AERADE Reports Archive ARC/R&M listing 1. Second report on the twisting of propeller blades. Supplementary to R. & M. 454 A. A. Griffith, and B. Hague The method of investigating the twist of propeller blades, which was developed in R. & M. 454, is interpreted mathematically by making a certain assumption as to the shape of the cross-sections. A general equation expressing the twist as a function of the radius is obtained, and an experimental method of solving it is evolved. It is shown that blades of certain shapes may be peculiarly liable to torsional vibration, and that a plan form.common in current practice possesses this property to an appreciable degree. It is further shown that the maximum stress due to torsion may determine fracture in this case. A method of calculating the shape of plan form in any given case, in order that the blade shall not twist, is deduced, and it is shown that this leads to a nearly symmetrical form in one instance. The effect of the large torsional hysteresis of timber in damping out vibrations is discussed, and it is suggested that herein may lie the reason for the comparative failure o5 metal propellers up to the present. Finally, suggestions are made for the modification of current practice in accordance with the indications of the present theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/455.pdf 2. The design of a sensitive yawmeter J. R. Pannell and R. Jones The investigation was undertaken in response to a request from the Technical Department of the Air Board for information as to the most sensitive form of yawmeter, and for a calibration curve for such an instrument. The original form of yawmeter suggested by Mr. (now Sir) Horace Darwin was used by Mr. E. T. Busk in his experiments in 1912 (see Rpt. 1912-13, p. 254) and a yawmeter on the same principle has been used in several wind channel investigations at the N.P.L. and has been described in R. and M. 156 and 371. A direct reading instrument of this type was described by Sir Horace Darwin in his Wilbur Wright Lecture of 1913. The variation of pressure with angle of inclination to the wind was determined on several sizes of pitot tubes, and from this curve it was predicted that the best angle between the axes of the two tubes of the yawmeter would be 120 deg. The sensitivity was found experimentally to be about 1.7 times as great as for the original form in which the angle was 90 deg. Various forms of yawmeter were tested until one was found which gave a result which could have been predicted from the experiment with the single pitot tube giving greatest sensitivity. The experiments indicate that, in plan view, the arms of the yawmeter should be straight and bevelled to a sharp edge at the end. The embraced angle should be 120 deg and the tube should not be of very small diameter. A tube of 0".30 internal diameter was found to be satisfactory, and a calibration curve for this instrument is given in the report. The instrument is capable of measuring angles with considerable accuracy, and can be used on aircraft or in the wind channel. If measurements are required in one plane only, they can be made very simply by turning the yawmeter till the pressure difference is zero, and reacting off the angle from a degree scale. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/445.pdf 3. Aerodynamic properties of a hemispherical cup with application to the hemispherical cup, windmill and anemometer F. B. Bradfield Windmills of the hemispherical cup anemometer type have been used on aeroplanes for driving auxiliary apparatus, and it therefore appeared desirable to be able to calculate their performance. To do this it was necessary to know the forces on a cup, and as this data was not available, the present work was set in hand. The lift, drag, and yawing moments of a hemispherical cup have been measured at several values of lv. Hence the characteristic curves for a windmill of this type when used as a means of obtaining power have been deduced. Two fans were tested in the wind channels for comparison with the calculated results. The effect of shielding the half revolution of the cups during which they return against the wind was ascertained, both with the anemometer half shielded by sinking it in the side of a large body, and with a windguard exposed to the wind. For the unshielded windmill the agreement obtained between the experimental torque and thrust and the calculated curves is very close. With a guard an approximate curve has been calculated, which gives good general agreement with the experimental results for the windmill as sunk in the side of a large body. The case with the exposed guard gives considerably larger values of torque and thrust, which effect is shown to be explained by the disturbance in the flow due to the guard. The aerodynamic properties of the cup, though investigated in this connection, are of more general interest and are therefore given in some detail. A note on the Robinson Anemometer is appended. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/712.pdf 4. Experiments on Balanced Control Surfaces for Rigid Airships R. Jones and D. H. Williams The experiments were conducted at the request of the Airship Design Department of the Admiralty in order to obtain data to assist in designing balanced control surfaces for airships of the R.38 class. Pitching moments (about C.G.) were measured on a model of R.33 (see R & M 361) with stabilising surfaces of the same overall dimensions. The balancing area did not, however, extend along the whole length of the control surfaces, but was confined to the outer end of the elevators, loss of length being partially balanced by increased width. Two different balancing areas were used. The effect of cutting off a piece of the fin immediately in front of the balancing area was investigated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/653.pdf 5. The distribution of pressure over the surface of airship model U.721, together with a comparison with the pressure over a spheroid R. Jones, M.A., and D. H. Williams, B.Sc. Undertaken to obtain data upon which to base nose-stiffening calculations on new airship. Distribution of pressure was measured over the whole length of the airship model at zero angle of incidence, with wind speed varying from 30 to 75 ft/sec. Also the pressures were measured on the nose of the model at different angles of yaw and roll at a wind speed of 40 ft/sec. A cone tangential to the model at a point near the nose was added, and the pressures aft of the circle of contact measured. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/600.pdf 6. Account of some experiments on rigid airship R.26 J. R. Pannell, and R. A. Frazer The Report gives experimental results obtained on four flights on R.26 during the period November, 1918-January, 1919. The following earlier Reports are quoted in the text :- R. & M. 668 (Airship R.33) ; R. & M. 537 and R. & M. 619 (23 Class Airships) ; R. & M. 460 and R. & M. 475 (Airscrew Thrust). The experiments may be classified under the following headings: (1) Unsuccessful attempt at pressure measurement over the horizontal stabilizing surfaces. (2) Turning trials with the rudders at 12Â° and 18Â°, port and starboard, for one speed only. See Tables 2 and 3, Figs. 2 and 3. (3) Deceleration tests from full speed. See Table 4, Fig. 4. (4) Airspeed for a number of combinations and rotational speeds of the engines. See Table 5. (5) Preliminary observations of airscrew thrdst by the method suggested by Dr. Stanton in R. & M. 460. See Appendix and Tables 6 and 7, Figs. 5 and 6. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/674.pdf 7. Experiments on rigid airship R.29 J. R. Pannell, and A. H. Bell Airship R.29. was the last ship of the 27 Class and it was considered desirable that a record of her performance should be obtained before she was placed out of commission. Arrangements were, therefore, made for the experiments described below to be carried out. Other reports dealing with full-scale experiments are :- R. & M. 537. "A flight in R.26." R. & M. 674. "Experiments on R.26." R. & M. 668. "Experiments on R.33." The principal experiments were :- Section (i).--Turning trials at various speeds and rudder angles for the original ship (R.29) ; with 303 sq. ft. of fabric removed from the upper fixed fin (R.29a) ; and with the whole of the fabric removed from the upper fixed fin (R.29b). Section (ii).--Course with rudders amidships or at small angles Section (iii).--Deceleration Trials. Section (iv).--Airspeed for various engine combinations. Section (v).--Attempted thrust measurements by pressure difference at amidships airscrew. Section (vi).--Distribution of speed in various localities. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/675.pdf 8. On the conditions at the boundary of a fluid in turbulent motion T. E. Stanton, Dorothy Marshall, and C. N. Bryant The object of the experiments was to determine the nature of the flow in the neighbourhood of the boundary of a fluid flowing in turbulent motion through a channel with parallel walls. The observations were made on air flowing through long pipes of circular cross section at mean rates of flow covering as wide a range as possible below and above the critical speed. The pipes used were 0. 269, 0. 714 and 12.7 cms. in diameter, and the range in experimental conditions varied from... The conclusions are that for speeds above the critical value as high as could be obtained, there is a layer of fluid of finite thickness at the boundary which is in laminar motion, and that the boundary condition is ... where the origin is taken in the boundary, and x is measured along the normal ; v is the velocity parallel to the boundary, mu is the coefficient of viscosity, R is the intensity of surface friction. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/720.pdf 9. Preliminary experiments on non-rigid airship "S.S.E.3 100,000," with a consideration of the performance data of various types of S.S. airship J. R. Pannell The experiments were carried out during a visit to Pulham Air Station when the trials of R.39. were temporarily interrupted. Other reports dealing with full-scale airship experiments are R. & M. 537, R. & M. 674, R. & M, 668 and R. & M. 675. A comparison is made between various ships of the S.S. type. The following experiments were carried out :- Section (i).---Turning trials with rudders hard over ; course with rudders approximately amidships. Section (ii).--Deceleration Trials. This section also includes a comparison between S.S.Z., S.S.E.3 90,000, S.S.T.14 and S.S.E.3 100,000. Section (iii).--Airspeed for various engine combinations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/693.pdf 10. Some Notes on the Theory of an Airscrew Working in a Wind Channel R. McK. Wood and R. G. Harris (a) Reasons for enquiry (l) The Momentum Theory of R. E. Fronde leads to equations which require some modification when the airscrew is working in a tunnel of dimensions comparable with the diameter of the screw. (2) Some correction to the speed of the air in a wind channel must be made to obtain the equivalent speed of advance of the airscrew in free air. (b) Conclusions - (l) Formu1ae for the thrust-momentum relation, inflow-outflow ratio and contraction ratio of the slipstream are deduced. (2) A method of correcting the speed of advance for the effect of channel constraint of flow is obtained based upon the Momentum Theory, which may probably be relied upon so long as the correction required is reasonably small. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/662.pdf 11. Vibrations of Rafwires R. G. Harris This report describes experimental and theoretical investigations of the vibrations of rafwires during "singing." The experimental work was confined to the laboratory. Observations were made on a rafwire in a wind channel at various angles of yaw, at various wind speeds and under various tensions. Subsidiary aerodynamic and other measurements were also made. The principal reason for the experiment was the wish to find an explanation for fractures which have occurred from time to time. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/759.pdf 12. A Generalised Type of Joukowski Aerofoil H. Glauert The present report gives a short account of a generalised type of Jankowski aerofoil which avoids the difficulty of extreme thinness near the trailing edge associated with the ordinary Jankowski aerofoils. Calculations have been made for three different aerofoils of this type which might form a suitable basis for an experimental test of the theory. Details are also given of a fourth aerofoil which should have a constant centre of pressure according to Munk’s theory of thin aerofoils. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/911.pdf 13. A Theory of Thin Aerofoils H. Glauert The present report develops a theory of thin aerofoils in two dimensional motion and simple integral expressions are obtained for the angle of incidence and moment coefficient at zero lift. A graphical method of integration is developed which can be used to determine the characteristics of any thin aerofoil. The method is applied successfully to three aerofoil sections and results are derived for a tail-plane and elevators. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/910.pdf 14. The Theory of the Design of Aerofoils with an Analysis of the Experimental Results for the Aerofoils R.A.F. 25, 26, 30 to 33 H. Glauert Recently a number of aerofoils have been designed with the object of obtaining (1) a good thick wing, and (2) a racing wing. Experimental results for these aerofoils are contained in reports R.&M. 915, R.&M. 928, and R.&M. 943. (b) Range of Investigation.-An account is given of the theory on which the aerofoils were designed, the essential feature being to curve the centre line of a good symmetrical section into a circular arc of suitable camber. In the case of high camber, a cubic curve was also tried for the centre line in order to reduce the movement of the centre of pressure. The experimental results are analysed for comparison with the theoretical predictions, and curves are drawn showing the relative merits of the aerofoils. (c) The theoretical basis of the method of design has been fully confirmed by the experimental results. In addition, it appears that the method leads to aerofoil shapes which compare very favourably with previous aerofoils. (d) Further progress may be obtained by seeking for the best possible symmetrical sections of suitable thickness, and further experimental investigation is also required on the effect of reflex curvature in thin and in thick aerofoils. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/946.pdf 15. A GENERAL THEORY OF THE AUTOGYRO H. Glauert An autogyro obtains remarkably high lift forces from a system of freely rotating blades and it is important to develop a theory which will explain the behaviour of an autogyro and will provide a method of estimating the effect of changes in the fundamental parameters of the system. A theory is developed depending on the assumptions that the angles of incidence of the blade elements are small, that the interference flow is similar to that caused by an ordinary aerofoil, and that only first order harmonics of periodic terms need be retained in the equations. An alternative method of analysis by considering the energy losses of an autogyro is developed in an appendix to the main report. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1111.pdf 16. Further development of autogyro theory. Parts 1 and 2 C. N. H. Lock The general theory of the autogyro given by Glauert in R. & M. 1111 is based on certain simplifying approximations and assumptions. The object of the present paper is to develop the theory still further by removing some of the approximations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1127.pdf 17. On the Flow of Air Behind an Inclined Flat Plate of Infinite Span A. Fage, F. C. Johansen The general form of the flow behind an infinitely long thin flat plate inclined at a large angle to a fluid stream of infinite extent has been known for many years past. The essential features of the motion are illustrated in the smoke photograph given in fig. 1. At the edges, thin bands of vorticity are generated, which separate the freely-moving fluid from the "dead-water" region at the back of the plate; and at some distance behind, these vortex bands on account of their lack of stability roll up and form what is now commonly known as a vortex streett (see fig. 2). Various theories for calculating the resistance of the plate have also been advanced from time to time. One of the earliest is the theory at "discontinuous" motion due to Kirchbofft and Rayleigh, who obtained the expression for the normal force per unit length of the plate. More recently Karman has obtained a formula for the resistance of a plate normal to the general flow, in terms of the dimensions of the vortex system at some distance behind the plate. In spite, however, of these and other important investigations, much more remains to be discovered before it can be said that the phenomenon of the flow is completely understood. No attempt has hitherto been made, as far as the writers are aware, to determine experimentally, at incidences below 90Â°, the frequency and speed with which the vortices pass downstream; the dimensions of the vortex system; the average strength of the individual vortices; or the rate at which vorticity is leaving the edges of the plate. The present investigation has been undertaken to furnish iniormation on these features of the flow. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1104.pdf 18. Theoretical Relationships for an Aerofoil with Hinged Flap H. Glauert The use of an aerofoil with a hinged flap is of very general importance both for control surfaces and for main supporting surfaces, and in particular information is required as to the effect of varying the size of the flap. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1095.pdf 19. An Investigation of Fluid Flow in Two Dimensions A. Thom, D.Sc., Ph.D., A.R.T.C. There are in existence several methods of obtaining numerical solutions to the two-dimensional flow of a perfect fluid for given boundary conditions Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1194.pdf 20. The Boundary Layer of the Front Portion of a Cylinder A. Thom A large amount of information is now available regarding the flow of water or air past a cylinder placed across the stream so far as the behaviour of the main body of the fluid is concerned; but the conditions in the layer close to the surface of the cylinder seem to be largely unknown. Accordingly it seemed advisable to explore the velocity, etc., close to the surface. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1176.pdf 21. The Theoretical Relationships for an Aerofoil with a Multiply Hinged Flap System W. G. A. Perring Theoretical expressions for the lift and pitching moment of an aerofoil in two dimensional motion were developed in R&M 910. This theory was extended in R&M 1095 to include the hinge moment of a flap in the case of a rectangular aerofoil of finite span. This analysis has now been extended to an aerofoil fitted with a multiply hinged flap system, and theoretical expressions for lift and pitching moment of the aerofoil, and the hinge moment about any hinge position have been deduced in the case of a rectangular aerofoil of finite span. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1171.pdf 22. Wind Tunnel Experiments on a Model Autogyro at Small Angles of Incidence C. N. H. Lock and H. C. H. Townend A wooden scale model, 6 feet in diameter, of the original 4-bladed rotating wing unit of the Cierva Autogyro, has been tested in the Duplex tunnel at blade angles of 0°, 1°, 1.8°, 2.30° and 3°. It has also been tested as a 2-blader at a blade angle of 1Â·8°. The extreme range of incidence was from 2° to 20° and of rotational speed from 3 to 12 revolutions per second. It was found that the model would not rotate at all at a blade angle of 4° while at 3° blade angle it would only rotate at angles of incidence above 12°. In order to supplement the measurement of forces and rotational speed at zero torque, observations of forces and angular accelerations were made over a more limited range at varying rotational speed, by means of a chronograph and stroboscope. These observations were interpreted as giving the forces and torque in steady motion when the torque was not zero. Observations were also made of the angular motion of the blades in flapping about their hinges.(Scan courtesy of Juergen Humt.) Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1154.pdf 23. The effects of turbulence and surface roughness on the drag of a cylinder A. Fage, A.R.C.Sc., and J. H. Warsap Experiments have been made on that type of flow around a circular cylinder which is peculiarly sensitive to changes in Reynolds' number and for which the drag coefficient falls from 0.6 to 0.2 approximately. A study has been made of the effects on the drag of methodical changes in a turbulence artificially created in the general stream, in the roughness of the entire surface, and finally in the size of the local excrescencies formed by generator wires. These methodical changes are shown to produce orderly changes in the drag, and it is concluded that the flow considered although sensitive to such extraneous disturbances is not of a critical nature. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1283.pdf 24. The Elasticity of Pintsch Crystals of Tungsten S. J. Wright Very little work has hitherto been done on the Elastic Properties of Single Crystals of Metals. In the case of Tungsten, which is the only cubic crystal whose elastic constants have been determined, the previous work of Bridgman based on static tests indicated that the constants satisfied the Isotropic relation. In the present investigation dynamical methods have been employed to redetermine these constants more accurately, and in particular to find out whether the crystals are truly isotropic. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1264.pdf 25. The Interference of a Wind Tunnel on a Symmetrical Body C. N. H. Lock The effect of the boundaries of a wind tunnel on the flow in the neighbourhood of a symmetrical body (i.e. (a) in two dimensions, a cylinder having a plane of symmetry parallel to the axis of the tunnel : (b) in three dimensions a body of revolution coaxial with the tunnel), may be represented on the assumption of irrotational flow to a first approximation as an increase in magnitude of the velocity at any point near the body in a constant ratio. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1275.pdf 26. The Application of Goldstein's Theory to the Practical Design of Airscrews C. N. H. Lock A recent paper on the Vortex theory of screw propellers, by Dr. S. Goldstein in the Proceedings of the Royal Society, contains a solution of the problem of the potential flow past a body consisting of a finite number of coaxial helicoids of infinite length but finite radius moving through a fluid with constant velocity. The results are applied to the case of an ideal airscrew having a finite number of blades and a particular distribution of circulation along the blade for small values of the thrust. The present paper contains a summary of Goldstein's results, which are then applied to the airscrew problem by a method which leads to formulae differing from the standard formulae of the "Vortex theory" by the addition of a factor to the formulae for the components of inflow; the value of this factor may be obtained from a chart embodying the results of Goldstein's calculations. The formulae of the Vortex theory are developed simultaneously from first principles by au analogous method which differs somewhat from the method used by its originator and brings out clearly the close analogy with the Prandtl theory of a monoplane wing; they also represent the limit of the Goldstein formulae for the case of an infinite number of blades. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1377.pdf 27. The Drag of Circular Cylinders and Spheres at High Values of Reynolds Number A. Fage The paper gives the results of experiments made recently to measure the drag of a circular cylinder of large diameter (23 in.). The more important measurements made in this country and abroad of the drags of circular cylinders and spheres at high values of Reynolds number are also included. An analysis of these measurements leads to the conclusion that the flow in an open-jet tunnel of the Gottingen type, with a contracting mouth and with the honeycomb at the larger end, is steadier than that in an N.P.L. type of tunnel. The drag coefficients of a circular cylinder and of a sphere appear to be slowly increasing, at the highest values of Reynolds number attained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1370.pdf 28. The Stability of a Body Towed by a Light Wire H. Glauert Summary.-Introductory (Purpose of Investigation.)-Owing to the practice of towing instruments belovv an aeroplane, the conditions for the stability of a towed body required investigation. Range of investigation.-The stability of a body towed by a light inextensible wire has been investigated on certain simplifying assumptions regarding the force experienced by the wire. Conclusions.-:-In addition to the pitching and yawing oscillations of the body there are three oscillations of the whole system. The most important oscillation is associated with a bowing of the wire in the plane of symmetry, and, even if the body has satisfactory statical stability, this oscillation may become unstable if the body is too short or if the drag of the body is low compared with that of the wire. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1312.pdf 29. Experiments on the Flow Past a Rotating Cylinder A. Thom Parts 1 -3. In 1925 the writer made a series of measurements of the direction and velocity of the air throughout the field about a rotating cylinder. The resulting velocity contours and streamlines were published at the time, but later the data were worked upto give the distribution of vorticity throughout the field. This was found by graphically differentiating the components of the velocity. Fig. 1 shows the observed air directions and Fig. 2 the vorticity values. The results of calculating the circulation round various contours in this field is shown in Fig. 3. It is seen that there is no very marked change in the circulation outside a contour of about twice the area of the cylinder section. It will also be seen that there is no circulation in the wake as a whole. The upper part contains positive vorticity and the lower an equal amount of (more concentrated) negative. This is in accordance with Prandtl's idea that a state of balance has been attained in the production of positive and negative eddying above and below. The circulation corresponding to the actual lift on this cylinder is about 16 ft./sec. The discrepancy is only apparent as the larger figure obtained in Fig. 3 refers to the centre section, where the lift is 15-20 per cent. greater than the mean as measured on the balance (see R. & M. 1082). As these experiments gave no information regarding the conditions close to the surface of the cylinder, a series of measurements in the boundary layer was made in 1927. These experiments are described in Parts 2 and 3. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1410.pdf 30. Further Experiments on the Flow Around a Circular Cylinder A. Fage and V. M. Falkner The intensity of friction on the surfaces of two cylinders of diameter 2Â·93 in. and 5Â·89 in. respectively have been determined from measurements of velocity taken at distances of about 0Â·0025 in. from the surface with small surface tubes. The sensitive range of Reynolds number (VoD/v) over which large changes in the flow characteristics are experienced was covered in the experiments on the larger cylinder. The character of the frictional distribution depends on the value of (VoD/v). At a relatively low value of (VoDv), the frictional intensity rises gradually to a maximum value and then rapidly falls to a zero value; whereas at a larger value of (VoD/v) within the sensitive range the frictional intensity after reaching its maximum value falls less abruptly to a minimum value, and then rises to a second maximum before the zero value is reached. A transition from laminar to turbulent flow occurs in the boundary layer where the frictional intensity is a minimum. The transition region is also clearly indicated by a marked inflexion in the curve of pressure distribution. The frictional distribution measured on the 5Â·89 in. cylinder is in reasonably close agreement with that predicted by modern boundary layer theory. Experiments have also been made to determine the effect of disturbances in the general stream on the characteristics of the flow. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1369.pdf 31. The Flutter of Monoplanes, Biplanes and Tail Units R. A. Frazer; W. J. Duncan The present report is the second in the Monograph series of the Aeronautical Research Committee to be devoted to the subject of flutter. The first, R. & M. 1155, appeared in 1928 and was entitled "The Flutter of Aeroplane Wings" ; ,it contained the essentials of a tolerably general theory of flutter, but the problem discussed in detail was the prevention of the wing flutter of monoplanes. As the outcome of this earlier investigation, a list of recommendations was drawn up for the guidance of designers. Since the publication of R. & M. 1155, research on wing flutter has been continued, and the subject of tail flutter has also received attention. The progress made is already recorded in separate reports issued from time to time in the R. & M. series; and these are, with slight modifications, now brought together under one cover. It is hoped that this compilation, which includes the recommendations regarding the design both of tail units in general and of the wings of biplanes, will be found convenient by designers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1255.pdf 32. The Interference on the Characteristics of an Aerofoil in a Wind Tunnel of Rectangular Section H. Glauert Approximate formulae for the interference on an aerofoil in a rectangular wind tunnel have been known and used for several years. More accurate formulae have been developed by Terazawa and Rosenhead, but their results are given in very complicated forms which are unsuitable for numerical computation. In this paper Rosenhead's formulae are reduced to a more convenient form and numerical results are derived for square and Duplex wind tunnels. The correction to the approximate formula is comparatively unimportant for a square tunnel, but important for a Duplex tunnel. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1459.pdf 33. Effect of Discs on the Air Forces on a Rotating Cylinder A. Thom The Potential Flow streamlines past a circular cylinder are as shown in Fig. la ... If a circulation is superimposed the streamlines become as in Fig. lb ... As the circulation is increased the stagnation points move together ... Thereafter if the circulation is further increased ti1e stagnation point leaves the surface and the flow pattern becomes as in Fig. 1d. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1623.pdf 34. Graphical Method of Calculating Performance of Airscrew C. N. H. Lock A rapid method is described of making calculations of airscrew performance by means of charts. The first application is to ordinary strip theory calculations on the basis of the formulae of Ref. 5. Six charts are required for each radius for which the value of thrust grading, etc., are to be derived; of these six, four depend on number of blades but are otherwise universal, since they are independent of shape of blade section, and do not involve the blade width or blade angle explicitly; they are based purely on the application of Prandtl theory to the airscrew and contain no empirical adjustments. The remaining two charts involve the lift and drag curves of the section. The second application gives a considerable further simplification in that the charts are required for a single standard radius (0.7) only; the thrust coefficient corresponding to a given working condition can then be deduced by a simple operation with three charts while the torque involves three further charts and a simple addition. The accuracy of the second method is increased if the lift and drag charts are deduced by analysis of observations on (model) airscrews, an analysis which can be performed rapidly by means of the remaining four charts; such an analysis of the results of the wind tunnel tests of high pitch airscrews shows that the method will give reasonably consistent results over a range of pitch ratio from 0.3 to 2.5, while there is little doubt that the method will cover the range of blade width likely to occur in practice. Changes of blade section and also of plan form and twist may be included if necessary by modifying the lift and drag curves. The second method has also been remarkably successful in its application to the stalled range of an airscrew, a range in which there is at present no other available method. It is further suggested that the first method might prove very convenient for analysing wind tunnel tests of model airscrews at high tip speed; the accuracy of application of the second method might be improved by basing the lift curves on full scale values of power, speed and revolutions, combined with an estimate of profile drag. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1675.pdf 35. Heavy Flexible Cable for Towing A Heavy Body Below An Aeroplane H. Glauert The mathematical expressions for the form of a heavy cable in a wind have been known for many years, but no systematic numerical results are available. Calculations have been made to derive a family of curves, depending on the weight-drag ratio of the cable, which should suffice to cover all practical problems, involving the towing of a heavy body. The use of the curves is illustrated by a typical numerical example. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1592.pdf 36. Tables for Use in an Improved Method of Airscrew Strip Theory Calculation C. N. H. Lock, D. Yeatman An improved method of calculating the performance of an airscrew has been described in prcv:ious reports (Refs. I and 2), which includes an allowance for tip loss. The present report contains tables of a parameter (x) required in the calculation of the blade interference by the new method ; these tables being available, the labour invloved is no greator than in a calculation by the standard vortex theory. A simplified method of calculation involving the use of charts is described in a separate report (Ref. 6). The tables given here cover the case of two-, three-, and four-bladed airscrews at a series of standard radii and for all values of pitch. Details of the method of calculation (due to Goldstein, Ref. 3) are given in an Appendix together with a method of interpolation which can be used to extend the results to any other number of blades. The results for three blades were interpolated by this method but are probably quite accurate enough for practical purposes. All formulae required in the present method of strip theory calculation are given here, together with complete details of a specimen calculation. A preliminary comparison is included between results of calculations by the present method and the new experiments on high pitch model airscrews described in Ref. 5, for two-bladed airscrews of pitch ratio 1.5 and 2.5 and a four-bladed airscrew of 2.5; these show satisfactory agreement (below the stall) and reasons are given to suggest that the agreement should be at least as good over the whole range of pitch ratio. It is concluded that the present formulae and tables may be used with confidence to calculate the performance of any airscrew below the stalling angle, provided that suitable aerofoil data are available. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1674.pdf 37. Wind Tunnel Tests of High Pitch Airscrews C. N. H. Lock, H. Bateman and H. L. Nixon The main series of tests of the original family of airscrews described in R&M 829 consisted of measurements of overall thrust and torque on 5 two-bladed and four-bladed airscrews of pitch diameter ratios 0.3, 0.5, 0.7, 1.0 and 1.5. These tests have now been extended to much higher pitch values and the original tests repeated at a uniform Reynolds number. The additional tests were made with the blades of P/D 1.5 rotated to the equivalent pitch values 1.0, 1.25, 1.8, 2.2 and 2.5. Some of the tests on the low pitch screws were made in a closed 7 ft. tunnel, but the tests of the highest pitch screws were made in the new open jet tunnel No.1 in order to use the higher maximum tunnel speed. Thus a comparison was obtained between observations in the closed and open jet tunnels for a number of airscrews and these support the standard methods of correction for tunnel interference. New apparatus was used including a new 15 H.P. induction motor of 9 in. diameter to drive the airscrew. The effect of the airscrew boss was eliminated by using a cylindrical guard body of 0.27 airscrew diameters with faired nose and tail of sufficient length to give a uniform flow in the absence of the screw. The thrust readings were corrected by pressure plotting the airscrew boss, so that the recorded thrust and torque coefficients refer to the exposed portions of the blades only. Instructions are given for correcting the performance data for the effect of interference when the screw is mounted on the fus elage of an actual aeroplane. The results show that the maximum thrust coefficient for the higher pitches is limited by the stalling of the blades, so that after reaching a value of about O.135 for the two-bladers and 0.26 for the four-bladers, the value of kT remains very roughly constant and independent of pitch for all smaller values of J. These values are however subject to a scale effect on maximum thrust coefficient of 5 to 10 per cent. for an increase of Reynolds number from 1.8 x 105 to 3 x 105 but there is some evidence to suggest that the full scale values will not differ greatly from those of the model. The torque coefficient increases with increase of pitch at all working conditions. The maximum efficiency for the two-bladers increases slightly from 88.4 per cent. at P/D 1.5 to an absolute maximum of 89.7 per cent at a P/D rather less than 2.5. For the 4-bladers the corresponding figures are 84.8 and 86.8. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1673.pdf 38. Cooling of Aircraft Engines with special reference to Ethylene Glycol Radiators enclosed in Ducts F. W. Meredith, B.A. The recent increase in the speed of aeroplanes has brought the question of cooling drag into prominence and forced the application of the principle of low velocity cooling. An analysis of the performance of a cooling system enclosed in a duct is required to guide further research and design. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1683.pdf 39. The reaction on a wing whose angle of incidence is changing rapidly. Wind tunnel experiments with a short period recording balance W. S. Farren A balance has been developed in the Aeronautics Laboratory at Cambridge by which the reaction on a wing whose angle of incidence is increasing or decreasing rapidly can be recorded. The reactions have been measured on eight aerofoils, including those used in R. & M. 1588. Large hysteresis effects at and above the stall have been found in two-dimensional conditions. It is considered that these form a basis for accounting for certain full scale observations which have not hitherto been satisfactorily explained. It is proposed to extend the work to three-dimensional conditions. The work is partly the outcome of that described in R. & M. 1561. It also forms part of the investigation of stalling described in R. & M. 1588, and in Professor Jones Wilbur Wright Lecture, 1934. A short account of the results was given by the author at the Fourth International Congress for Applied Mechanics, Cambridge, July, 1934. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1648.pdf 40. Wind Tunnel Tests of the characteristics of Wing Flaps and their Wakes K. W. Clark, B.Sc., D.I.C. and F. W. Kirkby To make a comparison of different types of flap on an aerofoil, preliminary to tests on a low wing monoplane. Plain, slotted and split flaps were tested. Lift, drag and pitching moments have been measured, and the position and intensity of the wake in the region of the tail planehave been observed by measuring total head and observing the behaviour of threads. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1698.pdf 41. Full scale trials on scion M.3 with a gouge flap J. Cohen Under review Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1753.pdf 42. The Effect of Blade Twist on the Characteristics of the C.30 Autogiro J. A. Beavan and C. N. H. Lock An analysis of the blade motion and force characteristics of the standard Cierva C.30 autogiro rotor is made, taking into account the torsional flexibility of the blades. The results are applied to the steady motion and pitching equilibrium of the whole machine. Using the physical constants of the blades, the analysis has been carried out for the cases of a mean profile drag coefficient over the blade elements equal to 0.014 and 0.012, and a speed range from zero to 130 m.p.h. The most important assumption of the present investigation is that the blades remain straight under all circumstances. The other approximations are not expected to have any great influence. The blades are found to twist to the extent of several degrees, in the sense that the mean pitch angle (at any radius) round the circle is decreased and that superimposed on this there is a periodic variation. Both effects increase with the forward speed until at the highest speed the outer portion of the advancing blade is twisted to below the no-lift angle of the section. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1727.pdf 43. Galerkin's Method in Mechanics and Differential Equations W. J. Duncan The method to be described here is attributed to the Russian investigator V. G. Galerkin, whose original papers are inaccessible to the present writer. His knowledge of the method is derived from a description given in a paper by E. P. Grossman. Grossman states that the method was given by Galerkin in his treatise 'Rods and Plates' (Vestnik Ingeneroff, 1915, p. 897) and that applications to oscillation problems were first made by V. P. Lyskov. It is pointed out by Grossman that Galerkin's process in applications to mechanics leads to the same results as Lagrange's principle of virtual work, but employs a special co-ordinate system. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1798.pdf 44. The Calculation of the Profile Drag of Aerofoils H. B. Squire; A. D. Young Owing to improvements in aerodynamic design it is desirable to be able to predict profile drag accurately. A method of calculating the profile drag of aerofoils is developed and is applied to investigate the drag of a flat plate and of two aerofoils of different thicknesses for three Reynolds numbers and three transition point positions. From the results curves are drawn which show the variation of profile drag for a range of aerofoil thickness, Reynolds number and transition point position. Comparison with experimental results shows satisfactory agreement. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1838.pdf 45. Torsional Vibration in Aircraft Power Plants: Methods of Calculation Part I. Introduction and General Comments Part II. Practical Treatment of the General Problem Part III. Practical Calculations for a Typical 12-Cylinder Vee engine B. C. Carter The object of this report is to assist designers of aircraft power plants to avoid harmful torsional vibration of the crankshaft-airscrew system. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2739.pdf 46. Flight tests of a falcon fitted with an irving flap J. Cohen and H. P. Fraser It has been stated that flaps for landing a clean, heavily loaded aeroplane, should provide a range of settings over which the lift is constant but the drag variable within wide limits, with low operating forces. The Irving flap aims to do this and it was decided to test it in flight, to see how nearly it approached the ideal and to gain experience of the landing technique to be employed with such a flap. The flap was fitted right across the span of a standard Falcon inboard of the ailerons; the changes in gliding angle and trim due to the flap, together with its contribution to maximum lift were determined. Measurements were made of the operating force, and the linkage and chord ratio varied with a view to reducing this to a minimum. By means of a 'gate' the flap movement could be kept within the constant lift range, when making landings, and the effect of variable drag explored. Handling trials were made by a large number of service and firms' pilots. The lift due to the flap increased uniformly until the half open position and thereafter remained constant, whilst the drag increased steadily. The total gliding angle change was 3Â½Â°, and trim change was negligible. The aerodynamic hinge moment was not as low as calculation suggests is possible for this type of flap. Tests indicated that it would be reduced were the chord ratio of the upper to the lower member increased from 1 to 2. Nevertheless, the present flap was quickly and easily operated and enabled pilots to reach a given point at a given spee d, without sideslipping, S-turns or use of engine. Pilots who tested the flap, generally considered it a definite help in facilitating the landing approach, but suggested that much more drag could be used with advantage. It is feasible in the landing technique, to control the gliding angle with a rapidly adjustable flap, which gives variable drag at constant lift. With the present Irving mechanism, quick movements of the flap are possible for aeroplanes up to about 3,000 lb. weight. With the Falcon, the flap was sufficiently large to show its advantage over the non-variable flap, but not large enough to enable the pilot to take full advantage of the landing technique used. A modification to the flap suggested by Mr. W. E. Gray, considerably reduces the operating load, and makes it applicable to larger and more heavily loaded aeroplanes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1863.pdf 47. A solution of the laminar boundary-layer equation for retarded flow D. R. Hartree The laminar boundary-layer equation, for a linearly retarded velocity in the main stream, U = 1 - 1/8x in reduced variables, has been solved numerically by working in finite intervals in x, with a correction for the finite length of x-interval. The method was first tried out on the region near the forward stagnation point, where the results could be checked from tables given by Howarth, and proved very satisfactory. The separation point has been determined by two independent methods to be close to x = 0.959, in excellent agreement with Howarth's value. The nature of the singularity at the separation point is discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2426.pdf 48. Abstracts of papers published externally
CONTENTS. The Continuous Beam. The Large Deflections of a Thin Circular Ring. Theoretical Discharge of Air from Ports in a Duct. The Estimation of Pipe Delivery from Pitot-Tube Measurements. The Influence of Wall Oscillations, Wall Rotation, and Entry Eddies, on the Breakdown of Laminar Flow in an Annular Pipe. Thermal Effects on Bodies in an Air Stream. An Experimental Determination of tile Spectrum of Turbulence. Sensitivity of Immersed Venturi-Pitot Head at Low Speeds. The Influence of the Mean Stress of the Cycle on the Resistance of Metals to Corrosion-Fatigue. The Resistance of some Special Bronzes to Fatigue and Corrosion-Fatigue. The Effect of Protective Coatings on the Corrosion-Fatigue Resistance of Steel. The Constitution of the Magnesium-Rich Alloys of Magnesium and Silver. Oscillatory Motion of a Fluid Along a Circular Tube. Relaxation Methods Applied to Engineering Problems. III. Problems Involving Two Independent Variables. Torsion of Built-Up and Reinforced Tubes. Application of the Galerkhl Method to the Torsion and Flexure of Cylinders and Prisms. The Elastic Stability of a Curved Plate under Axial Thrusts. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1868.pdf 49. General Investion into the Characteristics of the C.30 Autogiro P. A. Hufton, A. E. Woodward, F. J. Bigg and J. A. Beavan The present report on the performance of a gyro plane contains the first really satisfactory set of full scale data to be obtained in this country, and affords a valuable means of checking a body of theoretical investigation which has been growing up during the past twelve years. The greater part of this gyroplane theory can be transferred with little change to the case of the helicopter, on which full scale evidence is still almost completely lacking. In particular, the freedom of the blades to flap, which has played a considerable part in increasing the difficulty of gyroplane theory, seems likely to become an essential feature of all helicopters. (Scan courtesy of J. Humt) Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1859.pdf 50. Notes on the tail-first aeroplane S. B. Gates The tail-first aeroplane has certain strong attractions when combined with a tricycle undercarriage; in particular it has been suggested that it would represent a definite advance in the production of high lift. In these notes the main characteristics of a tail-first design are summarised and discussed, and an analysis is given of high-lift control with front and rear tails. It is shown that the high-lift claims made for the front tail are illusory in the present stage of development of high lift devices, owing to the high lift whick the tail must provide to balance the high lift of the wing. A front tail would immensely simplify the problem of longitudinal stability. The problem of getting enough directional stability and control without increasing drag would require research on a model. It could probably be arranged to work with a CLMAX of from 2 to 2.5 (i.e., with full-span slotted or split flaps), but is incapable of dealing with a CLMAX of 3 or over unless the point of application of high lift can be moved much further forward on the wing chord than at present. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2676.pdf 51. Stalling tests on a blenheim G. E. Pringle In extension of earlier flight tests it was required to investigate how accidental stalling and spinning of a Blenheim is affected by the setting of flaps, engine gills and throttles. The behaviour of the aircraft was tested at low speeds, both in straight stalls and also When one engine was cut in the climb. The tests included an investigation of some modifications to the wing. All of the above settings affect the behaviour of the Blenheim at and near the stall ; closing the gills and opening the throttles usually both have an adverse effect, either by reducing the warning of imminent stalling or by making the stall more violent. With gills closed and throttles partly open the stall is violent with flaps and undercarriage either up or down. In the engine-cutting tests the aircraft drops the corresponding wing suddenly, and at the lower speeds the falling wing partially stalls. The experiments with modified wing-section and wing-tip plan-form resulted in some improvement in stalling and behaviour after engine-cutting. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1966.pdf 52. The Calculation of the Total and Skin Friction Drags of Bodies of Revolution at Zero Incidence A. D. Young By a modification of the method used to calculate the profile drag of aerofoils a method has been developed for calculating the drag of smooth bodies of revolution. This method has been applied to three bodies at zero incidence, the calculations covering a wide range of fineness ratio, Reynolds number and transition position. It is hoped that the results of these calculations will be of particular value to those engaged in performance estimation and in research relating to the cleanness efficiency of aeroplanes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1874.pdf 53. The Effect of Openings on the Torsional Stiffness of Rectangular Section Tubes H. J. Allwright, B.Sc., D.I.C. It has been shown by Williams that holes or gaps in the cover skin of a stressed-skin wing may cause considerably increased stresses; it was desired to obtain quantitive information on the corresponding reduction in torsional stiffness. Following the analysis given by Williams, an expression is derived for the tortional stiffness of a rectangular section tube with an opening through the upper and lower cover skins, when a concentrated torque is applied at an intermediate section outboard of the opening. This stiffness is compared with the stiffness of a similar tube with no opening, and the effects of varying the length and position of the opening and of varying the flange area of the spars are examined for a torque applied at the three-quarter span section. Openings such as are necessary for fuel tanks and retractable undercarriages may cause serious losses of torsional stiffness, and should be made as short as possible in a spanwise direction. An opening of given dimension results in least loss of stiffness when very near the wing root, but it then causes larger local stresses than if positioned out along the span. Increase of spar flange area above that necessary for flexural strength has little effect in reducing the loss of torsional stiffness. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1993.pdf 54. An orifice method of producing a high velocity stream A. M. Binnie Earlier papers (Binnie 1938 and 1940) have dealt with the uniformity of the stream produced by a venturi flume and with the possibility of employing this device for testing model seaplane floats. If the velocity of the stream is to be as high as 40 ft./sec., a net head (i.e., vertical distance between the supply level and the surface of the channel) of 25 ft. is required. In a venturi flume with an expansion ratio of 2, and working at this net head, the ratio of downstream to upstream depth would be at least 0.25. Hence the gross head, or vertical distance between the supply level and the bottom of the channel, would be 33 ft., and the depth of the issuing stream would be 8 ft., which is unnecessarily large. It will be appreciated that to attain velocities of this magnitude a very great expenditure of power is required, and therefore the cross section of the stream should be as small as possible consistent with the requirements of the experiments. The expansion ratio might be increased to reduce the depth of the stream and to raise slightly its velocity, but only at the expense of its uniformity. It is, however, possible that a satisfactory and more economical stream might be produced by means of a rectangular orifice inserted in the side of a large tank near the bottom, and discharging direct into an open horizontal channel of the same cross-section (Fig. 1). To avoid contractions, the orifice must be fitted with a trumpet. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1887.pdf 55. Determination of Profile Drag at High Speeds by a Pitot Traverse Method C. N. H. Lock, M.A., F.R.Ae.S., W. F. Hilton, B.Sc., Ph.D., A.R.C.S. and S. Goldstein, M.A., Ph.D., F.R.S., of the Aerodynamics Division, N.P.L. At speeds at which the compressibility of the air can be neglected it is known that the profile drag of an aerofoil section can be determined with sufficient accuracy from measurements of total head and static pressure across a section of the wake. When compressibility is important measurement of a third quantity - e.g., air density - becomes theoretically necessary; but it appears that it is sufficiently accurate to assume that the total energy, E, per unit mass of the air is constant across a section of the wake, and then measurements of total head and static pressure suffice. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1971.pdf 56. Effect on hinge moment of fitting strips near aileron trailing edge, of increasing aileron chord and of extending aileron to wing tip with an appendix on pressures over surface of control fitted with strips A. S. Batson and J. H. Warsap To find a method Of modifying ailerons so that a machine may be more responsive in roll. (1) Hinge moment was measured on a 1/2.25 scale 'Hurricane' aileron with the following modifications:- (a) Strips (depth 0.02 in. and 0.04 in.) fitted near trailing edge. (b) Aileron chord increased from 0.18c to 0.22c and 0.26c. (c) Aileron chord 0.22c, extended to the wing tip. Strips (depth 0.04 in.) also fitted near trailing edge. Range of aileron angle 0Â° to Â±15Â° ; Range of incidence -4Â° to 8Â°. (2) Pressures were measured over the surface of a control (0.4c) of an aerofoil (N.A.C.A. 0020 section, 30 in. chord) with and without strips (depth 0.05 in.- 0.20 in.) or cords (0.09 in. diameter) by means of a static pressure tube : Angles of incidence 0Â°, 4Â° and 8Â°. Control angles Â±10Â° and Â±15Â°. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1936.pdf 57. Note on differential gearing as a means of aileron balance S. B. Gates It has been suggested in some American investigations that differential gearing, combined with adjustment of the aileron floating angle by means of a tab, may be a powerful method of balancing ailerons. This report sets out the theory of this method of balance and analysesit in relation to the most pressing problem of aileron design, which is to obtain close balance at high speed without overbalance in any part of the range, or uncomfortable lightness at slow speed. It is shown that this result can be achieved more directly by differential balance than by any other method if the differential and the tab setting are nicely adjusted to the natural floating properties of the aileron. Thus if the aileron tends to float up as incidence increases, a differential giving more downward than upward movement must be used, and this must be combined with an upward-set tab ; while if the aileron tends to float down as the incidence increases, a differential giving more upward than downward movement must be used, combined with a downset tab. After examining the possible disadvantages of the downward differential, and the loads set up by the tab, it is concluded that there is a strong case for exploration in flight of differential gearing as a major means of aileron balance. Some notes on the geometry of differential gearing are given in an Appendix. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2526.pdf 58. Tests in the compressed air tunnel on the aerofoils NACA 0015 and NACA 0030 with and without split flap and on other aerofoils of various thicknesses with a split flap R. Jones To obtain information on the effect of thickness on the aerodynamic characteristics of aerofoils with and without a split flap. The following 4 ft. by 8 in. rectangular aerofoils were tested :- NACA 0015 and NACA 0030 with and without a split flap 0.lc wide at 90 deg. to wing surface and at 0.lc from trailing edge. NACA 0012, NACA 23012, RAF 28 and RAF 48 with flap. The effect of rounding the edge of the flap was considered on NACA 0015. A comparison made with a 0.2c flap at 50 deg. to wing surface and at 0.2c from trailing edge on NACA 0015 and RAF 48. The effect of rounding the ends of NACA 0030 was also examined. C L, C D and C M were obtained over a range of Reynolds numbers with additional C D measurements at closer intervals of R on the two wings without flap. C D,0 was also determined by the momentnm method on NACA 0030. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2584.pdf 59. Tests on a whirlwind aircraft in the royal aircraft establishment 24-ft wind tunnel (in two parts) T. V. Somerville, R. R. Duddy and G. H. L. Buxton Tests were made in the 24-ft Wind Tunnel during March and April, 1940, on the Whirlwind aircraft to find if simple modifications can be introduced which will decrease its drag. The drag analysis is not complete and is focused chiefly on the drag due to leaks, cooling and excrescences. A complete record of the tests together with explanatory paragraphs is given in the tables of this note. The modifications which gave an appreciable saving in drag and which are considered possible to apply to the production aircraft are listed below. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2603.pdf 60. The resistance of aluminium and beryllium bronzes to fatigue and corrosion-fatigue D. G. Sopwith The investigation of the fatigue and corrosion-fatigue resistance of special bronzes (Gough and Sopwith, 1937) is extended to include (1) aluminium bronze (D.T.D.I60), (2) beryllium bronze (2.25 per cent. Be), each in two heat-treated conditions. In neither material is the fatigue or corrosion-fatigue resistance appreciably higher in the heat-treated condition than in the condition as received. The fatigue strength in air of the beryllium bronze is almost independent of the ultimate stress, which varied from 32 to 81 ton/in.². Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2486.pdf 61. A Further Investigation of Lateral Stability E. Priestley, B.A. Although lateral stability at high wing loadings is treated in R. & M. No. 1840, and a general outline of the problem of its estimation is given there, the above report does not include sufficient data to enable more than a rough estimation of lateral stability to be made for a particular aircraft. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1989.pdf 62. Comparison between plain and stringer-reinforced sheet from the shear lag standpoint M. Fine In R. & Ms. 2098, 2099, 2100 the stringer-sheet method of solving shear lag problems in stringer reinforced sheet was developed. The present report compares for two simple cases the solution for the plain sheet with that for the stringer-reinforced sheet. The solutions are practically identical by the two methods provided that the sheet is considered fully effective in taking end load. This leads to the conclusion that, in regions of tensile stress, at all events, all the skin area is to be included in the stringer area when applying this method. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2648.pdf 63. Derivative measurements and flutter tests on a model tapered wing W. P. Jones and N. C. Lambourne The influence of various parameters, such as wing density and flexural stiffness on the critical speed of a tapered wing was investigated theoretically in R. & M. 1782 using certain fundamental aerodynamic derivative coefficients. The principal object of the present wind-tunnel tests was to provide an experimental confirmation of the theory. A semi-rigid model wing of the R. & M. 1782 type was constructed with two tapered wooden spars of cruciform cross section. Its flexural axis lay at 0.3 chord and its inertia axis at 0.4 chord behind the leading edge. Measurements were made by the forced oscillation method of the following aerodynamical derivatives for a range of values of the frequency parameter: (i) Flexural Damping, (ii) Torsional Damping, (iii) Torsional Stiffness. The still air torsional damping which included the damping due to the internal structure of the wing was also measured, and the virtual inertia effects due to the external air were estimated by two-dimensional strip theory as described in Ref. 3. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1945.pdf 64. Flat Sandwich Panels under Compressive End Loads D. Williams, D.Sc., A.M.I.Mech.E., D. M. A. Leggett, Ph.D. and H. G. Hopkins, M.Sc. This report contains a theoretical investigation of the possibilities ofsandwich panels for transmitting compressive end loads, and also their behaviour under such conditions. The sandwich consists of two thin faces of a strong structural material, such as steel or duralumin, separated by a filling of a somewhat weaker character. The filling is designed to be stiff enough in shear to exploit the superior strength of the faces when the panel bends as a unit, and also to provide sufficient support against premature crinkling of the faces. Combinations are discussed in which steel or duralumin form the faces, and onazote, balsa wood or plywood provide the filling, and their merits are compared with each other. It is concluded that of the various types of sandwich considered, those having duralumin faces and a balsa wood filling are the most efficient. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1987.pdf 65. Flight tests of a youngman flap on fairey P.4/34. K.7555 M. B. Morgan and D. E. Morris Full-scale tests were required of the lift and drag characteristics of the Youngman flaps fitted to Fairey P.4/34 K.7555. These flaps are of the external aerofoil type, and can be lowered to two positions, one giving medium lift and low drag for take-off, the other (similar to a Fowler flap) giving high lift and drag for landing.CLMAX was determined when gliding and at full throttle. Glides and partial climbs were made in order to establish lift and drag curves. From the experimental results, the effect of flap setting on the minimum radius of horizontal turn was estimated. Further tests were made to determine the effect of adding an extra 12.1 sq. ft. to the flap area at the centre-section. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2547.pdf 66. Flight tests on a falcon with spoiler lateral control C. E. Kerr As part of a general investigation of tile use of spoilers for lateral control, flight tests were required on a Falcon with retractable circular-arc spoilers. In the first stage of the flight tests pilots' impressions and criticisms of response and stick feel were recorded and used as a basis for improving the,control. These tests were made at various speeds, flaps up and flaps down. In the second stage, after improving the control, flight tests were made with full-span flap in operation and landings were made with flap fully down. Finally, some measurements were made of time to bank at various speeds with-out flap and with flap fully down. By reducing the area of the top surface of the spoiler to a minimum and constructing it in the form of a cylindrical arc concentric with its hinge, a spoiler has been produced with zero aerodynamic hinge moment and no tendency to suck out of the wing surface. Provided that the inertia of the spoiler and the friction and backlash in the control circuit are reduced to a small amount pilots do not appear to find the resulting stick feel objectidnable after a little experience. The spoiler provides good response at cruising speeds and rapid though less even response at high speed. At low speed without flaps the response is poor. With a full-span split flap giving a CL MAX of 2.25 it is very good. For an aircraft fitted with full-span split flap, this type of spoiler appears to offer a satisfactory form of lateral control. There is no evidence of any time lag in response with these spoilers. Response for small control movements is not good at any speed, but at high speed the contrast between the initial stage of comparatively slow response and the succeeding stage of rapid response appears to become more marked, with the result, that when the control is applied in a normal manner the main response does not occur until the stick has been displaced somewhat. This effect is sometimes mistaken for time lag. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2491.pdf 67. Integrating Coefficients for Airscrew Analysis C. N. H. Lock, M.A., F.R.Ae.S., and A. E. Knowler, M.Sc., of Aerodynamics Division, N.P.L. In calculations of airscrew performance by the general graphical method of R&M 1849 or R&M 2035, the value of the thrust grading coefficient (t_{c}), or of a power loss coeeficient (such as (p_{c2}) is calculated for a definite series of values of the radius (r_{c} = 0.3, 0.45, 0.6, 0.7, 0.8, 0.9, 0.95, 0.975). These values are then plotted against r_{c}^{2}, a smooth curve is drawn and the area under the curve between the limits 0.09 and 1.0 determined by the use of a planimeter or by counting squares. In order to avoid the labour of plotting and integrating the curves and at the same time to secure more consistent results, it was suggested that the above method might be replaced by the use of integrating coefficients. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2043.pdf 68. Interference velocity for a close pair of contra-rotating airscrews C. N. H. Lock A method is developed of calculating the performance of a pair of contra-rotating airscrews, closely analogous to that described in R. & M. 2035 a for a single airscrew. The assumptions made are considered to be theoretically justifiable if the interference velocities are so small that their squares and products may be neglected. It is hoped to compare calculations by the present method with experimental results. The equations have been applied by an approximate single radius method to give the difference in blade setting between the front and back airscrews for equal power input; a comparison is also made between the efficiencies of single- and contra-rotating airscrews. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2084.pdf 69. Lateral control with high lift devices A. D. Young, R. R. Duddy The increasing attention which high-lift devices are receiving makes it desirable that a summary of the present information on lateral control with high-lift devices should be available. The devices considered are classified as - (A) those devices that can be used with full span flaps ; these include (i) spoilers, (ii) auxiliary aerofoils, (iii) ailerons behind Zap type flaps, (iv) ailerons behind slotted flaps, and (B) those devices which can be used only with nearly full-span flaps and which include (i) short span, wide chord ailerons (straight and skew hinge), (ii) floating tip ailerons, (iii) ailerons formed from part of rear flap of large double-slotted flap. A brief summary of the main characteristics of the various devices considered is found in Table 1. No satisfactory method of lateral control has yet been developed that permits full use of the high-lift devices covering the complete wing span, although there is a reasonable hope that a satisfactory spoiler control will yet be developed. For the present, methods of lateral control must be accepted which restrict to some extent the span or type of flap ; a number of such methods which are fairly satisfactory are available. The loss of possible lift increment incurred in their use need not be greater than about 15 per cent. of the increment due to full-span flaps. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2583.pdf 70. Notes on the lift and profile drag effects of split and slotted flaps A. D. Young and P. A. Hufton The existing data have been analysed and a method has been derived for predicting the lift and profile-drag increments of split and slotted flaps. It is suggested that the probable order of error involved in the method is within the accuracy required for most practical purposes. It is found that the proNe-drag increments of split flaps on wing-body combinations is somewhat lower than on wings alone, whilst the converse is tlue for slotted flaps. It is suggested that this may be due to wing-body-flap interference effects. Nevertheless, the available data from which these results are derived are scanty and most are comparatively unreliable ; further systematic tests are needed before definite conclusions can be drawn. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2545.pdf 71. On the periodic effects experienced by the blades of a contra-rotating airscrew pair A. R. Collar The present paper discusses the effects on the performance of a contra-rotating airscrew pair of the oscillatory nature of the flow round the blades. The blade sections at a representative radius are developed into two infinite cascades in a plane, and the two-dimensional flow in this plane is discussed : for simplicity the blade sections are replaced by vortices with strengths equal to tb.e circulations round the blades. On this basis, it is shown that if the two screws are to absorb equal powers at equal rotational speeds, the mean circulations round the blades must be equal ; however, this implies, for similar sections and equal chords, a coarser pitch setting for the front screw than for the rear. For this condition, the slipstream velocity has an oscillatory rotational component ; its mean rotation is, however, zero. In designing a contra-rotating airscrew pair; the most obvious way of assessing mean values for the local wind speed and direction is to imagine the number of blades to become infinite, while the blade settings and solidities are maintained; the slipstreams are then uniform. In the numerical example given it is shown that this method is quite good enough ; although the local thrust variations are of the order of Â±20 per cent. from their mean values, the latter are less than 0.5 per cent. different from those given by the assumption of an infinite number of blades. No account has been taken in the present paper of the vortices shed by the blades as the circulation changes; it may be anticipated that their effect will be to reduce the magnitude of the oscillatory variations in thrust, etc., to a degree defending on the value of the frequency parameter. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1995.pdf 72. On the static thrust of contra-rotating airscrews A. R. Collar, B.A., B.Sc., F.R.Ae.S. Under static conditions or at low rates of advance, the blades of a single airscrew are often stalled, except perhaps for the outer sections. At first sight, it would appear that the same conditions must apply to the blades of a contra-rotating pair of screws. However, some measurements made in America have shown that the static thrust of contra-rotating screws is considerably greater than that of a corresponding single screw; and the same conclusion has been inferred from the short take-off run of a particular aeroplane with contra-rotating screws. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1994.pdf 73. Propeller blade vibration nature and severity of vibration at edgewise resonance as influenced by coupling effects due to blade twist J. F. Shannon and J. R. Forshaw Information was required as to the stress distribution in propeller blades occurring at edgewise resonance, and the importance of this vibration relative to the other modes. Tests were carried out on a duralumin-bladed propeller so mounted that the dynamical system was equivalent to an engine and propeller subjected to engine torsional oscillation. The fundamental edgewise vibration and its interaction with the adjacent second overtone flapping vibration was investigated for non-rotating conditions. Edgewise resonance is important in so far as the twist of the blade causes unsymmetrical bending on the blade sections. In normal blades this twist results in large deflection in the plane of greatest flexibility, the accompanying stresses being of the order of 70 per cent. of those occurring at the second overtone flapping resonance for the same excitation. The effects of blade twist on the vibration of rotating propellers will be examined as opportunity affords. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2561.pdf 74. Spar depth and weight W. Tye and R. G. Thorne In all classes of structural design it is the usual practice to employ deep rather than shallow beams. This arises from the fact that, within limits defined partly by the web construction, the deeper the beam the less the quantity of material used. Also for beams of a given length and strength a deeper beam is stiffer. In the design of aircraft spars, where weight saving is of primary importance, and where too low a flexural stiffness might be a disadvantage, the greatest spar depth and the shortest span consistent with good aerodynamic properties are used. In discussions of wing design, it is customary to consider aspect ratio and thickness/chord ratio as primary design parameters, these quantities being intimately connected with the drag of the wing. The influence on wing weight of changes of either of these quantities is associated mainly with their effect on the semi-span/spar-depth ratio. For structural discussions, therefore, it is convenient to consider the ratio of wing semi-span to root thickness as the basic design parameter (root thickness is chosen here as the most representative depth and is most readily defined). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2569.pdf 75. Stress concentration due to four-point fixing at front end of monocoque fuselage, theoretical analysis M. Fine and D. Williams This report is a sequel to previous work by Williams, Starkey and Taylor (R. & M. 2098) and by Williams and Fine (R. & M. 2099) and treats the problem of the stress distribution in a stringer-reinforced cylindrical shell (representing a modern monocoque fuselage) under transverse loads when the reactions at the supported end are provided by four fixing points. It is assumed that these reactions are transmitted to the shell through four heavylongitudinal members, or longerons, and the purpose of the report is to discuss the manner in which the load in these members is passed on via the skin to the adjacent stringers. Two cases are considered. In the first the longerons are assumed to be of constant cross- section and to extend from end at end of the shell. In the second the longerons are tapered from the root outwards in such a way as to maintain a constant stress. Appendices I and III of the report treat the problems with some rigour and the solutions obtained are made the bases of quick approximate methods that can be applied with facilfty to any practical case. The results obtained by the approximate methods agree very satisfactorily with those derived by the far longer basic method. From working out typical cases it is inferred that for the end-to-end constant-section longerons the disturbance due to the four-point fixing does not extend a greater distance from the root fixing than Â½ to ¾ of the average root diameter, this distance being greater the greater the value of the ratio of total stringer area to total skin area in the cross-section. It is found that the constant-stress longeron tapers very quickly and appears to offer a good practical basis for design. The most important stress concentration in both cases is the shear stress in the skin immediately adjacent to the longerons at their root ends, and reinforcement of the skin thickness in this region is probably essential in all practical cases, especially for the constant stress longeron. The extent of this stress concentration is indicated by certain contour diagrams of stress distribution included in this report. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2100.pdf 76. Tests on the hurricane L.1696 in the 24-ft wind tunnel D. W. Bottle and T. V. Sommerville Tests on a Hurricane in the 24-ft Wind Tunnel at the Royal Aircraft Establishment were required to find if any simple modifications could be made which would reduce its drag. Measurements were made of :- (1) Leak drag. (2) Drag of miscellaneous excrescences. (3) Cooling drag. (4) Drag of the tail unit. The tests showed that the leak drag plus the drag due to the control gaps was 13 per cent of the total prone drag of the aircraft. Of this leak drag only one-third could be eliminated by methods which could be incorporated in production aircraft without serious modification. This emphasises the importance of eliminating leaks in the design stage. The drag of the cooling system was reasonably low, and tail-fuselage interference was small. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2562.pdf 77. The buckling of a square panel under shear when one pair of opposite edges is clamped, and the other pair is simply supported D. M. A. Leggett, Ph.D. For an efficient design of spar with thin sheet web it is important to know the load which will just cause the web to buckle. As stiffeners divide the web into panels, it is required to find the buckling stress of rectangular panels bounded on two sides by spar flanges and on the other two sides by stiffeners. Boundary conditions which represent closely this type of edge fixing are clamping (along the flanges) and simple support (along the stiffeners), and the object of this report is to find the critical shear stress for a square panel held in this way. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1991.pdf 78. The effect of variation of gear ratio on the performance of a variable-pitch airscrew for a high-speed aeroplane R. C. Pankhurst, A.R.C.S., B.Sc., J. F. C. Conn, B.Sc., M.I.N.A., R. G. Fowler and Miss E. M. Love The effect of change of gear ratio has been examined in the case of a four-bladed airscrew of 14 ft. diameter absorbing 2,000 b.h.p. at 37,000 ft. at a forward speed of 450 m.p.h. with a given engine speed (3,700 r.p.m.). Using the limited data at present available for the lift and drag of an airscrew blade section at high Mach number, it appears that for a sufficiently low gear ration the higher working lift coefficient of each blade element may increase the induced power loss such much that it is not off-set by the reduction in compressibility loss brought about by the decreased Mach numbers of the blade sections. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2039.pdf 79. The Mounting of Aero Engines : Transverse and Whirling Vibration of Some Idealised Systems Analysed by applying the Method of Admittances as extended by Duncan B. C. Carter, D.I.C., F.R.Ae.S. The following investigation was undertaken primarily to provide a rational design basis for the mounting of engines in single engined aircraft. An analysis has been made of the flexural vibrations of a uniform beam having a spring-supported mass at one end, the whole system being free in space, which is analogous to an engine flexibly mounted at the end of the fuselage. Special conditions examined include "de-coupling" spring mountings, gyroscopic coupling effects of airscrew inertia, and the case of an overhung mass. The results are applied to Defiant I, using experimental data. The analysis is extended to include cable-hangar systems. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1988.pdf 80. Water performance of a four-engined flying boat with step fairings of length 3, 6 and 9 times the step depth G. J. Evans, A. G. Smith, R. A. Shaw and W. Morris Tests were made to investigate the hydrodynamic qualities of the Sunderland flying boat, when fitted with step fairings of mean gradient 1 : 3, 1 : 6 and 1 : 9. Attitude and acce]eration measurements were made during take-offs, landings and constant-speed taxying runs. Water pressure measurements were made at various stations over the forebody and afterbody hull bottoms with and without the step fairings of 1 : 6 and 1 : 9 ratio. The fairings have no perceptib]e effect on water moments and water drag of the flying boat in steady conditions, although there appears to be a small reduction of the hump speed of 3 to 5 knots with the 6 and 9 : 1 step fairings. The 6 and 9 : 1 step fairings, however, introduce a bouncing type of porpoise in taxying runs at high speeds and high attitudes, although there is no evidence of the normal single- and two-step stability limits being affected. This bounce porpoise was not encountered during any take-off or landing with the 6 : 1 fairing, but was severe in landings with the 9 : 1 fairing whenever the datum attitude on touch-down was greater than 3 deg. The bounce porpoise is associated with a fluctuating water flow over the forebody and over the afterbody behind the fairing, and pressure and suctions of the order of 5 lb/sq in. and -- 2 lb/sq in. respectively were recorded on the afterbody. On the forebody, all pressures were positive. This bounce porpoising takes the form of violent pitching, combined with violent heaving in which the flying boat apparently bounces off the water once per complete cycle at less than stalling speed. Ordinary single- and two-step porpoising is accompanied by fluctuating water pressures on the forebody only. Zero pressures were recorded on the afterbody stations of the hull, with and without the fairings, for all stable hydroplaning conditions during take-off, landing and steady runs. The aft step was just immersed in some very high-attitude runs at high speed, but no recorders were located at the actual step. This bounce form of instability is undoubtedly due to afterbody interference with the wake from the forebody. The water flow from the forebody re-attaches itself periodically to the afterbody because of the presence of the step fairing. This probably occurs on the step fairings, but measurements were not obtained in these tests. The greater the fairing, the greater the re-attachment seems to be and, therefore, the more severe and the more frequent the attendant instability. A further programme of tests will be made to investigate the water flow conditions with the various fairings and means of making these efficient hydrodynamically. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2868.pdf 81. 24-ft tunnel tests on a high-lift model downwash and velocity measurements at the tailplane C. H. Naylor Pitching moment measurements in the 24 ft. tunnel have shown that the highlift model with double Fowler flaps down and slat open, although reasonably stable without slipstream, becomes unstable at the higher thrust coefficients required for level flight and climb. In some cases the tailplane contributed nothing to the longitudinal stability of the model. The present tests have been made to investigate the airflow in the neighbourhood of the tailplane. Pitching moment measurements in the 24 ft. tunnel have shown that the highlift model with double Fowler flaps down and slat open, although reasonably stable without slipstream, becomes unstable at the higher thrust coefficients required for level flight and climb. In some cases the tailplane contributed nothing to the longitudinal stability of the model. The present tests have been made to investigate the airflow in the neighbourhood of the tailplane. The effect of the increased velocity is main]y confined to the region of the slipstream, while the increase in downwash angle with thrust coefficient extends over a wider range in both directions. The variation in downwash angle and velocity is such as to make the tailplane a destabilising rather than a stabilising member, at constant throttle with the flaps and slat in operation with the tallplane in any practicable position. This is due to the large downwash angles associated with the relatively low aspect ratio wing. The stability could be improved by the use of a higher-aspect ratio wing. The effect of slipstream on the complete aeroplane, however, is not necessarily destabilising with flaps down because of the favourable effects of a high thrust line and of the slipstream velocity over the wing and flaps. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2649.pdf 82. A method of estimating the direct stress concentration round holes in reinforced sheet M. Fine and Anne Pellew It was shown in Aeronautical Research Council Report No. 5455 that the accurate stress-function solution of certain two-dimensional problems of stress distribution may be replaced, with negligible error, by the approximate stringer-sheet solution (R. & M. Nos. 2099, 2100). This report extends the comparison of the two methods to problems of stress concentration near holes. The stringer-sheet solution is not as accurate as before but the error in the direct stress is sufficiently low for the method to be of practical use. It is proposed to apply the method to rectangular holes and to the problem of a hole reinforced at its edge. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2604.pdf 83. A RÃ©sumÃ© of aerodynamic data on air brakes H. Davies, and F. N. Kirk A collection has been made of aerodynamic data on air brakes. The characteristics of wing brake flaps have been analysed, including the effect of venting or perforating the flaps. In particular, the design of brake flaps so as to have no appreciable effect on lift or trim is discussed, and in this connection the relative merits of double split trailing-edge flaps, Youngman flaps, air brakes behind the tail, etc., are compared. A brief description of some methods of balancing brake flaps is given. The small amount of data available on wing and tail buffeting due to brake flaps has also been analysed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2614.pdf 84. A Review of Some Stalling Research With an Appendix on Wing Sections and their Stalling Characteristics A. D. Young, H. B. Squire Over a period of years a considerable amount of stalling research on various aeroplanes was completed at the Royal Aircraft Establishment and it was considered desirable that the main results should be summarised and reviewed. The report includes a general discussion of the effect on stalling b~haviour of wing section, plan form, washout, flaps, nacelles, gills, slipstream, antomatic wing-tip slots and Hudson-type slits. The important part that is played by the longitudinal trim and stability at incidences near the stall is emphasised. The relation between wing sections and their stalling characteristics is discussed and it is shown that the stalling characteristics can be broadly predicted from an examination of the form of the wing-section upper-surface pressure distribution at high incidences. The results indicate that vicious stalling behaviou) can be avoided by the use of wing sections towards the tip of fairly high camber (3 to 4 per cent.) and moderate thickness (>12 per cent.). For some types of aeroplanes there are, however, serious objections to the use of high camber towards the tips ; the designer is then advised to avoid wing sections which experiments and theory indicate have particularly bad stalling characteristics. The worst tip thickness for stalling appears to be in the region of 9 per cent. High taper tends to worsen the stalling behaviour and it is advisable to consider taper ratios greater than 2:1 only in conjunction with wing-tip sections having good stalling characteristics. The use of part-span flaps does not appear to cause any marked deterioration in stalling behaviour, and frequently it improves the behaviour ; but there is some evidence, though not yet conclusive, that the use of full-span flaps may be accompanied by an appreciable worsening in stalling behaviour. Attention is drawn to the advisability of examining the flow at high incidences in the neighbourhood of the tail-plane of an aeroplane in the design stage, with a view to assessing its probable stalling behaviour ; in particular, the possibilities of designing for some stall warning can then be examined. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2609.pdf 85. A theoretical analysis of longitudinal dynamic stability in gliding flight H.M. Lyon, et al As part of a general investigation of stability problems a review of the theoretical aspects of dynamic longitudinal stability was required. A summary is given of the theory of dynamic stability in gliding flight, including an approximate method of calculating the period and damping of the phugoid. The effects of weights and springs in the elevator circuit are examined and compared with qualitative evidence from flight tests. Stability at altitudes is also considered. It is shown that, with positive static stability, the low degree of phugoid damping on some modern aircraft cannot be attributed to low drag or to inadequate tail area for damping out the pitching motion, unless there is a large loss of tail-plane effectiveness on freeing the stick. It is more probably due to too small a static margin combined with friction in the elevator circuit. A weight moment about the elevator hinge improves static stability, but with the assumptions made here, it does not appear to be as efficient dynamically as an equivalent change in static margin by an increase in tail effectiveness or a movement of the centre of gravity. A spring or inertialess weight moment improves static stability, but may have a very unfavourable effect on dynamic stability, particularly at high altitudes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2075.pdf 86. An approximation simplifying wing flutter calculations G. A. Naylor This report shows that the application of classical flutter theory to the determination of wing flexural-torsional flutter speeds is considerably simplified by the omission of a term which is usually the very small difference between two small quantities. With this simplification it is possible to derive a formula giving the critical speed explicitly in terms of the dynamical coefficients. Numerical examples show that this approximation gives practically the same flutter speeds as the complete classical theory, even when the coefficients are given values which do not normally occur. A simpler approximate formula is obtained by a combination of the first approximation with Pugsley's simplified theory; this second approximation gives flutter speeds for normal wings which agree with those from classical theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2605.pdf 87. Binary aileron--spring-tab flutter G. A. Naylor and Anne Pellew This note deals with binary aileron-spring-tab flutter involving rotation of the aileron and spring tab about their hinge lines. The methods of R. & M. 1155 are used to calculate the variation of flutter speed with various parameters. Particular attention has been given to the magnitude and position of the tab mass-balance weight. It is concluded that binary aileron-spring-tab flutter can be prevented by mass-balancing the tab provided the balance weight is not placed further than a certain distande ahead of the tab hinge. This distance is in agreement with the limit suggested by Frazer and Jones. Although flutter can be prevented by adding mass at this limiting distance, the mass required is impracticably large; it becomes practicable if the arm is reduced to about three-quarters of the limiting distance. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2576.pdf 88. Calibration of the Royal Aircraft Establishment 24-ft wind tunnel J. E. Allen, and K. V. Diprose Evidence from several check experiments indicated that the results of the preliminary calibration of 1935 were in error. The object of the described experiment was to investigate this and to calibrate the wind tunnel in greater detail than previously. The velocity distribution across the jet in three planes has been found at several tunnel speeds. The distribution of static pressure throughout the jet and the relation between the dynamic head at various positions in the tunnel and the hole-in-side pressure has been investigated. A complete list of all previous calibrations together with results and reasons for the discrepancies is included. A new tunnel calibration is given in Tables 1 and 2. The plane of reference is taken as 12.5 ft from the jet face, and the mean velocity over the section is greater than the standard value used up to the present by about ½ per cent at high speeds and 2 per cent at low speeds. The mean velocity falls as the jet face is approached, and a correction factor for this is given in Table 2. The revised corrections will be incorporated in all reports issued after 30th June, 1942. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2566.pdf 89. Contra-flow turbo-compressor tests A. D. Baxter and C. W. R. Smith Several methods of constructing contra-flow turbo-compiessor wheels have been investigated by mechanical tests on single-stage wheels. The results have been incorporated in a complete unit which has been designed and tested at the Royal Aircraft Establishment for research purposes. It was designed to pass 200 lb/min of air at 25,000 It with a compression ratio of 2.7 : 1 and a temperature at inlet to the turbine of 145 deg C. In designing, the compressor results from aerofoil cascade tests were extrapolated beyond the limits then covered (1938). Subsequent cascade experiments showed that the compressor efficiency would be low and that the blading used would be stalled under design conditions. Tests on the unit confirmed this, indicating that a compressor efficiency of about 70 per cent was the maximum obtainable, whereas the designed efficiency was 83 per cent, a figure which with present day knowledge is easily obtainable. A slight modification to the compressor-blade heights improved the efficiency and enabled the range of operation to be extended. In the contra-flow unit the leakage between the shrouds separating the compressor and turbine annuli is a special problem. Owing to the departure from design conditions and the intake air boost the leakage observed on the unit was at times as much as 50 per cent of the entering air. The leakage likely to be obtained in a unit operating under designed conditions is estimated at 4 per cent. Most Of the remainder of the running time was devoted to investigation of mechanical problems. These included the temperature gradients in the wheels, bearing cooling and lubrication, and constructional features. At a gas temperature of 400 deg C. the constricting section in the wheel disc caused a drop of temperature of 150 deg C. above the high pressure bearing housing. By increasing the cooling air mass flow this drop was increased to 250 deg C. The bearings were found to be satisfactory provided their temperature could be maintained at less than 200 deg C., but the oil metering supply was unsatisfactory. Some movement of the blades in the rotors was observed and relative axial expansion of t.he rotors andcasing led to rubbing at the high-pressure end. Trouble was also experienced with the large gland leakage areas at the shrouds and around the bearing housings. It was concluded that, in spite of the poor aerodynamic performance, there was no fundamental reason why similar units should not operate efficiently and why a good mechanical performance should not be obtained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2607.pdf 90. Design and development of a torsiograph having a serrated-condenser pick-up unit B. C. Carter, and J. R. Forshaw The instrument that forms the subject for this report has a condenser pick-up unit to which a carrier wave is applied : it measures, directly, instantaneous angular displacements due to shaft twist. The pick-up originated in a surface-strain gauge (embodying serrated-condenser elements) which had been the subject of some preliminary experimental work. Two main types of torsiograph are contrasted in relation to their application and the present torsiograph is described. Results of calibration tests with different serrations and air-gaps are given, together with a general account of experience gained during a total of some 10 hours running with the instrument fitted to a Merlin II engine. Some typical records are included but not the results of the torsional vibration investigation - which will form the subject of a separate report. Calibration resultg are given from which the serrations appropriate to particular applications can be decided. The torsiograph gives very satisfactory results when due care is taken with electronic equipment. The natural frequency of the instrument is such that torsional vibrations having a frequency as high as 80,000 cycles per minute can be recorded with ease. The instrument provides a means of making continuous observations of torsional vibration at a moderately remote station and it can be adapted for making observations in flight. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1982.pdf 91. Estimation of wing flutter speeds from the curves of R. & M. 1869 Mary E. K. Graham Normal classical theory is somewhat complicated for design use, and this report describes a simple method for the use. of designers : briefly, this is to estimate a straight-tapered wing equivalent to the'wing under consideration, and to apply the results of R. & M. 1869 to determine its flutter characteristics. A graph is given, in which flutter speeds calculated by the classical theory for a number of typical aeroplane wings, are plotted against the speeds found by the use of the curves given in R. & M. 1869. The method strictly applies only to plain cantilever wings, but would probably give conservative results for wings with wing engines. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2608.pdf 92. Experiments on laminar-flow aerofoil EQH 1260 in the William Froude national tank and the 13ft. x 9ft. and 9ft. x 7ft. wind tunnels at the National Physical Laboratory A. Fage and W. S. Walker To determine Whether the flow conditions in the William Froude National Tank and the new 13 ft. x 9 ft. and 9 ft. Ã— 7 ft. tunnels at the National Physical Laboratory are sufficiently steady to allow the properties of laminar-flow aerofoils to be investigated at high Reynolds numbers: and to obtain information on the behaviour of laminar-flow aerofoil section EQH 1260. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2165.pdf 93. Flutter of control surface tabs G. A. Naylor Oscillation of control-surface tabs has occurred in flight. General experience and the investigations of this report suggest that the oscillations were flutter, involving translation of the tab, arising from bending of the local control-surface structure, coupled with rotation of the tab about its hinge, arising from either backlash or elasticity of the tab controlling me&anism. Binary flutter calculations show that, for this coupling, the normal remedy, i.e. mass-balancing, is only partially effective (static mass-balancing roughly doubles the backlash flutter speed but may decrease the elastic flutter speed). If the tab controlling mechanism is adequately stiff, elimination of backlash gives higher flutter speeds than would be obtained by mass-balancing alone and in practice probably removes the danger of flutter. Flutter is completely prevented by aerodynamically balancing and dynamically mass-balancing (C.G. on hinge line) the tab. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2606.pdf 94. Free-flight tests on kites in the 24-ft wind tunnel S. B. Jackson Tests were required to be made on six kites over a greater range of wind speed than for previous large-tunnel tests. The kites used during the investigation were (A) 3-ft Cody kite Mk. II, (B) 3-ft reversed Cody or Dyco kite, (C)3-ft Haldon kite, (D) 2 X 3-ft Cody storm kite with lateral cross-bracing, (E) 2-ft Cody kite Mk. III with bifurcated inner bridle and (F) 2-ft Cody kite Mk. III with longitudinal bracing. Tests were made over the whole stable range of the kites and up to the highest safe wind speed. The kites were flown from a pylon and values of lift, drag and incidence of the forward and rear bridles were measured. Attempts were also made on two of the 3-ft kites (A and C) to improve their stability at higher wind speeds and low incidences. The maximum value of (L-W)/D was below 2.5 and values of Cz, based on the fabric surface area, excluding the vertical panels, were not greater than 0.9. The unmodified kites are unsuitable for high wind speeds. At low incidences, the kites tend to fall away from their flying position at speeds above 70 ft/sec, but this can be temporarily delayed by diagonal cross-bracing to lift the centre of the leading edges of the front lifting panels, and by tying the wing tips together. At high incidences, bending of the bamboos may disrupt the kite and it is recommended that a bifurcated bridle, which picks up at four points on each lower longitudinal, be used to prevent this bending. The parallel-rigged wing canes tend to take up a negative incidence as tile lower longitudinals bend under load, and thus cause bending of the transverse bamboos. This can be avoided by using cross-rigging, the wing canes then taking up a slight positive incidence. The flapping of the vertical panels, which limits the usefulness of the kites at higher speeds, can be moderated by stiffening canes sewn in the fabric in a fore and aft direction. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2599.pdf 95. Graphical treatment of binary mass-balancing problems R. A. Frazer A graphical method, based on 'classical' flutter theory, is described which provides a simple test of the effectiveness of mass-balancing in the prevention of flutter at various heights. Illustrative applications are made to flexural-aileron and servo-rudder flutter. It is suggested that diagrams of this type may be a useful aid in design. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2551.pdf 96. Heat Transfer Calculation for Aerofoils H. B. Squire, M.A. A method of calculation of the rate of heat transfer from the surface of an aerofoil maintained at a temperature above that of the stream was required, including allowance for the effect of dissipation of energy in the boundary layer. A convenient method of calculation is developed for laminar boundary layers, and the best method of applying Reynold's analogy to the turbulent layer is discussed. The methods are applied to calculate the heat transfer from the aerofoils N.A.C.A. 2409 and 2415 at C_{L} = 0.24 and C_{L} = 0.8. Simple formulae for the rise in surface temperature due to dissipation are derived. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1986.pdf 97. Measurements of cabin noise in bomber aircraft D. Cameron, and W. J. D. Annand Measurements of cabin noise level, by means of an objective noisemeter and octave filter, have been made on a number of multi-seater aeroplanes. It was desired to examine these results to determine whether they could be predicted from the geometry and other features of the aeroplanes, and whether they could be correlated with noise assessments by the crew. Curves of noise level in decibels against frequency have been obtained for eight aeroplanes, in various flight conditions, at different crew stations, and on one aeroplane with and without soundproofing. These curves have been examined in conjunction with details of the geometry of the aeroplanes, the frequencies of airscrew and engine rotation and of the engine explosions, and assessments of the aeroplane noise made by pilots and observers. The principal sources of noise are airscrew rotation and engine exhaust at low frequencies and aerodynamic noise at high frequencies; in certain cases, other factors such as airscrew torsional vibration and engine vibrations appear to contribute. The noise level to be expected can be predicted roughly from a consideration of the distance of the crew stations from exhausts and airscrews, the area of perspex present, the aerodynamic cleanness of the windscreen and the degree of soundproofing. The curve of noise level against frequency does not in all cases agree with an-assessment by the crew, and it appears that some other measurement is necessary to complete the picture. It is suggested that a more complete determination of the noise characteristics would be given by a combination of three tests--frequency analysis, a measurement of peak values, and an aural investigation of rattles, etc. The introduction of some degree of soundproofing is considered to be desirable in the majority of British bombers. The material used must not interfere with maintenance by making pipelines, etc., inaccessible, and it is for consideration whether some local thickening of the fuselage skin and windows in the plane of the airscrews would not be of advantage in reducing the amount of internal material required. Care should be taken to eliminate noises such as rattles, buzzes, whistles and drumming panels which can be very irritating to the crew even when they are not very loud. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2296.pdf 98. On the stressing of polygonal tubes with particular reference to the torsion of tapered tubes of trapezoidal section H. L. Cox A general method for stressing polygonal tubes is described and applied to the torsion of parallel and tapered tubes of rectangular and trapezoidal section. It is assumed that the shape of the tube is maintained by a limited number of frames. In treating parallel tubes deformation of these frames in their own planes is taken into account; the effect Of this deformation is shown to be small, and in treating tapered tubes the frames are assumed to be rigid in their own planes. The method of stressing tapered tubes in torsion is applicable to any tube of trapezoidal section with one plane of symmetry, no matter how the dimensions may vary along the length of the tube; in particular the method is directly applicable to tubes having portions of their walls cut away. The successive stages in the computation are set out in tabular form and illustrated by worked examples, including cases with 'cut-outs'. The final stage in the computation involves the solution of a set of simultaneous equations equal in number to the number of frames, but these equations are of a special type, readily soluble by a straightforward process without danger of any serious loss of accuracy. The length of the computation is directly proportional to the number of frames, but it is demonstrated by examples that the stress distribution is affected only slightly by the addition of extra frames, so that in practice it should normally be permissible to ignore all but a few of the frames. In the special case of a conically tapered tube in which the wall thicknesses are uniform along the length of the tube, the results can be generalized to include the case of a tube with an infinite number of rigid frames. In this case the results obtained by the present method become identical with those obtained by Williams in R. & M. 1761 and by others using Williams's method. The author wishes gratefully to acknowledge the help he has received in the preparation of this paper from Messrs. H. E. Smith and A. E. Johnson of the National Physical Laboratory, Mr. W. S. Hemp of the Bristol Aeroplane Co., Ltd., and Mr.E.H. Atkin of Messrs. A. V. Roeand Co., Ltd. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1908.pdf 99. Possio's subsonic derivative theory and its application to flexural-torsional wing flutter parts 1 and 2 R. A. Frazer and Sylvia W. Skan Part I. Possio's Derivative Theory for an Infinite Aerofoil Moving at Subsonic Speeds. The derivative theory due to C. Possio for an infinite aerofoil moving at subsonic speeds is reviewed, and certain modifications are proposed. Derivative values are calculated for a Mach number of 0.7, and for values of the frequency parameter lambda ranging from 0 to 5.0. For lambda < 1 the derivative values based on a three-point collocation method are in fair agreement with those given by Possio. For the range 1.0 < 2 < 2.0 five-point collocation is necessary, while for lambda = 5.0 even seven-point collocation may prove unsatisfactory. The numerical results obtained are applied in Part II to estimate the influence of compressibility and flying height on the critical speed for flutter of a tapered cantilever wing. Part II. Influence of Compressibility on the Flexural-Torsional Flutter of a Tapered Cantilever Wing Moving at Subsonic Speed. Calculations based on Possio's subsonic derivative theory and:on vortex strip theory were made to obtain preliminary information on the influence of compressibility and flying height on the critical speed for flexural torsional flutter. The results are summarised by curves corresponding to constant altitude H, which show the variation of N with wing stiffness ratio r, where N denotes the ratio of the critical speed for flutter of the wing in compressible air at a Math number of 0.7 to the critical speed for flutter of the same wing in incompressible air. The results indicate that for 1 =< r =<3 the compressibility correction is insignificant at sea level, and that N is of the order 0.95 to 0.92 at H = 30,000 ft. More extensive test calculations are very desirable. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2553.pdf 100. Propellors in high-speed dives J. F. C. Conn, B.Sc., M.I.N.A., and Miss E. M. Love The performance of a variable-pitch, 3-bladed propellor has been calculated for conditions of fixed power absorption, fixed rotational speed and varying advance speed. Curves of efficiency and power-loss ratios are given to a base of V/a (advance speed/velocity of sound, Fig 1), together with thrust, torque grading and compressibility loss curves to a base of (radius) squared (Fig. 2). Increasing values of V/a (up to 0.85 or 600 m.p.h. at 21,000 ft.) representing the conditions of a high-speed dive, are accompanied by marked decreases in efficiency and under these conditions the thrust becomes negative over the tips of the blades. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2040.pdf 101. Proposal for an elevator maneuverability criterion S. B. Gates The approximate theory of response to elevator developed by Bryant, Gandy and Gates yields a compact formula for a criterion of manmuvrability Q, the 'stick force per increment in g' ; there is an anMogous but less useful criterion 51 terms of stick travel. It is recommended that Q be adopted for designers' use, that its limits of validity be checked by careful tests on one aeroplane, and that more force measurements in pull out from dives be made on a number of aeroplanes in order that numerical standards may be attached to Q. Reference is made to American standards and to experimental work already done in this country. The rate of growth of acceleration, which is not represented in the criterion, is discussed and illustrated by a numerical example. From this it appears that within limits which probably apply to a pilot's normal control movements :-- (1) The rate of application of force affects the time to reach maximum acceleration but not the value reached. (2) The acceleration produced by a given stick force is independent of speed if the static margin is fixed, but the time to reach it is inversely proportional to the speed. (3) The acceleration produced by a given stick force increases with altitude ; this effect is the greater the less the static stability. The bearing of this on the difficult control of high altitude fighters near the ceiling is discussed. The close connection between the problems of maneuvrability and safety is noticed throughout. The inertia weight is not ideal as a deterrent to the production of high acceleration, and more promising variants of this device are referred to. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2677.pdf 102. Some wind-tunnel developments of the spoiler as a form of lateral control W. S. Coleman, and G. H. Tidbury The following investigation formed part of a more general research on problems associated with high-lift flaps. To obtain the maximum advantage from such devices, a satisfactory alternative to the conventional aileron is required, permitting the flap to extend over the full wing span. Spoilers meet this condition, but further development to improve their hinge moment and response characteristics was clearly necessary at the time. The present work was undertaken for this reason. The static rolling, yawing and hinge moments were examined on (1) a series of hinged-plate spoilers, (2) a series of circular-arc spoilers, particular attention being given to the development of satisfactory hinge moment characteristics. Subsequently, the latter, which proved to be of considerably greater promise with respect to the above consideration, were investigated for response. For a spoiler of the type illustrated in Fig. 2b, the hinge moment is sensitive to the degree of bevel y. By hinging the surface concerned, so that y can vary with displacement of the spoiler, it is shown, by means of an example, that promising hinge-moment characteristics are obtainable with a quite simple link system for controlling the bevel angle in the necessary manner. The present experiments, however, are mainly of interest in emphasizing the value of this device as a very effective way in which the required hinge-moment characteristics can be approached, and are by no means an exhaustive survey of what may be achieved in this direction. From the dynamic experiments, it is concluded that a spoiler-aileron fitted to a wing with full-span flap of the dimensions considered in the present investigation will have a satisfactory response under high speed or cruising and climb conditions in flight, but may become deficient in this respect as the stall is approached. An intersurface slot behind the spoiler, when the latter has to be located so far from the trailing edge (at approximately 80 per cent. of the wing chord), proves to be essential both in promoting a satisfactory initial development of static rolling moment, and in preventing an inadequate response. The slot, however, if unsealed when the control is not in operation, introduces a drag increment which would be excessive for high performance. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2586.pdf 103. Spring Tab Flutter Part I A Theoretical Investigation on Wing-Aileron-Tab Flutter Part II Experiments on Binary Aileron-Tab Flutter R. A. Frazer et al Part I. A theoretical discussion is given of wing-aileron-tab flutter, with special reference to the influence of spring tab control. Numerical applications of the theory are made to two representative types of spring tab, and with the aid of special stability diagrams certain conclusions are drawn regarding the conditions for flutter prevention. In relation to binary aileron-tab flutter it is shown that certain restrictions on the aileron-tab density ratio should be observed, and that when a balancing mass for the tab is fitted its arms should be limited to a certain length. Calculations relating to ternary flutter indicate that the possibility of ternary flutter occurring when all the possible binary types are absent is very remote. Part II. A theoretical discussion of the effect of non-preloaded spring tab control on wing-aileron-tab flutter, in which the binary aileron-tab case is included, is given by Frazer and Jones in Part I. The experiments here described were made to test certain of their conclusions for binary aileron-tab flutter. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2952.pdf 104. Stress diffusion adjacent to gaps in the inter-spar skin of a stressed-skin wing M. Fine and H. G. Hopkins The diffusion of stress in the .neighbourhood of chordwise gaps in the wing surface is an important structural design problem. Such gaps occur at wing joints and at undercarriage and bomb-bay cut-outs, and can involve local stress concentrations which require to be estimated. This report gives, subject to certain simplifications (including representation of the stringers by an equivalent sheet, carrying direct end load only), a theoretical analysis of the problem, and derives formulae for the stress distribution. Approximate formulae are found for (i) the direct stress in the flanges and (ii) the shear stress in the skin at the flanges and at the chordwise gap. These approximate formulae, applicable with negligible error when chordwise gaps are not closer than about one and a half times the inter-spar distance, enable a rapid estimate to be made of the stress concentration. A numerical example to illustrate the application to design is given, and shows that the maximum additional skin shear stress can be as much as two to three times the maximum additional flange direct stress. Although various factors (for example, flexibility of riveted joints between the spar flanges and the skin, local buckling and plastic flow) are likely to reduce the stress concentration if present calculations predict it to be high, some reinforcement of the skin is likely to be necessary. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2618.pdf 105. The Application of a "Wattmeter" Harmonic Analyser to the Measurement of Aerodynamic Damping for Pitching Oscillations J. B. Bratt, B.A., B.Sc., K. C. Wight and V. J. Tilly, of the Aerodynamics Department, N.P.L. In the application of the magneto-striction stress-indicator to the measurement of the forces on an oscillating aerofoil the method employed is to obtain a photographic record of the stress indicator output by means of a cathode ray tube and moving film camera. The analysis of the records so obtained is laborious, particularly on account of the presence of extraneous vibrations, and the accuracy is low. The present paper describes a method in which the modulated output from the stress-indicator is first rectified and then analysed electrically by means of an electronic wattmeter, results being obtained in terms of meter readings. The method is sensitive and rapid, and the accuracy is much higher than that of the photographic method, whilst extraneous vibrations are smoothed out electrically. Also the greater sensitivity of the method has shown up certain undesirable features in the stress indicator, e.g. hysteresis in the sensitive unit and somewhat rapid variation of calibration with time. The need for a more satisfactory type of indicator for measuring oscillatory forces is emphasised. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2063.pdf 106. The Buckling of a Long Curved Panel under Axial Compression D. M. A. Leggett In modern aeroplane design a detailed knowledge of the behaviour of thin panels is very necessary. The problem of flat panels may be regarded as largely solved. This is not true, however, of curved panels and the object of this report is to obtain further information on the behaviour of curved panels under axial loading. The problem falls naturally into two parts, according as the Invesngat lon is concerned with the initial buckling of the panel or with its subsequent behaviour. The second part of the problem will be treated later, and attention is here confined to obtaining an accurate expression for the initial buckling stress of a slightly curved and perfectly fanned panel, the two straight edges of which are either simply supported or fixed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1899.pdf 107. The correlation of aeroplane loading and accident statistics A. G. Pugsley The general problem is to predict the probableeffect of a given change of structural strength upon the accident rate, the available data usually being in the form of rather meagre loading and accident statistics together with a knowledge of the strength of the structure concerned. A method of treating this problem is given and is illustrated by an application to undercarriages. The method is simple and quick and requires no specialist knowledge of statistical mathematics. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2682.pdf 108. The Experimental Determination of the Interference on a Large Chord Symmetrical Joukowski Aerofoil Spanning a Closed Tunnel J. H. Preston, B.Sc., Ph.D and N. E. Sweeting, of the Aerodynamics Division, N.P.L. The interference on a 20 in. chord simple Joukowski aerofoil approximately 12 per cent thick has been measured in the 4 ft. No. 2 tunnel at the National Physical Laboratory. Tunnel constraint was removed by shaping the walls over a limited distance fore and aft of the model to the calculated streamlines of the unbounded flow about the wing. When the model chord is less than half the tunnel height, and the incidence is less than 9 deg., the wing can be replaced by its equivalent doublet at the position of maximum thickness, together with a vortex with the same circulation at the centre of pressure, for the purpose of calculating the streamlines. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1997.pdf 109. The induced drag of flapped elliptic wings with cut-out and with flaps that extend the local chord A. D. Young Calculations have been made of the induced drag of flapped elliptic wings covering a range of aspect ratios from about 4 to about 12, a range Of flap spans from 0.2 to 1.0 of the wing span, and a range of flap cut-outs from 0 to 0.6 of the wing span. The results are presented in charts in a convenient form for application. Calculations have also been made of the induced drag of elliptic wings of an aspect ratio of about 6 with flaps that extend the local chord by 40 per cent when in operation ; flap spans of 0.26, 0.5 and 0.77 of the wing span were examined. It is concluded that for a given net flap span and lift increment minimum induced drag will be obtained with a cut-out of about 0.1 wing span. The effect of local chord extension due to a flap was found to be negligible. These results apply strictly to elliptic wings but they probably apply with fair accuracy to wings of taper ratio of the order of 2 : 1. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2544.pdf 110. The theory of parachutes with cords over the canopy G. W. H. Stevens and T. F. Johns The basis for designing parachutes of R. & M. 862 did not appear to be correct for parachutes with cords over the canopy. Moreover, the presence of these cords was essential in a practical design for heavy duty purposes and it was obvious from appearance that their presence produced a stress distribution considerably different from that of the earlier theory. This report investigates the distribution of stress in a parachute with cords over the canopy, particularly when the cords are kept shorter than the length of the fabric gore which is permitted to bulge out between the cords under the excess pressure of the air inside the parachute. An approximate theory of shape and of the distribution of stress is developed by making certain assumptions, particularly that the tension in the fabric in any axial section can be reduced to a negligible amount, and that the pressure difference all over the parachute can be regarded as uniform. On the basis of this theory a method of calculating the shape of a gore is developed and an example given. A brief statement is made on the degree to which a parachute so designed departs from the shape and maximum stress calculated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2320.pdf 111. Wind-tunnel tests on the Shetland C. H. E. Warren and R. E. W. Harland Wind-tunnel tests were needed to obtain aerodynamic data on the Shetland. The following measurements were made: 1. Lift, drag and pitching moment for various conditions of the model over the complete flight range, with flaps up and down. 2. Directional and lateral stability. 3. Ele+ator, rudder and aileron effectiveness. 4. Effect of return-flow nacelles on lift and pitching moment. The lift and drag increments due to the flaps suggest that their design is satisfactory, and no modifications have been recommended. There is a sufficient margin of stick-fixed longitndinal stability without slipstream at normal speeds, but with flaps up there is a loss in stability near the stall. With flaps down there are appreciable changes in longitudinal stability and trim. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2571.pdf 112. Wind-tunnel tests on the spoiling effects of engine cooling gills on radial air-cooled installations on a wing J. Seddon and J. A. Kirk Information was required on the spoiling drag associated with opening cooling gills on radial air-cooled engine installations on a wing. Maximum lift, drag up to high CL, and cooling flow were measured on a 1/12 scale model of a flying boat, showing 1. the effect of opening cooling gills to 25 deg. and the variation of these effects with gill position relative to the wing; 2. the results of emitting the cooling air at specified regions of the exit; 3. comparison with a scheme for return-flow cooling. The spoiling drag associated with fuliy open gills at high Cz can be very large (of the same order as the wing induced drag) if the gill exit is nearer to the wing leading edge than about 10 per cent. of the local wing chord; but the effect diminishes rapidly as this distance is increased. To avoid the effect it is recommended that the exit of the gills should be at least 15 per cent. of the chord forward of the wing leading edge. The drag due to spoiling is also reduced if the cooling air is kept away from the nacelle-wing junction by emitting it at specified regions round the exit, preferably at the bottom where the lift is a minimum. Larger gill angles would be needed to satisfy maximum flow requirements in this way. The return-flow cooling system, with nose-exit, shows no evidence of large spoiling drag at high cooling flow. The data obtained may be useful for estimating the effects of other forms of discharge of low-energy air in front of a wing leading edge. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2558.pdf 113. A method for determining the water stability of a seaplane in take-off and landing H. G. White, and A. G. Smith A direct method of determining the water stability in take-off and landing of full-scale seaplanes is described. The customary method of measuring full-scale stability is by steady runs over a range of speed and attitudes. This is tedious ; it does not give the true take-off stability and does not give the landing stability. The steady-run stability is assumed to correspond very closely to the take-off stability but was originally used to obtain fun-scale conditions comparable with model scale. This report gives a method of analysis of take-off records of attitude against speed, and results Obtained by this method are compared with the steady-run results. Results on the Scion fitted with a Â½ scale Sunderland hull and Saro with a 1/2.75 scale Shetland hull are used to establish the method, but it has also been checked against the available date on the full-scale Seal and Sunderland I. The take-off stability limits show remarkable agreement with the corresponding steady run limits (to within Â½ dec) of the Scion and Saro. Evidence on the Seal and Sunderland is insufficient for a definite conclusion in these cases, but there is no disagreement between the results obtained. The method is accurate and quick to use, but takes no account of of the amplitude of porpoising so that a few steady runs would still be necessary to establish this where required. By use of this method the investigation of the stability characteristics of a seaplane under different conditions of weight, c.g. and flap angle can proceed quickly on the evidence of about eight take-off records at each condition, these records covering the full attitude range. The method may also be applied to find landing stability from landing records. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2719.pdf 114. A note on side and floor aperture jumping G. W. Carling The occasional complete or partial failures of "X" type parachute equipment are, so far as is known, always associated with one or more of the three following faults:- 1. Somersaulting of the man. 2. Twisted rigging lines. 3. Tangled rigging lines. Present research and development work is primarily directed to reducing or eliminating these faults. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2395.pdf 115. An aerofoil designed to give laminar flow over the whole surface with boundary-layer suction E. J. Richards and C. H. Burge A new type of aerofoil is described over the whole of which it is possible to maintain laminar flow by means of a small amount of boundary-layer suction. Preliminary small scale experiments at Reynolds numbers of about 0.37 Ã— 10power6 show that the mass flow it is necessary to remove by suction is less than that in the laminar boundary layer at the slot. On the basis of these small-scale experiments the effective drag of this aerofoil at a Reynolds number R is estimated to be approximately 6.0Rpower-1/2. Thus at the Reynolds numbers reached in present day flight (say 25 Ã— 10power6) an effective drag coefficient of 0.0012 may be expected. These figures are all subject to experimental confirmation at higher Reynolds numbers. More elaborate tests are to be made in the National Physical Laboratory 13 ft. Ã— 9 ft. wind tunnel at Reynolds numbers up to 5 Ã— 10power6. Other experiments are also planned in the N.P L. Rectangular High-Speed Tunnel. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2263.pdf 116. Effect on aerofoil drag of boundary-layer suction behind a shock wave A. Fage, and R. F. Sargent To measure, at Mach numbers near the critical value, the reduction in drag due to boundarydayei suction on the upper surface of an aerofoil. To determine whether this reduction can be obtained with an economic use of power. The experiments were made on 2 in. chord aerofoils, NACA 0020 section, at 0 deg. and 4 deg. Drag was determined from pitot tube traverses at one chord behind the trailing edge of the model. Information on the flow over the upper surface was obtained from pitot tube traverses at 0.02 chord behind the trailing edge, from visual observation of shock waves, from surface tube observations just forward of the slot, and from normal pressure measurements. The cases considered are those for which shock waves cause boundary-layer separation and those for which shock waves are not present or are too weak to cause separation. Estimates of the power absorbed by the compressor, ignoring duct losses, are Obtained from (i) measurements of the mass of air sucked and the maximum stagnation pressure of the air issuing from the slot, and (ii) a boundary-layer relation which includes entry shock losses but not the losses in the slot. Suction has little effect on the critical Mach numbers, Mc = 0.65 for α = 0 deg. and 0.57 for α = 4 deg., but the minimum drags with suction on the upper surface are 40 per cent., α = 0 deg., and 50 per cent., α = 4 deg. lower than the aerofoil drags without suction, 0.45 < M < 0.735. The drag coefficients measured at the critical Mach numbers without suction are obtained with suction at Mach numbers which are 0.08, α = 0 deg., and 0.105, α = 4 deg., higher. The drag falls to its minimum value when about 0.6 of the mass of air in the boundary layer is sucked. In the present experiments, the power saved by the reduction in drag due to suction is about the same as the estimated power absorbed by the compressor. The experiments give promise that, at the Reynolds numbers of flight and for an efficient slot and suction system, the drag coefficient of a wing at the critical Mach number without suction can be maintained at the same value and. with an economic use of power to a higher Mach number, say 0.1 higher, by boundary-layer suction. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1913.pdf 117. Experiments giving hinge moment and lift on a NACA 0015 aerofoil fitted with a 40 per cent control, with especial reference to effect of curvature of control surface A. S. Batson, J. H. Preston, and J. H. Warsap To add to the available data regarding lift and hinge moment on a control, and to test further the ideas developed in R. & M. 20O8, with especial reference to the effect of curvature of control surface. Measurement of lift and hinge moment on a two-dimensional aerofoil (section NACA 0015, chord 18 in.) fitted with a 40 per cent control (radius-nose). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2698.pdf 118. Flutter at High Incidence Mary Victory This report describes work which has been done to investigate the possibility that the flexure-torsion flutter speed of a wing may be less at high incidences than at low incidences, and that this decrease may be due primarily to reduction of aerodynamic torsional damping with incidence. The main discussion is contained in Part I., but the evidence dealt with here is obtained from tests made at relatively very low Reynolds numbers. Part II. (p.11), however, discusses the application of the results to full scale, and is based on more recent tests at larger Reynolds numbers. It is concluded that for modern aircraft the variation of critical speed with incidence is likely to be small. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2048.pdf 119. Frequency "admittance" curves for coupled engine crankshaft (torsional) and contra-revolving propeller (flexural) vibrations J. Morris In this report the "admittance" method, for dealing with coupled vibrations of engine crankshaft propeller systems, is adapted to cover the case of contra-revolving propellers. The treatment is quite general in that the propellers may or may not be equal or may or may not revolve at equal speeds. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2012.pdf 120. Lateral stability of tailless aircraft A. W. Thorpe and M. F. Curtis Information was required on the probable effect on lateral behaviour of a change from conventional to tailless types. The essential features of a tailless design are represented by large reductions in the absolute values of the derivatives yv, nv, nr. As few tailless models have been studied, a numerical survey of stability boundaries has been made over a range of these parameters which probably covers the limits set by the all-wing design without end fins. Curves of constant period and constant damping have been drawn in a few cases and from these curves a numerical comparison of the stability characteristics of conventional and tailless aircraft has been made. For the larger values of n~ and y,, considered, oscillatory instability is more likely to occur at low speed than at high, and instability at high speed is unlikely. For the smaller values of n, and y~, oscillatory instability is more likely at high speed than at low speed, and stability at high speed can be attained only with a small value of -- l,. Spiral instability is probable at all speeds, but at high speed the rate of growth.of this motion will be small. The survey stresses the need for systematic measurements of y~, n,., n, (particularly the last) in the tailless range. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2074.pdf 121. Methods of Predicting Flexure-Torsion Flutter of Cantilever Wings J. Williams, B.Sc., of the Aerodynamics Division, N.P.L. It is assumed that, for the purposes of flexure-torsion flutter analysis, the cantilever wing may be treated as a semi-rigid body possessing two degrees of freedom. Part I of the report - "Comparison of Methods by Inertia-stiffness Diagrams" - describes six methods for the prediction of critical flexure-torsion flutter speeds of such a wing. The methods are compared by use of the inertia-stiffness diagram, which allows the two moments of inertia and the two elastic stiffnesses to be left free for choice. Part II - "The Two-dimensional Classical Formula" - develops a formula, such that when the structural mass and plan-form data together with the fundamental resonance frequencies are available for a specific cantilever wing the lowest critical flutter speed of that wing can be calculated directly from the formula. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1990.pdf 122. Note on the influence of aspect ratio on the variation with mach number of the lift and hinge-moment characteristics of a wing and full-span control A. D. Young and P. R. Owen It is shown on the basis of the linearised theory that the effects of compressibility on the lift and hinge-moment characteristics of a wing and full-span control are functions of aspect ratio. With reduction in aspect ratio the increase of the lift characteristics with Mach number is reduced appreciably (see equation 12 and Table 1). The same effect is noted for the hinge-moment characteristic b1 (equation 13). The effects on the hinge-moment characteristics b2 and b3 are rather more complicated (equations 14 and 15), but in many practical cases the influence of aspect ratio will be very small. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2767.pdf 123. The Calculation of Aerodynamic Loading on Surfaces of any Shape V. M. Falkner The object of the report is to establish a routine method for the calculation of aerodynamic loads on wings of arbitrary shape. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1910.pdf 124. The Difference between the Spinning of Model and Full-scale Aircraft G. E. Pringle, PH.D. It was required to review the technique of model spinning tests with the object of improving the reliability of model standards as applied to full scale. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1967.pdf 125. The flexural axis of thin-walled sections that have no plane of symmetry D. Williams, and B.V.S.C. Rae A method of finding the fiexural axis of unsymmetrical thin-walled sections is described that not only obviates the necessity for first finding the principal axes of inertia, but also simplifies the wtlole procedure. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2939.pdf 126. The hull launching tank (descriptive) A. G. Smith, G. C. Abel, and W. Morris The hull launching tank has been built in order that systematic measurements of impact pressures can be made on large model seaplane hulls to supplement full scale tests, and to cover conditions of impact which would be dangerous full scale. The object is to obtain generalised formula for the maximum local pressures, the total impact load and the simultaneous distribution of pressure on any hull form for any impact condition. The report describes the hull launching tank and apparatus, the range of impact conditions possible for test, and the methods developed for measuring the parameters which affect the impact loads. Theoretical considerations, the results of tests and further developments, will be found in existing or in subsequent reports. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2723.pdf 127. The initial buckling of slightly curved panels under combined shear and compression D. M. A. Leggett The initial buckling of flat rectangular panels under combined shear and compression has been investigated theoretically in R. & M. 1965. This report extends the results given there to panels which are long and slightly curved. On aircraft with laminar flow wing sections, it is desirable that the wing cover should remain smooth up to a factor of 1¼g, and to achieve this a possible type of construction is one in which stringers are dispensed with, and the cover is reinforced with closely spaced ribs and stiffeners. These divide the cover into a large number of long and slightly curved panels, and the results given in this report should be of value in estimating the combined shear and compression which such panels can carry without buckling and so developing waviness. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1972.pdf 128. The prevention of flutter of spring tabs A. R. Collar The present report gives a correlation of the results of earlier researches into the prevention of flutter of spring tabs. The restrictions on the way in which tab mass-balance must be applied, which are given in the earlier work, are shown to be very simply derivable from the conditions necessary for the elimination of elastic and inertia couplings; and from these considerations an optimum length of tab balancing arm is deduced. The recommendations for avoidance of spring tab flutter are summarised in Â§9. Two Appendices deal respectively with the optimum length of arm when the aerodynamic actions are taken into account, and the relation between the results of the earlier work and the recommendations of Â§9. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2034.pdf 129. The Smallest Size of a Spanwise Surface Corrugation which affects Boundary-layer Transition on an Aerofoil A. Fage, F.R.S. The effect of a spawise surface corrugation on the position of transition from laminar to turbulent flow in the boundary layer of an aerofoil depends on the local disturbances caused by the corrugation and on the stability of flow in the boundary layer beyond. The report describes wind-tunnel experiments made for bulges, hollows and ridges on an aerofoil and on a flat plate to obtain relations for the minimum height of a spanwise surface corugation which affects the position of boundary-layer transition, and so the drag, of a laminar-flow aerofoil. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2120.pdf 130. The Turbulent Boundary Layer in Compressible Flow W. F. Cope The flow of a compressible gas past a fiat plate is investigated for a turbulent boundary layer. The local and mean skin-friction coefficients are calculated for both power and log laws of velocity distribution. The calculations show a considerable reduction of both coefficients with increasing M. In the course of the analysis assumptions have been made whose accuracy is not proven, though they are consistent with those made in incompressible gas dynamics. The results are applied to calculate the contribution to fR of skin friction for a typical projectile of various calibres. The calculation shows that it should be possible by a properly selected series of wind-tunnel and full-scale experiments to ascertain if the large reduction in skin friction occurs, but that it is unlikely that it will be possible to discriminate between the two hypotheses about velocity distribution. Historical Note.--The introduction proper gives the reasons which lead to the writing of this paper and for a long time security considerations prevented its publication. Recently, however, work on similar lines both at the Royal Aircraft Establishment and in America (e.g., van Driest or Wilson in J.Ae.Sc.) have both confirmed the general accuracy of the picture presented and to a considerable extent superseded it as a technical contribution. Nevertheless it seems still to have some value technically and to be of great interest historically as a very early contribution to the literature of the subject. The preparation of a paper of this kind for publication raises questions of rewriting so as to bring it up to date which are very difficult to decide. In the present case it has been decided to leave it untouched except to change the details of the references if the subject matter has since been published. The main reasons for this decision are that adequate modern treatments (such as those cited above) now exist, and that therefore to rewrite it would merely add one more to them and to no useful purpose, while at the same time it would diminish almost to vanishing point the historical value of the paper. The work was carried out as part of the National Physical Laboratory programme of work for the fighting services. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2840.pdf 131. The variation of power with height of a Merlin 46 engine as determined by flight tests on a spitfire Vc G. S. Hislop The variation of full throttle engine power with height was required on a Spitfire Vc (Mellin 46) for comparison with that obtained previously by the same method on a Hurricane II (Merlin XX). This, the locked propeller method, gives the ratio of full throttle powers at any two altitudes and in the present tests the ratio was obtained at the following altitudes :- 37,000 ft. and 16,000 ft. 35,000 ft. and 16,000 ft. 83,000 ft. and 16,000 ft. 37,000 ft. represents the maximum height at which accurate performance measurements can be made with this aircraft. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2213.pdf 132. Torsiograph Observations on a Merlin II Engine, using a Serrated-Condenser Pick-Up, with Five Different Pitch Settings of the Propeller Blade B. C. Carter and J. R. Forshaw This report is based upon the first application of the torsiograph described in Reference I, the observations being made in the course of development of the instrument. Subsequent applications have been to Merlin 61 and Sabre engines, with results which are given elsewhere. The torsiograph pick-up unit was fixed into the pinion-driving shaft of a Merlin II engine on a hangar test-bed and records were obtained at various crankshaft speeds from 900 r.p.m. to 3,000 r.p.m., and with blade settings ; 16.5 deg., 20.5 deg., 22.5 deg., 25.5 deg. and 29 deg., measured from tile propeller disc at 42 inches from the shaft axis. The observed cyclical torque oscillations have been analysed into harmonic components and the causes of the corresponding modes of vibration are examined in the report. To assist this examination, some vibrograph observations were made and also a mathematical analysis, which is given in the Appendix. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1983.pdf 133. Wind-tunnel experiments on the squidding of parachutes L. F. G. Simmons, R. W. F. Gould and C. F. Cowdrey To determine the underlying cause of the collapse of a parachute, known as 'squidding.' Measurements of pressure were made in a wind tunnel at a number of positions over the surfaces of rigid models representing (a) a fully inflated canopy (b) a semi-squidded shape, and also at points over the surface of a small parachute. Each rigid model was uniformly perforated with holes representing a degree of porosity which was varied in some of the tests by covering different areas of the surface. Tests on the parachute were made with it tethered, (1) with rigging lines to a fixed point, (2) by wires to the sides of the tunnel. Directional measurements of flow required for tracing streamlines were made in the neighbourhood of the parachute both before and after the fabric had been rendered non-porous. It was found that, through the lack of deformable areas near each mouth, the rigid models did not reproduce adequately the prerequisite conditions of flow which normally lead to squidding. Radial outward forces tending to prevent collapse were shown to depend not only on the pressure inside the canopy but also on the strength and direction of the local flow. Any change which brings the direction nearer to that of the axis of the parachute decreases the incidence of the lip of each gore, and hence reduces the outward radial force. Such a change results from an increase in porosity of the fabric, and since an increase in porosity usually occurs with rise of speed, the process of squidding starts at a speed when the lips of the gores become deformed inwards. Similar changes of flow were not observed with a non-porous parachute, which remained fully inflated at the highest speeds attainable in the tests. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2523.pdf 134. A general treatment of static longitudinal stability with propellers, with application to single-engined aircraft E. Priestley A general method of treatment of stick-fixed static longitudinal stability with propellers is given, distortion and compressibility effects being neglected. Model full-throttle data on some single-engined fighters are analysed for the flaps-up condition to establish a basis of estimation of effect of propeller on stability for this type of design. The general effect of propellers on manceuvre point, more particularly the effect on Hm - Kn, is considered in an appendix. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2732.pdf 135. A note on a rotating bending-fatigue machine for tests at 200 deg. C C. E. Phillips and R. C. A. Thurston An experimental adaptation of an air temperature rotating bending-fatigue testing machine has been made for tests on light alloys at temperatures up to 200 deg. C. The machine is shown photographically in Figs. 1 and 2. It consists of a shaft rotating in a pair of self aligning ball bearings, driven by a direct current variable speed motor at one end, and with a chuck at the other end to hold circular-section test-pieces. The latter are held in the chuck by six set-screws. A two-point loading system is adopted and arranged with one scale pan to obviate the possibility of overstressing a test-piece during the application of the weights. Fracture or vibration of the test-piece operates a switch which stops the motor; the number of revolutions are indicated by the usual form of counter. The variable speed control permits critical speeds due to resonances of the test-piece assembly being avoided. For tests at 200 deg. C., a somewhat longer test-piece (see Fig. 3) than the standard air temperature type is used, and the temperature measurements are made by two thermo-couples (ironeureka) secured one to each end of the effective portion of the test-piece. The thermo-couples are connected directly to four insulated terminals on the chuck, which are permanently joined by wires through the middle of the main shaft to the brass slip-rings seen in the photographs. The thermal E.M.F. is picked up from the slip-rings by carbon brushes, so arranged that the contact pressure is obtained by dead-weight loading ; the brushes are only in contact with the rings whilst observations are being made; at other times a cam lifts them clear. The usual potentiometer method, with sensitive galvanometer, is adopted for the E.M.F. determinations, so that troubles due to variation of contact resistance at the brushes are minimised. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2674.pdf 136. A review of porpoising instability of seaplanes A. G. Smith, and H. G. White A review has been made of the evidence on take-off and landing porpoising instability of seaplanes. The basic types of porpoising and their occurrence have been examined ; full-scale results have been correlated with model-scale and theoretical results. Porpoising instability has been divided into three basic types, (a) forebody, (b) forebody-afterbody, (c) step Lnstability. The first occurs during planing on the forebody only whenever the attitude decreases below a critical value. It is associated with a positive water pressure distribution over the forebody near the step ; there is no flow on the afterbody. The instability corresponds theoretically to that of a single planing surface. The second type occurs during planing on the front and rear steps whenever the attitude exceeds a critical value. It is associated with a positive water pressure distribution over the forebody and afterbody in tile neighbourhood of the steps only. There is no flow on the first 70 to 80 per cent of the afterbody. This porpoising corresponds to the theoretical case of two planing surfaces in tandem. The third type occurs when the water flow is not separated efficiently from the hull bottom at the main step. Large negative pressures alternate with positive pressures on the whole afterbody, the combination causing violent instability. Step instability is only present at high speeds but may occur down to quite low attitudes, and well below the stalling speed. Full-scale stability limits are measured in both steady and accelerated speeds. Under operational conditions a 2 deg amplitude porpoise has been chosen as the maximum permissible for safety. Three degrees of stable range are then defined : (i) the minimum stable range, corresponding to the limits given by undamped porpoising of any amplitude-- these limits are obtained from steady or accelerated speed tests ; (ii) the minimum stable range during steady speeds where limits are drawn to exclude porpoising of under 2 deg ; (iii) the operational stable range where limits are drawn to exclude porpoising of under 2 deg amplitude under accelerated conditions. The first is of predominantly research interest, the second is the operational case for zero acceleration (i.e., over load take-off), the third is of greatest operational importance. The stability limits are to some extent dependent on the degree of disturbance encountered, but once started, porpoising instability is independen t of disturbance. Step porpoising is particularly sensitive to disturbance ; in bad cases it often occurs at high speeds whenever the afterbody becomes even slightly immersed. A maximum value of disturbance should be laid down for design purposes. Model tests at steady speeds give the minimum stable range. At high speeds the Royal Aircraft Establishment range is probably smaller than the full-scale because of the disturbance used and represents the extreme case. R.A.E. model limits are 1 to 3 deg higher than the full-scale limits on the same seaplane, but are otherwise ill good qualitative agreement. The differences are probably due in part to the accumulated effect of differences in displacement, stalling angle and lift, damping, moment of inertia and radius of gyration, to differences in applied disturbance, and to scale effect. The first can be reduced by use of slipstream and care ill aerodynamic design ; the second by use of a laid down full-scale design disturbance. The theory of porpoising instability will give accurate results for forebody instability if accurate values of the derivatives are available. There is not as yet sufficient accurate generalised data for this and experimental determinations are as lengthy as measuring the actual limits. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2852.pdf 137. A simple method of computing CD from wake traverses at high-subsonic speeds J. S. Thompson This note gives a convenient method of obtaining CD from a pitot-static traverse in an aerofoil wake, using Jones' equation as modified by Lock, Hilton and Goldstein for compressible flow. Charts are provided from which the integrand CD' can easily be obtained for any point in the traverse, but it is shown that in nearly all cases an accuracy of 1 per cent in CD can be obtained by applying an integrating factor to the area under the total-head loss curve. Three Appendices give (a) a summary of the standard theory and equations, (b) details of the construction of the charts and (c) an empirical equation giving CD' in a simple analytical form. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2914.pdf 138. An air-injection method of fixing transition from laminar to turbulent flow in a boundary layer A. Fage, and R. F. Sargent The paper deals with a simple method of fixing transition by the injection of small air jets into a boundary layer from a row of surface holes, and describes experiments which establish the effectiveness of the method. A merit of the method is that the rate of air injection can be adjusted to give, at each speed of test, a minimum disturbance of flow necessary to fix transition at the position selected. The minimum rate of air injection for transition is small, about 0.015 times the rate of mass-flow in the boundary layer. The method is especially suitable for high-speed tests since it does not give a local shock wave, which is sometimes present when a surface wire is used to fix transition. The experiments show that a large increase in drag may be caused by a very small leakage of air into the laminar boundary layer of a low-drag wing. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2106.pdf 139. An experimental investigation of the effect of localised masses on the flutter of a model wing N. C. Lambourne and D. Weston This report contains an account of some experiments on the effect of concentrated masses (representing wing engines, etc.) on the flutter characteristics of a model cantilever wing. Flutter critical speeds and frequencies were measured for an extensive range of mass loading and the results are presented in the form of diagrams. The flutter motions for a few representative conditions of mass loading were determined by an analysis of cinematograph pictures. The results of experiments on the influence of the flexibility of an engine mounting are also included. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2533.pdf 140. Application of thin aerofoil theory to the design of double flap controls of small chord H. H. B. M. Thomas, and M. Lofts Recent experimental investigations on small-chord controls in two-dimensional flow suggest that such controls are more efficient than wide-chord controls. The experiments also suggest that a further gain is obtained if the control or flap is broken, hinged and geared at some point along its chord. This Note examines, on the basis of the thin aerofoil theory, the control efficiency of such double flap systems, as ailerons and as elevators. A range of values of total chord ratio is covered, and the optimum arrangement determined in each case. The theory suffers from the limitations of the thin aerofoil theory, which fails to take account of the thickness/chord ratio and the boundary layer effects ; these can be large for the thicker sections. It does, however, provide an indication of the effect of variations of the various parameters and also the ratio of the flap chords defining the optimum. In general terms the problem considered here is to find the minimum control column force to produce a given rolling moment. Throughout the present work the lift is fixed at that produced by the 0.50 chord flap. It is shown that the smaller chord single- and double-flap systems are more efficient than a wide-chord arrangement and that a double flap is more efficient than a single flap of the same total chord. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2017.pdf 141. Creep Tests on some Cast Magnesium Alloys. Parts I, II and III A. E. Johnson, H.J. Tapsell, and H. D. Conway PART I - Creep Tests of 150 hours Duration at 100 deg., 150 deg. and 200 deg. C. on some Cast Magnesium Alloys. PART II - Comparison of the Creep Properties of Three Cast Magnesium Alloys Based on Tests of 1,000 hours Duration. PART III - Effect of Various Heat Treatments on the Short-time Creep Behaviour at 3 ton/sq.in., 150 deg. C., of Four Cast Magnesium Alloys. The National Physical Laboratory was represented at a meeting held at the Ministry of Aircraft Produ.ction on 21st July, 1943, when certain proposals for research into the properties of magnesium alloys at temperatures up to 200 deg. C. were discussed. It was decided that the N.P.L. should be asked to undertake some short-time creep tests on a number of magnesium alloys with a view to selecting suitable alloys for fuller investigations. It was agreed that creep tests of short duration at 100, 150 and 200 deg. C., and at one stress to be selected for each temperature, should first be undertaken, and that subsequent tests should be made on those alloys which appeared to warrant more prolonged creep testing. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2675.pdf 142. Design of suction slots A. Fage and R. F. Sargent Boundary-layer suction is likely to have important applications in the future, particularly on jet-driven low-drag aircraft and in the design of cooling systems. Information will then be needed on the optimum entry shape of two-dimensional slots suitable for boundary-layer suction. The present work, presented in Parts I and II, has been undertaken to obtain such information. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2127.pdf 143. Gas turbine design based on free vortex flow E. A. Simonis and J. Reeman The design of a turbine stage is considered on the basis of free vortex flow from the nozzles and blades and some of the factors which limit the design of an efficient turbine stage are discussed. As the flow conditions at the root of the blades are of greater importance in limiting the design than those at the mean diameter, calculations of the stage performance are made for various values of nozzle angle, reaction and exhaust swirl at the inner diameter of the nozzles and blades. The results of these calculations are presented in the form of a series of curves which show how the design conditions, such as mass flow per unit annulus area, rim speed and Mach numbers relative to the blades, vary with work output from the turbine stage. These curves enable a quick estimate to be made of a suitable turbine stage design to meet given requirements of mass flow and work output, and an example is given showing their application. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2541.pdf 144. Lift, and pitching moment measurements on an EC 1240 tailplane elevator at high speeds with elevator gap sealed W. F. Hilton and A. E. Knowler Previous measurements at high speeds made in the 12-in. Circular High Speed Tunnel of the lift, drag and pitching moment for an aerofoil with elevator have now been repeated for lift and moment with the gap between aerofoil and elevator sealed. It was found previously that there was no serious loss of control until a Mach number of M = 0.75 to 0.78 was reached and this result has now been found to hold good for the 'gap sealed' condition. Above M = 0.78 the control falls rapidly, reaching one half its low-speed value at about M = 0.81. This result holds good whether the gap is sealed o rnot. With the gap unsealed, a2 was practically independent of Mach number at a value 3.0 from M = 0.45 to 0.73 ; with the gap sealed the value of a2 approximated to the value 3.6/~/(1 - M2), following the Glauert formula, over the range M = 0.4 to 0.7. The effect of sealing the gap is to increase a2 by 40 per cent. at M = 0.4 and 60 per cent. at M = 0.7. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2227.pdf 145. Prediction of undercarriage reactions G. Temple The object of this report is to give a connected account of the methods which have been developed at the Royal Aircraft Establishment by Messrs. D. D. Lindsay, R. G. Thorne and S. A. Makovski for the prediction of undercarriage loads under symmetric landing conditions; to extend these methods to deal with other landing manoeuvres; and to formulate a simplified system of step by step computation of the loads. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1927.pdf 146. Round Jets in a General Stream H. B. Squire, M.A. and J. Trouncer, B.A. The flow in a round jet issuing from an orifice in the same direction as a general external stream is investigated theoretically as an extension of the problem of a jet issuing into still air. The flow in the upstream part of the jet (Region A of Fig. 1), in which a core of fluid of uniform velocity exists, and the flow in the downstream or developed part of the jet (Region B of Fig. 1), are investigated separately; the solutions fitted together at the section at which the core disappears. The deviation of the outside stream due to inflow into the jet is also considered. Numerical solutions are derived for several values of the ratio of jet exit velocity to stream velocity. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1974.pdf 147. Tests of a griffith aerofoil in the 13 ft. x 9 ft. wind tunnel. Parts I. II, III and IV E. J. Richards, W. S. Walker and J. R. Greening PART I. Wind-tunnel Technique and Interim Note. PART II. Effect of Concavity on Drag. PART III. The Effects of Wide Slots and of Premature Transition to Turbulence. PART IV. Lift, Drag, Pitching Moments and Velocity Distributions. This report describes tests carried out on a 16 per cent. thick Griffith suction aerofoil in the 13 ft. x 9 ft. wind tunnel. Prior to these tests being carried out, the principle involved in the design of these aerofoils had only been justified experimentally by tests on a very small scale in the National Physical Laboratory 4-ft. wind tunnel 1 ; the purpose of the present tests was to verify the feasibility of the Griffith 'discontinuity' principle on a satisfactory scale, and to obtain quantitative data on the aerofoil characteristics with and without suction, the amount of suction needed to prevent separation and to develop the optimum slot shape and width for maximum efficiency. Part I describes the technique used in the experiments, and the method of interpretation of the results to include in the drag a term to account for the power used to develop the necessary suction. The experiments show that separation of the flow on the surface can be fully prevented on this type of aerofoil by sucking less than half the air in the laminar boundary layer at the design position of the slot. If the flow is turbulent from the wing leading edge, the amount of air that must be sucked away is very little greater than that if the flow is laminar to the slot. In the experiments of Ref. 1, it was found that the flow to the rear of the suction slot remained laminar to the trailing edge of the aerofoil. In the present experiments this was not found to be so, transition to turbulence occurring some distance rear of the slot. Part II (page 7) of this report describes an investigation of this effect and shows that this instability results from the dynamic instability of the boundary layer along a concave surface, and that it is impossible to design any practicable aerofoil shape over which this instability can be prevented at the Reynolds numbers of flight. Part III (page 11) of the report extends the investigation of slot design to greater slot widths and less extreme shapes and includes the effect on suction mass flow of premature transition to turbulence forward. In Part IV (page 16) aerofoil characteristics are discussed both with and without suction, including the velocity distribution over the aeroIoil, lift coefficient, pitching moments and hinge moment variation with incidence. The effective drag coefficient variation is examined and extrapolation to full-scale Reynolds numbers carried out. It is shown that even with turbulent flow aft of the suction slot, a low-drag coefficient may be anticipated at the Reynolds numbers of flight. The effect of nacelles on suction wings is also examined. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2148.pdf 148. Tests on a model body-wing combination at supersonic speed P. J. Wingham The tests described in this report were made in the 1-ft Circular Tunnel at the National Physical Laboratory at a Nach number of about 1.4. The main object was to determine the lift obtainable from wings of very short span and in particular to see whether tile lift curve departed much from a straight line at incidences up to about 12 deg., it being already known that the lift curve for a two-dimensional aerofoil was sensibly straight up to 20 deg. or so of incidence. Unfortunately it was not possible to measure the drag load, so that only normal force and pitching moment values are available. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2711.pdf 149. The case for factors of safety of 1.5 instead of 2.0, with special reference to the flight envelope P. E. Montagnon The purpose of this note is to show the desirability of using a factor of safety of 1.5 throughout all design strength requirements, in particular in the first instance for all requirements directly connected with the symmetric flight envelope. Alongside this is shown the desirability of changing the flight envelope to agree more nearly, with results obtained in practice (from V-g records). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2578.pdf 150. The effect of differing thickness distributions on a propellor's efficiency A. B. Haines, B.Sc. Calculations of the efficiency of propellors having five different thickness distributions (effects of other variants having been eliminated) have been made for forward speeds from 300 to 600 m.p.h. at 20,000 ft. It is shown that the efficiency becomes very sensitive to the thickness (particularly of the root end of the blade) as the speed is increased beyond 500 m.p.h., but that at this speed the effects of tip thickness are relatively minor provided the blade is at least as thin as, say, a modern compressed propellor. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1992.pdf 151. The effect of model size on measurements in the R.A.E. high speed tunnel. Drag of two-dimensional symmetrical aerofoils at zero incidence W. A. Mair, and H. E. Gamble Pitot traverse drag measurements were made at zero incidence on three NACA 0015 aerofoils of different sizes. Pressures at the tunnel walls were also measured. For each aerofoil, tests were made at two different Reynolds numbers by changing the tunnel pressure. From the results it has been possible to separate the effects of varying Reynolds number and tunnel wall interference. It has been shown that the blockage corrections in current use (based on linear theory) are not large enough to equalise drag measurements made on different sizes of aerofoil at the same Reynolds number. Empirically increased corrections which bring the results into agreement have been found. The results have also shown that at high Mach numbers there is a fairly large variation of drag coefficient with Reynolds number, especially between Reynolds numbers of about 0.2 x 10power6 and 1.4 x 10power6. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2527.pdf 152. The prevention of binary flutter by artificial damping R. A. Frazer Formulae are obtained which provide an estimate of the amount of artificial control needed to prevent binary flutter. Results are expressed in terms of a 'minimum damping multiplier' R, defined as the ratio of the least direct damping coefficient required for absolute flutter prevention to the 'natural' direct aerodynamic damping coefficient of the control surface concerned. Numerical results are obtained for five different types of aircraft. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2552.pdf 153. Tunnel interference at compressibility speeds using the flexible walls of the rectangular high-speed tunnel C. N. H. Lock and J. A. Beavan The results of various measurements made in the National Physical Laboratory Rectangular High-speed Tunnel using the flexible walls are compared with theory in order to throw further light on the problem of tunnel interference at very high speeds. The dependence of the wall pressures and overall aerofoil forces on the wall shape has been investigated for two-dimensional tests of various aerofoils, though most of the work relates only to the low drag section EC 1250. It is concluded that the standard methods of 'streamlining' the walls to simulate free air conditions are satisfactory up to speeds at which the shockwave from the aerofoil first reaches one wall, which in ordinary cases occurs above about M = 0.85 for a low-drag 12 per cent. t/c section, or 0.81 for a conventional 18 per cent, t/c. The 5-in. chord is about as large as should normally be used, and in this case lift can be estimated from the streamline wall pressures, a correction being made for insufficient length of tunnel. If straight walls are used, the theoretical corrections to free air seem applicable up to top speed, and in this case the lift can be obtained from the wall pressures without addition beyond the end of the tunnel. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2005.pdf 154. A method of testing smooth wings for initial shape and resistance to distortion under load J. C. King and D. H. Trollope The development of special smooth wing constructions for laminar-flow aerofoils calls for a simple testing technique to check the suitability of these new designs. In the method now used a short parallel length of wing bounded by ribs is tested under uniform bending with torsion and internal pressure superimposed when necessary. A standard specimen and standard testing technique are described. A review of the existing instruments for measuring surface irregularities is included. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2531.pdf 155. A new method of numerical integration of the equations of the laminar boundary layer T. G. Cowling A new method for the numerical soiution of the boundary-layer equations is described. This rests in essence on the fact that the equations of steady flow are special cases of the equations of general motion. The velocity profiles are found at successive sections across the boundary layer. Trial values of the velocity are assumed at any section; from these, space derivatives of the velocity are deduced by using finite differences, and time derivatives by using the equations of motion. The trial values are then adjusted to give zero time derivatives of the velocity at the section. The method in some respects resembles Southwell's relaxation method. The method has been applied to two problems already discussed numerically by Hartree. It is not suitable for use with a differential analyser, though the development of new calculating machines may bring it within the range of machine integration; but rather less labour was required to achieve manually with it results rather more accurate than obtained by Hartree with the differential analyser. The results did not, however, differ greatly from Hartree's. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2575.pdf 156. A New Method of Two-dimensional Aerodynamic Design M. J. Lighthill The main object of this report is to describe and illustrate a fairly simple exact method by which aerofoils and other surfaces may be constructed to have desired velocity distributions. Its subsidiary interest is as a progress report on shapes already constructed, which are described in the Appendices and Figures, but should not be regarded as the best which, after further development, the method may be capable of producing. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2112.pdf 157. A theoretical calculation of the reduction in drag obtainable by ejector action of the exhaust gases when mixed with the cooling air-flow of a typical air-cooled engine A. B. P. Beeton The formulae which give the thrust theoretically obtainable in a system where the ejector exhaust is mixed with the engine cooling air are of considerable mathematical complexity, and it is not therefore evident under what conditions the greatest benefit can be obtained from such a system. By considering a special case, it is shown that there is an optimum size of the mixing duct in relation to the exhaust-pipe diameter; and also that the effect of mixing the exhaust gas and cooling air streams is only beneficial when the available total pressure head behind the engine is small. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2302.pdf 158. A theoretical discussion of wings with leading-edge suction M. J. Lighthill Suction slots on wings are of two kinds: those into which only the boundary layer is sucked away, and those which also receive a considerable portion of the free air outside the boundary layer. The purpose of the former is to overcome a discontinuous drop in the velocity at the surface of the aerofoil and so obviate the need for extended regions of adverse pressure gradient where transition or separation may occur unpleasantly soon. This requires special design of the aerofoil (to have a discontinuity in velocity at some point or points) and conversely an aerofoil so designed essentially requires to have such slots at these points and nowhere else. Hitherto their position has generally been well to the rear of the aerofoil and the aim has been to make the velocity non-decreasing as far as the slots on both surfaces for as wide a range of CL as possible. The purpose of the second kind of suction slot is to eliminate large adverse pressure gradients occurring immediately behind it, by the action of sink effect. Such a slot could be placed anywhere on any wing, and would always have this effect. Naturally the most satisfactory position is near the summit of any large suction peak. These occur most frequently and with the greatest detriment near the leading edge at high lifts. Hence a slot suitably placed in the forward region may be expected to increase the maximum lift of some wings. This report will study the use of slots near the leading edge ; both when they act solely by sink effect, and when the ideas of the two foregoing paragraphs are combined and the same slots used for both purposes (obviously the most economical method). The following discussion is based on the theory of R. & M. 2112, of which at least Â§ 1 should be read and the rest lightly skimmed before the reader goes any further. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2162.pdf 159. A theoretical investigation of the response of a highspeed aeroplane to the application of ailerons and rudder K. Mitchell, A. W. Thorpe and E. M. Frayn The response of a fast moving aeroplane to a lateral gust, and to applied rolling and yawing moments, is examined by means of the differential analyser, taking a range of values of the principal lateral stability parameters, and including sufficient ranges of the other stability and inertia parameters to make the conclusions of general validity for high-speed flight. The motion following a sharp-edged side-gust is shown to be of a markedly oscillatory character, with an unpleasantly short period, particularly in small aeroplanes. The shortness of the period is probably the worst feature. A general survey is made of the dependence of the motion upon the various parameters, the differential analyser results being supplemented by the use of approximate formulae, which were developed with a view to this application. Particular attention is paid to the amplitudes of the motion in roll, yaw, and sideslip, and it is seen that it may be difficult to make the motion less unpleasant. The period may be lengthened by reducing nv, but the improvement that is possible in this way is limited. Damping can be improved by reducing dihedral, or by increasing body side area: the addition of a forward fin, ahead of the centre of gravity, would therefore be doubly helpful, lengthening the period and improving the damping. In studying response to applied moments attention is chiefly concentrated upon response to ailerons, and the theoretical results are compared with a theoretical standard motion produced by a constant roiling moment together with a yawing moment varied so as to suppress sideslip. Response at high speeds is shown to be insensitive to changes in lv and nv within their normal ranges, and good response to pure rolling moment is assured for all lateral stability characteristics other than those associated with the combination of small fin with large dihedral: this combination is worst at high values of the lateral relative density. The effect of adverse yawing moment from the ailerons is detrimental, and becomes worse as the dihedral is increased or fin area decreased. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2294.pdf 160. Aerodynamic forces on wings in simple harmonic motion W. Prichard Jones A theory for the calculation of the aerodynamic forces acting on wings of finite span and any plan form is developed, and from it an approximate method which reduces the amount of numerical work is derived. Satisfactory agreement with the experimental evidence available is obtained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2026.pdf 161. An Analysis of the Lift Slope of Aerofoils of Small Aspect Ratio, including Fins, with Design Charts for Aerofoils and Control Surfaces D J Lyons And F/O P L Bisgood The analysis of R.A.E. Report No. Aero. 1840 has been extended to cover the lift slope of aerofoils of small aspect ratio and of fins in place upon an aeroplane. The charts of that report for the estimation of lifting characteristics of aerofoil controls have been included in this report with some small modifications, and those necessary for the estimation of fin and rudder lifting characteristics added. In general it is possible to estimate the lift slope of the aerofoils on an aircraft, taking account of interference effects, to within about ± 5 per cent. and control powers to within about ± 10 per cent. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2308.pdf 162. An experimental investigation into the suitability of a corrugated construction wing for a laminar-flow aerofoil J. C. King This report describes a detailed experimental investigation into the structural features of a 6-ft chord wing specimen having thick skin reinforced by spanwise corrugations. The tests included surface distortion, proof and ultimate tests on the specimen and compression tests on two panels. A short length of parallel specimen was used with a simplified test rig built for the purpose. These tests showed that for this specimen, provided the wing can be made smooth in the first place, it will not be adversely affected by loads imposed in service. The major portion of the surface distortion in flight will be due to the aerodynamic suction; the effect of direct and shear stresses being negligible. In the ultimate tests failure was due to elastic instability of the skin and corrugations at a compressive stress of 11.1 t/sq in. This compares favourably with the compressive stress at failure of the panels, which, when corrected for the shear stress present in the wing, reduces to 11.3 t/sq in. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2530.pdf 163. Blockage Corrections in a Closed Rectangular Tunnel A. D. Young and H. B. Squire PART I. Simple, Approximate Formulae for General Application. PART II. Note on the Blockage Correction for Streamline Bodies of Revolution Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1984.pdf 164. Calculation of the effect of slipstream on lift and induced drag. Part 1. Wing of infinite span Aeronautical Research Council The lift distribution along a wing of infinite span with a central jet of higher velocity is calculated by standard methods of aerofoil theory for several values of (jet velocity/stream velocity) and of (jet diameter/wing chord). The lift increment and the induced drag are determined and the application of the results to practical cases is discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2368.pdf 165. Compression Tests on Seven Panels of Monocoque Construction H. L. Cox, M.A., F. R. Thurston, B.Sc., A.Inst.P. and E. P. Coleman, with Appendix by H. E. Smith, B.Sc., of the Engineering Division, N.P.L. The primary purpose of the present tests was to provide specific data for application to a particular design problem; but the opportunity has been taken to develop a technique of testing, by which comparison of experimental results with theoretical conclusions may be facilitated. All the panels tested were 20.5 in. wide by 12.5 in. long and the sheet cover was 0.08 in. thick; the panels were stiffened by stringers at 3.3, 4 or 5 in. spacing, the area of cross-section of each stringer being about 0.05 in.^{2}; the stringers were thus abnormally light in comparison with the sheet cover. The stringers were attached to the sheet cover by thread-cutting screws, screwed in the cover, and one principal object of the tests was to determine the maximum permissible spacing of screws along the stringer consistent with a certain desired minimum load at failure. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2042.pdf 166. Experiments on the measurements of transition position by chemical methods J. H. Preston, and N. E. Sweeting, F. H. Burstall The smoke filament technique for detecting transition points is limited to speeds below 180 ft./sec, for orthodox atmospheric tunnels with good lighting and viewing conditions. Also many tunnels are of the enclosed pressure type in which observation is impossible, whilst many atmospheric wind tunnels have poor facilities for lighting and viewing. Hence the need for methods which will supplement the smoke filament technique at high gpeeds, and which can be applied to pressure tunnels and to flight. The work was almost wholly confined to a particular technique, which consisted in allowing a gas in high concentration to ooze out of an orifice near the nose and flow over the wing surface, which was coated with a suitable sensitive paint, thus producing a stain. Various combinations of gases and paints were tried as suggested by well-known 'indicator' tests in chemical analysis. The flow of smoke from the orifice was also studied. With suitable choice of gas and paint the transition position can be determined satisfactorily. The controlling factor which decides the definition of the stain in the laminar region is the 'threshold' of the paint to the action of the gas. This should be such that only a very faint trace is produced in the turbulent region, whilst an intense and well defined stain occurs in tile laminar region. Care must be taken at moderate Reynolds numbers, when laminar separation is likely to be present. With gas oozing from a hole in the nose only, its presence is likely to pass undetected, but it can be found by introducing the gas near the end of the laminar flow region. For this reason, if facilities for observation exist, it is recommended that the smoke filament technique be used at low wind speeds. If a permanent or semi-permanent record is desired, then ammoniff in conjunction with mercurous chloride is very good, as also is hydrogen sulphide on white lead, and ammonia on congo-red (an organic pigment). A 'fugitive' stain which disappears in about 10 minutes can be produced by passing ammonia over Brom-cresol-purple which has been given a suitable 'threshold'. Very small amounts of gas are used - from 3 to 6 cubic inches, supplied at a rate of about 1 cubic inch per minute. A rough metering arrangement is desirable. 'Evaporation' methods are being investigated at the Royal Aircraft Establishment and the National Physical Laboratory. It is desirable that the technique described in this report should be applied to flow at high speeds and high Reynolds numbers; if successful, then it can be extended to pressure tunnels and to flight. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2014.pdf 167. Flight tests at high mach number on E28/39 W4041 (single-engined jet-propelled aircraft) A. W. Thom, F. Smith and J. Brotherton This report describes fright tests at Mach numbers up to 0.816 on the E 28/39 W4041, the first iet-propelled aircraft to be flown in this country. For these tests the aircraft was fitted with wings of "high-speed" section (EC 1240/0640). Alternative wings of conventional section (NACA 23012) were also available ; it was intended to repeat the tests with these wings, but before this could be done the aircraft was required for other purposes. Measurements of incidence, aileron and elevator angles, stick force and aircraft drag were made. In addition, measurements of pressure distribution were made at a section of the wing, and the profile drag of the same wing section was measured by the "pitot comb" method. The results showed that, as the Mach number increased above about 0.75, there was a large nosedown trim change and an increase of drag. For a given Mach number, both these effects were found to be more serious on this aircraft than on a Spitfire, suggesting that this "high-speed" type of section (EC 1240/0640) may be less suitable for flight at high Mach numbers than the conventional section (NACA 2212) of the Spitfire. A pronounced "hysteresis" effect was observed in the wing pressure distributions at high Mach numbers, leading to different results for increasing and decreasing Mach number, at the same Mach number and lift coefficient. This apparent "hysteresis" has not been explained and no corresponding effect was found in the profile drag measurements. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2264.pdf 168. Flight Tests on "King Cobra" FZ.440 to investigate the Practical Requirements for the Achievement of Low Profile Drag Coefficients on a "Low Drag" Aerofoil F. Smith and D. J. Higton This report describes measurements of profile drag made on the wing of the King Cobra aircraft, which has a low-drag profile of X.A.C.A. design. The profile drag was high with the original surface finish and although it was improved when the surface was polished the profile drag was still much too high for a low-drag aerofoil. By reduction of the surface waviness to ± one thousandth of an inch low drag coefficients of the order of 0.0028 were obtained. The report describes the technique used to reduce the waviness and also the effect of flies, dust, water, high Mach number and normal acceleration upon the low drag characteristics of the wing. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2375.pdf 169. Fracture of Glass Rods in Bending and under Radial Pressure C. Gurney and P. W. Rowe A simple theoretical argument leads to the conclusion that if Griffith's crack hypothesis is true, rods of brittle materials when subjected to radial pressure should fracture at a mean pressure equal to the average tensile stress at failure in a tensile test. In practice, it is not convenient to do tensile tests on account of the difficulty of gripping the test pieces and of procuring axial loading. In the present series of tests, the mean radial pressure at fracture of three types of glass rod has been compared with the tensile stress at fracture computed from bending tests. The mean fracture stresses developed in the two types of test differ significantly though not greatly. When departures of the experimental test conditions from ideal conditions are considered, they appear adequate to account for the difference. The results, therefore, are not in disagreement with the deduction made from Griffith's crack hypothesis that fracture in radial pressure occurs at a pressure numerically equal to the tensile breaking stress. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2284.pdf 170. High-speed Wind-tunnel Tests on Models of Four Single-engined Fighters (Spitfire, Spiteful, Attacker and Mustang) Parts 1-5 W. A. Mair et al Part I - Tests on the Spitfire I. Part II - Tests on the Spiteful (F. 1/43). Part III - Tests on Cabins for the Spiteful. Part IV - Tests on the Attacker (E. 10/44). Part V - Tests on the Mustang I. This report describes measurements of lift, drag, and pitching moment made in the R.A.E. High Speed Wind Tunnel on models of the Spitfire, Spiteful (F.1/43), Attacker (E.10/44), and Mustang. On the Spiteful model, pressure distributions on the front radiator flap were also measured. An introduction (written in 1949) gives a general account of the tests described in the separate parts of the report. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2535.pdf 171. Influence of the testing machine on the flexural failure of panels W. S. Hemp The pin-ended length of a panel tested fiat-elided in a compression testing machine is influenced by the flexibility of the machine. A system of elastic constants is defined to describe this influence (section 2) and equations for the critical load developed (section 3). These constants are detmmined by stiffness measurements made on the testing machine (section 4) and by calculation of the platten deformation at the area of contact with the panel (section 5). Finally, the degree of fixation achieved in the testing of typical panels is calculated and the results given in graphical form (section 6). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2539.pdf 172. Kinetic temperature of wet surfaces. A method of calculating the amount of alcohol required to prevent ice, and the derivation of the psychrometric equation J. K. Hardy A method is given for calculating the temperature of a surface wetted either by a pure liquid, such as water, or by a mixture, such as alcohol and water. The method is applied to the problem of protecting; by alcohol, propellers and the induction system of theengine against ice. The minimum quantity of alcohol required is calculated for a number of arbitrarily chosen conditions. The effect of evaporation of alcohol is shown by repeating the calculations for a non-volatile fluid. The method can be applied to other problems in evaporation, for instance, to the evaporation of fuel in the induction system of the engine. The psychrometric equation, used in wet-bulb hygrometry, is deduced in its general form. The effect of kinetic heating is included in this equation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2830.pdf 173. Notes on the design of converging channels S. Goldstein The design of two-dimensional converging channels is considered, with special reference to (i) the lengths of the channels and (ii) the occurrence or absence of unfavourable velocity gradients at the walls. It is shown that it is not possible to have a short channel unless the velocity at the wall decreases at the beginning (the upstream end) of the channel; and it is further shown how a series of channels may be designed of decreasing lengths with increasingly unfavourable velocity gradients at the walls. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2643.pdf 174. On fundamental sets of solutions of the equations of lateral motion, and the rapid calculation of general solutions K. Mitchell The lateral motion of a symmetrical aeroplane slightly disturbed from steady flight is determined, to the first order of small quantities, by the solution of a system of six simultaneous linear differential equations with constant coefficients, in which the inhomogeneous terms, representing control forces or the effects of gusts, may be arbitrary functions of time. In virtue of the general properties of such equations, as is well known, their most general solution can always be written down in a form involving definite integrals. Calculations of such theoretical expressions can be very tedious, and it is now shown that the most general solution can be much more simply obtained, by processes of addition, multiplication, and integration, from a set of three fundamental solutions. A large number of such sets of fundamental solutions has already been obtained by means of the differential analyser, and the application to these of the methods of this report will make possible a large range of more special response calculations, some of which may well develop into important matters of routine. After an introductory statement of the equations of motion, the three fundamental solutions are defined in sect. 3.1, with four further solutions which are conveniently regarded as fundamental, though they can be derived from the original three. Relations between these seven solutions are given in sects. 3.2 to 3.6. Sect. 4 is concerned with the derivation of other solutions corresponding to constant or piecewise constant disturbances, and generalisation to disturbances given as any functions of time is made in sect. 5. A few particular examples of the technique developed are given in sect. 6, the fundamental solutions used being chosen from the differential analyser results mentioned above. A brief account of the scope of these is given in an Appendix, which includes in tabular form an index to the complete series of 1188 figures in which the results are contained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2182.pdf 175. Report on the flow phenomena at supersonic speed in the neighbourhood of the entry of a propulsive duct G. H. Lean The present work continued that reported in Ref. 1 and extended some of the results there described to lower entry Mach numbers (1.3 to 1.9). It was found, as in Ref. 1, that with a parallel entry duct followed by a straight divergent diffuser of 10 deg total angle the flow inside the parallel tube was supersonic provided the outlet pressure of the diffuser was less than a certain critical value (about 0.93 of the upstream pitot pressure). In this case the mass flow of air through the tube was equal to that calculated, assuming that all the air incident on the internal section of the tube entry passed through it. For pressures higher than the critical value the flow became subsonic at the duct entry, a shock-wave was formed at the entrance lip and the rate of airflow through the tube decreased. Similar results were obtained for a uniformly divergent tube of 7 deg total angle; in this case, however, an outlet pressure equal to 0.97 of the upstream pitot pressure was attained before the shock-wave left the lip. For outlet pressures less than the critical the flow was supersonic for a distance inside the duct entry depending on the outlet pressure, the flow becoming subsonic further along the duct. The assumption of unidimensional flow in the duct led to results which showed considerable disagreement with the observed pressure distribution more especially in the subsonic flow region. This could be explained by assuming that the flow in this region separated from the duct wall. The results of tests on models of two forms of annular entry (the Q1 and E24/43 entries respectively) showed that two types of flow rdgime were possible depending on the outlet pressure. For low outlet pressures a shock-wave was formed at the lip of the entry and the flow passed into the entry but for higher outlet diffuser pressures there was no distinct shock-wave from the annular lip and the flow through the annulus was reversed. The outlet diffuser pressure at which the flow changed direction for each entry tested was about 0.5 of the free-stream pitot pressure and was thus considerably lower than for the unobstructed type of duct. With the airflow passing into the annulus the flow through the Q1 entry was independent of the outlet pressure over the range of Mach numbers tested and was about 0.88 of the flow through an area equal to the intake area in the free stream. For the E24/43 entry the airflow decreased as the outlet diffuser pressure increased probably due to changes in the boundary-layer thictmess at the annulus. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2827.pdf 176. Review of remote indicating systems for aircraft instruments F. Postlethwaite As aircraft have increased in size it has become necessary to use remote indicating systems to transmit many readings to the pilot's or/and flight engineer's instrument panels. Such systems will be essential for future large civil and transport aircraft, and a number already exist operating on different principles and power supplies. Many operate from a low voltage d.c. electric supply, but it seems certain that a higher voltage a.c. supply will be used in the type of aircraft under consideration. A review was therefore required of all known and possible remote indicating systems, whether operated by a.c., d.c., or by any other source of power, in order to indicate how activities could be directed into the most promising channels, and to see if an ideal system for all remote indications is possible or known. Information about remote indicating systems already in use in aircraft has been collected from systems still being developed, from applications in other fields of engineering, and from published information concerning devices which might be applied to the problem of remote indication. Some original contributions are also included. The main conclusion arising from the review is that it is considered that electrically operated systems are more promising than anv of the other systems, and that, apart from coping with the transmission of unrestricted rotation, much can be done in devising an ideal system for dealing with all other remote indications. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2199.pdf 177. Sandwich Contruction and Core Materials Part III. Instability of Sandwich Struts and Beams H. L. Cox The purpose of the core in a sandwich structure is to stabilize the skins against local failure and to enable them to work together as a single beam, having a moment of section relatively much greater than that of the two skins separately. To fulfil these functions the core must restrain the skins from relative lateral movement and also limit relative shear movement between them; a core which resisted shear only would permit out-of-phase buckling at a load determined purely by instability of the skins as struts; whereas a core which resisted only lateral separation of the skins would permit in-phase buckling at the same load. In Ref 2 the incidence of these two types of instability was examined in respect of an artificial structure, in which in effect the core had an infinite stiffness longitudinally. This analysis indicated that the in-phase type of instability was of the modified Euler type over a long wavelength, the true Euler load being reduced by shear deformation of the core; and that the out-of-phase mode should occur over a short wavelength and should depend principally on the modulus of the core material in the transverse direction. The formula derived for the critical strain in this out-of-phase mode included also an additive term proportional to the shear stiffness of the core; owing to the inherent assumption that the core material was infinitely stiff longitudinally this effect was known to be overestimated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2125.pdf 178. Strip Theory Method of Calculation for Airscrews on High-Speed Aeroplanes C. N. H. Lock, R. C. Pankhurst and J. F. C. Conn The report describes a simplified 8-point strip theory method of calculating the free-air performance of a propeller up to tip Mach numbers near the velocity of sound. It is based on the assumptions of R. & M. 1674 and 1849 together with the further simplifying assumption that the curve is straight (valid below the stall) and that the curve also is straight (valid for J > 1.0). The report includes tables of parameters which are required in the calculations as functions of J, r, and N for eight standard radii (r, = 0.3, 0.45, 0.6, 0.7, 0.8, 0.9, 0.95, 0.975) for the range of values of J from 1.0 t o 7.0; these are of universal application. In addition, tables of section data for various section shapes are required; these are given for Clark Y sections over a range of thickness in R. & M. 2036; they were derived, by methods described in R. & M. 2020, from overall measurements of thrust and torque on full scale propellers at low values of J in the Royal Aircraft Establishment 24-ft. tunnel and are subject to revision in the light of subsequent experimental research. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2035.pdf 179. Tank Tests on a Hull with the Main Step Faired in Planform and Elevation D. I. T. P. Llewelyn-Davies Tank tests were required to find out whether the water characteristics of a hull with a main step, faired in both planform and elevation, were comparable with those of a hull with a conventional Vee or transverse step. Stability diagrams and spray and resistance characteristics were obtained over a large range of loadings (CDelta0 = 0.616 to CDelta0 = 1.440). The fully faired step offers more possibility of designing a longitudinally stable flying boat hull than does the conventional transverse or Vee step, but a hull with such a step is 5 to 10 per cent. less efficient hydrodynamically except at high speed. In order to avoid running too fine at high speed, it is recommended that the centre of gravity should not be more than 0.46b ahead of the apex of the step. The modification to the step planform makes little difference to the main spray characteristics, but increase in all-up-weight reduces wing, tailplane and propeller clearances. The effect of increase in load on the porpoising stability characterictics is to raise both limits, with a tendency for the upper limit to rise more rapidly, but less regularly, than the lower limit. The free-to-trim attitudes also rise with increase in all-up-weight. The planing efficiency of the hull increases with increase of load, especially at high speeds. There is evidence of a second resistance hump at high speeds and also of a critical variation of planing efficiency with attitude under similar conditions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2708.pdf 180. Tests of Contra-rotating Propellers of 2 7/8-ft. Diameter at Negative Pitch on a "Typhoon" Aircraft Model R. C. Pankhurst, J. N. Veasey, J. R. Greening and Miss E. M. Love The previous tests of a pair of contra-rotating two-bladed propellers have been extended to the propeller 'braking' condition by covering the range of pitch setting from 0 deg. to - 30 deg. at the 0.7 radius. Measurements of overall thrust and individual torques were made up to an advance ratio (J) of 4.0, except that the 0 deg. settings were not tested beyond an advance ratio of 1.0 where the torque had already become negative. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2218.pdf 181. Tests of model propellers in the high speed tunnel thrust and torque measurements on a 2-blade, 6 per cent. thick, Clark Y section propeller G. S. Hislop, J. Caldwell, M. Jones High-speed wind tunnel tests of various model propellers were required as part ofa general research programme dealing with propellers for high-speed aircraft. A two-blade 4 ft 6 in diameter Clark Y section propeller of 6 per cent. thickness ratio and 7 per cent. total solidity was tested at three fixed blade angles over a range of forward Mach numbers up to 0.8 and rates of advance up to J = 4. In addition, the forward Reynolds number based on 1 ft. chord, was varied from 1 million to 4 millions at one blade angle, the forward Mach number being held constant at 0.3. (i) The experimental technique employed for measurement of overall thrust and torque of model propellers in the Royal Aircraft Establishment High Speed Tunnel was proved successful and capable of yielding reasonably consistent results. (ii) No appreciable scale effect was present on the tests made at low Mach number, but this does not necessarily hold at high Mach numbers, for which condition no evidence is available. (iii) The variation of thrust and torque coefficientsand propulsive efficiency with increasing Mach number at constant rates of advance show no serious departure from the variations to he expected from such a blade section operating at high Mach numbers. (iv) A maximum efficiency of 0.9 was attained with this propeller at low forward speeds and tip Mach numbers. With increase in Mach number the efficiency fell slowly but steadily until some critical Mach number was reached when the rate of decrease became serious. The critical tip Mach number varied between 0.9 and 1.2 depending upon the operating conditions. At a forward Mach number of 0.7 and upwards the rate of decrease in efficiency became large, though the maximum efficiency at M = 0.7 was still quite high at 0.76. It might be possible to reduce this rate of decrease at a given Mach number by operating at still greater blade settings. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2595.pdf 182. Tests on a 5-per-cent Biconvex Aerofoil in the Compressed-Air Tunnel D. H. Williams, A. H. Bell A symmetrical 5 per cent. biconvex aerofoil has been tested from R = 0.3 x 10(to power 6) to R = 7.5 x l0(to power 6). No scale effect was found on Cz. To show the effect of camber, comparative curves are given for circular-back aerofoils. Cz .... increases linearly with camber from 0.7 for the symmetrical wing to 1.18 for a wing with 6 per cent camber. The aerofoil was also tested with a 15 per cent. split flap. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2413.pdf 183. The behaviour in compression of aluminium alloy panels having a flat skin with corrugated reinforcement E. A. Brook This report describes compression tests on 36 panels, made of D.T.D. 390 and D.T.D. 546. Each panel consisted of a flat skin reinforced with continuous corrugations, and the object of the test was to investigate the effect of rivet pitch and arrangement, corrugation width, and skin and corrugation thickness, on the buckling and failing loads of the panels. The results indicate that for the thicknesses of skin and corrugations considered in this report, the inter-rivet buckling stress is considerably less than the stress at which the skin between rivets would buckle, when considered as an Euler strut with encastre ends. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2598.pdf 184. The buckling of a Flat Rectangular Plate under Axial Compression and its Behaviour after Buckling H. L. Cox, M.A., of the Engineering Division, N.P.L. To rehearse the theory of buckling of a flat rectangular plate with particular reference to the effect of restraint at the edges of the plate against movement in the plane of the plate. The effects of various types and degrees of edge restraint on the behaviour of the plate are considered with regard both to the value of the critical stress and to the behaviour after buckling. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2041.pdf 185. The design of suction aerofoils with a very large CL-range M. B. Glauert The use of suction slots to remove the boundary layer at points where the air velocity has a discontinuity opens up wide new fields in aerofoil design. It becomes possible to envisage aerofoils which have laminar flow characteristics over the greater part of the surface throughout a Q-range so large as to completely cover the normal flight range, and which are also thick enough to provide ample room for the stowage of engines, passengers and other loads at much lower all-up weights than have hitherto been feasible. This paper considers four aerofoils designed on the basis of their velocity distributions in two-dimensional incompressible potential flow. The design method used was that of Lighthill's exact theory, set out in R. & M. 2112, which involves prescribing the velocity over the aerofoil surface as a function of position on the circle into which the aerofoil may be transformed. A few additional techniques to procure suitable velocity distributions were employed, and an exposition of these will be the subject of a later paper. The principal feature in the design is the replacement of the region of falling velocffy over the rear part of the aerofoll by a single discontinuity in velocity, at which point boundary-layer suction is applied. Thus adverse pressure gradients are completely eliminated throughout a wide range of incidence. The boundary layer remains thin and laminar flow may be achieved, even on aerofoils of very great thickness. At the discontinuity the mathematical shape is a logarithmic spiral, but this must be modified in practice to include the suction slot. In one aerofoil the spiral is avoided by having a steep fall of velocity over a short distance of the surface instead of a complete discontinuity, but this may detract from the performance. The paper discusses the relative merits of the aerofoils and considers possible improvements. Zero pitching moment is very desirable and can readily be achieved. A suction slot on the lower surface proves to be unnecessary for aerofoils cambered as these are so as to be efficient at high lifts, but it may be unavoidable if a less cambered design is required in an effort to get a higher critical Mach number. This is inevitably low with aerofoils of this thickness, and is the chief drawback of thick suction wings. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2111.pdf 186. The Effect of Mean Incidence, Amplitude of Oscillation, Profile and Aspect Ratio on Pitching Moment Derivatives J. B. Bratt, B.A., B.Sc., and K. C. Wight of the Aerodynamics Division, N.P.L. The wattmeter harmonic analyser used in conjunction with the magnetostriction stress indicator has been extended to give both the in-phase and the out-of-phase components of the fundamental in the aerodynamic pitching moment on an aerofoil oscillating about a spanwise axis. With this apparatus measurements have been made to determine how the components of pitching moment variation are influenced by mean incidence, axis of oscillation, profile, aspect ratio, amplitude of oscillation, Reynolds number and frequency parameter. In the cases where the pitching moment variation is sinusoidal these results may be expressed in terms of pitching moment derivatives. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2064.pdf 187. The experimental determination of the boundary layer and wake characteristics of a piercy 12/40 aerofoil, with particular reference to the trailing edge region J. H. Preston, N. E. Sweeting and D. K. Cox To carry out on a Piercy 12/40 aerofoil an experimental investigation similar to that which was made using a Simple Joukowski aerofoil, and which is described in R. & M. 1998. The aim being to provide data relating to boundary layer and wake characteristics on two aerofoils, one cusped and the other with a finite trailing edge angle (22.1 deg.), from which a start could be made on the theoretical prediction of the chordwise load distribution taking due account of the boundary layer and wake, and to replace or substantiate the empirical corrections which were introduced, in R. & M. 1996, which describes an attempt to predict the lift of an aerofoil. The tests were carried out on a 20-in. chord aerofoil in the 4-ft. No. 2 tunnel under conditions of zero interference. The Reynolds number was 0.42 x 10power6. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2013.pdf 188. The Ideal Drag Due to a Shock Wave. Parts I and II C. N. H. Lock Part 1. The subject of the present note is the increase of the drag of an aerofoil which arises from the presence of limited shock waves when the forward speed lies between the so-called shock stalling speed and the velocity of sound. Evidence from photographs and other sources shows that under certain conditions a single limited shock wave exists on one or both surfaces of an aerofoil when the local speed at some point of the surface exceeds the velocity of sound. It is therefore suggested that ideal two-dimensional motions about an aerofoil may exist, which satisfy the equations of motion of a non-viscous non-conducting compressible fluid, at all points of the field outside a limited shock wave attached to one or both surfaces of the aerofoil. The shock wave is to be considered merely as a surface of discontinuity across which the usual conditions of continuity of flow, momentum, total energy and velocity parallel to the surface, are satisfied; it forms the rear boundary of a limited region in which the flow is supersonic and its intensity falls to zero at its outer edge where the velocity is equal to the local velocity of sound. As a result of the increase of entropy on passing through the shock wave, the density and velocity at a large distance behind the aerofoil of a particle of fluid that has passed through the shock wave will both be reduced below their free-stream values; the pressure will have regained its free-stream value. The ordinary momentum integrals taken across lines far in front of, and far behind, the aerofoil thus determine the drag in the ideal case; this may be considered as the ideal (lowest possible) drag due to an actual shock wave. Part 2. The method given in Part I of calculating a first approximation to the ideal theoretical drag rise due to a shock wave on an aerofoil is extended to cover the use of the Karman-Tsien solution in place of the Glauert relation. It is shown how the drag rise can be calculated from the thooretical critical Mach number and the geometrical curvature of the surface at the point of maximum suction. In particular for two aerofoils having the same critical Mach number the drag rise is proportional to the radius of curvature; thus the drag rise on a 17.3% ellipse at zero incidence will be three times that for an NACA 0012 section having the same critical Mach number. Comparison with experiment in the N.P.L. 20 in x 8 in HighÂ·Speed Tunnel shows that for a number of aerofoil shapes the theoretical rise occurs consistently from M = 0.1 to 0.13 later than the observed rise. The present method is simple and should give at least a better indication of the relative merits of different aerofoil shapes than a knowledge of the theoretical critical speed alone. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2512.pdf 189. The increase in thrust obtainable from a power plant installation using the cooling-air as a propulsive jet A. B. P. Beeton The net thrust or drag of a power-plant cooling system has been estimated for various flight speeds. The effect of using the exhaust heat inside the duct is considered, and also the effect of burning additional fuel behind the engine. Typical figures are taken to produce a set of curves, from which the respective merits of the various systems considered can be assessed in a general manner. It is concluded that useful gains in total thrust might be obtained at top speed by the use of internally discharging exhausts. The gain from auxiliary fuel burners behind the engine would only be considerable at very high speeds. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2147.pdf 190. The investigation of air loads in flight from measurements of strain in the structure J. Taylor Strain measurements in flight involve considerably more work than on ground tests and should be restricted to problems which cannot be solvedby ground tests. Limited experience available suggests that for most flight work the overall bending and shear actions at each of about five sections of a major component are all that is required. These can be determined by suitable selection of positions of gauges, with no more than four to eight measuring stations at each section. It is advisable to check any particular installation by ground tests using known loads. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2408.pdf 191. The theoretical effect of flight path angle on the lateral stability and response of an aircraft E. M. Frayn, and M. V. Parnell The response of a typical aircraft of the dive-bomber class to various disturbances has been calculated at four angles of dive covering tile range 0 to 90 deg and for four pairs of values of lv, nv. The most notable effect on stability is the marked increase in spiral damping with increasing dive angle at the same T.A.S. This has little effect on the response, since in most components, this mode is scarcely excited. For dive angles up to 30 deg the variations in response are so slight as to be negligible, while for larger angles of dive the variation is small for the first 2 airsecs. Calculations of response in level flight, which slightly underestimate the response in a dive, can thus be assumed to give a sufficiently accurate picture of the behaviour at small flight path angles for most requirements. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2529.pdf 192. Theoretical velocity distribution in a high-speed tunnel contraction M. Jones and P. Bright By an arithmetical method, contours of constant Mach number have been determined in the contraction cone of a circular tunnel whose axial distribution of area was assumed to be the same as that in the Royal Aircraft Establishment High Speed Tunnel. The results show a definite tendency for the velocity to be lower on the centre line than on the wall, the difference becoming smaller as tbe working section is entered. Sufficient work has been done to show that the method described can be used to obtain solutions for the flow of a compressible fluid in a pipe of varying cross section, provided that there are no discontinuities in the boundaries. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2601.pdf 193. Wind-tunnel tests on a 30 per cent. suction wing E. J. Richards, W. S. Walker and C. R. Taylor Tests carried out on a 16 per cent. suction wing have shown that it is impossible to maintain laminar flow aft of the suction slot at high Reynolds numbers, because of the dynamic instability of the laminar layer over the concave surface. As a result of this finding it was concluded that compared with a normal low-drag wing very little was to be gained by this means on wings of normal thickness-chord ratio except at very high Reynolds numbers. Since however the maximum thickness-chord ratio allowable on low-drag wings is of the order of 18 to 20 per cent., it was realised at once that a considerable gain could be obtained from the new designs by virtue of the fact that there appeared to be no limit to the thickness-chord ratios allowable on this type of wing and that wing thickness-chord ratios of 30-40 per cent. could be used which would give low drags and high maximum lifts. It was further shown in the 16 per cent. tests that the amount of suction necessary if transition could not be delayed to the slot, and the quantity of air that needed removal from the boundary layer were not changed to any great extent ; thus the scheme appeared promising even in the absence of extensive laminar flow because of the structural and storage gains obtained thereby. The present paper describes tests carried out in the National Physical Laboratory 13 ft. x 9 ft. Wind Tunnel at Reynolds numbers between 0.8 and 3 millions on such a 30 per cent. suction wing to determine whether the suction principle is satisfactory and to investigate the general characteristics of the wing. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2149.pdf 194. 24-ft. tunnel tests on a Rotol wooden Spitfire propeller. Test results, and data for single radius calculations A. B. Haines and P. B. Chater This note contains the results of tests made in the Royal Aircraft Establishment 24-ft. tunnel on the Rotol hydulignum propeller RA.10046 designed for the Spitfire IX aircraft. The overall thrust and torque measurements have been analysed to give mean lift-drag data, and these have been compared with those for other propellers. When account is taken of the comparative root thickness and pitch distributions, it is shown that in general, the present results confirm conclusions from earlier analyses particularly as to the large influence of root thickness on the start of the stall. The blade has however a higher CDmin at low Mach number than was expected. For the take off condition on the Spitfire IX, the propeller gives almost 25 per cent. more thrust than does the corresponding Rotol metal design. Part of this increase results from the 15 per cent. greater solidity of the wooden propeller. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2357.pdf 195. A brief review of the problem of exhaust silencing F. L. West This note reviews past and present work on noise reduction of the reciprocating engine exhaust. Collected measurements of the noise level surrounding various engine installations and the effect of silencing experiments on engine and aircraft performance are presented. In view of the growing application of the gas turbine, some recent observations of its noise characteristics are included. The adverse effects of simple baffle silencers on engine power illustrate the need for renewed investigation of silencing by acoustical interference methods allowing unrestricted gas flow. In this respect, limitations of past work on the theory of silencers are discussed and possible improvements suggested. In conclusion, a tentative method of calculating the influence of engine and exhaust pipe design on the noise spectrum is applied to a typical system. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2803.pdf 196. A criterion for the prevention of spring-tab flutter A. R. Collar and G. D. Sharpe The present paper advances a formula which can be used as a criterion for the degree of mass-balance necessary for the avoidance of spring-tab flutter. The formula shows that if the tab is of sufficiently light construction, mass-balance may not be required at all; on the other hand, the usual static balance may be inadequate for a tab of high inertia. The criterion comprehends within itself the requirement (given elsewhere) limiting the length of a mass-balance arm. While the formula is based on theoretical considerations (which are set out in the Appendix) the numerical values for the quantities to be used have been deduced from flight experience, which shows excellent correlation with the theory. Two forms for the criterion are given: a simple form suitable for general application, and a slightly elaborated form intended for application to unusually large tabs. The Appendix, besides containing the main analysis, also gives consideration to certain factors which for simplicity are omitted in the main text. In particular it is shown that the 'limiting length' for a balance arm may be generalised to a 'limiting circle' for the position of the balance mass: the circle can often be found from simple geometrical considerations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2637.pdf 197. A theoretical approach to the design of hydrofoils C. H. E. Warren An investigation has been made into the application of the theory of thin sections to the design of hydrofoils having high cavitation speeds. Consideration is given to both symmetrical sections, which themselves are suitable for struts, and camber-lines, which, when used with the symmetrical sections, lead to cambered sections which are suitable for lifting surfaces. In all the aim has been to keep the peak local velocities to a minimum, and the sections developed differ from' low-drag' aeroIoil sections mainly in that, being hydrofoils, the sections have sharp leading edges. The theoretical optimum section consists of an elliptic symmetrical section superimposed on a logarithmic camber-line. Typical practical sections will cavitate at a speed lower by about 5 knots than the theoretical optimum section of the same thickness/chord ratio and at the same lift coefficient. For strut sections it is shown that sections having high cavitation speeds at zero incidence tend to be inferior to other sections at incidences as small as 2 deg. For lifting surface sections it is shown that although a high cavitation speed demands a low design lift coefficient, a high loading at cavitation demands a high design lift coefficient. Operation above cavitation speeds or over wide ranges of lift coefficient are not considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2836.pdf 198. Aerofoil theory of a flat delta wing at supersonic speeds A. Robinson Lift, drag, and pressure distribution of a triangular flat plate moving at a small incidence at supersonic speeds are given for arbitrary Mach number and aspect ratio. The values obtained for lift and drag are compared with the corresponding values obtained by strip theory. The possibility of further applications of the analysis leading up to the above results is indicated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2548.pdf 199. An approximate solution of two flat plate boundary layer problems E. J. Watson, J. H. Preston The method presented here for obtaining an approximate solution of the laminar boundary-layer equations is based on the iteration process of Piercy and Preston. It leads to a simple analytical approximation of good accuracy for Blasius' solution of the boundary-layer flow past a flat plate. The main purpose of this paper is, however, the application of the method to a generalisation of Blasius' problem, namely the case of a flat plate in a uniform stream when there is a suction velocity normal to the plate proportional to xpower-1/2 where x is the distance along the plate from its leading edge. This generalisation was first given by Schlichting and Bussmann, and has also been considered by Thwaites and Watson. For the simpler problem of the flat plate in a uniform stream it is well known that by means of Blasius' transformation the solution is obtained from that of a third-order non-linear differential equation. The iteration method of Piercy and Preston for the solution of this consists in replacing the velocity where it occursÂ·in the equation by an inferior approximation and solving the resultant linear equation to obtain a superior approximation. To start the process the velocity was assumed to be that of the stream, giving Oseen's solution as the next approximation. Here the start is made in a different manner. We take as the initial approximation to the velocity one of two choices - (i) a constant value or (ii) a linear function-and in either case have a parameter at our disposal. The iteration is performed, giving a second approximation containing this parameter, which we then determine by substituting the second approximation in the momentum equation. The necessary integrations can be performed analytically, and the quantities which characterise the boundary layer are readily determined. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2537.pdf 200. An exact solution of the boundary-layer equations under particular conditions of porous surface suction B. Thwaites No hitherto successful attempts except one (by Griffith and Meredith) have been made to provide an exact solution of the boundary-layer equations of motion when there is a continuous normal velocity at the boundary. At the suggestion of Preston a solution is given in this report when this suction velocity is proportional to xpower-1/2, x being the distance along the plate, and there is a constant velocity outside the boundary layer. The solution is merely an extension of the well-known Blasius' solution, and does not contain any new mathematical technique. Being exact, however, it can command a certain interest, since the treatment of the boundary-layer equations with suction through the boundary is very difficult (Thwaites). The solutions of the differential equation below were obtained on the differential analyser, at Manchester University, at present on loan to the Mathematics Division, N.P.L. Acknowledgements are made to the Analyser Group of this Division for providing these solutions, and in particular to E. C. Lloyd, who was concerned in this particular problem. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2241.pdf 201. Asymptotic solution of a boundary layer suction problem E. J. Watson The theory of the boundary layer on a flat plate in a uniform stream with a velocity of suction proportional to xpower-1/2 (x being the distance from the leading edge of the plate), has been developed by Thwaites a in a report which contains numerical solutions of the problem obtained on the differential analyser. The behaviour of the solution when the rate of suction is large is investigated here, and it is found that the velocity distribution in the boundary layer approximates to the Griffith-Meredith or asymptotic suction profile. The solution is developed in the form of a series of descending powers of the suction velocity and the coefficients of this series are obtained successively by the so1ution of linear differential equations. The first four coefficients are obtained explicitly and numerical values are given in Table 1. Series are also obtained for the displacement and momentum thicknesses and for the skin friction and form parameter H. Comparisons are made with Thwaites's solutions, and good agreement is found when the rate of suction is large. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2298.pdf 202. Combustion in the gas turbine a survey of war-time research and development Peter Lloyd The present report attempts a general survey of the whole field of gas-turbine combustion. The report covers both research and development, and while it is mainly concerned with British work, some mention is also made of German work on the same subject. The related processes of combustion in propulsive ducts are briefly touched on. The report is based on a paper to the Institution of Mechanical Engineers, but with much fresh material, including a comprehensive bibliography. There have been many groups of investigators concerned in this work at the Royal Aircraft Establishment, Power Jets, Joseph Lucas & Co., the Asiatic Petroleum Co., Metropolitan Vickers Ltd., Rolls-Royce, Armstrong Siddeley's, De Havillands and the City and Guilds College. In preparing the present report, full use has been made of the work of all these groups and of the Combustion Panel of the Ministry of Aircraft Production's Gas Turbine Collaboration Committee through which they co-operated; this debt is gratefully acknowledged. On the other hand the interpretation and assessment of the work are the author's, and for these full responsibility is taken. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2579.pdf 203. Compression tests on dural-celluboard sandwich panels K. H. V. Britten Results are given of compression tests made on 56 Dural-Celluboard Sandwich Panels with Birch Spruce or Whitewood centres. These are compared with results from similar tests on Dural-Balsa sandwich and all-metal panels, and it is seen that over the range of sizes and weights considered Dural-Celluboard can be equally or more efficient for carrying end loads. The birch Celluboard was more efficient than the spruce or whitewood and the thicker sandwiches, and those with thicker skins were more efficient than the thinner specimens. The maximum stress reached in the skin, 48,000 lb/sq in., was equal to the 0.1 per cent tensile proof stress of the material. The birch filling had also reached its maximum compression stress, 8,000 lb/sq in. The design had therefore exploited these materials to their fullest extent. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2658.pdf 204. Diffusion of antisymmetrical loads into, and bending under, transverse loads of parallel stiffened panels J. H. Argyris To present the general theory of diffusion of antisymmetrical concentrated end loads and edge loads into parallel stiffened panels, including the theory of bending of a parallel stiffened panel under arbitrary transverse loads. By combining the results of this paper with the results on diffusion of symmetrical loads given in R. & M. 1969 and R. & M. 2038 or in Appendix I to this paper it is possible to analyse the diffusion in a parallel panel under any arbitrary load or edge stress distribution. The methods developed in this paper permit a simplification and slight generalisation of the results obtained in R. & M. 1969 and 2038 for the symmetrical diffusion case in a parallel panel. The relevant formulae are given in Appendix I to this report. An alternative approach to the diffusion problem in parallel panels with given boom areas is presented in Appendix II. In general diffusion in parallel panels is determined by three parameters : the diffusion constant as defined by Cox (R. & M. 1860), the ratio of total area of edge members to total area of stringers plus effective sheet, and the ratio of total area of stringers plus effective sheet to the product of length of panel and sheet thickness. It is shown that the effect of transverse loads on the direct stresses in a parallel panel is equivalent to that of antisymmetrical edge loads producing the same bending moment at each section. The shear stress distributions differ by a constant value across each section. This difference is the shear stress produced by the shear force of the transverse load system assumed uniformly distributed over each cross-section. In all loading cases as mu increases the stress distribution in the panel approaches that indicated by the ordinary engineer's theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2822.pdf 205. Flight tests on Hurricane II, Z.3687 fitted with special wings of 'low-drag' design R. H. Plascott, D. J. Higton, F. Smith and A. R. Bramwell This report describes flight tests to investigate the proNe-drag characteristics of a 'low-drag' section wing built by Armstrong Whitworth, Ltd., using a new type of construction of their own design. During the first series of tests, a section of the wing was pressure-plotted and the results showed that it should'be possible to obtain laminar flow over a range of lift coefficient from 0.12 to 0.50. A few preliminary profile-drag measurements were also made and a fairly low profile-drag coefficient (CD = 0.0046 to 0.0050) was recorded over a lift Coefficient range of 0.20 to 0.40; there was, however, a rapid rise in the profile drag coefficient at lift coefficients less than 0.20, and investigation of the surface waviness showed that the failure to maintain laminar flow at higher speeds was probably due to the excessive waviness present, which amounted to a variation of about ± 2½ thousandths of an inch from the mean deflection curve on a two-inch gauge length. A further series of profile-drag measurements was made when the surface waviness had been reduced to ±1 thousandth of an inch variation from the mean deflection curve on a two-inch gauge length. It was found that, provided no flies or other insects were picked up during the flight, the drag coefficient had been reduced to 0.0044 over a range of lift coefficient from 0.12 to 0.50. This corresponds to transition from 50 to 60 per cent. chord. With the reduced surface waviness, it was possible to maintain laminar flow up to Reynolds numbers of nearly twenty millions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2546.pdf 206. Further wind tunnel tests on a 30 per cent. symmetrical suction aerofoil with a movable flap N. Gregory and W. S. Walker The present work was undertaken in order to extend the existing experimental information on the 30 per cent. Griffith suction aerofoil obtained by Richards, Walker and Taylor (1945), in particular: (a) to investigate the behaviour of the wing when the flap was deflected, (b) to test a wider slot and improved internal ducting system, (c) to investigate further the variation of suction quantity with speed, and (d) to find the variation of CD with suction quantity and with different surface conditions. Tests with zero suction were carried out at a Reynolds number of 2.88 Ã— 10power6 for a range of incidence of 0-20 deg. and for flap angles of 0-14 deg. With boundary layer suction applied, tests were carried out at this Reynolds number to 6 deg. incidence only, owing to insufficient suction head. At a Reynolds number of 0.96 Ã— l0power6 the pump power was sufficient to prevent separation up to an incidence of 16 deg. where the maximum CNF recorded was 2.3 with 14 deg. flap angle. The flap is effective as a high-lift device. A given CL can be obtained at a much smaller angle of incidence when there is a positive flap setting than with zero flap angle, and less suction is required to prevent separation. There is considerable scale effect present between the two speeds at which tests were made, and it is desirable to test the wing in the Compressed Air Tunnel in order to estimate flight performance, particularly in the event of suction failure. The suction quantity is high at R = 0.96 x 10power6 but now shows a continuous decrease with increase of Reynolds number in contrast to the irregular variation found by Richards. With no suction and with laminar flow to the slot, the CD has the low value, for the thickness of the aerofoil, of 0.010. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2287.pdf 207. General performance calculations for gas turbine engines D. H. Mallinson In this report an attempt is made to summarise the theoretical work carried out during the past few years aimed at discovering the potentialities of the gas turbine as a power plant in many fields of application, but especially as an aircraft power unit. To do this the performance of the various modifications of the ideal gas turbine cycle is considered in some detail, and the works of various authors are then combined and edited in order to depict the performance attainable by practical engines. The influence of component efficiencies on this latter performance is examined and the effects of modifications, such as reheating the gas after partial expansion or introducing a heat exchanger, are compared with the effects predictable from the ideal cycle calculations. The association between the gas turbine and jet reaction as a means of aircraft propulsion is considered and the probable performance of several simple jet engines estimated over a speed range from 0 to 1,500 m.p.h. The influence of forward speed and altitude on the output and efficiency of the gas turbine is obtained and combined with the influence of varying operating conditions upon the propulsive efficiency of the jet to give the overall performance of a jet-turbine combination. Finally a method of estimating the performance of a simple jet engine from the non-dimensional characteristics of its components is detailed and the results of an example employing this method are used to illustrate the influence of several factors, such as propelling nozzle size, upon the equilibrium running conditions of such an engine. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2684.pdf 208. Influence of Tuned Dampers on Flexure-Aileron Flutter. Parts I-III. R.A. Frazer et al Part I - Theoretical Investigation on the Influence of Tuned Damping Devices on Flexure-Aileron Flutter. Part II - Some Further Calculations on the Influence of Tuned Damping Devices on Flexure-Aileron Flutter. Part III - Experiments on the Effect of Tuned Damping Devices on Flexure-Aileron Flutter. In Part I a general theory has been developed for the investigation of the influence of damping devices of various types on flexure-aileron flutter. The numerical applications refer to a large transport aircraft, and they are restricted to the case of a mass-balanced aileron-carried damper. From the diagrams given at the end of the Part it is inferred that this type of damper would be unsatisfactory as a flutter preventive. Part II supplements Part I and gives results for a partly balanced and for a completely balanced aileron-damper system. It is concluded that tuned dampers of these types would also prove unreliable. Part III describes an experimental investigation into the effect on flexure-aileron flutter of a tuned damping device attached to the aileron. The results confirm the theoretical conclusion that the use of an aileron-carried damper would not be a reliable flutter preventive. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2559.pdf 209. Investigation of the flow past finite wedges of 20 deg. and 40 deg. apex angle at subsonic and supersonic speeds, using a Mach-Zehnder interferometer with appendix: sensitivity and accuracy of the interference method applied to pressure measurements D. C. Pack, E. Groth An investigation has been made in the high-speed wind tunnel A 7 of the Luftfahrtforschungsanstalt. Brunswick, of the flow past finite wedges of 20 deg. and 40 deg. apex angle at both subsonic and supersonic speeds, the Mach numbers lying between 0.6 and 0.85 on the one hand, and between 1.4 and 2.8 on the other. The pressure distributions on the models have been evaluated from photographs of density contours obtained by the use of a Mach- Zehnder interferometer. The interferometer technique is briefly described, and also the method of evaluation of the photographs. The results are discussed in detail, and are compared with the theoretical predictions of Maccoll and Codd. A selection of photographs, and a number of diagrams showing the pressure distribution, are included. In the Appendix, the sensitivity and accuracy of the interference method applied to pressure measurements are discussed. It is shown that requirements for both, in the particular case of the A 7 tunnel, are satisfied in a range of Mach numbers between 0.5 and 3.0. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2321.pdf 210. Limitations of Use of Busemann's Second-order Supersonic Aerofoil Theory W. F. Hilton The author has found the Busemann theory very rapid in use for the determination of pressure coefficients. It has been tacitly assumed in the past that Busemann's second-order theory of aerofoils at supersonic speeds was subject to the same limitations of wedge angle as the exact theory given by Lighthill and others, namely, the wedge angle at which the bow wave detaches. The range of angles for which Busemann's theory gives a pressure coefficient in error by less than 1 per cent is shown to be smaller than the angle range for the shock wave to be attached. There is also a limit to the application of Busemann's method to angles of expansion as well as to angles of compression, unlike the exact theory, which can be extended to expansive angles of tile order of one right-angle without breaking down, in fact far beyond the useful range. The limits of angle given for the use of Busemann's theory are conservative, since they give the pressures to 1 per cent, and tile force coefficients will be more accurately determined since the errors tend to cancel out when integrating pressures to obtain forces. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2524.pdf 211. Measurements of the degree of smoothness attained in a laminar-flow wing speciment (Short Bros.) R. B. Coles This report describes tests made to determine the degree of surface smoothness attained in a 6-ft. chord wing specimen having two spars and a thin skin stiffened between spars by ribs and channel section chordwise members. The specimen was designed and made by Short Bros. of Rochester. The tests included measurements of the initial surface smoothness, distortion under load, proof and ultimate tests and compression tests on two short lengths of the upper front spar flange. These tests show that in order to reduce the amplitude of the skin distortions to the required limits the rigidity of the channel section stiffeners should be increased and possibly additional local stiffening near the front spar added. No permanent distortions of the wing beyond the allowed limits are likely to occur under service conditions. The compressive stress in the spar flanges at failure was 37,500 lb./sq, inch. Strut tests on 6-in. and 12-in. lengths of the upper front spar flange gave failing stresses of 59,000 lb./sq, in. and 48,000 lb./sq, in respectively. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2253.pdf 212. No. 2, 11 1/2-ft wind-tunnel tests of a small span, small chord double aileron for use as a lateral control on a high-lift aircraft A. D. Young and W. S. D. Marshall Tests were made on a 1/2.25 scale model of a half wing of the Master. The span of the aileron was 0.22s and the chords were 0.2c and 0.15c; the aileron was fitted with a balance tab of 0.05c chord. Measurements were made of the hinge moments, lift increments (from which the rolling moments were deduced) and the pressures in the aileron gaps just above and below the seals. The latter were required for estimating the effect of internal shrouded nose (or pressure) balances. Tests were also made of the effect on the hinge and rolling moments of a small spoiler situated just aft of the front aileron vent ; the spoiler was assumed to emerge on the lower surface of the down-going aileron and on the upper surface of the up-going aileron. The main conclusions are: (1) A double aileron will give much the same rolling moment as a single aileron of the same total chord and at the same total deflection. (2) The double aileron offers no advantage where total deflections of magnitude not greater than about 20 deg are required (as for ailerons of normal span and area). For ailerons of small span and chord, for which deflections of the order of 50 deg are required, the double aileron offers definite advantages over the single aileron. (3) An inter-aileron gearing of about 2 is probably the optimum. (4) For a representative carrier-borne aircraft it is estimated that, even with this inter-aileron gearing, either the tab balance plus a nose balance of upwards of 40 per cent or a nose balance approaching 50 per cent is required to keep the stick forces for full control at landing speeds down to an acceptable figure. (5) The effect of the spoiler is only apparent for control movements of less than about 20 deg. Its possibilities on ailerons of normal span and angular range are worth investigating. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2536.pdf 213. Note on profile drag calculations for low-drag wings with cusped trailing edges R. C. Lock In R. & M. 1838 calculations of profile drag were made based on wing sections of conventional design, and were later extended in an Addendum to "low-drag" wing sections with convex trailing edges. Further calculations were required for low-drag sections of more recent design with cusped trailing edges. Calculations were made on sections of the NACA 65-family of thickness 0.12c and 0.23c with maximum thickness at 0.4c from the leading edge, over a range of Reynolds number and position of the transition points. The results were found to differ considerably from those of Ref. 2 when the transition points were far back from the leading edge, the calculated values of the drag coefficient being in some cases as much as 25 per cent. less than the previous calculations. The results were in good agreement with wind-tunnel tests made at the National Physical Laboratory and the Royal Aircraft Establishment, but showed a large discrepancy with flight tests made at the Royal Aircraft Establishment. In these flight tests transition was fixed by means of tapes, but no account was taken of the possibility that transition may have occurred behind the tapes and not necessarily at the tapes themselves. In this way the drag for a supposed mean transition point may have been underestimated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2419.pdf 214. Note on the influence of spanwise flow on lift distribution W. P. Jones The influence of spanwise flow on the lift distribution for a thin flexible wing of any plan form is considered. By the use of Eulel's equations for incompressible, inviscid flow, it is shown that the lift distribution is not appreciably affected provided the displacements of the wing are small. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2181.pdf 215. Notes on the Induced Drag of a Wing-Tail Combination C. H. Naylor An expression has been derived for the factor to he applied to ideal induced drag to allow for Wing-tail interference. This factor is primarily dependant on the wing-taillift and span ratios. It is of the order of 1.1 for a normal aircraft when the tailplane carries 10 per cent of the weight of the aircraft, and can reach unexpectedly large values at high speed. Charts, generalised curves, and sufficient information are included to permit rapid evaluation of the factor for any particular case. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2528.pdf 216. On an aspect of the accident history of aircraft taking off at night A. R. Collar, George White An investigation is described into the cause of a series of accidents to aircraft taking off at night; it depends on the fact that the direction of the net reaction on a pilot's body during acceleration is the same as that corresponding to a steady climb. The analysis and a numerical illustration are given in Part I. The results of flight tests designed to check the analysis are summarised in Part II: the results confirm the theoretical findings. It is concluded that the only faculty which can be safely used is that of vision, and this implies the use of instruments throughout the whole of the take-off at night. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2277.pdf 217. On certain types of boundary-layer flow with continuous surface suction B. Thwaites In this report, two matters are dealt with which were left in an unsatisfactory state in the Appendices of Reference 1. The first concerns the conditions obtaining near the front of a flat plate in a uniform stream with constant continuous suction through the plate. We now satisfactorily prove that the boundary-layer velocity profile tends to the well-known Blasius profile as the front end of the plate is approached. The second matter concerns the solution of the boundary-layer equations of motion when 'similar' velocity profiles are assumed - it is shown that only two types of outside stream velocity distributions lead to 'similar' profiles, under ordinary conditions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2243.pdf 218. On the flow past a flat plate with uniform suction B. Thwaites A new method of performing boundary-layer calculations is introduced in this paper, and is applied to the problem of finding the characteristics of uniform flow past a flat plate through which there is a constant normal velocity. An exact solution to this problem has not yet been found and it is therefore difficult to assess the accuracy of the results obtained. The results, however, are compared with those of two other methods. The new method will be applied to other problems and is explained in detail in Ref. 5. When the momentum equation is being used, one obvious advantage of the method is that, in 'adding' velocity profiles, the momentum thickness of each may be added to give the momentum thickness of the whole. This is not so in the usual methods of boundary-layer calculations, and great simplification is thereby obtained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2481.pdf 219. Part 1 Tabulated Thermal Data for Hydrocarbon Oxidation Products at High Temperatures. Part 2 The Effect of Dissociation on Rocket Performance Calculations A. B. P. Beeton Part 1. Tables are given of the total heat and entropy of H2O, CO2, 02, CO, H2, OH, O and H for the range of temperature 1500-4000 °K. Values are also given for the corresponding equilibrium constants over the same temperature range. The tables have been compiled with a view to their use in calculating the performance of liquid-fuel rockets. Part 2. The equilibrium constants and thermal properties of all the important gas components have been used to calculate some theoretical combustion chamber temperatures and specific impulses allowing for all dissociation effects. The results are compared with a previous method which ignored dissociation (into OH, O and H components), in the case of a propellant consisting of a 3 to 1 mixture ratio of oxygen and hydrocarbon fuel. The combustion chamber temperature is found to be about 300°C lower and the specific impulse about 10 seconds smaller than the figures given previously. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2542.pdf 220. Research on High Speed Aerodynamics at the Royal Aircraft Establishment from 1942 to 1945 The Staffs Of The High Speed Tunnel And High Speed Flight Sections Summary.-A brief description of the Royal Aircraft Establishment (R.A.E.) High Speed Wind Tunnel is given, together with an account of the methods used for calibrating the tunnel and for testing models in it. This is followed by a survey of the more important results obtained from tests on models in the tunnel. An account is then given of the technique which has been used at the R.A.E. for the investigation of compressibility effects in flight. Flight experiments at high speeds are described, and some comparisons are made with the results of wind tunnel tests. Future developments in wind tunnel and flight research at high speeds are briefly discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2222.pdf 221. Service failures in aircraft structures associated with fatigue, repeated or dynamic loads J. B. B. Owen This note gives examples and photographs of several structural defects which have occurred in service and shows that, although many failures may be due to fatigue or the application of excessive static-loads, some are probably influenced by the repeated application of loads of high intensity, and by loads of a dynamic character. It is suggested that changes in design aimed at (1) eliminating the loads causing failure, e.g., reducing in one case tab backlash, and (2) alleviating stress concentrations, are ways of reducing the incidence of defects due to repeated loading. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2688.pdf 222. Some Preliminary Results from V-g Recorders Installed in Military and Civil Aircraft R. Hain Taylor During the latter half of the 1939-45 war, V-g recorder slides were collected from a number of operational and training aircraft types, and about April, 1944, the scope was widened to include some commercial transport aircraft. A number of the results has been given limited circulation as Aeronautical Research Council papers, from heavy bombers in October, 1943, from fighters in January, 1944, and from twin-engined aircraft in April, 1944, and a summary of readings from commercial aircraft in 1946; this Report collects these scattered results into one body. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2610.pdf 223. Swept wings in supersonic flight S. B. Gates Opinion seems still unsettled on the aerodymamic merit of swept wings in supersonic flight. To elucidate this, Ackeret's theory of two-dimensional wave reaction is here extended to include sweep. The formulae so derived are used to compare the performance of a straight wing with one swept through 45 deg, making some allowance for frictional drag. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2818.pdf 224. Tank tests on a jet-propelled boat-seaplane fighter (saunders-roe E6/44) G. L. Fletcher Investigations into porpoising stability, water resistance, and seaworthiness have been made on the hull design of the E6/44. The original lines were unsatisfactory for seaworthiness and porpoising stability at overload and modifications to improve these qualities have been made. Results on the final lines indicate that porpoising stability should be adequate at all loads up to the design overload, and take-off time should be well within the specified limit. Seaworthiness tests show that the limiting condition for satisfactory operation at normal load is a 2-ft sea. The hump-spray is severe and due to likelihood of damage, full advantage of flaps may not be gained unless a preselector control be used. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2718.pdf 225. The boundary-layer flow over a permeable surface through which suction is applied J. H. Preston A brief review of existing work is given and the possibility of certain simple solutions for velocity distributions of the type U = kxpowerm with their appropriate suction distributions is indicated. An improved approximate calculation of the 'entry flow' along a flat plate, through which constant suction is applied, is given in some detail. Also Prandtl's original calculation (based on the momentum equation) for boundary-layer flow with constant suction and a constant adverse Velocity gradient is repeated, using Howarth's accurate solution for flow without suction. It is also demonstrated (subject to the accuracy of the approximations) that distributed suction should be much more economical in quantity than suction flow through the minimum number of isolated slots required to prevent separation in the flow under a constant adverse velocity gradient. Practical applications of porous suction are then considered and illustrated by simple examples. These fall under two headings :--(a) the stabilisation of laminar flow against disturbances, (b). the prevention of separation. If the stability calculations made by Pretsch are correct, then a suction velocity vl, given by v1/U>= 1.82 Ã— 10power-5, where U is the free-stream velocity, should make the boundary-layer flow past a flat plate stable against all small disturbances. Thus by use of a very small suction flow it may be possible to stabilise the flow over a laminar flow type wing against the adverse effects of waviness. The prevention of laminar separation, coupled with the increase of stability, makes possible a wing with 100 per cent. laminar flow. Bluff shapes as extreme as a circular cylinder require only a comparatively small suction flow to overcome laminar separation. The application of porous suction to the attainment of a high CL MAX is also considered, and it is demonstrated that, even for a thin wing, a very high CL MAX should be made possible by a surprisingly small suction flow applied over less than 10 per cent. of the chord. It is also suggested that porous suction could be used as a valuable research tool to thin the boundary layer and thus simulate high Reynolds number conditions at small test Reynolds numbers for both incompressible and compressible flOW. Some consideration is given to the practical realisation of a porous surface which approximates to the mathematical concept. It is concluded that porous bronze, made by sintering metallic powder, is the most suitable existing material for laboratory experiments. There seems to be no reason why a similar 'surface' should not be made in light alloy for the flight applications. It is considered that the simulation of a porous surface by the use of isolated slots is not suitable unless their spacing and width are small compared with the boundary-layer thickness. It is concluded therefore that porous suction may have important practical applications to flight at both small and large CLs. Experiments are needed to confirm the ideas put forward in this report. Also accurate solutions of the boundary-layer equations for the flow under an adverse pressure gradient with porous suction are required to check the approximate treatment used herein. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2244.pdf 226. The Effect of Tab Mass-balance on Flutter Part I Ternary Tailplane-Elevator-Tab Flutter Part II Experiments on the Influence of Tab Mass-balance on Flutter G. H. L. Buxton, G. D. Sharpe, C. Scruton, P. M. Ray and D. V. Dunsdon Part I. Following an accident to a Mosquito fitted experimentally by the Royal Aircraft Establishment with a g-restriction device involving heavy mass-overbalance of an elevator tab, an investigation has been made into the flutter characteristics of tailplanes carrying elevators and tabs. The degrees of freedom considered were vertical bending of the fuselage, elevator rotation and tab rotation. The tab was assumed to be spring-connected to the elevator, while the elevator was taken to be free. The effect of variation of the stiffness ratio, of the states of mass balance of the tab and elevator, and of horn balance of the elevator, was investigated. It was found that, with a statically balanced elevator and a statically overbalanced tab, ternary flutter could occur at low speeds while all binary motion involving two only of the degrees of freedom was stable at all speeds, Such flutter could be eliminated by a mass overbalance of the elevator. It is thought that similar results would apply to spring-tab systems, but this is to be investigated. It is considered that flutter of this nature was a likely cause of the Mosquito accident, and it is recommended that in no circumstances should tabs be overbalanced unless a detailed investigation involving at least three degrees of freedom has shown the system to be flutter free. Part II. Tests made to investigate the effect of tab mass-balance on wing-flexure-aileron-tab flutter show that the ternary flutter may arise from over mass-balance of the tab although the binary types of flutter are stable. This conclusion is in agreement with that reached theoretically in Part I for flutter involving tabs and elevator with fuselage vertical bending. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2418.pdf 227. The high-speed laboratory of the aerodynamics Division, N.P.L. Part I - description of the installation. Part II - experimental techniques. Part III - experimental results. D. W. Holder The first part of this report describes the Ngh-speed tunnel installation in the Aerodynamics Division of the National Physical Laboratory. The installation consists of the 12-in. diameter High-Speed Tunnel, the 20 x 8-in. High-Speed Tunnel and a number of smaller tunnels all of which are operated on the induction principle from a common compressed-air storage capacity. An account is included of a series of experiments which were made to investigate the influence of the design on the efficiency of an induced-flow tunnel, and finally the new 18 Ã— 14-in. High-Speed tunnel is described. The second part describes some of the experimental techniques which have been used. Many of these are similar in principle to those of low-speed tunnel practice, but some of them (e.g., the schlieren and shadowgraph techniques) are Peculiar to compressible-flow experiments. The third part of the report reviews the experimental results obtained in tile high-speed tunnels during and immediately before the war. The phenomena which occur on a particular aerofoil as the Maeh number is increased from a low value are described in detail and the effects of the aerofoil shape are then discussed. This approach is used also for supersonic flow where the flow round a particular aerofoil is again described in detail and the effects of aerofoil shape and. Mach number are discussed. The flow round an aerofoil with a control flap is discussed for both subsonic and supersonic flow and an account is included of a number of other fundamental and ad hoc investigations. The report was written in 1946 as a contribution to the series of monographs intended for the Scientific War Records. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2560.pdf 228. The laminar boundary layer associated with the retarded flow of a compressible fluid C. R. Illingworth Two aspects of the solution of the equations governing steady gas flow in a laminar boundary layer, when the main stream velocity is non-uniform, are considered. In the first place it is shown that the equations can be reduced to ordinary differential equations, whose solution implies the similarity of the distributions of velocity and temperature in planes perpendicular to the boundary, only in the case when the main stream velocity is uniform. In the second part, an extension of Pohlhausen's method is used to determine the point of separation of the boundary layer in an air flow in which the pressure increases with a uniform gradient. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2590.pdf 229. The yawing vibrations of an aircraft J. Morris, and G. S. Green This report gives a theoretical method for calculating the natural frequencies and modes of yawing vibration of a complete aircraft. The basic feature of the treatment is the replacement of the continuous mass system by one consisting of a finite number of discrete masses elastically interconnected. In the, course of the analysis, use is made of the deflection coefficient artifice in the formation of the equations of motion, and the escalator process in their marshalling and numerical solution. The method has been applied to a single-engined fighter aircraft, for which the results of a resonance test were available. These results appear to be some 40 per cent. in excess of their calculated counterparts and no satisfactory explanation occurs to the authors to account for this incompatability. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2525.pdf 230. Wind-tunnel tests on the 30 per cent. symmetrical griffith aerofoil with ejection of air at the slots N. Gregory, W. S. Walker and W. G. Raymer It has been shown by Preston(1946) that ejection of air at the point of velocity discontinuity on a 16.2 per cent thick Griffith suction aerofoil prevents separation, and that if sufficient air is ejected, the drag is reduced. The present tests were undertaken to apply this principle to the 30 per cent. Griffith aerofoil and to investigate the effect on lift by pressure-plotting the aerofoil. Ejection of air was found to prevent separation, but about 66 per cent. more air was required than with suction. Three times the suction quantity of air, when ejected, reduced the drag to the low values associated with suction. Curves of Cnf,Cq,Cm Ch, Cd and velocity distribution when blowing are given, and comparisons are made with corresponding curves obtained with suction and with no suction. The same lift and pitching moments are obtained at any incidence with blowing and with suction, but tile suction quantities are about 40 per cent. less than the blowing quantities. The hinge moments are greatly different with blowing, and increase with increase of the normal force. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2475.pdf 231. A method of performance reduction for helicopters F. O'Hara The equations for helicopter performance are derived in a form suitable for the development of performance reduction methods, and the equations obtained provide also a simple method of performance estimation. Formulae are determined for reducing observed performance data to standard temperature conditions and for estimating the effect of weight changes on performance. Charts of the relationships are given for typical values of helicopter and engine characteristics. The general equations are divided into two groups dealing respectively with forward and vertical flight. Performance reduction methods are then outlined for the three cases of climbing, level and vertical flight and are applied to show the effect of weight changes in each case. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2770.pdf 232. A new law of similarity for profiles, valid in the transonic region K. Oswatitsch A new law of similarity is given, valid for slender profiles in mixed transonic flow with negligible viscosity, according to which the cube of the Prandtl factor of any critical Mach number is proportional to the thickness ratio. It is shown that this rule, and that of yon Karman for flow at sonic speed, are valid for shock-waves within the range over which the shock loss is proportional to the cube of the pressure rise. Experimental pressure distributions plotted according to this rule show good agreement, except for the position of the shock-wave on the surface. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2715.pdf 233. A review of the essentials of impact force theories for seaplanes and suggestions for approximate design formulae R. J. Monaghan Classical theories of impact of seaplanes on water have been based on the assumption of a transfer of momentum to a hypothetical associated mass of water attached to the seaplane, such that the total momentum of the two remains constant. Recent developments of the theory show that this treatment fails to take account of momentum shed to the wake formed behind a seaplane when it has forward speed, i.e., it neglects the planing forces. This report reviews the essential theory and assumptions underlying recent work, and puts forward an approximate design formula for the maximum deceleration during a main step impact which is directly a function of the initial impact conditions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2720.pdf 234. Aileron reversal and wing divergence of swept wings E.G. Broadbent and Ola Mansfield A method of solution for the aileron reversal speed of a swept wing (with emphasis on sweepback) is developed on the lines of strip and semi-rigid theories. The influence of the following parameters is investigated :-- (a) The degree of sweep. (b) Wing torsional and flexural stiffness. (c) Wing plan-form. (d) Aileron plan form. Families of curves are given for extended variation of these parameters which may be used for the direct estimation of the reversal speed of a given wing by interpolation. A solution is given for the wing divergence speed of a swept wing. The general results have been obtained using simple modes of wing deformation but equations are quoted for any given modes of deformation and the adopted modes are compared with the actual deformations produced by the aerodynamic loading for an extreme case. A suggestion is put forward for improving the accuracy of the semi-rigid approach by an iterative method of solution and the flexural mode of distortion is investigated for a particular case. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2817.pdf 235. An examination of the technique of the measurement of the longitudinal manoeuvring characteristics of an aeroplane, and a proposal for a standardised method D. J. Lyons It is demonstrated in this report that the 'steady stick force per g' as defined by Gates and Lyon in R. & M. 2027 is the best criterion for the measurement of manoeuvrability of an aircraft because: (a) practically, it indicates the minimum stick force that has to be exerted by the pilot to break the aircraft, and (b) its value is obtainable in flight by a perfectly definite test procedure. It is further concluded that some additional criterion may be necessary to ensure that unduly heavy forces are not encountered during sharp pull-outs. A method of measuring the steady stick force per g, has been developed at the Royal Aircraft Establishment which it is suggested should be standardised for such tests throughout the country. The results of this method have been demonstrated on two aircraft, a Mosquito and a Lancaster. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2597.pdf 236. An example in wing theory at supersonic speed H. B. Squire Calculations of the pressure on a flat elliptic cone and on a flat elliptic hyper-cone at supersonic speeds and zero incidence are made for the case when the cones lie inside the Mach cone of the apex. The results are combined to give the pressure distribution and drag of a wing-like surface at zero incidence in a supersonic stream. It is found that the pressure is constant along straight lines on this surface which are normal to the wind direction. The drag results show the effect of sweepback on drag at supersonic speeds. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2549.pdf 237. An experimental investigation on the flutter characteristics of a model flying wing N. C. Lambourne This report describes some preliminary experimental work that has been carried out in an attempt to gain information on the flexural-torsional flutter characteristics of flying wing types of aircraft. Tests were made with two flexible tip-to-tip models : (A) Rectangular plan form; (B) Cranked and tapered plan form. The method of supporting the models in the wind tunnel allowed certain bodily freedoms to be present either singly or simultaneously, and measurements were made of critical speeds and frequencies, and in a few cases the flutter motion was analysed by means of cinematograph records. The experimental results are in no way conclusive and cannot be directly applied to full-scale problems, but they do point to some of the difficulties in the treatment of the flutter of flying wings. Further, the difficulties encountered during the flutter tests themselves lead to suggested modifications in the technique of providing a model in a wind tunnel with the bodily freedoms appropriate to free flight conditions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2626.pdf 238. An investigation into the effect of forced and natural afterbody ventilation on the hydrodynamic characteristics of a small flying boat (saro 37) with a 1 : 20 fairing over the main step J. A. Hamilton In continuation of the tests reported in R. & M. 2463, an investigation was made into the hydrodynamic qualities of a small flying boat (Saro 37) with a 1 : 20 double curvature fairing over the main step. As before, the aircraft was equipped with means for forced and natural ventilation of the afterbody. Apart from the 1 : 20 fairing, the Saro 37 hull is a 1 : 2-75 scale model of a larger flying boat (Shetland), of 19.0,000 lb all-up-weight. Forced ventilation was supplied by an auxiliary power unit driving a centrifugal air compressor. The fairing was ventilated by three sets of ventilating ducts--one set immediately behind the main step, an intermediate set at 30 per cent beam aft of the step, and an aft set at 90 per cent beam aft of the step, i.e., at the inflexion line of the 1 : 20 fairing. Only the forward ducts were force ventilated in the present tests. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2714.pdf 239. An investigation into the suitability of proposed aircraft design memoranda tests for deck-landing aircraft. Part I. Seafire IIc and Barracuda II. Part II. Hellcat I and Avenger I D. Lean, J. R. Stott, P. A. Hufton and D. Johnson A series of requirements for deck-landing aircraft has been proposed and the suggested programme of tests has been carried out on two Naval aircraft. The results of these tests are given in this report, and their significance has been discussed in the light of the accepted deck-landing qualities of these two aircraft. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2407.pdf 240. Bound and trailing vortices in the linearised theory of supersonic flow, and the downwash in the wake of a delta wing A. Robinson, and J. H. Hunter-Tod Summary.--The field of flow round a flat aerofoil at incidence can be regarded in linearised theory as the result of both bound and trailing vortices for supersonic as well as for low-speed flight. This leads to a convenient method, given the lift distribution over an aerofoil, for calculating the flow round it at supersonic speeds. As an application of the results the downwash is calculated in the wake of a delta wing lying within the Mach cone emanating from its apex. The downwash is found to be least just aft the trailing edge and is everywhere less than the downflow at the aerofoil. It increases steadily to a limiting value which is attained virtually within two chord lengths of the trailing edge. The ratio of the downwash at any point in the wake to the downflow at the aerofoil decreases with increasing Mach number and apex angle. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2409.pdf 241. Calculated aerodynamic characteristics of two infinite wings with constant chord V. M. Falkner The report gives solutions obtained by the vortex lattice method for the aerodynamic loading of two infinite wings of constant chord with sweepback of 45 deg, one with a V-joint at the centre, the other rounded off with arcs of radius four times the chord. The true mathematical solution for these problems is exceedingly difficult to find, and the accuracy has been verified by considering the convergence of solutions of varying complexity. The V-wing shows a reduction in circulation near the joint with accompanying backward movement of the local centre of pressure, while the rounded wing has increased circulation without appreciable variation of the centre of pressure from the 0.25-chord position. The results will be used to modify loading functions used in vortex lattice theory in order to improve solutions for wings of small aspect ratio, particularly when the leading or trailing edges meet at an included angle which differs considerably from 180 deg. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2594.pdf 242. Calculated data for the combustion with liquid oxygen of water-diluted alcohols and paraffin in rocket motors I. C. Hutcheon and S. W. Green Flame compositions, combustion temperatures, and specific impulses have been calculated for the combustion with liquid oxygen of (1) methyl alcohol with varying additions of water, (2) ethyl alcohol with varying additions of water, (3) aviation turbine paraffin. Calculations have been confined to propellant combinations with an excess of alcohol or paraffin and which produce combustion temperatures below about 2,700 deg K. An expansion ratio of 20:1 has been assumed in obtaining the specific impulses, and the methods of calculation are fully explained. The various propellant combinations are assessed from several points of view as to their usefulness for rocket propulsion. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2572.pdf 243. Calculation of the influence of a body on the position of the aerodynamic centre of aircraft with sweptback wings H. Schlichting From systematic three-component measurements of wing-body combinations with swept wings it has been found that the movement of the aerodynamic centre due to the influence of the body is greater for a swept forward than for a straight wing and less for a sweptback wing. The forward shift of the aerodynamic centre due to the body for normal wing body combinations is about 0.06c for a straight wing, about 0.12c for a 30 degrees swept forward, but about zero for a 45 degrees sweptback wing. A simple theoretical method is given for calculating this movement of the aerodynamic centre due to the influence of the body, and it is shown that the agreement with experimental results is quite good. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2582.pdf 244. Comparative tests of thick and thin turning vanes in the royal aircraft establishment 4 X 3-ft wind tunnel K. G. Winter The tests were made by replacing the existing centre six thick vanes at the first corner of the 4 x 3-ft wind tunnel by vanes of sheet metal. The thin vanes reduced the-corner loss, estimated from a wake traverse behind one vane, without any deterioration in outflow, and are therefore recommended for use in future wind tunnels. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2589.pdf 245. Concerning the annular air intake in supersonic flight I. M. Davidson and L. E. Umney The stability of an annular air intake at a Mach number of 1.4 and with Reynolds numbers of about 1.5 x 10power6 is considered in detail and a method is described whereby the experimental results might be extrapolated for preliminary full-scale design purposes. This extrapolation has yet to be checked experimentally, but suggests that a typical aircraft intake would have an overall isentropic efficiency of about 85 per cent. The results also indicate that both the stability and the efficiency of an intake could be improved by controlling the boundary layer on its nacelle, and as an alternative to boundary-layer suction a device which is described as a segregation ring is suggested. This, it appears, might raise the efficiency by some 2 or 3 per cent. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2651.pdf 246. Electronics applied to the measurement of physical quantities G. E. Bennett, G. R. Richards and E. C. Voss The report describes the application of electromechanical and electronic principles to the design of instruments for the measurement of physical quantities such as movement, strain, pressure, acceleration, and vibratory motion, with particular reference to the special requirements of aeronautical engineering. The dynamic characteristics of pick-ups are considered, and sub-divided on an electrical basis into electromagnetic, capacitance and resistance types, a detailed description of each type being given. This is illustrated by an historical survey of their development, and by reference to a number of various recent designs and their characteristics. Piezoelectric, magnetostrictive, photoelectric, hot-wire, vibrating wire, and vacuum tube pick-ups are also considered briefly, and reference is made 'to calibrating devices and techniques. An account is given of the circuits used for the conversion of the electrical variation produced in each type of pick-up into a corresponding voltage or current, particular mention being made of bridge circuits and resonance circuit methods. The special requirements of amplifiers, and the best basic circuits for satisfying them, are considered and illustrated by detailed reference to a number of particular amplifier designs ; in particular, direct-coupled and carrier amplifiers are considered. The requirements of recording equipment and the various recording methods are discussed, and a detailed account given of photographic recording and various oscillograph cameras, their optical arrangements, components and timing devices. Single and multi-channel recording equipments are considered with a brief survey of existing literature and more detailed reference to new developments of single-channel equipments designed for specific purposes, and four-, six- and twelve-channel general purpose equipments using either cathode-ray tubes or recording moving-coil galvanometers. Finally, the application of the techniques and instruments to typical measurements undertaken since 1940 are described in order to illustrate the type of work which may he undertaken by such methods and the form and nature of the results obtained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2627.pdf 247. Evaporation of drops of liquid J. K. Hardy An analysis has been made of the processes which follow when a drop of liquid is subjected to a sudden change in the condition of the air in which it is suspended. Equations are given from which either the temperature of the drop, or the rate at which it will evaporate, can be calculated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2805.pdf 248. Forced flow against a rotating disc D. M. Hannah The steady motion of an incompressible viscous fluid due to an infinite rotating plane lamina has been considered by Von Karman and by Cochran: the motion of fluid flowing with axial symmetry towards an infinite stationary plane lamina has been dealt with by Homann. The present paper deals with the general question of steady irrotational flow with axial symmetry against an infinite rotating lamina, of which the above are two special cases. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2772.pdf 249. Heat transference and pressure loss for air flowing in passages of small dimensions J. Remfry This investigation had as its primary object the experimental determination of the heat-transfer and pressure-loss characteristics for air flowing in small triangular, square, hexagonal and round passages. The heat interchanger models, with a frontage six inches square, each comprised from just under 150 to over 2,250 passages, according to their size and spacing. The hydraulic diameter of the smallest tubes was about 0.08 inch. Previously, little information of this kind had been available for any except round tubes of more than 0.5 inch diameter. The heat transfer in small smooth passages was found to be less than that usually measured for turbulent flow in tubes of larger size, and there was a tendency for a prolonged transition. The investigation was extended to determine the greater heat flow obtained in bulged or waved passages and outside a nest of hexagonal tubes. The influence of variation of passage length, pitch and end shape was also examined. A simplified theoretical analysis furnished a basis for separation of the components of pressure loss due to friction, increase of momentum, turbulence and end losses. Because of the uncertainty regarding conditions in transitional flow, a more precise theoretical treatment was considered to be unjustified. The interdependence of friction and heat transfer was emphasised by estimating the useful friction from the measured heat transfer coefficient, using the relationship deduced by von Karman on the hypothesis of the existence of a buffer layer between the laminar boundary flow and the turbulent core. The pressure losses measured in the experiments were found to be represented with good accuracy by coefficients, which may confidently be used to predict the air pressure drop in similar types of passage when the rate of heat transference is known. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2638.pdf 250. Investigation of skin buckling D. J. Farrar The present tests were conducted on aluminium alloy plates in endwise compression, with varying conditions of edge support, to provide data on the buckling stress and post-buckling behaviour of aircraft skins. All the plates tested were 35 in. long and nominally 0.064 in. thick. The plate width between the supports was varied between 35 and 120 times its thickness. Both clad (D.T.D. 546) and unclad (D.T.D. 646) material were tested. Three types of edge support were used: rows of steel balls in vee-grooved blocks, intended to imitate pin-edged conditions; rows of steel rollers in recessed blocks, intended to imitate clamp-edged conditions; and a single type of stringer used in previous panel tests. Measurements were made of the plate load and mean strain, and of tile shape of the skin buckles. The test technique is discussed and the experimental results compared with theory. The ball edge supports did not accurately represent pin-edged conditions, neither did the roller edge supports accurately represent clamped-edged conditions. The tests provided some data on the effect of plasticity in seriously reducing the load carried by the plate after buckling, and on the effect of cladding in reducing the buckling stress. The buckling stresses measured for the panels with stringer edge supports were in good agreement with theory. The load carried by the plate after buckling ill this case was further reduced by tile effect of plasticity in the stringers: a simplified theory is developed whose results are in agreement with the experimental observations. The testing technique used is applicable to further investigations of the buckling of plates as part of a panel. The information obtained on the effect of plasticity has an important bearing on the load-carrying capacity of panels, and while the present results may form the basis of design data sheets, it is desirable that the range of investigation be extended to cover other material specifications. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2652.pdf 251. Investigations on stalling behaviour, rudder oscillations, take-off swing and flow round nacelles on the Tudor 1 aircraft D. J. Lyons During the development of the Tudor I aircraft, the Royal Aircraft Establishment co-operated in the flight tests. This report summarises the results, which are felt to be of general interest. The importance of 'deep tufting' in leading to an understanding of varied aerodynamic problems has again been forcibly demonstrated; namely in showing that: (a) early buffeting of the Tudor as the stall is approached was due to a very small airleak around the leading edge of the wing root causing a breakaway of flow, the resultant wake of which hit the tailplane, (b) early wing-tip stalling was shown to be due to small mal-fitment of the T.K.S. de-icers, (c) rudder "kicking" arose from flow through the hinge cutouts, (d) excessive take-off swing was due to poor rudder control as a result of the early rudder stall, and to the fact that the aircraft was stalled in the ground attitude, (e) the inner nacelle needed considerable lengthening. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2789.pdf 252. Kinetic temperature of propeller blades in conditions of icing J. K. Hardy and C. D. Brown The kinetic temperature of a section of a propeller blade has been calculated for a blade with high thermal conductivity, and also for a blade which is non-conducting. Calculations have been made for clear air, and for conditions of icing to find the extent to which kinetic heating is effective against ice. On a non-conducting blade the temperature is lowest at the position, on the cambered face, where the velocity of the air is greatest. At this position there is practically no protection from kinetic heating. In .the case of a blade which is a good conductor, the average temperature is calculated by balancing the flow of heat by convection to and from the blade. The average temperature is substantially above the minimum temperature on a non-conducting blade. The average temperature has been calculated for a range both of conditions of icing and of operation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2806.pdf 253. Landing of an aircraft on a suspended sheet J. Taylor An investigation is made into the characteristics of a freely suspended flexible sheet as a shock absorber replacing the conventional under-carriage, particular attention being given to the inertia of the sheet. It is found that when an aircraft is dropped vertically on to the sheet the retarding force is first produced by the inertia of the sheet itself, and not until later in the descent by the reactions from the side supports of the sheet. By careful adjustments of the mass and tension of the sheet 'retardation efficiencies' exceeding 80 per cent can be achieved. The effect of the aircraft having a forward component of velocity increases the contribution of sheet momentum. For reasonably practical laliding speeds and sheet dimensions, virtually the whole of the momentum of descent is absorbed by sheet inertia. Under such conditions still higher retardation efficiencies are obtainable and, with a suitable design of aircraft keel, rebound may be entirely eliminated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2574.pdf 254. Low-speed model tests on two "V" wings J. Trouncer, and D. Kettle Wind tunnel tests were required for comparison with flight tests on two "V" wing tailless gliders of 28.4 deg. and 36.4 deg. sweepback. The main part of the work consisted of longitudinal, lateral and directional stability tests on the two wings, but pressure-plotting tests on the wing of larger sweepback and an investigation of anti-tip stalling devices was also included. Tip slats were found to be the most effective of the devices tried in the present experiments for overcoming the drawback of the premature tip stall. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2364.pdf 255. Low-speed wind-tunnel tests on a model of a jet tailles aircraft J. Trouncer and G. F. Moss This report gives the results of longitudinal and lateral stability tests made on a model of a jet tailless aircraft. It includes the effects of split flaps, trimming flaps, dive-recovery flaps and four types of anti-tip-stalling device (slats, nose flaps, double split flaps and letter-box slots). It also includes the effect of the ground in the landing condition. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2843.pdf 256. Low-speed wind-tunnel tests on two 45 deg sweptback wings of aspect ratios 4.5 and 3.0 (Models A and B) J. Trouncer and G. F. Moss A general programme of tests on sweptback wings is being made in the high and lowspeed wind-tunnels of the Royal Aircraft Establishment to supplement existing data. Low-speed stability tests have been made on two wings of aspect ratio 4.5 and 3.0 (Models A and B). Both wings were of 45 deg sweepback, 4:1 taper ratio and 14 per cent thickness ratio. The present report covers the tests made on these wings and is given in three parts :- Part I Stability tests on the two wings without body or tail unit. Part II Stability tests on the two wings with a body, fin and tailplane fitted (varying tail angle). Part III Tests made with two types of nose flap on Model A (aspect ratio 4.5). The results give the effect of aspect ratio on longitudinal, lateral and directional stability for a 'wing alone' and a wing, body and tail unit combination. They also give the value of the downwash at a constant distance behind the two wings. The nose flaps tested on Model A did not prove effective as a means of improving the stability. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2710.pdf 257. Measurement of aircraft attitude relative to flight path during dives J. E. H. Braybon This report deals with the development of a technique for direct recording of the attitude of an aircraft relative to-flight path during dives, i.e., the direction of incidence of free airflow relative to aircraft datum, using a wind vane coupled to a Desynn transmitter. Results obtained in dives under steady conditions of dive angle and A.S.I. show agreement with those deduced from level flight results using the conventional airflow-ncidence/lift-coefficient relation. Included are the details of the instrumentation required to obtain simultaneous records of the flight conditions (A.S.I. height, dive angle) and corresponding incidence under non-steady conditions such as exist during rocketry attacks. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2564.pdf 258. Measurements of mid-chord pitching moment derivatives at high speeds J. B. Bratt, and A. Chinneck Measurements of the pitching moment derivative coefficients for a 7½ per cent bi-convex aerofoil oscillating about the mid-chord axis were made in a high-speed wind tunnel by the method of decaying oscillations. The tests were made at Mach numbers of 1.275, 1.455 and 1.515 for supersonic flow, and covered a range extending from 0.4 to 0.9 at subsonic speeds. The effect of variation of frequency parameter was also investigated, and conditions giving rise to sustained or growing oscillations at subsonic speeds were examined. Comparison with existing flat plate theories for supersonic flow shows complete disagreement in the trend of the damping with Math number change, the linearized theory for a flat plate giving an increasing negative value as M is reduced below 1.41, whereas experiment gives an increasing positive value. A recent theory which takes into account the shape of the profile agrees in trend with experiment, suggesting that profile is of vital importance in this field. The results of the subsonic tests exhibit a narrow region of Mach number extending from approximately 0.87 to 0.89 within which negative damping can arise. It is thought that this effect is bound up with the formation of shock-waves at the surface of the model. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2680.pdf 259. Note on the characteristic curve for an airscrew or helicopter C. N. H. Lock On reading Dr. Hislop's paper I on experiments on a Hoverfly I aircraft which reproduces the 'characteristic' curve of an airscrew as given in R. & M. 1026, and on re-reading the latter report and R. & M. 1014 after an interval of twenty years, it occurred to me that a modification of the method of plotting adopted in these reports would have certain advantages. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2673.pdf 260. Note on the effect of boundary-layer suction on separation E. J. Watson It is well known that the separation point of a boundary-layer flowing over an impermeable surface is defined by the vanishing of the skin friction at that point. Previous investigations have assumed that this condition applies equally to the flow over a porous surface through which the boundary layer is being withdrawn by suction. This appears, however, not to be strictly accurate, and the object of this note is to examine the significance of the distinction and to suggest by means of physical arguments the general character of the flow near a separation point. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2538.pdf 261. Note on the effect of size of aircraft upon the difficulties involved in landing an aircraft D. Adamson The effect of aircraft size upon the response of an aircraft during those manoeuvres which are commonly employed in landing has been examined, and in this way an assessment has been made of the way in which the difficulties experienced by the pilot will go up as aircraft size increases. On the basis of the work summarised in this note it is concluded that the problems associated with landing (from the pilot's point of view at any rate) are unlikely to be aggravated to such an extent, as the size of aircraft increases up to the limiting size considered in this report (300 ft span), as to make landing really difficult. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2567.pdf 262. Note on the maintenance of laminar-flow wings W. E. Gray, and H. Davies The maintenance of laminar-flow wings involves two problems:-- (1) The prevention of deterioration in the surface itself (e.g. cracking of the paint or filler, increase in roughness or waviness, etc., whether due to weathering, stresses in flight, or accidental damage). (2) The prevention of contamination of the surface with flies, etc. This Note gives an account of experience gained at the Royal Aircraft Establishment in dealing with these problems during flight tests on the characteristics of low-drag wings. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2485.pdf 263. Note on the southwell method for estimating critical loads H. L. Cox (a) Purpose of Note.--To draw attention to certain restrictions on the use of the 'Southwell plot' to estimate critical loads in cases differing in conditions from those which the method was first proposed. (b) Range of Note.--The effects on the 'Southwell plot' of variation of stress distribution, of elastic failure of the material and of other variation of critical stress, however it may be occasioned, is examined. (c) Conclusions. The 'Southwell plot' is strictly applicable only to deflections which go to infinity at a definite critical load. In other cases the plot usually over-estimates the buckling load; but the error should seldom be important. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2696.pdf 264. Notes on the technique employed at the R.A.E. in low-speed wind-tunnel tests in the period 1939-1945 F. B. Bradfield Very little has been recorded during the war years as to the details of technique used in low-speed wind-tunnel tests. The size and type of tunnel used during this period will remain in use at firms and colleges for some time after newer equipment is available at research establishments, so it has been decided to issue some record of the technique in use at the Royal Aircraft Establishment during the war years, both with a view to establishing a standard technique where it is satisfactory, and to consider weaknesses where it has failed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2556.pdf 265. On the design of aerofoils for which the lift is independent of the incidence B. Thwaites It has been shown in R. & M. 2611 how lift may be obtained on aerofoils independently of the incidence. In this paper mathematical processes are set out of designing such aerofoils to have specified velocity distributions at certain incidences and lift-coefficients. Approximate and exact methods are given, corresponding to the methods employed in the design of ordinary aerofoils. Several shapes are worked out, some of them being the product of ideas not given in R. & M. 2611. A full discussion of the characteristics of such aerofoils is given. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2612.pdf 266. On the momentum equation in laminar boundary-layer flow a new method of uniparametric calculation B. Thwaites Summary.--The general method of Pohlhausen, which is discussed in detail in Ref. 1, uses a uniparametric system of velocity distributions of the form u/U = f(y/delta) + lamda.g(y/delta). Pohlhausen, by choosing simple forms for the functions f and g, then uses the momentum equation to find the distribution of delta with x and thence the distributions with x of the other boundary-layer characteristics. Several awkwardnesses exist in his method, especially when it is applied to problems dealing with a normal velocity at the boundary. In this paper, a new method is described of combining velocity distributions in the form y/theta = F(u/U) + lamda.G(u/U), and it is shown that such a combination avoids several difficulties. This method of combination also allows a second parameter apart from lamda, which might be found valuable in certain problems. The method has been briefly described before as part of an investigation into the effect of continuous suction on laminar boundary-layer flow under adverse pressure gradients. In that paper (R&M 2514) a numerical example of its use was given. In this paper no example will be given because, as far as the author can see, the practical use of the method is superseded by the generalised method of Ref. 1 : however it possessed considerable analytical interest. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2587.pdf 267. On the solution of linear simultaneous differential equations with constant coefficients by a process of isolation J. Morris In this report a process is given for the solution of linear differential equations with constant coefficients. The operative artifice is closely akin to Routh's method of Isolation by means of which the constants of integration are found separately for each root of the characteristic equation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2623.pdf 268. Performance calculations for a double-compound turbo-jet engine of 12:1 design compressor pressure ratio D. H. Mallinson and W. G. E. Lewis This report describes.a theoretical investigation using conventional component-characteristics to discover that division of work between the low and high-pressure compressors of a double-compound simple-jet gas turbine of 12 : 1 design pressure ratio which is likely to result in the most desirable equilibrium operation over the normal engine speed range. Having decided in favour of a pressure ratio of 3 : 1 in the low-pressure compressor and 4 : 1 in the other, a study is then made using more realistic compressor characteristics to determine the probable performance of such an engine under all flight conditions when the design maximum temperature is 900 deg C (1173 deg K). The equilibrium running conditions of the engine are investigated with special reference to the problems introduced by the double-compound type of design. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2645.pdf 269. Photo-elastic examination of a cylindrical strut intended for recording compressive loads W. A. P. Fisher Photo-elastic methods are used to establish how much of a cylindrical steel strut mounted for measurement of compressive force by strain-gauges, has uniform stress distribution, even when the end load is concentrated near the axis of the strut. It is found that a strut 16 in long, and 6 in diameter has virtually uniform stress distribution over the middle 21 in. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2532.pdf 270. Photographs of shock wave movement W. F. Hilton and R. G. Fowler Consecutive photographs were taken at millisecond intervals of the flow past a low-drag aerofoil at compressibility speeds. At a Mach number 0.1 above the 'pressure critical' the shock wave was found to oscillate rapidly but aperiodically, whereas the edge of the associated boundary layer remained quite steady, at least for periods of 1/50 sec. At the critical Mach number and just below it a series of small shock waves was observed, apparently moving against the direction of flow. Note. The photographs reproduced in this paper were taken in January, 1944. Their issue was postponed in view of possible improvement in technique. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2692.pdf 271. Pressure distributions at high speed on EC 1250 (data report) J. A. Beavan, and G. A. M. Hyde This report puts on record, as data, pressure distributions measured on a 5-in. chord aerofoil of EC 1250 section in the 20 x 8 in. Rectangular High-Speed Tunnel, at the National Physical Laboratory. The pressure distributions given here were obtained some years ago, and give detailed results on an aerofoil which has some interesting properties but differs in shape from those now used for aircraft wings. Some discussion of the results has been made elsewhere, for example in R. & M.'s 2560 and 2222. The curves show the now well-known phenomenon of the backward movement of shock waves and spread of the supersonic region ahead of them at a fairly constant limiting local Mach number along the surface, for a symmetrical aerofoil at moderate incidences. The changes of lift, pitching moment, etc., with Mach number can be estimated from the pressure distributions. The results resemble those obtained from German tests at higher Reynold's number, but smaller incidence range. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2625.pdf 272. Pressure plotting tests in the Royal Aircraft Establishment high speed wind tunnel on a 21 per cent thick, low drag aerofoil (Brabazon 1 wing root section) A. B. Haines and W. Port Pressure plotting tests have been made on the 21 per cent thick wing root section for the Brabazon I aircraft as a two-dimensional aerofoil spanning the Royal Aircraft Establishment High Speed Tunnel The tests covered a Mach number range up to 0.7 at a Reynolds number of about 3 x 10power6 and low speed tests were extended up to R =9.45 x 10power6. It appears that there is adequate margin between the cruising and stalling conditions to provide manoeuvrability and safety in up-gusts. The results ... may be pessimistic because the tunnel tests had to be made by covering the speed range at a series of certain fixed incidences. Also the incidence range covered was not large enough. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2617.pdf 273. Sandwich construction and core materials part 5 W. J. Pullen Section 1, some physical properties of an extruded cellular cellulose acetate. Section 2, the determination of poisson's ratio in compression of certain low density materials. Tensile, Compressive and Creep tests have been carried out on four different samples of Extruded Cellular Cellulose Acetate. It is concluded that the material is comparable with calcium alginate and other low-density materials so far handled in the Engineering Division, N.P.L. In particular, the samples are not subject to the same degree of 'softening' as has been the case with some similar materials. The 'filled' samples are more efficient than the 'unfilled' ones and are worth considering as possible low-density stabilizers in sandwich construction. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2686.pdf 274. Some data pertaining to the supersonic axial-flow compressor I. M. Davidson Together with some random considerations concerning possible compressor development, data concerning the flow of air at high speeds is presented in this note in a form suitable for use in the design of supersonic axial-flow compressors. A brief history and description is also given of the work of the German pioneers Weise, Encke and Betz. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2554.pdf 275. Suction-slot ducting design A. G. Rawcliffe Summary.--Purpose of Ducting.--To provide uniform suction through a narrow slot along tile span of a wing, with the lowest possible losses, when the pump is situated at the root of the wing. Range of Investigation.--Models of various design were tested and modified in the light of the results obtained. From these experiments, together with a qualitative analysis of the flow through the type of ducting proposed, specific recommendations have been formulated for the attainment of uniformity of suction combined with low power losses. Investigations were confined to suction from still air. Results.--Losses of about 0.2ql were obtained with the broad partition and with the guide-vane ducts, compared with about 0.7ql for the earlier models, and the distribution of velocity at the slot was quite satisfactory. The circular collector duct appeared to be more efficient, but suction was much higher at the tip than at the root. Future Developments.--Suction ducting is to be tested in the wall of a small wind-tunnel, so that the effect of the tunnel boundary layer may be studied. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2580.pdf 276. Tests on a 'glauert' nose-suction aerofoil in the N.P.L. 4-ft. no. 2 wind tunnel F. Cheers and Ola Douglas Tests on an 8.65 per cent thick nose-suction aerofoil designed by Glauert have been made in the 4 ft No. 2 wind tunnel at the National Physical Laboratory at Reynolds numbers 0.385 and 0.577 x l0 (to the power of 6). The results show that the section stalls at a lift coefficient of 1.13 without suction. With suction quantities of 0.003, 0.0045, 0.006 and (with a wider slot) 0.012, the values of Cl(max) were respectively 1.32, 1.34, 1.36 and 1.57. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2356.pdf 277. Tests on a 'lighthill' nose-suction aerofoil in the N.P.L. 4-ft. no. 2 wind tunnel F. Cheers, W. G. Raymer, and Ola Douglas A series of tests on an 8.6 per cent thick nose-suction aerofoil designed by Lighthill has been made in the 4 ft No. 2 Wind Tunnel at the National Physical Laboratory at Reynolds numbers of 0.385 and 0.577 x 10(to the power of 6). The results show that the wing stalls at alpha ~= 3 deg (Cl = 1.12) without suction, the lift coefficient at the stall increasing approximately linearly with suction quantity and reaching 1.93 at Cq = 0.019 and 23 deg incidence. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2355.pdf 278. Tests on a working model ram jet in a supersonic wind tunnel J. R. Singham, F. W. Pruden and R. C. Tomlinson The report describes experiments with a small scale model of a ram jet burning hydrogen in the 1-ft diameter Circular High-speed Tunnel of the National Physical Laboratory adapted to run at a (nominal) Mach number of 1.4. The purpose of the tests was twofold. First, to examine how far it was practicable to test such a small scale model in a wind tunnel. Secondly, to determine to what extent the external drag of a model duct tested hot would differ from that of the same model tested cold. The design, development and construction of a suitable model was carried out by R. P. Probert and the staff of Power Jets (Research and Development) Ltd., (now National Gas Turbine Establishment) whilst the testing was done jointly with the staff of the National Physical Laboratory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2568.pdf 279. Tests on yawed aerofoils in the 20 x 8-in. high speed tunnel J. A. Beavan and N. Bumstead Tests on NACA 0020 sections of 1.2 and 2.0-in. chord completely spanning the tunnel showed that there was no appreciable difference in compressibility drag rise due to wind-tunnel interference. This was the case both with the aerofoil yawed (40 deg) and straight across the tunnel. The results, and further measurements on a Piercy aerofoil previously tested, showed also that the gain in Mach number has been increased from 65 to about 80 per cent of the theoretical value that assumes infinite span and no boundary-layer effects, now that the air is dried to a large extent by use of return ducts. Some explorations of the flow behind the aerofoil are considered to justify these conclusions at Mach numbers up to at least 0.92. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2458.pdf 280. The aerodynamic characteristics of flaps A. D. Young This report collects and summarises the results of work that has been done both in this and other countries on the aerodynamic characteristics of flaps prior to and during the period of the war. The report has both a philosophical and practical aim, viz., to demonstrate, as far as possible, such underlying unity as exists in the behaviour of the large variety of flaps that have been developed and investigated, and hence to present charts and tables which will enable designers to predict with acceptable accuracy the characteristics of any particular flap arrangement. In section 2 a brief description of the various flaps considered is given, and these are also illustrated in Fig. 1. Section 3 is devoted to a discussion of the definitions of the lift, drag and pitching moment increments, based on the normal and on the effective (extended or reduced) wing chords. Section 4 deals in some detail with split and plain flaps, whilst section 5 is devoted to the simple slotted flaps of the Handley Page and N.A.C.A. types. A large variety of flaps classified as high-lift flaps are considered in section 6, these include Fowler flaps, double Fowler flaps, N.A.C.A. single and doubleslotted flaps, single and double Blackburn flaps, Blackburn flaps with flap leading-edge slots, Blackburn flaps with inset slots, Blackburn flaps with deflected shrouds and Venetian-blind flaps. The main characteristics of these high-lift flaps are also summarised in Table 2. The effect of wing-body interference on the drag and lift increments of split and slotted flaps is discussed in section 7, whilst section 8 summarises the aerodynamic effects of wing leading-edge slots. The effect of flaps on induced drag is dealt with in section 9. A discussion of the characteristics of nose flaps, with particular reference to the type developed and tested by Kruger in Germany is given in section 10. A brief discussion on brake flaps is given in section 11, whilst the allied subject of dive recovery flaps is examined in section 12. Because of its topical interest, such information as is available on the characteristics of flaps on swept-back wings is summarised in section 13. Section 14 is devoted to a summary of the main formulae and conclusions developed in the report. The bibliography at the end was compiled with the object of providing as representative a list as possible of the main reports and papers to which a reader might wish to refer for more detailed information. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2622.pdf 281. The aerodynamic derivatives with respect to sideslip for a delta wing with small dihedral at zero incidence at supersonic speeds A. Robinson and J. H. Hunter-Tod Summary.--Expressions are derived for the sideslip derivatives on the assumptions of the linearised theory of flow for a delta wing with small dihedral flying at supersonic speeds. A discussion is included in the Appendix on the relation between two methods that have been evolved for the treatmenf of aerodynamic force problems of the delta wing lying within its apex Mach cone. When the leading edges are within the Mach cone from the apex, the pressure distribution and the rolling moment are independent of Mach number but dependent on aspect ratio. When the leading edges are outside the apex Mach cone, the non-dimensional rolling derivative is, in contrast to the other case, dependent on Mach number and independent of aspect ratio : the other derivatives and the pressure, however, are dependent on both variables. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2410.pdf 282. The application of the exact method of aerofoil design M. B. Glauert This report considers in detail the design of aerofoils by Lighthill's exact method, in which the velocity over the aerofoil surface is prescribed as a function of the angular co-ordinate on the circle into which the aerofoil may be transformed. The mathematical basis of the method is set out, means for obtaining desired characteristics for the aerofoil are developed, and the procedure to be followed in the actual design is fully discussed. Various special functions are introduced to increase the range and practical utility of the velocity distributions obtainable, and these and other functions are fully tabulated. The calculations for the design of a particular thick suction aerofoil are set out in detail. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2683.pdf 283. The asymptotic theory of boundary-layer flow with suction part 1 the theory of similar velocity distributions part 2 flow with uniform suction part 3 flow with variation of suction velocity E. J. Watson General Summary.--The subject of this report is the steady two-dimensional flow of a boundary layer over a permeable surface through which the fluid is withdrawn at a known rate of suction. This rate of suction is assumed, in accordance with the hypotheses of the boundary layer, to be small compared with the stream velocity, and of order R (to the minus 0.5) where R is the Reynolds number. It is supposed here that the suction is relatively large, though still of the same order. Part I deals with the similar solutions of the boundary-layer equations, Part II with an arbitrary pressure distribution but constant suction velocity, and Part III with the general problem. Thus the results of Parts I and II can be obtained from Part III, but they are of interest in themselves. Attempts are made in both Parts I and II to find when separation occurs, but only rough estimates can be made as the series do not converge well. In Part II the theory is applied to the flow over a porous circular cylinder in a uniform stream, and also to the use of suction round the nose of an aerofoil to prevent stalling at high incidence. The only previous work on this approach appears to be a report by Pretsch, which according to Mangler contains a study of the similar profiles on the same lines as Part I. The report by Pretsch has not been examined, and it is therefore not known if his results agree with those given here. A special case of Part I is in course of publication. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2619.pdf 284. The design and installation of small compressed air turbines for testing powered dynamic models in the Royal Aircraft Establishment seaplane tank D. I. T. P. Llewelyn-Davies, W. D. Tye and D. C. MacPhail This report describes the development of small lightweight air turbines for powering dynamic models in the R.A.E. Seaplane Tank. The units have proved to be rugged and reliable and power/weight ratios of 0.4 lb/b.h.p. have been achieved. The installation of the turbines in dynamic models and the provision of their air supply are also discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2620.pdf 285. The drag increase at high subsonic speeds K. Oswatitsch The drag increase beyond the critical Mach number is calculated by modifying the supersonic part of the Karman-Tsien pressure distribution on a profile. This is possible when the supersonic regions are not too large. The formula giving the modified pressure distribution is derived very roughly. It may give only one of the main effects appearing when supersonic speeds occur in the flow, and may be changed and calculated more exactly later. For the calculation of the drag increase the formula is sufficient and the agreement of theory and experiment in all examples calculated is good. Within the approximation of the theory the lift coefficient is practically unchanged. Calculations of the centre of pressure are not made. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2716.pdf 286. The effect of spanwise rib-boom stiffness on the stress distribution near a wing cut-out E. H. Mansfield A theoretical investigation is made into the effect of spanwise rib-boom stiffness on the stress distribution at a cut-out in the inter-spar skin of a stressed skin wing in bending. Both shear and bending stiffness of the rib-boom are taken into account, and attention is concentrated on the case in which the rib-boom is built-in to the spar flanges. Curves are included which determine, for any particular case, the magnitude of the peak shear stress adjacent to the flange, the approximate spanwise variation of this shear stress, the proportion of load transferred by the rib-boom to the skin and stringers, and the bending moment in the rib-boom at its points of attachment to the spar flanges. By suitable design of the rib-boom it is possible to lower the shear stresses adjacent to the flange with little or no increase in structure weight. Available experimental results for the peak shear stresses are in good agreement with this theoretical work; previously developed methods a give over-estimates of the order of 100 per cent. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2663.pdf 287. The effect of uniformly spaced flexible ribs on the stresses due to self-equilibrating systems applied to long thin-walled cylinders E. H. Mansfield and M. Fine In many problems relating to the stressing of thin-walled cylinders, and in particular those concerned with the stresses set up in a cylinder under torsion when one section is restrained against warping, it has been commonly assumed that sections have their shape retained by closely spaced stiff ribs. Justification for this assumption is that, for certain types of loading, the ribs of most practical structures do little work in maintaining the section shape (and the analysis is considerably simplified). In this report the effect of discrete, flexible ribs has been investigated and the results have been incorporated in a number of graphs which show the effect of rib-flexibility in a long thin-walled cylinder of arbitrary shape under end constraint. Some of the results of these investigations are, as would be expected, of a negative character, in that they show that for certain types of end conditions (roughly, those in which the predominating self-equilibrating loads act parallel to the cylinder axis) the effect of rib-flexibility is negligible. But rib-flexibility is of paramount importance when self-equilibrating shear-distorting forces are applied to a cylinder--such as occur at a wing cut-out or near an overhanging engine--and this report makes the stress distribution in such a case readily determinable. It is shown that the complete stress die-away pattern depends, apart from the boundary conditions, on two nondimensional parameters. These parameters are functions of the type of end constraint as well as of the structure dimensions and elastic constants. Expressions are given for determining these parameters when the cylinder shape and loading are arbitrary. The simplified case of a four-boom cylinder Of rectangular section under torque is treated separately in a second appendix. The solution is strictly true for a four-boom cylinder or when the self-equilibrating end-load system is orthogonal (eigenload); but as minimum-energy methods are used in the analysis, the results are believed to be substantially correct for a smoothly varying end-load system applied to a cylinder of arbitrary shape. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2832.pdf 288. The efficiency of a pitot intake inclined to the air stream E. L. Place and R. Lecavalier In an earlier report on intake ducting for supersonic flight, the efficiency of a 'pitot' type intake was discussed and shown to have a marked effect on the performance of gas turbine engines. The present report is supplementary in that it describes the effect of inclining the pitot intake to the main air stream direction in the transonic Mach number range 0.7 to 1.5, an effect which is at present incalculable. Curves are presented showing the influence of inclination on intake adiabatic efficiency and air mass flow into the intake. These experimental results are then illustrated by application to the performance of a typical turbine engine and a propulsive duct in sonic and supersonic flight. At a flight Mach number of 1.5, it is found that, for both turbine engine and propulsive duct, an inclination of 5 deg reduces the net thrust by roughly 2 per cent compared with the normal flight thrust. For inclinations greater than 5 deg, however, thrust falls off more rapidly, and at 10 deg inclination, it is reduced by roughly 6.5 per cent for the turbine engine and 7.5 for the propulsive duct. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2621.pdf 289. The influence of thickness/chord ratio on supersonic derivatives for oscillating aerofoils W. P. Jones By the use of Temple and Jahn's theory for the oscillating flat plate and Busemann's theory for aerofoils in steady motion, derivatives are obtained for symmetrical circular-arc and double-wedge aerofoils describing low frequency oscillations at supersonic speeds. It is known that theoretically the torsional aerodynamic damping for a flat plate oscillating about an axis forward of the two-thirds chord position is negative at low frequencies for a limited range of supersonic speeds. In this report, however, it is shown that the effect of increasing thickness/chord ratio is to decrease the range of speeds for which the aerodynamic damping is negative, and for which one degree of freedom flutter is possible. The present theory also allows for the forward movement of the centre of pressure from the half-chord position as the aerofoil thickness is increased, and leads to better estimates of the stiffness derivatives for an actual aerofoil. In practice, the centre of pressure is not at half-chord as predicted by linear theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2679.pdf 290. The production of lift independently of incidence--the Thwaites Flap, Parts I and II B. Thwaites In Part I of this paper, the possibility of obtaining lift on a body in a uniform stream independently of the incidence is discussed, and a practical method which obtains this effect is given. It is shown that a small thin 'flap' which may be moved about a well-rounded trailing edge through which, for example, continuous suction is applied will produce circulation about the aerofoil. A necessary feature of this method is tile prevention of separation of flow by boundary-layer suction, which is also used to reduce substantially the width of the wake. The method uses principles quite different from those which have been proposed in the past for obtaining increased lift on aerofoils. The practical applications of the device are briefly discussed, and some interesting consequences pointed out. It will, for instance, be possible to fly with an aerofoil always at zero incidence. Again, the stall in which the flow separates from near tile leading edge may be completely avoided, for as the circulation and lift increase, the incidence may be decreased so that severe adverse velocity gradients occur nowhere but near the trailing edge. In Part II of the paper, a report is given of a preliminary experiment which was set up to investigate whether the theoretical predictions made about the efficacy of the Flap were largely confirmed. A wholly porous circular cylinder was fitted with the Flap and measurements were made of the pressure distribution round the cylinder for various positions of the Flap. These observations shewed that for angular deflection of the Flap of less than 20 deg, about 85 per cent of the theoretical value of CL was realised : a maximum CL of about 5-6 was obtained. These results are taken to shew that tile physical principles of Part I are sound and that the Thwaites Flap does, in fact, enable lift to be generated independently of incidence. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2611.pdf 291. The solution by lifting-line theory of problems involving discontinuities V. M. Falkner The report, which has been written as a preliminary to a later account of similar work in lifting-plane theory, describes how wing loading problems involving discontinuities are solved by lifting-line theory. The four discontinuities considered are (a) direction of leading or trailing edge, (b) incidence, (c) two-dimensional lift slope and (d) chord. As the effects of the first are of minor importance in lifting-line theory, attention is mainly confined to the last three, the solution being based on the use of a few terms of a Fourier series in conjunction with special functions tabulated elsewhere. The work is limited to straight unyawed flight and includes lift, induced drag, and pitching, rolling and yawing moments, all with or without deflected landing flaps and ailerons. The method of formation of the equations, and the solutions of a representative range of problems for a hypothetical wing, including loading due to incidence, symmetrical wing twist, uniform roll, and deflected flaps and ailerons, are fully described. An indication is given of how induced drag and yawing moment calculations will later be simplified by the use of special derived functions. Absolute values of wing properties as given by lifting-line theory are usually too high, but the specification of correction factors for viscosity is beyond the scope of the report. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2592.pdf 292. The solution of lifting-plane problems by vortex-lattice theory (with seven appendices) V. M. Falkner The report describes in detail the methods by which the principles of vortex-lattice theory, introduced in a previous report, R. & M. 1910, are applied to the calculation of the aerodynamic loading of wings by lifting-plane theory. The scope of the paper is limited to the application of these principles to symmetrical incidence solutions and symmetrical and anti-symmetrical wing twist solutions, for which standard solutions can be treated by comparatively simple loading functions. The effect of discontinuity of direction of leading or trailing edge cannot be avoided even in the simplest solutions, and it has been found necessary to include an investigation of this problem in order to cover the prescribed usage of the method. Special standard functions tabulated in another report are used to allow for the rounding off effects due to change of direction of leading or trailing edge. The general problem of discontinuities is under investigation and will be dealt with in a later report. A comprehensive set of solutions for a delta wing is included in the report in order to show the convergence of and relation between solutions of varying complexity, and to indicate which solution should be used in order to satisfy the accuracy prescribed for any given problem. The case of the delta wing is not completely general, and the exposition in respect to induced drag and yawing moment will be completed in a later report. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2591.pdf 293. Velocity distribution on straight and swept-back wings of small thickness and infinite aspect ratio at zero incidence S. Neumark A solution by H. Ludwieg, giving the velocity distribution in tile central section of a thin swept-back wing of infinite aspect ratio with a biconvex profile at zero incidence, has been found erroneous. In connection with this problem, the approximate method of sources and sinks for determining velocity distribution on straight and swept-back wings is critically examined, its limitations established, and proper ways of its application to threedimensional problems indicated. A correct solution of Ludwieg's problem is found, and generalized to give the velocity distribution over the entire wing. The method is further extended to cover a wide class of thin symmetrical wing profiles, those with rounded leading edge being, however, often intractable by this particular method. The ultimate purpose of the investigation is to provide a reliable basis for determining the critical Mach number for swept-back wings. Further work is needed to embrace wings of finite aspect ratio and tapered wings, in particular delta-wings. The method seems adequate to deal with these more complex cases. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2713.pdf 294. Wind-tunnel measurements of yawing moment due to yawing (nr) on a 1/5.5 scale model of the meteor Mark F.III J. G. Ross and R. C. Lock During recent investigations into the self-excited oscillations ill yaw, experienced on Meteor aircraft, the lateral stability derivative, nr, was measured in flight, and found to differ considerably during initial experiments from the theoretical estimate. A new technique was therefore devised to measure nr in the wind-tnnnel; and, with its aid, modifications were tested on a model with the object of reducing the self-excited oscillations in flight. Measurements of nr were made over a range of Reynolds numbers, and for different periods of oscillation of the model. The final comparison of the flight and wind-tunnel tests, after certain refinements in technique of the former, and after corrections for solid friction to the latter had been made, showed that the full-scale measurement of nr was about 10 per cent less than-that obtained in the tunnel. Considering the difficulties involved, this agreement may be considered as satisfactory. For the model in the standard condition, the value of nr was about 20 per cent less than the estimated figure of -0.108 at zero lift, but with dorsal fins (see sections 5.7 and 5.8). It was found possible, without altering the value of nv to increase the value of nr to the estimated value. The 'snaking' tendencies of the model, which were more pronounced at small angles of incidence, could be greatly reduced by fitting an upper dorsal fin (described in section 5.7). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2791.pdf 295. Wing parachutes for recovery from the spin. Part I - General design requirements. Part II - Wake Phenomena. G. E. Pringle, T. V. Somerville, D. J. Harper, J. R. Mitchell, J. Picken, G. E. Pringle Part I. The suggestion to use parachutes attached near the wing tips for recovery from bad spins is not news, but was considered -before tail parachutes were introduced. With the increasing interest in tailless types it has become necessary to reconsider the wing parachute as a safety device, and wind-tunnel tests have showvn that it can be of powerful assistance. Part II. The wing parachutes of a tailless aircraft prototype failed to open when streamed in an accidental spin. This gave a clue to the existence of a marked wake effect when a parachute is deployed on a tow cable behind a stalled wing. This wake effect is such as greatly to reduce the critical closing speed of the parachute. The effect measured in a wind tunnel diminishes as the cable is lengthened. It is recommended that the cables should be made as long as possible up to one and a half spans in length; here the danger of entanglement becomes real. The centrifugal forces in spinning may also be turned to good account in making the parachutes ride outside the wing wake; for the same reason, attachment at the extreme tip is preferred to attachment inboard. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2543.pdf 296. Wing-fuselage flutter of large aeroplanes W. P. Jones A general theoretical method is described which takes into account a large number of degrees of freedom and is based on the design data for the aeroplane. The problem specifically investigated is the symmetrical flutter of a particular aircraft. Twelve degrees of freedom are assumed to cover pitching and translational motion of the whole aeroplane, flexure and torsion of the wings, and fuselage vertical bending. The tailplane is regarded as rigid. In the case considered, estimates indicate that the lowest critical speed is well above tile maximum design speed of the aeroplane. The influence of the additional degrees of freedom associated with movements of the control surfaces is not considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2656.pdf 297. 24-ft wind tunnel tests on a propeller with NACA 16 series sections. Test results and analysis into mean lift-drag data A. R. C. MacDougall and A. B. Haines This report gives the results of tests made in the Royal Aircraft Establishment 24-ft Wind Tunnel on the de Havilland propeller for the Aeronautical Research Council research programme initiated in 1943. The propeller was designed to give a good performance at high forward speeds and the aim of these tests was to check whether, as a result, serious losses in take-off performance had been incurred. The results are more reassuring than was expected. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2602.pdf 298. A distant reading manometer with particular application to the measurement of small pressures A. S. Halliday, and H. Deacon The function of the manometer is to enable small pressure differences to be measured at a distance. The instrument will measure either the difference of two pressures or a single pressure relative to atmosphere. The accurate measurement of small pressures at a distance remote from the source is not very satisfactory by the orthodox methods using long lengths of tubing. The chief difficulty is that due to lag. This problem became apparent when exploring the wind velocity and direction on the Whirling Arm at the National Physical Laboratory. From the yawmeter to the Chattock gauge, which one normally uses for pressure measurements, the length of tubing required for each lead is of the order of 120 ft. This means that a considerable time must elapse before a reliable reading can be obtained, particularly if the pressure difference is very small. The sensitivity of the manometer described is comparable with that of a 26 in. Chattock gauge and is capable of measuring pressures up to about 3 in. of water. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2744.pdf 299. A review of the problem of choosing a climb technique, with proposals for a new climb technique for high performance aircraft K. J. Lush The climb techniques at present used on modern aircraft entail quite high true air speeds and high kinetic energies. It was desired to investigate the effect of kinetic energy variation with height, which is ignored in present methods, on the choice of climb technique. The problem of choosing the best climbing technique is considered and the limitations of the present technique discussed. A new approach is made to the general problem of choosing the best climb technique between any specified end conditions, and with the aid of a geometrical illustration tentative conclusions are deduced concerning the choice of climb technique. These are presented for discussion prior to a fuller investigation. It is concluded that the application of present methods of choosing a climb technique to aircraft whose speeds on the climb are high is open to question. Introduction of 'energy height' as a variable permits a more exact treatment to be attempted and enables a geometrical illustration to be developed of the general problem of optimum climb between specified end conditions. From discussion of this illustration it is tentatively concluded that a revised climb technique, outlined in the Report, will give improved performance by building up a relatively high kinetic energy at low altitudes, where the thrust available is high, for conversion into potential energy (i.e. height) at high altitudes. In a particular example the new technique reduced the times required to climb to 40,000 ft and 45,000 ft by 1.4 minutes (9 per cent) and 2-5 minutes (10 per cent) respectively. It is hoped to investigate the proposed technique experimentally with a view to confirming its superiority over present methods. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2557.pdf 300. A theoretical investigation into the lateral stability of an aeroplane controlled by an automatic pilot, with particular reference to the effect of flight path angle T. W. Prescott Several autopilots produce aileron deflection proportional to the movement between the aeroplane and the outer gimbal of a vertical gyroscope. In non-level flight this relative movement is not equal to the rotation of the aeroplane about its x-axis, and it was desirable to investigate the lateral stability for steep angles of climb and dive. Calculations show that instability does occur, but that stability can be restored either by making the rudder deflection dependent on aileron movement in order to counteract,the aileron drag coefficient, or by adding a rate of yaw term to the rudder circuit. The addition of both aileron and rate terms to the rudder circuit is greatly superior to the addition of either term alone. The aileron drag coefficient can also have a detrimental effect at the start of an automatic turn, and response curves during entry into the turn have been calculated for various degrees of aileron drag compensation. The bank angle and sideslip response curves are unaffected by the compensation. The rate of turn response is improved during the first second but subsequently is little affected by aileron drag compensation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2640.pdf 301. A wind-tunnel investigation of entry loss on propeller turbine installations. Parts 1 and 2 J. Seddon and A. Spence The report is in two parts, following a general introduction. Part I describes wind-tunnel tests on (a) a series of models of annular entries, with and without propeller, in the 5-ft tunnel ; (b) a set of large circular blade roots on a full-size nacelle in the 24-ft tunnel. The models were based on two representative propeller turbine engines of different sizes. Various shapes and sizes of spinner and duct were tested, including 'vertical' and 'sloped' entries and 'elliptical' and 'conical' spinners. The work follows on from past tests, model and full-scale, on entries for radial air-cooled reciprocating engines. The smaller engine tends to have the higher entry loss, owing to the blade roots being relatively thicker. In a typical case, under cruising conditions, the total entry loss on the model is 25 per cent of free-stream dynamic head, of which 18 per cent is caused by the blade roots. Scale effect is likely to be small. In these circumstances a large diameter spinner gives the best result. Sloped entries are not recommended. From a generalised analysis of the results empirical rules are suggested for the estimation of spinner loss, duct loss, and blade-root loss, making up the total entry loss in flight. The additional duct loss which is usually present in ground running is also considered in general terms. Part II describes wind-tunnel tests on models of a number of alternative ducted spinners for a typical engine, and, for comparison, one annular entry similar to those tested in Part I. It is shown that the ducted spinners give 90 to 95 per cent total head in cruising flight compared with about 75 per cent for the annular entry. Most of the gain is in a reduction of blade root loss from 17 per cent total head to about 2 per cent. The results are not sensitive to the shape of the blade root fairing. Low velocity must be maintained as far as possible, both in the spinner itself and in the rear duct. Expansion of the duct in the neighbourhood of the leak should be avoided, however. The leak gap should be kept small, to minimise the extra flow taken through the spinner. A short cowl version, in which the outer cowl of the spinner terminates just ahead of the propeller, is satisfactory for practical purposes, and has the advantage of being lighter in weight than a long cowl spinner with nose entry. A detailed analysis of the loss is given, using methods evolved in Part I. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2894.pdf 302. Aerofoil oscillations at high mean incidences W. P. Jones Summary.--The problem of the estimation of the aerodynamic forces acting on two-dimensional aerofoils oscillating at mean incidences below the stall is considered. A method of calculation is suggested which makes use of the steady motion characteristics of the aerofoil. At low frequencies, good agreement with the measured aerodynamic derivatives should be obtained as the method is such that it gives the correct values at zero frequency. A comparison between the estimated and measured values of the pitching-moment derivatives for a particular aerofoil is made, and this shows that the method suggested gives better agreement with experiment than the usual vortex-sheet theory. The method can be extended for the calculation of control-surface derivatives. To some extent, the influence of compressibility could also be taken into account. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2654.pdf 303. Aircraft landing gear ground loads when spinning-up the wheels at touch-down J. W. Blinkhorn The investigation covers all combinations of landing speed, coefficient of friction between the tyre and the ground, and harshness of landing, for any type of pneumatic tyre and wheel unit. Particular attention has been given to landing speeds between 50 and 150 m.p.h., coefficients of friction from 0 to 2.0, and landings giving vertical wheel accelerations of lg, 2g, 3g, 4g. It was found that for any landing, the vertical reaction at any wheel which has just finished spinning-up increases with increase in the moment of inertia of the wheel and tyre unit, and the landing speed, and decreases with increase in the free tyre radius, the aircraft weight, the time to reach the maximum vertical wheel reaction, and the coefficient of friction between the tyre and the ground. It should be noted, of course, that there is a relation between the moment of inertia, the free tyre radius and the aircraft weight, - in general the free tyre radius and the moment of inertia will increase with aircraft weight. For any wheel and tyre unit it is shown that there are various combinations of landing speed and coefficient of friction which will cause the wheel spinning up to iust cease at the same instant as the maximum vertical wheel reaction is reached, and except for very gentle landings, the maximum value of μ required is usually much less than 1.0. Figs. 1 to 7, together with the notation given in Section 8, are self-explanatory and expand the above observations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2588.pdf 304. Assessment of the relative performance of the by-pass engine and the orthodox double compound jet engine E. A. Bridle The by-pass engine can be described as a form of ducted fan engine in which the fan boosts the main compressor. Two possible forms of by-pass engine are described, and their estimated performance is compared with that of the orthodox double compound jet engine under various flight conditions, the calculations being extended to include the case of thrust boosting by means of exhaust reheat. It is concluded that the by-pass engine can offer an appreciable gain in respect of fuel economy over the orthodox double compound jet engine even at 650 m.p.h, in the stratosphere, at the expense, however, of increased frontal area for a given thrust. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2862.pdf 305. Boundary-layer and wake investigation in supersonic flow J. Lukasiewicz and J. K. Royle The report describes the results of traverses of the boundary-layer and wake encountered in a small supersonic tunnel at a Mach number of 2.5. The tunnel was arranged with two throats in parallel formed by two shaped walls enclosing a shaped central element. Both the laminar and turbulent boundary-layers were encountered and compared with existing experimental and theoretical results. The frictional drag of the central element as deduced from the wake traverses is in close agreement with that calculated from considerations of laminar boundary-layer growth over the surface of the element. The tests also provide information relating to the design of nozzle profiles, particularly at the point of inflexion, where the changes of pressure gradient may have a serious effect on the boundary-layer and on the velocity distribution. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2613.pdf 306. Boundary-layer flow along a flat plate with uniform suction J. M. Kay Summary.--Experiments have been carried out in the closed-circuit wind-tunnel at Cambridge University to determine the effectiveness of distributed suction as a means of controlling and stabilizing the flow in a boundary layer. These experiments have shown that the laminar exponential suction profile can be established and retained, provided the boundary layer is in an undisturbed laminar condition at the start of the suction region. Good agreement has been obtained between the measured velocity profiles and the theoretical exponential form. It has also been shown that the laminar suction profile, when once established, is able to surmount small disturbances which would normally be sufficient to promote transition in the absence of suction. There is, however, no evidence whatever to suggest that laminar flow can be re-established if transition once occurs. The variation with rate of suction of the total effective drag of a flat plate has been investigated. It has been established that, from the point of view of drag reduction, the optimum rate of suction is the minimum rate which is sufficient to maintain laminar flow under the prevailing conditions of stream turbulence and surface finish. A suction velocity ratio of approximately 0.0010 has proved necessary in order to ensure the preservation of laminar flow with the conditions prevailing in the wind-tunnel at Cambridge, although a lower figure may be adequate under the steadier air conditions of free flight. As far as turbulent flow is concerned, it has been shown that distributed suction provides an effective method of thinning a turbulent boundary layer. Some evidence has also been accumulated to show that an asymptotic turbulent suction profile may be closely approached at sufficient values of suction velocity. A theoretical basis has been suggested for this type of boundary-layer flow, using the vorticity transfer theory, which has given good agreement with the experimental results. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2628.pdf 307. Calculated loadings due to incidence of a number of straight and swept-back wings V. M. Falkner, Doris Lehrian In this report are collected together the calculated aerodynamic loadings due to incidence of a number of straight and swept-back wings. The calculations follow in the main the routine described previously in another report, but include additions concerned with induced camber and induced drag. An additional investigation is made of the effect of the N.A.C.A. camber on the properties at zero lift of a rectangular wing of aspect ratio 6. A table is given of loading functions for use in auxiliary solutions when the wing plan has a discontinuity of direction at an arbitrary position along the span. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2596.pdf 308. Comparative flutter tests on two, three, four and five-blade propellers H. G. Ewing, J. Kettlewell, and D. R. Gaukroger This report describes comparative flutter tests on two, three, four-and five-blade Duralumin propellers with the same blade design. The tests were made on the No. 3 spinning tower, Royal Aircraft Establishment. Straingauges were used for determining the vibratory stresses and the phase relations between the blades. A wide range of blade angles above and below the stalling region was explored. Stalling flutter was the only form encountered. The phase relation of the blades was found to be dependent on number of blades and speed of rotation, and to influence the amplitude of the vibratory stresses. It is shown that no direct comparison of the flutter characteristics of the two, three, four and five-blade propellers can be made. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2634.pdf 309. Conical flow as a result of shock and boundary-layer interaction on a probe J. Lukasiewicz The formation of a conical shock and a conical region of flow separation originating from the tip of a thin traversing tube was observed in a supersonic tunnel as a result of interaction of a strong shock with the boundary layer on the tube surface. The angles of the conical shock and separation surfaces and the static pressure in the separation region are in good agreement with the theoretical conical flow solutions. The extent of the conical flow illustrated should act as a warning against the use of static pressure tubes for measuring pressures in the regions of strong shocks. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2669.pdf 310. Dynamic Longitudinal Stability Measurements on a Single-rotor Helicopter (Hoverfly Mk. I) W. Stewart Flight measurements have been made of the phugoid motion of the Hoverfly Mk. I helicopter, following an arbitrary longitudinal displacement of the control, the latter being returned to its initial position and held fixed. The tests were done throughout the speed range for power-on conditions and in autorotation for various centre of gravity positions and for forward and backward initial displacement of the stick. In power-on flight there is a large variation in the dynamic stick-fixed stability with speed. From zero airspeed up to 35 m.p.h. and at airspeeds above 50 m.p.h, the phugoid motion is divergent, but for the speed range 35 to 50 m.p.h. the helicopter is stable. In autorotation, there is little change in the dynamic stability with speed. Below about 30 m.p.h. the phugoid amplitude tends to increase slowly, and above this speed the amplitude tends to decrease slowly. There is no variation in the character of the longitudinal phugoid motion with change in centre of gravity position. Neither was any difference detected in the character of the oscillations produced by initial backward movement of the stick, compared with those produced from initial forward displacement. The theoretical estimation of the power-on stability agrees with the flight tests at low airspeeds, but it shows little variation in stability with speed. In autorotation, the theoretical work agrees very well with the flight tests throughout the speed range. The discrepancy in the power-on tests is felt to be due to a large variation of the fuselage pitching moment with speed, particularly due to the effects of the induced flow from the rotor. (Scan courtesy of Juergen Humt.) Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2505.pdf 311. Effects of air humidity in supersonic wind tunnels Julius Lukasiewicz and J. K. Royle The available theoretical and experimental information on condensation of water vapour in the supersonic flow of air is reviewed and the influence of condensation on operation of supersonic tunnels is considered. The mechanism of condensation in supersonic flow is of molecular nature and does not depend on the presence of solid condensation nuclei in the air. As estimated by Oswatitsch and confirmed by experimental results, the condensation in supersonic flow of air is primarily a function of the adiabatic supercooling DeltaT h to ad (defined in Fig. l), which determines the conditions at which the condensation shock occurs. For medium-sized supersonic tunnels (say 1-ft square working section) the adiabatic supercooling is of the order of 50 deg C. For most test purposes it is essential to eliminate the detrimental effects of condensation, on flow distribution in the tunnel working section. The usual method is to use highly dried air, and the question of the required dryness is considered. It is shown that by increasing stagnation temperature condensation can be avoided usually only at Mach numbers smaller than 1.5. Alternatively, condensation can be eliminated from the tunnel nozzle by pre-expansion in an auxiliary nozzle, as verified experimentally. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2563.pdf 312. Experiments in the compressed air tunnel on swept-back wings including two delta wings R. Jones, C. J. W. Miles and P. S. Pusey The experiments considered in the present report form part of an investigation into the characteristics at high values of Reynolds number, of swept-back wings, particularly swept-back wings of triangular plan form, commonly known as Delta wings. The work was carried out in conjunction with the Royal Aircraft Establishment where the wings were made. Also some experiments had already been carried out on one model at a low value of R by Hills, Lock and Ross, at the Royal Aircraft Establishment (1947). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2871.pdf 313. Flight tests on swinging during take-off on a single-engined fighter-bomber (Typhoon Ib) W. Stewart Flight tests have been carried out on a Typhoon aircraft to compare the values of the aerodynamic side forces and yawing moments, during take-off, with the wind-tunnel measurements, and to compare various methods of estimating the rudder angles required to trim during a take-off run. The side forces can be checked fairly simply by estimating the various component side forces acting at each instant during the run and comparing the summation with the resultant side force measured by an accelerometer. The aerodynamic side forces were evaluated from the wind-tunnel tests under the corresponding conditions and the side force from the undercarriage was estimated from the load on the wheels and the angle of crab of the wheels to their instantaneous direction of motion. It is more difficult to compare the yawing moments operating as there is no direct method, at present, of measuring an angular acceleration. Angular accelerations are difficult to obtain by differentiation of the observed angular displacements of the aircraft, due to the rapid variations in angle produced by the pilot's over-corrections on the rudder. Nevertheless, it was possible in some of the runs to evolve the resultant yawing moment from double differentiation of the heading angles and where this could be done successfully, good agreement was obtained between this resultant moment and the summation of the estimated components. By integrating the summation of the estimated yawing moments along a take-off run, which should be approximately zero, a further check on the comparison of the flight and wind-tunnel yawing moments can be made. The results show very good agreement with the wind-tunnel tests. As runs have been done under various crosswind conditions on the aerodrome (i.e., different angles of sideslip) the order of each of the aerodynamic components was verified. A method of evaluating the rudder angles required to trim is suggested, by solving the side-force and yawing moment equations simultaneously, using the wind-tunnel measurements for the aerodynamic components and introducing the side force from the undercarriage, in terms of the crab angle of the wheels. In the yawing-moment equation, the second-order differential inertia terms is neglected as the changes of angle in the theoretical calculations (representing a straight take-off run) are very small. The effect of the tail wheel has been disregarded as it is only in operation during the initial stages of the run. Due to considerable over-correction by the pilot, it is desirable to design for a rudder range at least 20 per cent in excess of that required to trim. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2660.pdf 314. Four- and eight-channel desynn graphical recorders F. R. J. Spearman A 4-channel recorder, providing continuous traces against time on photographic film, has been developed for use with any instruments embodying Desynn transmitters. It is suitable for the measurement of quantities which vary with a maximum frequency of 3 c.p.s. It is made from F.24 camera component parts, and uses the standard magazine and 5-in. wide film. It has been successfully used for flight trials; manufacturing drawings are available. An 8-channel version, of which two or three may be coupled together, is under development. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2636.pdf 315. High-speed tunnel tests of a 5 per cent. Chord dive-recovery flap on a NACA 0015 aerofoil D. A. Clarke Pressure plotting tests were made in the Royal Aircraft Establishment High Speed Tunnel on a parallel wooden NACA 0015 wing with dive-recovery flap. The Mach number was varied between 0.30 and 0.80, and the Reynolds number was kept constant at 1.4 x 10power6. All combinations of the following were tested :--flap position 0.2c, 0.3c, 0.4c ; flap angle 20 deg, 40 deg, incidence 0 deg, 4 deg. The flap-chord/wing-chord ratio was 0.05. The report presents a general picture of the action of a dive-recovery flap on a wing. The data are, however, too limited to permit the formulation of general design recommendations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2689.pdf 316. Landing gear with twin tandem wheel units: cornering characteristics as determined by model tests J. W. Blinkhorn For twin tandem units the wheel loading conditions which arise when aircraft are turned on the ground may be critical for the landing gear. To estimate the magnitude of these loads, cornering tests were made on a small scale model of the main undercarriage unit proposed for the Brabazon I, Mk. II. These tests showed that for zero turning radius, i.e., turning about the central vertical axis of the model undercarriage, the wheel side loads were almost equal to the vertical load multiplied by the coefficient of sliding friction between the tyres and the ground. The side loads rapidly decreased as the turning radius increased, and with the turning radius equal to three times the wheel base, the wheel side loads were only about half of those at zero turning radius. The severity of the design loads for turning on the ground will therefore be considerably reduced if it can be ensured that the centre of the minimum turning circle of the aircraft is a short distance outboard of either main undercarriage unit. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2668.pdf 317. Load diffusion at an interspar opening theoretical methods of analysis compared with strain measurements on a large wing D. C. Allen The diffusion of load from spar flanges into skin and stringers near an opening was investigated experimentally in a large wing structure undergoing strength tests. A comparison of measured strains with those given by theoretical methods shows that in general the flange loads are represented with reasonable accuracy. Any theory, however, in which the chordwise rib at the edge of the opening is ignored gives shear stresses much greater than those measured. Allowance for the bending stiffness of this rib produces values of shear stress comparable with those obtained experimentally. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2664.pdf 318. Low-speed wind-tunnel tests of fowler flaps, slats and nose flaps on a model of a jet aircraft with a 40 deg swept-back wing A. Spence This report presents the results of tests with Fowler flaps on a model of a single-jet aircraft with a 40 deg swept-back 10 per cent thick wing. Slats and nose flaps were also tested as means of delaying the tip stall. The maximum trimmed lift coefficient without flaps or slats was 1.055 (R = 2.7 x 10power6). With half-span Fowler flaps (leaving a gap across the fuselage) and slats over the outer half of the span, this value was increased to 1.64, and there was adequate stability. Tests in which the spanwise extent of the nose flap was varied, indicated that about 50 per cent. wing semi-span per side was the optimum length of slat or nose flap for avoiding instability at the stall. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2752.pdf 319. Measurements of maximum lift on 26 aerofoil sections at high mach number. Part I tests on 19 aerofoils. Part II Tests on a Further 7 Aerofoils J.A. Beavan et al The lift on a number of aerofoil sections mostly of 2-in. chord has been determined over a wide range of incidence and Mach number by measuring tile pressures on the walls of the 20 x 8 in. High Speed Tunnel. There is some evidence that the low Reynolds number of the tests is not important. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2678.pdf 320. Methods of approaching an accurate three-dimensional potential solution for a wing H. C. Garner There is a great need for more accurate data on the aerodynamic derivatives of swept-back wings in order to solve problems of stability, control and flutter. As one step in the search for these data the estimation of the three-dimensional potential solution is essential, and if it is to be of value the degree of accuracy of any approximation must be known beyond question. This report gives attention to some fundamental aspects of the vortex-sheet theory for determining the distribution of lift on a finite wing. The accuracy and limitations of some existing approximate forms of the theory are discussed. With special reference to the labour of computation an iterative approach to an accurate solution is suggested, and the general mathematical expression for the distribution of lift required to give an exact solution for a Vee wing is considered. It is proposed - (a) That, with the specific purpose of checking the Falkner (R. & M. 1910, 1943) vortex-lattice theory, the iterative procedure should be applied to a wing of constant chord with acute hyperbolic leading and trailing edges (see Fig. 3). (b) That by choosing suitable functions calculations should be undertaken to determine a reliable potential solution for a Vee wing (see Fig. 2) in an inclined stream. (c) That further study is needed before calculations can usefully be nudertaken to improve the accuracy of existing methods of estimating the characteristics of deflected controls. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2721.pdf 321. Methods of testing reinforced plastics, parts I and II F. T. Barwell PART I. Measurement of Tensile Strength. An experimental comparison has been made between five types of tensile tests including novel types designed to enable axial loading conditions to be approached more readily than is the case with established methods. Examination of the results of two hundred and forty tests indicates that significant differences can occur between the results of different tests and that there is also a significant variation between the properties of material cut from different parts of the same sheet. It is concluded that the results, obtained when testing paper-base material by novel methods, are sufficiently good to justify development of a simplified apparatus of similar type for general use. PART II. Measurement of Interlaminar Strength. The strength of reinforced plastics depends almost entirely on their fibrous reinforcement, and when, as in laminated plastics, this reinforcement is arranged to lie in parallel planes, there is marked interlaminar weikness. For example, the tensile strength measured in a direction at right-angles to the laminations is shown to be from one-sixth to one-ninth of the corresponding value measured in the direction of the laminations. In spite of the obvious concern of the designer in tile value of interlaminar strength and of the indication of previous research that this quantity is markedly affected by variations in manufacturing conditions, measurements of this quantity are not generally made in this country: It has been the practice in the National Physical Laboratory however to carry out certain tests of interlaminar strength and it was considered desirable to compare and to assess the accuracy of these tests together with those used in U.S.A. and Germany. Besides providing the basis for the rational interpretation of the results, it was hoped that the investigation would enable one particular type of test to be selected for further work. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2702.pdf 322. Model tests in the 24-ft wind tunnel to determine the optimum angle for release of a cockpit hood R. Fail For some time now, it has been recommended that mechanical assistance be incorporated in jettisonable cockpit-hood designs. Some firms have preferred designs in which the hood is constrained to rotate through a definite angle before the final release. A short series of tests has, therefore, been made in the 24-ft Wind Tunnel to determine the optimum angle for release. This was found to he about 10 deg, which is considerably less than has been suggested in the past. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2644.pdf 323. Model tests on an air interchange system for removing engine exhaust products from a wind tunnel K. W. Newby, E. G. Barnes and D. W. Bottle Model tests have been made to investigate the functioning of an air interchange system for removing from a return-circuit wind tunnel a high proportion of the exhaust products from propulsive units under test. The tests were planned to assist the design of an engine altitude tunnel. With changing circumstances the priority of this tunnel has been reduced, but the tests were continued to give general information on the extraction of engine exhaust products from this type of wind tunnel. The tests were made on a partial model of a tunnel, which had an air interchange exhaust collector designed to remove 15 per cent of the tunnel mass flow. This was installed on the tunnel axis at the downstream end of the working section. Tests were also made on 10 per cent and 5 per cent collector entries designed to be interchangeable with the 15 per cent entry. The tests have confirmed that the interchange system tested was generally very satisfactory for the specified requirements, and that in the interests of power economy, the interchange ratio should be reduced as far as possible. In other tunnels with less exacting requirements the collector duct would of course be placed in a region where the wind speed was low, in order to reduce the losses and hence the fan power. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2639.pdf 324. Note on semi-experimental methods for the determination of aerodynamic derivatives for an oscillating wing-aileron system P. F. Jordan A brief survey is given of existing semi-experimental methods for the determination of two-dimensional aerodynamic derivatives for unsteady motion of a wing-aileron system (and, in particular, for aerodynamically balanced controls); a comparison with (partly unpublished) esperimental data is made. The result is encouraging for further investigations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2706.pdf 325. Note on the dynamic characteristics of servo-tab systems of control D. Adamson and D. J. Lyons Generalised curves have been constructed from which estimates can be made of those dynamic characteristics of the servo-tab-type of control which are of chief interest to the designer, viz., (i) the magnitude of the first overshoot of the main flying control beyond its equilibrium position, (ii) the lag of the main control surface behind the tab movement, (iii) the damping of the main control surface oscillation, (iv) the angular velocity possessed by the main control when it first passes through its equilibrium position. The characteristics evaluated for two specific cases, a 50,000-1b and a 300,000-1b aircraft, indicate no special problems to the designer or pilot except with regard to overshoot of the control at low flying speeds. Elastic stops are considered to be the most promising solution to this. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2853.pdf 326. On a theory of sandwich construction W. S. Hemp The theory of sandwich construction developed in this paper proceeds from the simple assumption that the filling has only transverse direct and shear stiffnesses, corresponding to its functional requirements. This supposition permits integration of the equilibrium equations for the filling. The resulting integrals are used to study the compression buckling of a flat sandwich plate. The formulae obtained are complex, but may be simplified in practical cases. A second approach to sandwich problems is made in section 5, where a theory of 'bending' of plates is outlined. This generalises the usual theory, malting allowance for flexibility in shear. This approach is applied to overall compression buckling of a plate, and agreement with the previous calculations is found. This suggests the possibility of calculating budding loads Ior curved sandwich shells. A simple example, the symmetrical buckling of a circular cylinder in compression is worked out. The theory developed would seem applicable to all cases of buckling of not too short a wave length. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2672.pdf 327. Regenerator heat exchangers for gas-turbines J. E. Johnson Information was required from which the performance of regenerators suitable for heat exchangers for gas-turbines could readily be estimated. A series of tables and curves have been prepared from which the efficiency of a regenerator can be calculated if the operating conditions and heat transfer coefficients are known. The tables and curves cover a range of lengths and blow times appropriate to gas-turbine conditions. Measurements of heat transfer and pressure drop coefficients have been made on several examples of matrix of both the gauze and flame trap type in conditions similar to those in a gas turbine. A number of examples have been worked out from the experimental results to show the relative importance of the different variables on the performance of typical regenerators. A gauze matrix of fine wire and open mesh has a much lower weight and only slightly higher pressure drop than a flame-trap matrix for the same efficiency. The recommended size of gauze is a wire diameter of 0.002 in. to 0.004 in: and a mesh of 20 to 40 wires per inch, the material should be stainless steel. Further design study is necessary to determine whether this advantage can be maintained in a complete regenerator. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2630.pdf 328. Sandwich Construction and Core Materials, Part VI W. J. Pullen et al A range of struts each consisting of 'Balsolite' filler sandwiched between two faces of one-sixteenth inch thick birch plywood has been tested in order to assess the efficiency of Balsolite as a stabilizer in sandwich structures. It is concluded that this material compares favourably with other low density materials when used as a stabilizer. Modification of the material, namely the use of transverse and longitudinal tubes alternately, does not appear to be beneficial. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2687.pdf 329. Some electrical integrating circuits and their use in the measurement of low frequency vibration amplitudes G. R. Richards The note investigates the possibility of making low frequency vibration measurements by the use of electronic acceleration measuring equipment in conjunction with electrical doubly integrating circuits. It is shown that by this method many of the disadvantages associated with the use of seismic displacement units can be obviated particularly over the frequency range 2 to 40 c.p.s. Three electrical integrating methods are discussed, the correct circuit conditions for the integration of periodic sinusoidal, rectangular and triangular waveforms are derived. A description is given of an existing acceleration measuring equipment incorporating two of the described integration networks; its sensitivity, frequency response and methods of increasing these factors are discussed in detail. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2724.pdf 330. Some tests on compressor cascades of related aerofoils having different positions of maximum camber A. D. S. Carter One of the major variables defining the shape of any blade is its position of maximum camber, and there are several indications that its choice considerably effects the performance of the cascade. Tests have therefore been carried out on a series of aerodynamically equivalent cascades in which the position of maximum camber was varied systematically. The tests covered a full incidence range up to choking. From the results and consideration of other work the following conclusions were reached. (1) Bringing the position of maximum camber forward gives a wider working range and a higher choking mass flow. (2) Moving the position of maximum camber back gives a higher work capacity and a higher drag critical Mach number. (3) With the present design rules there can be little doubt that the best all-round performance is obtained with blades having their positions of maximum camber 50 per cent of the chord from the leading edge provided adequate throat area Call be provided with this design. (4) With improved methods of design it is anticipated that the performance for the other positions of maximum camber could be improved, but even so the best combination of large working range and good high-speed performance appears to occur for a blade having its position of maximum camber as in (3) above. These conclusions apply to the two-dimensional performance of a cascade of blades : in an actual compressor the results may have to be modified to accommodate the three-dimensional nature of the flow. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2694.pdf 331. Speeds and Normal Accelerations of .Boeing Clipper Aircraft on North and South Atlantic Routes D. T. Jones This report presents results obtained from V-g recorders fitted to Boeing Clipper aircraft on the North and South Atlantic routes between September, 1944 and May, 1946. The records cover about 3,300 flying hours and show that the maximum speed recorded is 215 m.p.h. (I.A.S.) and the maximum upward and downward accelerations are 2.3g and -0.3g respectively. The two main groups of records considered differ from one another not only in respect of route but also in seasonal conditions and in proportion of flights made in wartime. Therefore, differences between the results cannot be simply ascribed to differences of route. It appears from the analysis that tile maximum speed likely to be attained in a large flying time is somewhat greater in one group (North Atlantic) than in the other (South Atlantic) and that the maximum accelerations on the other hand are likely to be less for the former than the latter. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2633.pdf 332. Supersonic theory for oscillating wings of any plan form W. P. Jones Summary.--A theory for thin wings of any plan form describing simple harmonic oscillations of small amplitude in a supersonic air stream is developed. It is based on the use of the generalised Green\'s Theorem in conjunction with particular solutions which vanish over the charadteristic cone with vertex at any point in the field of flow. The theory can be used to calculate tile aerodynamic forces acting on fluttering wings when the modes of distortion are known. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2655.pdf 333. Systematic wind-tunnel tests with slats on a 10 per cent thick symmetrical wing section (EQ 1040 profile) G. F. Moss It was thought that present rules for the design of Handley Page slats might be inadequate for modern high-speed aerofoil sections. These tests were made on the EQ 1040 wing section to determine the optimum slat setting for this type of wing profile. Three slats were tested whose chords were 10 per cent, 20 per cent and 30 per cent of the wing chord, over a wide range of positions. Lift coefficients were measured over the stall in each case. Some tests were made with a split flap. Best results for the 10 per cent chord slat are obtained with very small gap and large dip. Zero gap, i.e., using the slat as a nose flap, may in fact give the optimum. Optimum positions for the larger chord slats are more conventional, but require larger forward extensions than are given by the old rules. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2705.pdf 334. Tables of multhopp and other functions for use in lifting-line and lifting-plane theory V. M. Falkner, E. J. Watson The report gives the derivation and computed tables of two classes of functions suitable for the solution of problems of spanwise aerodynamic loading of wings either by lifting-line or lifting-plane theory. The functions are based on lifting-line theory, but, by a consideration of the connection between lifting-line and lifting-plane theory through the application of I~nnk's stagger theorem to the calculation of induced drag, it is deduced that the functions must be equally suitable for lifting-plane theory. The first range of functions, called Multhopp or M functions, is associated with discontinuities of induced downwash, while the second, called P functions because of the polygonal representation of induced downwash, is connected with discontinuities in rate of change of induced downwash. Examples are given of the combination of functions to produce given curves of induced downwash, and evidence of the close relation between the results for a continuous and stepped downwash curve suggests that the functions tabulated will be sufficient to cover almost any problem in wing loading. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2593.pdf 335. Tests on a Glas 2 wing without suction in the compressed air wind tunnel C. Salter, C. J. W. Miles and R. Owen Summary.--In this report the results are given of an investigation, without the application of suction, into the lift, drag and pitching moment of an aerofoil of 31.5 per cent thickness/chord ratio designed specifically for use with a single suction slot at 0.69c from the leading edge. The object of the tests was primarily the estimation of the behaviour of the wing at high Reynolds numbers in the event of the failure of the suction, but it was also hoped to obtain information concerning some reasonable method of countering any serious effects that might arise. Consequently, the tail of the aerofoil was hinged to form an unslotted main flap and fitted with a detachable split flap. Tests were also made with a slotted main flap. The Reynolds number range extended from 0.3 × 10(to the power of 6) to 7.3 x 10(to the power of 6). Critical regions were observed and the scale effects were found to be large. The influence of the flaps was generally more or less normal, although the increase in CL max. was less than half that for a conventional aerofoil of similar thickness/chord ratio, the NACA 0030. At R - 7.25 × 10(to the power of 6) without flaps, CL max. for the Glas II was 1.21 compared with 0.7 for the NACA 0030. A 15 per cent split flap at 90 deg on the latter increased CL max. to 2.2 whereas the values for the Glas If only reached 1.71 with a similar split flap and 1.64 with a main flap angle of 40 deg. The effect of the slot between the main flap and the forward portion of the wing was found to be comparatively small. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2540.pdf 336. The calculated performance of ethyl alcohol-water mixtures as rocket fuels with liquid oxygen A. B. P. Beeton Specific impulses and combustion temperatures have been circulated for rocket propellants consisting of liquid oxygen and ethyl alcohol-water mixtures. This system appears to have a number of advantages compared with the corresponding liquid oxygen and petrol system. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2816.pdf 337. The calculation of whirling speeds of a system of rotors keyed to co-axial shafts T. S. Wilson The whirling of shafts carrying rotors is a subject which has attracted the attention of many engineers and mathematicians notably Dunkerley, Chree, Stodola, Jeffcott and Morris during the past fifty years. The last mentioned writer has given some valuable historical surveys and criticisms in addition to his own elucidation of several aspects of the general problem. The main purpose of this paper is to bring the calculation of whiffing speeds of an important class of systems within the scope of the iterative technique of Duncan and Collar, and to demonstrate by theory and example that problems involving large numbers of degrees of freedom may thereby be efficiently dealt with. It would appear that the power of this iterative method is not so widely appreciated as it might be. One erroneous belief is that the utility of the method ceases whenever slow convergence of the iteration ensues. An additional refinement of procedure, which the writer has exploited, allows two or more modes to be extracted more or less simultaneously from an iteration which is converging slowly. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2709.pdf 338. The derivation of airworthiness performance climb standards F. G. R. Cook, and A. K. Weaver From the first, civil airworthiness requirements have included climb performance among the safety criteria. Hitherto climb performance standards have been empirical, and magnitudes have been chosen by reference to current aircraft types regarded as satisfactory. A weakness of this empirical type of requirement is that no method is provided for modifying the standards to meet new operating procedures and aircraft design features. To overcome this difficulty, a more rational basis for deriving the climb standards is proposed. The conception is introduced of a 'datum' performance, below which conditions predisposing to an accident exist, and the level of safety judged by an 'incident rate' which is the frequency with which the operational performance of aircraft falls below this datum. A standard is chosen so that when the aircraft type complies, the incident rate will not exceed some tolerable value. To derive such a standard, account must be taken of the various conditions such as weather and airframe state which affect performance. The standard need only be framed in terms of some of these conditions; the effect of others may be included on a statistical basis by providing an appropriate 'performance margin' over the datum. It is shown how the treatment of the conditions affects the form and efficiency of the standard. The margin appropriate to a given incident rate is obtained from the distribution function of the climb performance; this function is, in turn, derived from the distribution functions of the conditions treated statistically, and their effect on climb performance in a given aircraft configuration. The effect of engine failure is included by taking account of the probability of engine failure and the associated loss in performance. To simplify the treatment of changes in aircraft configuration, the flights are divided into stages, such as take-off climb, in which the configuration, except for the incidence of engine failure, is sensibly constant. It is then shown that the required standard (datum plus margin) for any stage may be specified in terms of a single case (i.e., number of operative engines); the case chosen is that found to be dominant in incident causation. Numerical examples are given of the derivation of standards by the method described. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2631.pdf 339. The determination of the natural frequencies of a full-scale airframe-engine system by the admittance method J. R. Forshaw and F. T. Mountford The development of the method of the measurement of admittances and the solution of the frequency equation for a complex full-scale airframe-engine system is given, dividing the dynamical system at the attachment of the engine to the airframe, and using a force system of equal and opposite bending moments and shearing forces. The values of the resonance frequencies obtained from the graphical solution of the frequency equation and from the resonance test are compared and found to be in good agreement. The method is applicable to the matching of an engine to an airframe by adjusting the flexibility of the mounting units. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2667.pdf 340. The diffusion of load into a panel bounded by constant stress booms and a transverse beam E. H. Mansfield A theoretical investigation is made into the diffusion of symmetrical, concentrated loads into a long stiffened panel having constant stress edge members and a transverse loading beam. Both pin-jointed and clamped end conditions for the beam are considered. Curves are given for determining the peak shear stress near the boom, the variation of this shear stress along the length of the panel, the proportion of load transferred by the beam, and the bending moment at the ends of the beam. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2729.pdf 341. The diffusion of load into a semi-infinite sheet Parts 1 and 2 E. H. Mansfield In Part 1, the rigorous and the 'stringer-sheet' stress solutions are given for a point load applied in the plane of a semi-infinite sheet and at a finite distance from the boundary which is assumed to be free. From these are derived, by integration, some of the stresses produced by distributed loads applied along lines normal to the free boundary; attention is concentrated on the stresses along the line of action of the applied loads. The problem of finding the shear stresses adjacent to a load-carrying boom attached to the sheet and normal to the free edge is also investigated and integral equations for the shear stresses are derived. The integral equation obtained from the rigorous theory is not readily soluble, but it is shown that, as in the stringer-sheet solution, very large shear stresses are present adjacent to the boom and near the free edge of the sheet. The required variation of boom cross-sectional area along its length to cause any particular variation of shear stress adjacent to the boom is also given. In Part II, a theoretical investigation is made into the problem of stiffening a sheet to relieve the high stresses near the free edge and adjacent to a direct load-carrying boom attached to the sheet. For booms of constant cross-section the stress distribution depends, with certain assumptions, on two non-dimensional parameters, and curves are included for determining the peak stresses in the sheet and the loads in the stiffening structure over the practical range of these parameters. It is shown that if a given weight of stiffening material is to be distributed uniformly along the free edge of the sheet there is a particular shape of stiffener which gives lowest peak stresses in the sheet. The influence of rivet flexibility between boom and sheet is examined theoretically. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2670.pdf 342. The dynamic landing loads of flying boats with special reference to measurements made on Sunderland TX.293 Anne Burns and A. J. Fairclough An account is given of a full-scale investigation into the stresses occurring in the wing members of a Sunderland flying boat during landing impacts. It is found that the main dynamic effect is caused by the wing oscillating in its fundamental mode. These dynamic loads have a spanwise distribution similar to the normal lift load and, if the level flight lift load is taken as unity, a magnitude (in the most severe impact recorded) of 1.4 upwards and 1.5 downwards. Generalizing this result, one concludes that whereas down loads in landing may be a deciding factor in design the up loads are amply covered by existing requirements. Comparison of calculated and experimental loads found in these tests indicates that satisfactory agreement can be attained by using recently introduced modifications of standard dynamical methods. Although the investigation is primarily a structural one some interesting results on general water load phenomena are obtained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2629.pdf 343. The effect of compressibility on the attitude of aircraft in rectilinear flight K. J. Lush The attitude of aircraft (i.e., the angle between the aircraft datum and the flight path) is of considerable importance in the aiming of certain airborne armament. An investigation was therefore made of the effect of compressibility on the attitude of aircraft in flight in a straight path. The application of the results of linear perturbation theory to the problem was examined, and the deductions made compared with the results of attitude measurements on a Spitfire IX over a wide range of altitude and air speed. As is well known, linear perturbation theory indicates a reduction of the slope of the curve of attitude against lift coefficient with increase in Mach number. The theorv indicates, however, that in straight flight at a constant ratio of wing lift to air pressure the variation of Mach number with lift coefficient is such that to a first approximation the slope of the curve of attitude against lift coefficient remains unchanged at the low Mach number value, only the intercept, or apparent no-lift angle, being altered (Fig. 1). This reduction in no-lift angle is proportional to the ratio of the lift to the air pressure but is not directly affected by Mach number or air speed. The experiments show a reduction in no-lift angle which agrees with that predicted by theory for the aspect ratio of wing tested. The change in apparent no-lift angle is of the order of half a degree between sea level and 40,000 ft. The above conclusions should not be applied to wings over 15 per cent thick. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2776.pdf 344. The effect of slipstream on the longitudinal stability of multi-engined aircraft D. E. Morris and J. C. Morrall Flight measurements of longitudinal stability power-off and power-on made on numerous aircraft have been analysed and a generalised curve for estimating the contribution of slipstream to longitudinal stability, applicable to both flaps-up and flaps-down cases, has been derived. Using this curve the change in stability due to slipstream at a given value of CL can be estimated with a probable error of less than ± 0.02 in the position of the neutral point. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2701.pdf 345. The Flow in an Axially-Symmetric Supersonic Jet from a Nearly-Sonic Orifice into a Vacuum P. L. Owen and C. K. Thornhill The numerical method of characteristics is used to calculate the flow in a steady supersonic jet of air issuing from a slightly supersonic circular orifice into a vacuum. The calculations are entirely numerical, and no recourse is made to graphical methods. The characteristic equations for steady supersonic flow with rotational symmetry are first derived, and then special consideration is given to the flow near the axis of symmetry, where the normal step-by,step numerical process breaks down. In the calculation, the Mach angle in the plane of the orifice is taken as 85 deg to obviate the difficulties of a sonic orifice at which the initial characteristics would be perpendicular to the flow, and the potential equation parabolic. The results should be practically the same as for a sonic orifice. An alternative method of dealing with a sonic boundary-plane would have been the use of analytical solutions for the initial flow in this region (cf. Ref. 3). The results of the calculations are presented in diagrams. The solution is a universal solution in so far that it applies to any similar jet, flowing into any external pressure, in that region bounded by the orifice and the first wave front which registers the existence of an external pressure outside the jet. This fact allows the calculated pressure distribution along the axis of symmetry to be compared with experimental measurements in air jets with finite pressure ratios, and good agreement is obtained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2616.pdf 346. The numerical method of characteristics for hyperbolic problems in three independent variables C. K. Thornhill Introduction and Summary.--Recent advances in electronic computing devices suggest that it may soon be feasible to attempt numerical solutions of problems involving three independent variables. In this paper, preliminary consideration is given to the extension of the numerical method of characteristics for hyperbolic equations to the case of three independent variables. A general quasi-linear second order partial differential equation in three variables is first considered, and the characteristic surfaces and curves are derived, together with the differential relations which hold along them. It is shown that numerical integration should be possible along the faces or edges of a hexahedral grid. The equations are developed in more detail for two special cases of compressible flow, namely steady isentropic supersonic flow in three-dimensional space, and unsteady flow in two dimensions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2615.pdf 347. The physical characteristics of wire resistance strain gauges E. Jones and K. R. Maslen This report deals with the fundamental principles of the wire resistance strain gauge. Types of strain gauge in common use and their methods of construction are described, and the mechanism whereby strain effects change of resistance is discussed. A sub-section is devoted to the behaviour of fine wires, in general, under strain. Possible causes of error, including the effects of humidity and temperature, are discussed, and as far as possible methods are given of overcoming these difficulties. The effect of the passage of current on the strain gauges is described, and methods of increasing the output are suggested. The final section is devoted to miscellaneous properties of the wire resistance strain gauge, on several of which very little information is at present available. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2661.pdf 348. The Royal Aircraft Establishment 4 ft x 3 ft experimental low turbulence wind tunnel. Part 1 general flow characteristics H. B. Squire and K. G. Winter The 4 x 3 ft Wind Tunnel was erected as a model of larger tunnels to investigate unconventional design features directed towards obtaining a high standard of flow. Diffusers of 5 deg cone angle are used, except for the rapid expansion through three wireTgauze screens up to tile maximum section. The contraction ratio is 31.2 : 1 and nine screens are fitted in the maximum section. A speed control is used operating independently of the fan by means of a by-pass duct. The velocity distribution across the working-section is constant to ± ¼ per cent. The standard deviation of the velocity with time measured over a period of 50 sec is 0.03 per cent. The flow in the diffusers shows no tendency to separate and the velocity distribution approaching tile first screen is very satisfactory. The installation of cascades with gap/chord ratio of ¼ gives uniform outlet flow without appreciable increase in the pressure drop. There is no separation in the rapid expansion of the bulge, but the flow in the contraction cone is not satisfactory. A longer contraction would have been advantageous. The power factor has been measured as 0.27 with.all screens fitted but could be improved slightly if all the leaks were sealed. The speed control is satisfactory in operation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2690.pdf 349. The theoretical estimation of power requirements for slot-suction aerofoils, with numerical results for two thick griffith type sections J. H. Preston, N. Gregory, and A. G. Rawcliffe Summary.--This report describes a method for assessing the performance of slot-suction aerofoils in terms of an effective drag coefficient, which takes into account the power requirements of the suction pump neglecting slot entry and duct losses. When the suction-slot is located at a velocity discontinuity the suction flow required to prevent separation can be calculated, using the elementary theory suggested by Sir Geoffrey Taylor. The method is applied to two Griffith type aerofoils (30 per cent and 31.5 per cent thick) and the drags are compared with those of normal thin aerofoils 20 per cent thick. When transition is forward the drags are nearly equal; but when transition is at the slot the drags of the suction aerofoils are very much less than that of a normal thin aerofoil with transition at its most rearward feasible position. The gains afforded by the use of suction near the trailing edge of an aerofoil arise partly from reduction of form drag, and partly from an economy in power when the loss of head in the boundary layer is restored by means of a pump instead of appearing as a loss of momentum in the wake to be overcome by a thrust. Further gains will result if the pump efficiency is greater than the propulsive efficiency. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2577.pdf 350. Theoretical investigations of ternary lifting surface - control surface - trimming tab flutter and derivation of a flutter criterion H. Wittmeyer Theoretical investigations have been made of the flutter of an idealised trimming tab system having three degrees of freedom - normal translation of the main lifting surface, rotation of the control surface and rotation of the tab. All the structural parameters of the system have been varied except the out-of-balance moment of the control surface. The cases in which the system is free from flutter have been particularly investigated. From these investigations criteria for the avoidance of flutter have been derived. If the structural parameters of the system satisfy these criteria, flutter of the system with these three degrees of freedom should be impossible. The resutts are applicable to trimming tabs, servo-tabs with zero follow-up ratio, and generally to all systems in which the tab can be regarded as connected elastically only to the control surface. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2671.pdf 351. Towing tank tests on a large six-engine flying boat seaplane, to specification 10/46 Princess. Part 1 General porpoising stability, trim and spray clearance A.G. Smith, G. L. Fletcher, T. B. Owen and D. F. Wright This report gives the results of the first series of towing tank tests made at the Royal Aircraft Establishment Towing Tank (up to May 1947) on a powered dynamic model of a six-engine transport flying boat, later named the Princess class, and designed to specification 10/46, on the basis of which full-scale hull construction was started; later tests have been made to further improve the hull step and afterbody and test the effect of modifications to the aerodynamic superstructure and power units. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2641.pdf 352. Wind-tunnel tests of the stalling properties of an 8 per cent thick symmetrical section with nose suction through a porous surface R. C. Pankhurst, W. G. Raymer and A. N. Devereux Summary.--The stalling properties of an 8 per cent thick symmetrical aerofoil with large leading-edge radius of curvature and continuous (distributed) suction over the nose have been tested in the 4-ft No. 2 Wind Tunnel of the National Physical Laboratory. It was found that suction postponed the stall to higher angles of incidence by suppressing separation at the leading edge. The suction also produced beneficial effects in delaying transition. Moreover it prevented the development of boundary-layer turbulence behind a single excrescence or spanwise corrugation, provided the suction was applied over a sufficient chordwise extent of the aerofoil surface. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2666.pdf 353. Wind-tunnel tests on a thick suction aerofoil with a single slot M.B. Glauert et al Summary.---This report describes the two-dimensional wind-tunnel \'tests carried out in the National Physical Laboratory 13 × 9 ft wind tunnel on a 31.5 per cent thick suction aerofoil, GLAS-II, which has a single slot on the upper surface at 69 per cent chord. Both suction and blowing were used to prevent separation. Lift, drag, pitching moment, and the flow through the slot were measured. Tests without suction were made at Reynolds numbers of 0.96 and 2.88 millions. The results at the two Reynolds numbers were markedly different, and at the higher speed widely varying values of the drag-coefficient were recorded in the same conditions, there apparently being several possible rdgimes of flow. With suction, the pump power available only enabled tests to be made at the lower Reynolds number, and with the boundary layer on the upper surface laminar to the slot. At low incidences suction quantities agreeing well with theoretical estimates sufficed to maintain unseparated flow, but at higher incidences the flow tended to break down. Three or four times as much suction was required at all incidences to make the separated flow re-adhere. With blowing, still larger quantities were necessary, but the spanwise distribution of the flow from the slot was unsatisfactory. Two different slot shapes were tested on the model, one with a sharp beak to the front lip, the other with a rounded entry. Intermittent separation of the flow occurred in each case. The phenomena may be of a fundamental character and associated with the profile shape rather than with the shape of the slot entry. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2646.pdf 354. Wind-tunnel tests on the 30 per cent symmetrical griffith aerofoil with distributed suction over the nose N. Gregory, W. S. Walker and A. N. Devereux This report describes tests carried out on tile 30 per cent Griffith symmetricM aerofoil with continuous suction applied through a porous capping fitted over tile front 15 per cent of the upper surface. Throughout the range of incidence covered in the experiments, distributed suction was found to decrease the slot suction necessary to prevent separation, especially when the distributed suction caused rearward movement of the transition position. The profile drag of the aerofoil was measured, and estimates were made of the equivalent drag coefficients for the work done by the suction pumps. Assuming no losses additional to those in the boundary layer, it was found that the effect of distributed suction was to reduce slightly the overall drag of the aerofoil. Measurements of the velocity within the boundary layer were made at various chordwise positions on the porous surface; the profiles recorded were very close to the theoretical. Distributed suction was able to delay transition when this would otherwise be precipitated by a ridge on the surface, or by adverse pressure gradients, but a turbulent boundary layer remained turbulent when suction was applied. The characteristic spread of turbulent flow in the wake of a small particle on the surface was much reduced by distributed suction; under favourable conditions, the wake was entirely eliminated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2647.pdf 355. A calculation of the complete downwash in three dimensions due to a rectangular vortex Doris E. Lehrian A calculation of the complete downwash in three dimensions due to a rectangular vortex, is given for the limited range Z = ± 4. The downwash is computed at selected positions, in planes normal to the plane of the vortex; these planes are spaced at even integral multiples of the semi-width of the vortex, measured from the line of symmetry. Values are tabulated for Z in the range (0,4) and a set of graphs is also included for 0 < Z < 2; they are to be used in conjunction with the 'Tables of Complete Downwash due to a Rectangular Vortex' (R. & M. 2461). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2771.pdf 356. A comparison of two methods of calculating wing loading with allowance for compressibility with appendix: note on Falkner's method for calculating compressibility effects on wing loading V. M. Falkner, W. P. Jones The report gives the results of a comparison by two different methods of the aerodynamic loading of a tapered V wing of aspect ratio 5.8 and 45 deg sweepback at M = 0.8, based on the Prandtl-Glauert factor or linear perturbation theory; the first method, associated particularly with vortex-lattice theory, deals with changes in Mach number by preserving the plan of the wing and using special Tables of downwash, while the second uses the solution for Mach number 0 on a wing with the lateral dimensions reduced by a specified factor. The two methods are shown to be in good general agreement at M = 0.8 and, although it can be argued that the second method is more accurate on theoretical grounds, this is offset by the fact that the first has considerable advantages in ease of calculation, and in the possibility of extension to more accurate solutions when the Prandtl-Glauert factor fails at high subsonic speeds. Examples of the application of the theory are also given for a delta wing, for a straight tapered wing without sweep, and for a tapered wing with 28-4 deg sweepback. It is possible to give a general and reasonable explanation of the nature of the variations of load grading and local aerodynamic centre which occur with increasing Mach number, and with the information given, there should be no difficulty in the prediction of Mach number effects on a wide range of plan forms. Since the completion of the work, a mathematical examination of the limitations of the first method has been made by W. P. Jones who has calculated exact values of downwash due to a rectangular vortex over a range of Mach numbers for comparison with those obtained by the approximate formula. His work, which is included as an Appendix, confirms the accuracy of the approximate method at high Mach numbers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2685.pdf 357. A high-speed camera for the photography of shock-wave oscillations in a wind tunnel D. W. Holder et al A camera has been developed which enables oscillations of shock-waves and of other quasi-stationary phenomena in a wind tunnel to be photographed by either the schlieren method or the shadowgraph method at speeds up to 2000 frames per second, and with exposures of the order of 1 microsecond. Photographs of an oscillation which occurs when the critical Mach number is exceeded at low Reynolds number on an EC 1250 aerofoil are included as examples. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2901.pdf 358. A revised index of mathematical tables for compressible flow R. C. Tomlinson This revision of the original 'Index of Mathematical Tables for Compressible Flow' by A. O. L. Atkin (A.R.C. 9893, August, 1946) has been prepared at the request of the Fluid Motion Sub-Committee of the Aeronautical Research Council. It contains information of all the relevant tables known to the author, which can be obtained by workers outside the establishment of origin. The purpose of the index is to make available to workers in the field of compressible flow a reference from which they may trace a tabulation of any function they require, if it exists. It is also hoped that it may help to prevent waste of effort by unnecessary duplication of tables. The first revision of this Index by the present author in June, 1948, showed that there were in existence tabulations of most of the functions required by workers in this field. These tabulations were, however, scattered throughout a large number of reports, some of which were not easily accessible. As a consequence of this, it was often necessary to use an inferior table or do without. Furthermore, there was no guarantee of the accuracy of t~he Various tables, and there was good reason to be suspicious of some of the tables that would have been the most useful if they had been accurate. It was recommended that a book of collected tables should be prepared, and the Compressible Flow Tables Panel of the Aeronautical Research Council was set up to do this. The book together with a companion volume of graphs, is to be published by the Clarendon Press. In preparing for the book a number of mistakes were found in the tables listed in this Index, but no systematic checks were made. There seems little point in listing here the few mistakes found--it is sufficient to offer a warning. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2691.pdf 359. A theoretical examination of the effect of deadrise on wetted area and associated mass in seaplane-water impacts R. J. Monaghan A theoretical examination is made of the deadrise effect on associated mass and wetted area in the two-dimensional impact case (vertical drop of an infinitely long wedge at zero attitude). Available estimates are summarised and a new theoretical formula is developed by means of an expanding prism flow which gives results for associated mass in very close agreement with those given by Wagner's semi-empirical formula (on which most of the estimates of three-dimensional associated mass have so far been based). In addition the new treatment gives a formula for wetted area which is not available from Wagner's treatment except for very small values of deadrise angle. Comparison is made between these and other formulae in the light both of theory and experiment and a brief survey is made (in Appendix I) of the assumptions involved in applying associated mass methods to motions through a free surface. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2681.pdf 360. Abstracts of papers published externally
CONTENTS: Spring Tabs on Frise Ailerons. Why Shear Webs? A Boundary Value Problem for a Hyperbolic Differential Equation Arising in the Theory of the Non-uniform Supersonic Motion of an Aerofoil. A Study by a Double-refraction Method of the Development of Turbulence in a Long Circular Tube. Notes on the Linearised Equation for the Velocity Potential of the Supersonic Flow of a Compressible Fluid. Technique of tile Step-by-Step Integration of Ordinary Differential Equations. Control Reversal Effects on Sweptback Wings. The Radial Focusing Effect in Axially-symmetrical Supersonic Flow. On Source and Vortex Distributions in the Linearised Theory of Steady Supersonic Flow. Assessment of Errors in Approximate Solutions of Differential Equations. Notes on the Linear Theory of Incompressible Flow Round Symmetrical Sweptback Wings at Zero Lift. Flutter of Systems with Many Freedoms. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2565.pdf 361. An approximate solution of the compressible laminar boundary layer on a flat plate R. J. Monaghan Following a major assumption that enthalpy and velocity are dependent only on local conditions, an enthalpy-velocity relation ... is obtained for the laminar boundary layer on a flat plate where subscripts p refer to the plate, 1 to the free stream and e to the equilibrium temperature condition at the plate. When compared with general results, this relation (exact for Prandtl number a = 1) gives a close approximation to Crocco's numerical results for a = 0.725 and 1.25, up to u/us = 0.8. Using the above relation in conjunction with the approximate viscosity-temperature relation suggested by Chapman and Rubesin, and with Young's suggested first approximation for shearing stress it is shown that close approximations to displacement thickness and velocity distribution are given by ... These have the advantage of being algebraic in form whereas previous results have involved complex numerical integrations for individual cases. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2760.pdf 362. An electric tank for the determination of theoretical velocity distributions T. J. Hargest An analogy due to Relf has been applied to the design of apparatus for quickly determining the theoretical velocity distributions around an aerofoil in cascade. The accuracy of the apparatus was tested By determining the velocity distribution around a cylinder. An accuracy of within 1 per cent of the approach velocity was obtained for this case. The apparatus has since been applied to determine the theoretical velocity distribution around various aerofoils in cascades; an example is given of the pressure distribution around an aerofoil at zero incidence. An application to determine the theoretical velocity distribution around the central aerofoil of a nozzle cascade where the effect of the ducting side wails is included, is also given. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2699.pdf 363. An experimental investigation of the flow through a helicopter rotor in forward flight P. Brotherhood and W. Stewart Experiments have been made to determine the flow conditions through a helicopter rotor in forward flight using the smoke filament technique. This method consisted of flying the helicopter behind an aircraft from which smoke generators were suspended on a long wire. The smoke trails passed through the main rotor of the helicopter, and photographs were taken from another aircraft in a side position. Flow conditions at the rotor disc over a narrow bend on the side of the advancing blade were investigated in this way. The range of speeds covered was from 44 m.p.h. to 60 m.p.h, corresponding to a range of tip speed ratios 0.138 to 0.188. An increase in induced velocity from front to rear of the rotor disc was obtained. The results are in reasonable agreement with theoretical predictions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2734.pdf 364. An experimental study of three-dimensional high-speed air conditions in a cascade of axial-flow compressor blades K. W. Todd Detailed investigations have been made by optical and physical methods in a high-speed wind tunnel of the flow characteristics of two compressor blade cascades. In Part 1 a representative high-camber cascade was examined at zero incidence over entry air velocities ranging from low to critical. Traverses were made of discharge angles and wake losses at all heights so that a relation between two and three-dimensional losses could be obtained. Some records were also made of the nature of the vortices induced in the discharge flow. In Part 2 the blade and passage designwas conditioned by the findings of Part 1, with the aim of so modifying the cascade that its efficiency in the critical flow region would be improved. Optical and physical examinations were again carried out over a range of both incidence and velocity. The results from Part 1 indicate that although fully developed shock formations can be used to bring about reduction in profile drag, the net performance of a conventional cascade is prohibitively low when shock occurs, by reason of the shock losses themselves. The results from Part 2 show that by delaying the advent of shock, and by reducing its intensity and complexity, an improvement in high-speed performance can be achieved, although at a somewhat limited incidence range. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2792.pdf 365. Choking effects and some reynolds number effects on the mach number distribution round a two-dimensional aerofoil in the RAE 10-ft x 7-ft high-speed tunnel D. A. Clarke, and H. E. Gamble A two-dimensional aerofoil of NACA 0015 section was tested at zero incidence in the Royal Aircraft Establishment 10 ft x 7 ft High-speed Wind Tunnel and measurements were made of (a) Static pressure on the aerofoil surface at Reynolds numbers of 1.4 x 10power6 to 5.5 x 10power6 (b) Static pressure on the aerofoil surface, on the tunnel walls and in the stream between the aerofoil and the walls at R = 2.8 x 10power6. All the tests were made at Mach numbers of 0.7 upwards and were continued past the choking Mach number of 0.764 until either the maximum permissible fan speed was reached or the maximum available power was being used. The results showed that the choking Mach number was about 0.764 at Reynolds numbers from 1.4 x 10power6 to 2.8 x 10power6. Above M = 0.760 the development of the supersonic region towards the walls was extremely rapid in terms of tunnel Mach number. At M = 0.761 the sonic line was only about half-way out to the tunnel walls and at M = 0.764 it had reached them. Before and during choking quite large changes in the aerofoil pressure distributions were produced by varying the Reynolds number. At M = 0.73 and 0.75 the shape of the pressure distribution curves indicated the possibility of a λ-shock at the lower Reynolds numbers and a single shock at the higher Reynolds numbers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2912.pdf 366. Corrections to velocity for wall constraint in any 10 x 7 rectangular subsonic wind tunnel J. Y. G. Evans The validity and accuracy of method's of determining corrections to the measured velocity in a wind tunnel to compensate for the constraining effect of the wails are reviewed following recent experimental evidence from the R.A.E. 10 x 7 ft subsonic wind tunnel. It is concluded that such corrections, commonly known as 'blockage' corrections, can be successfully applied at Mach numbers up to 0.96 but some modifications are necessary to the formulae at present in use. The more important of these are outlined below. (1) The compressibility factor should be based on the corrected Mach number of the stream. (2) The ratio of 'solid' blockage (i.e., the blockage due to model excluding wake) to the peak wall velocity increment is not constant but depends on the length of the model and the Mach number of the stream. (3) The calculated solid blockage of a wing must be increased to allow for the presence of local supersonic flow. For wings of usual plan form, this may be done by an empirical factor which is a function of the rise in drag coefficient. (4) Addition of corner fillets to the tunnel gives rise to a larger percentage increase of the solid blockage than of the wall velocity increments. Formulae for the calculation of the longitudinal distribution of blockage increment due to any model, necessary to check the validity of the method in particular cases, are presented in a form which, it is hoped, will facilitate their use in any 10 x 7 wind tunnel. Formulae for the corresponding wall velocity increments, used to check the accuracy of the method by comparison with measured wail pressures, are also given. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2662.pdf 367. Critical Mach numbers for thin untapered swept wings at zero incidence S. Neumark In this paper, which is a continuation of two earlier ones (R. & M.'s 2713 & 2717), the subsonic flow past untapered swept wings, at zero incidence, is further investigated using linear theory. Methods for calculating 'lower' and 'upper' critical Mach numbers are given, the solution of the main problem being preceded by a short analysis of critical Mach numbers for the simpler cases of infinite wings (straight, sheared and yawed). The determination of critical Mach numbers depends on the knowledge of velocity distribution over the wing surface, the problem dealt with in the previous reports mostly for the case of the simple biconvex parabolic profile. These earlier results have been extended here to cover a wide class of profiles. Hence it has been possible to determine critical Mach numbers for wings with four different profiles, showing the effect of thickness ratio and of angle of sweep-back (or sweep-forward) in each case. The method applies strictly to wings of large aspect ratio, but no significant corrections are necessary except for very low aspect ratios. The results and examples, illustrated by a number of tables and graphs, provide a basis for more general discussion. Several conclusions concerning the practical use of swept-wing design are presented. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2821.pdf 368. Downwash measurements behind a 12-ft diameter helicopter rotor in the 24-ft wind tunnel R. A. Fail and R. C. W. Eyre Some measurements of downwash have been made in a plane behind a 12-ft diameter helicopter rotor over a range of shaft inclination and tip speed ratio. In the various operating conditions, the tunnel tests are in reasonable agreement with the theoretical results for the appropriate type of loading. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2810.pdf 369. Effects of rate and duration of loading on the strength of aircraft structures K. D. Raithby The effects of rate and duration of loading on the structural strength of aircraft have been investigated by comparing the failing loads of both wooden and metal tailplanes when tested at different rates of loading, the duration of test varying from about 6 seconds to 3¾ hours. With wooden structures, differences in strength due to rate of loading were much less than those predicted from the results of American tests on wood. With metal structures neither rate of loading nor sustained high loading had any appreciable effect on the failing load. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2736.pdf 370. Elasticity of a sheet reinforced by stringers and skew ribs, with applications to swept wings E. H. Mansfield A rigorous theory has been developed for determining the stresses and displacements in a sheet reinforced by stringers and ribs which are not at right-angles to the stringers. The solution of many problems of practical importance has been facilitated by the introduction of a stress function. The theory has been applied to a cylinder oI rectangular section stiffened with such skew ribs (a simplified representation of a swept wing). It is shown that there are axes about which applied moments produce pure twist or pure curvature of the cylinder. There are simple formulae for determining these axes and the relationships between twist and curvature and the applied moments. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2758.pdf 371. Flow through a helicopter rotor in vertical descent P. Brotherhood Flight tests have been made on a Hoverfly I helicopter to investigate the types of flow associated with various rates of vertical descent. At the same time measurements of the performance were made. The results are analysed by two different methods to produce characteristic curves for the rotor and are compared with data obtained from wind tunnel tests on model propellers at negative rates of advance. The information was obtained from the Hoverfly I helicopter but it is thought that the results can be applied to any other helicopter of similar size. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2735.pdf 372. Flutter problems of high-speed aircraft E. G. Broadbent The flutter problems of high-speed aircraft are considered generally and specific consideration is then given to the new problems introduced by the use of new wing plan forms. The theoretical and experimental results on the coupled ('classical') symmetrical flutter of swept (including 'barbed' and cranked forms) and delta wings is reviewed and presented to show the effect and importance of the body freedoms of the aircraft on the critical flutter speed and frequency. A criterion is proposed for deciding the 'dangerous type' of fundamental normal mode to be considered in flutter calculations. The danger here is that the fundamental normal mode can combine with the body freedoms and give rise to a form of flutter which is independent of the wing torsional stiffness. It is suggested that the deciding feature is the shape of the nodal line in the fundamental mode. If it is such as to indicate rotation of the fore-and-aft wing sections near the tip, then the mode is considered to be dangerous. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2828.pdf 373. Formulae for estimating the forces in seaplane-water impacts without rotation or chine immersion R. J. Monaghan, and P. R. Crewe This report presents formulae and curves for estimating the maximum forces, together with the times and drafts associated with these forces, in main-step landings of seaplanes, provided that there is no rotation and that the chines do not become immersed. It also compares the values estimated by these formulae with the results of model tests made by the N.A.C.A. under controlled conditions in their Impact Basin, when good agreement is found. The basic formulae and curves given are considered to be the simplest and most accurate which can be evolved at present from the many proposed in various reports in recent years and reviewed in R. & M. 2720. They involve the use of a new basic 'impact parameter' and a new estimate for associated mass, which is based on three- rather than on two-dimensional concepts. It was convenient to split the report into two parts. Part I contains a statement of the formulae recommended for use in design estimates, together with numerical examples. Part II contains the comparison with experimental data. A simplified theoretical treatment and all mathematical details relevant to both parts is given in Appendix I. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2804.pdf 374. Interim report on V-g records on helicopters H. I. Birds V-g records have been obtained during the past year on Hoverfly I helicopters. Some data have also been obtained on a Hoverfly II and a Sikorsky S.51. The V-g records on these aircraft were obtained mainly during test flying, which included blind flying and some general flying. It was not possible to separate the flight accelerations from the landing accelerations, but these were small except in the case-of engine-off landings which were the subject of separate tests. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2746.pdf 375. Low-speed measurements of the pressure distribution at the surface of a swept-back wing V. M. Falkner, and Doris E. Lehrian Low-speed measurements of the pressure distribution have been made at selected stations on a swept-back wing with and without body. The wing was of 45 deg sweep-back, with a sharp discontinuity at the centre-section, and of aspect ratio 3 with uniform chord. The aerofoil section was chosen to be suitable for work at low Reynolds number, and the wing plan to be of the maximum utility for comparison of observed and calculated pressure distribution. The work is the first part of a programme designed to give results of the greatest assistance to the development of mathematical methods, and the model was of exceptionally clean design to avoid extraneous effects. The symmetry of the model allowed the work to be duplicated by coveIing a range of positive and negative incidences, and by averaging, it has been possible to remove zero irregularities due to wind-tunnel flow and present accurate values of pressure distribution, distribution of local lift coefficient and centre of pressure of normal force for a range of incidence 0 to 16 degrees. Wind-tunnel balance measurements of overall lift appear to be in reasonable agreement with the pressure plots. A selection of chordwise pressure distributions is plotted and it is shown that at zero lift for the wing along there is good agreement with curves calculated at the Royal Aircraft Establishment. A comparison of a potential solution for load grading and local aerodynamic chord with the wind-tunnel measurements at finite lift shows approximately the variation due to the effects of wing thickness and viscosity. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2741.pdf 376. Measurements of the aerodynamic derivatives for a horn-balanced elevator N. C. Lambourne, A. Chinneck and D. B. Betts This report gives the results of measurements by a forced oscillation method of the direct derivatives (aerodynalaic stiffness and damping) for a horn-balanced elevator. The tests were made at low airspeeds on a complete wing-fuselage-tail model at 0 deg and 10 deg incidence in a wind tunnel. Some information was obtained on the effect of mean elevator angle on the derivatives when the model was at the high incidence. Measurements were also made with trailing-edge cords and transition wires in position. The experiments suggest that none of the above factors causes a reduction in damping, but the stiffness derivative was found to be considerably influenced by the elevator angle and by the presence ot trailing-edge cords and transition wires. In general the measured values are numerically considerably less than those calculated by simple strip theory using two-dimensional vortex sheet theory results. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2653.pdf 377. Note on the application of Thwaites' numerical method for the design of cambered aerofoils A. R. Curtis Some minor developments ill the technique of Thwaites' Numerical Method of Aerofoil Design I are described. In particular, the process of obtaining the camber-line ordinates from the Goldstein Approximation I velocity distribution is discussed in detail; the relevant tables of constants are given. An opportunity is taken to include a complete set of 20-point tables of Conjugation Factors needed in any actual application of the Numerical Methods. The theory underlying these tables is given by Watson in R. & M. 2716. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2665.pdf 378. Notes on helicopter rotor behaviour after engine failure in hovering flight W. Stewart, and G. J. Sissingh Calculations have been made of the changes in rotor speed following engine failure on a typical helicopter in hovering flight. Various time functions for the collective pitch operation are considered. The results are in excellent agreement with the one recorded case of an actual power failure in hovering flight. Rapid pilot action in reducing the collective pitch after engine failure is essential to prevent dangerously low rotational speed of the blades. The possibilities of automatic pitch reduction or of a power failure warning to the pilot are considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2659.pdf 379. Notes on the dynamic response of an aircraft to gusts and on the variation of gust velocity along the flight path with special reference to measurements made in Lancaster P.D. 119 Anne Burns A collection of records showing the time histories of strains and accelerations at various parts of a Lancaster flying in turbulent air is presented and discussed. The records include specimens taken in cloud at moderate altitudes and in clear air at low altitudes. Two points of interest regarding the response of the aircraft to gusts are brought to light :- (i) The amount of fundamental oscillation excited by a gust appears to be affected to a marked extent by the variation of gust velocity across the span. (ii) The amount of oscillation excited does not appear to show any marked decrease as the airspeed of the aircraft is increased. Some decrease in the oscillation excited might be expected due to increase in aerodynamic damping. An attempt is made to deduce the variation of gust velocity along the flight path from the measured response of the aircraft. The results indicate that a large up-gust is often closely followed by a large down-gust and vice versa. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2759.pdf 380. Notes on the transonic movement of wing aerodynamic centre S. B. Gates These notes aim at providing a framework to display what is known of the backward movement of the aerodynamic centre of wing shapes likely to be used for transonic operation, as the flow progresses from incompressible through subsonic to supersonic, the shock-wave regime being ignored. A new geometrical parameter (see Figs. 1, 2) is taken as the main variable because (a) it gives a neat classification of the various wing shapes, (b) it expresses the results of supersonic theory in a simple form, (c) it simplifies the subsonic analysis by making direct use of the similarity law for three-dimensional compressible flow, and so (d) it is possible to display on one diagram most of the theoretical and experimental data at present available. On the supersonic side, where very little experimental data is known in this country, the analysis is based on the conical solution by Puckett and Stewart for pointed tips; this has been extended on a simple but questionable assumption to cover blunt tips. On the subsonic side the laborious approximate theoretical methods have not yet yielded much data that is both systematic and reliable, and though model data is accumulating it inevitably lacks cohesion except in the case of delta wings. The work of R. T. Jones on the aerodynamic centre of shapes so slender that it is independent of Mach number is linked up, so far as it goes, with the supersonic data, and should be extended. When the existing fragments of the subject are assembled within this framework as in Table 1 and Fig. 13, the problem begins to get into focus and certain general trends are broadly discernible, but no very definite conclusions can be drawn except for pointed tips in general and delta wings in particular. These summaries do however show what will be the most profitable lines of research to illuminate quickly the whole subject, and recommendations are made to this end (see conclusions, section 9). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2785.pdf 381. Polymethyl methacrylate (perspex type) plastics; crazing, thermal and mechanical properties H. Warburton Hall and E. W. Russell The report summarises the more practical aspects of the results of a long-term investigation of the basic physical and chemical properties of polymethyl methacrylate ('Perspex' type) plastic. Thermal, elastic, crazing, solvent absorption and mechanical properties are included and the effect of these on the service efficiency of a plastic structure is described. Experimental evidence is given concerning the essential role of tensile stress and absorbed solvent in causing crazing and recommendations concerning means to reduce or avoid the incidence of crazing are included. The basic thermal properties are compared with those of metals and the dangers of differential expansion in combined metal-plastic structures are noted, together with the serious effects of chilling of plastic structures during the 'hot-forming' operation. Details are given of appropriate heat treatments designed to remove casting and workshop strains without causing distortion. The elastic behaviour of the plastic is explained on the basis of its long chain-like molecular structure and the change from a rigid glass-like type of mechanical behavionr to that of a rubber-like material with rise of temperature, such as in the hot-forming process, is described. The various strain components produced by mechanical stress, namely the instantaneously reversible, the long-range reversible 'creep' type and the irreversible 'viscous' type are examined. The low degree of 'permanent set' obtained even at hot-forming temperatures is explained. Tensile, impact and flexural strengths, together with the effects of temperature, notch sensitivity, solvent and crazing on them, are given in detail. References to the original reports of the investigations summarised are included in the text. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2764.pdf 382. Pressure plotting and balance measurements in the high speed wind tunnel on a half-model of a 90-deg-apex delta wing with fuselage A. C. S. Pindar, and J. R. Collingbourne Tests were made at a Reynolds number of 1.8 x 10power6 and Mach numbers up to 0.93. The wing tip was cropped to a taper of 1/7 and the wing section was RAE 102, symmetrical, 10 per cent thickness/chord at 35 per cent chord. Form drag is highly localised near the root at low speed. Above M = 0.88, rearward movement of the strong shock causes a rapid rise of drag at all sections. Spanwise loading at low incidence is close to potential theory for wing without body up to M = 0.9. A tip stall occurs at M > 0.9 for α = 3.65 deg and at M > 0.8 for α= 7.7 deg, and causes a nose-down moment. Overall lift slope at low CL's increases to a maximum at about M = 0.89, then falls off with signs of a recovery at M = 0.92. Local aerodynamic centres at low CL agree with potential theory for wing alone at low speeds, but move backwards beyond M = 0.8. The overall aerodynamic centre for the wing moves back about 10 per cent mean chord by M = 0.92. There is a loss of elevon power for angles up to - 5 deg above M = 0.92, as found on a complete model at lower Reynolds number. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2844.pdf 383. Records of major strength tests P. B. Walker The strength attained in major strength tests, made over a period of ten years, is given for twenty-four wing systems and ten fuselages. A preliminary analysis is also presented from the standpoints of safety and design efficiency. One third of all the wing systems tested are found to be seriously understrength as originally designed, and it is concluded that wing and fuselage testing for all new types is essential for safety. The majority of understrength aircraft, however, were brought up to the required standard by local strengthening, and it is concluded that this has an important bearing on design efficiency. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2790.pdf 384. Schlieren tests on some conventional turbine cascades J. A. Dunsby Schlieren tests on a series of conventionM turbine cascades have shown that the variations in performance at high speed can be accounted for by shock-wave and boundary-layer interaction. The rise in loss coefficient sometimes encountered at outlet Mach numbers of 0-6 to 0.8 is shown to be due to the formation of a λ-shock series on the upper surface of the blade, the subsequent fall in loss coefficient and increase in deflection as the outlet Mach number rises to unity being caused by the formation Of a shock system at outlet which forces the separated part of the boundary layer back on to the blade Surface. It is shown that a λ-shock series may form on a boundary layer which is apparently turbulent. This has not been observed before. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2728.pdf 385. Some high-speed tests on turbine cascades E. A. Bridle High-speed wind-tunnel tests on seven cascades of turbine blades are described, the blades having conventional sections including both reaction and impulse designs. The two-dimensional performance over wide ranges of incidence at Mach numbers up to 1.0 is discussed, special importance being attached to the effects of compressibility. It is shown that the effect of increasing the degree of reaction is to reduce the total-head loss and to increase the unstalled incidence range. High Mach numbers alone are not found to cause a catastrophic increase in loss with these particular blade designs, while the cos -1 throat/pitch rule is found to be approximately true only at high Mach numbers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2697.pdf 386. Some related oscillation problems W. J. Duncan Two simple means for establishing a relation between a pair of oscillation problems are briefly discussed. In the first, the displacements are connected by use of a differential operator. The set of natural frequencies is identical for the two problems and results of interest are obtained when the transformed boundary conditions can be physically interpreted. In this manner it is shown, for example, that a flywheel on a uniform shaft can be transformed into a flexible coupling and a mass carried on a uniform beam into a flexible hinge. In the second, the connection is established by use of the concept of mechanical admittance. Here the frequency equations are simply related but the frequencies are not. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2707.pdf 387. Stresses in built-up beams due to an abrupt change in shear stress at a loading station J. Taylor Owing to the abrupt change in shear stress at loading sections of beams there is a concentration of direct stress in the outer fibres of the beam near the loading section. A method of calculating this concentration is described. The highest stress concentrations occur in short deep beams and are greater for wooden than metal beams. The method is applied to the spars of two wooden aircraft and stress concentrations 1.06 and 1.4 are found at the fuselage attachments. Strain measurements were made at positions on a wooden beam under load and the theoretical predictions verified. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2775.pdf 388. Tests related to the effect of profile shape and camberline on compressor cascade performance S. J. Andrews Cascade tests have been made to obtain information on the related questions of whether simpler sections than the normal aerofoil C4 can be used without loss o~ efficiency, and whether a particular section should be constructed on a circular-arc or a parabolic-arc camber-line. Of the large possible number of simple shapes, three only were chosen for comparison with the aerofoil. They were a flat plate with rounded leading and trailing edges, a flat plate with sharpened leading and trailing edges, and an approximately biconvex shape. A representative cascade shape was chosen (blade inlet angle 55 deg, outlet angle 30 deg, and pitch/chord ratio 0.75) and four cascades with the four sections mentioned above mounted on circular-arc camber-lines were made up. In addition, to provide data on the relative advantage of circular-arc and parabolic-arc camber-line, two cascades were made up on parabolic-arcs. The main conclusions to be drawn are that the approximately biconvex profile, which is a very simple shape to make, is superior to the aerofoil at Mach numbers above 0.75, and that the circular-arc camber-line is on the whole superior to the parabolic-arc. The 'plate' blades with blunt leading and trailing edges are poor in performance, but the 'plate with sharpened edges' is reasonably good. It is suggested that very thin blades of the 'plate' type may have certain applications. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2743.pdf 389. The 9 x 3 in. induced-flow high-speed wind tunnel at the national physical laboratory D. W. Holder and R. J. North A 9 X 3 in. high-speed wind tunnel driven by a compressed-air injector has been built in the Aerodynamics Division of the National Physical Laboratory. The tunnel operates at roughly atmospheric stagnation pressure and has so far been used to give Mach numbers up to 1.8. The general arrangement of the tunnel and the preliminary calibration, which is generally satisfactory, are described. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2781.pdf 390. The buckling in compression of panels with square top-hat section stringers W. S. Hemp, and K. H. Griffin A simplified panel model is described, together with a number of assumptions about the mode of its buckling. The approach to the calculation of the buckling stress is by splitting the panel into a number of flat plates and treating these by the ordinary plate theory. Use of the boundary conditions between these plates leads to a relation between the buckling stress and the variables of the panel geometry. The results thus obtained are compared with two sets of recent experimental work; and an appendix is included to show the effect of initial panel irregularities on the experimental determination of buckling stresses. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2635.pdf 391. The calculation of lift taking account of the boundary layer J. H. Preston The purpose of this paper is to fred a sound approach to the problem of the theoretical prediction of sectional characteristics taking account of the boundary layer. Attention is mainly concentrated on the lift, since it is on the accuracy of this calculation that the accuracy of calculations for other characteristics such as pressure distribution and moments must depend. Calculations of the lift and of the velocity at the edge of the boundary layer near tile trailing edge have been made for two dissimilar symmetrical aerofoils at an incidence of 6 deg, using boundary-layer data taken from experiment. The method of calculation satisfies the fundamental theorem that no net vorticity is discharged into tile wake at the trailing edge and in contrast to tile earlier calculations of R. & M. 1996, full account is now taken of the effect of the boundary layer on the velocity field outside tile boundary layer, so that the empiricism of that report is avoided. The present calculations harmonise the two different methods of approach which have been used in the past, namely, the one in which the loss of lift below the Joukowski value was attributed entirely to the incidence and camber effects of the boundary layer, and the other in which the vorticity theorem was satisfied, but boundary-layer camber effects were ignored. The main conclusions are as follows :--The calculated values of the lift and the velocity at the edge of the boundary layer at the trailing edge are in satisfactory agreement with experiment. Incidence and camber effects of the boundary layer account for a large proportion of the loss of lift, which is much greater for the Piercy 1240 aerofoil (trailing edge angle 22.15 deg) than for the cusped Joukowski aerofoil. Curvature effects may be important near the trailing edge. Prediction of the other characteristics such as pressure distribution and moments should be possible, but the work involved will be considerable. Given a satisfactory method of computing the details of tile turbulent boundary layer up to the separation position, prediction of scale effects and Mach number effects on sectional characteristics below the stall should also be possible, using the methods of this paper in conjunction with an iterative process. More boundary-layer explorations should be undertaken in the neighbourhood of the trailing edge of large chord aerofoils with zero and finite trailing-edge angles. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2725.pdf 392. The elastic stability of sandwich plates J. H. Hunter-Tod This paper treats the elastic stability of supported rectangular plates of sandwich construction with isotropic and aeolotropic fillings under compression and shear loading. Formulae are developed for critical stresses for flat and curved panels in compression and flat panels in shear for the buckling of the whole panel, also for the wrinkling or local failure of the faces of flat panels in compression. It is established that for a wide range of conditions the critical stress for panels buckling in compression is independent of the form of the filling providing it is symmetrical about the normal; of the elastic constants of the filling only the transverse shear is of concern. As a result a simple extension of the equivalent plate theory of greatly improved accuracy is developed enabling the use of equations treating the plate as a whole. NOTE: This paper was presented as a thesis for the Diploma of the College of Aeronautics, June 1948. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2778.pdf 393. The improvement in pressure recovery in supersonic wind tunnels H. Eggink The inefficient pressure recovery of present day supersonic wind tunnels, which leads to high costs of plant installation and operation, is discussed and methods of improvement suggested. In particular, the diffuser system, where most of the losses occur, is studied in detail ; the improvement to be expected in the pressure recovery by the use of convergent-divergent types is explained and methods of overcoming the necessity for high starting powers with this arrangement are presented. Diffuser experiments based on recent investigations into breakaway phenomena in supersonic flow are described which result in a considerable improvement of pressure recovery. A deceleration from M = 2.48 at the working section to M = 1.42 at the diffuser throat was obtained using a variable diffuser throat. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2703.pdf 394. The initial buckling of a long and slightly bowed panel under combined shear and normal pressure E. H. Brown and H. G. Hopkins Recent American experimental work has suggested that the resistance to buckling of wing skin panels under compression or shear loads is improved by aerodynamic suction. A complete theoretical analysis of this problem is very difficult, because compression load necessarily involves the consideration of post-buckling behaviour. An approach is made in this report by considering the restricted problem of the initial buckling of a long, thin and slightly bowed panel under combined shear and normal pressure. The theoretical values of the initial shear buckling stress, which agree well with American experimental values increase with both pressure and curvature; the wavelength of the buckles also increases with pressure, but decreases with curvature. The difference between the buckling stresses for simply supported and clamped edges is considerable for a flat panel under shear alone but decreases rapidly with curvature and pressure, thus making the indeterminacy of practical edge conditions of less importance. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2766.pdf 395. The loss in climb performance, relative to the optimum, arising from the use of a practical climb technique K. J. Lush A practical climb technique will not in general comply with the condition for optimum climb performance and will give an inferior climb. An assessment of the loss of performance involved is, therefore, desirable. A practical climb technique is considered which is defined by a fixed relation between equivalent air speed (or Mach number) and pressure altitude, and a rough estimate made of the loss in performance involved in using such a technique with a turbine jet aircraft over a range of air temperature, engine speed, thrust, or aircraft weight. An approximate method of calculating a suitable relation is given in an Appendix. If the technique for optimum climb is not fixed by compressibility effects, use of such a practical climb technique will result in a loss of performance, relative to the optimum, less than the greater of 1 per cent and ½ ft/sec in rate of climb over a wide range of aircraft weight or a moderate range of air temperature, engine speed or thrust. Approximate limits are quoted in Table 2. More precise limits may be estimated for any particular aircraft. If the technique for optimum climb is determined by compressibility effects such a practical climb technique can give optimum performance over a wide range of weight, air temperature and engine speed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2756.pdf 396. The measurement of the overall drag of an aircraft at High Mach Numbers D. J. Higton, R. H. Plascott, and D. A. Clarke This report describes the technique which has been developed to measure the overall drag of an aircraft at high Mach numbers in both level flight and dives. It shows how improvements have been made both in flight and tunnel technique so that comparisons between full-scale and model tests have now become possible. Flight results from Meteor IV aircraft show close agreement between drag measured in level flight and in dives and later tests compare well with high-speed wind-tunnel measurements on a 1/12th scale model. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2748.pdf 397. The numerical solution of two-dimensional fluid motion in the neighbourhood of stagnation points and sharp corners L. C. Woods Methods are given in this paper of dealing with singularities of functions satisfying certain two dimensional partial differential equations. For a numerical solution the differential equations are replaced by difference equations on a square mesh. Log (I/q) where q is the Velocity, becomes infinite at stagnation points, sharp corners, sinks, etc., while the conjugate function 0 (flow direction) becomes multi-valued. The method consists in finding a series expansion for the function (log 1/q or 0) in the neighbourhood of the singularity. This expansion is then used to find relationships between the function values at points of the mesh adjacent to the singularity. A method of working directly in the transformed flow plane (in which the aerofoil is a slit), and thus avoiding irregular squares on the boundary, is also given. The method is developed for incompressible flow, but an approximation suitable for compressible flow is given. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2726.pdf 398. The pressure distribution, at supersonic speeds and zero lift, on some swept-back wings having symmetrical sections with rounded leading edges G. M. Roper Formulae are found for the pressure distribution at supersonic speeds and at zero incidence for certain symmetrical surfaces of small finite thickness, with swept-back leading edges, the surfaces being set symmetrically to the wind direction. The solutions are only valid if the surfaces lie wholly within the Mach cone of the apex. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2700.pdf 399. The scope and accuracy of vortex lattice theory V. M. Falkner The report gives an outline of the development of the principles on which potential problems in lifting plane theory are solved by the use of a vortex lattice for the purpose of computing downwash. The conditions of convergence necessary for an accurate solution are defined, and the main purpose of the report is to show that those connected with the lattice have been, or can easily be satisfied. Published solutions by this method have been mainly concerned with spanwise load grading and local aerodynamic centre and examples are given here of earlier checks on accuracy for rectangular and triangular wings, and a yawed infinite wing, based either on an alteration of the lattice spacing or on comparison with downwash obtained by surface integrals. The study of accuracy is now advanced by a comparison based on exact values calculated from surface integrals given by W. P. Jones, and applied to a rectangular and a sweptback wing. The downwashes obtained from the lattice are shown to converge to the exact values, but by a comparison of two solutions for the sweptback wing it is shown that the beneficial coupling effect of the lattice makes it unnecessary to obtain individual downwash values to great accuracy, at least for spanwise load grading and aerodynamic centre calculations. Trial calculations reveal that there would be no difficulty in extending the convergence to detailed pressure distribution or other properties of any thin wing, but it is desirable to give prior attention to the main effects of wing thickness and viscosity. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2740.pdf 400. The simple harmonic motion of a helicopter rotor with hinged blades J. K. Zbrozek In simple harmonic oscillation of the helicopter with hinged blades, the tip-path plane is tilted with respect to the shaft in the plane of oscillation and in the plane perpendicular to it. The angles of tilt can be expressed as functions of angular velocity and acceleration. The influence of the acceleration term on the dynamic stability of the helicopter is small. The expressions for angles of tilt due to angular velocity can be simplified to the expressions obtained in previous work under assumptions of quasi-static conditions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2813.pdf 401. The use of tensor notation to develop characteristic equations of supersonic flow C. N. H. Lock, and R. C. Tomlinson The general equations of the steady motion of a non-viscous fluid are given in tensor notation. It is then assumed that one family of co-ordinate surfaces are characteristic surfaces, i.e., surfaces on which the transverse derivatives of the flow-variables are not determined by their values on the surface itself. The condition for this is given by the relation which can be interpreted to give the well-known result that the velocity normal to the surface is sonic. The relation which must then hold between the variables on the surface itself is also determined (characteristic equation). The special cases of axisymmetric and two-dimensional flow are also considered and the results interpreted to give the well-known relationships. As an example, the flow in a simple wave, i.e., a flow in which one fatuity of characteristic lines are straight, is treated in detail. While no new results have been obtained, the authors feel that the extra simplicity resulting from the use of quite general co-ordinates gives a deeper insight into the behaviour of such flows. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2632.pdf 402. Theoretical calculations of the distribution of aerodynamic loading on a delta wing H. C. Garner Summary.--The distribution of velocity potential difference has been calculated for a thin flat plate in the form of a delta wing at small incidence. The method introduces novel functions with 10 arbitrary constants to expless the doublet distribution over the wing and a special numerical integration to evaluate the downwash at 10 chosen points on the surface. Three different forms of the doublet distribution (a), (b) and (c) are employed and lead to three independent solutions of the resulting simultaneous equations ; solution (c) is considered to be the most accurate. The plan form selected for this investigation is that of a delta wing, of aspect ratio 3, shown in Fig. 1. One object of the laborious calculations is to form the first step towards a fundamental comparison with pressure distributions measured on a model of the wing in the National Physical Laboratory Duplex Wind Tunnel. Solution (c) has been compared with two solutions of the identical problem by vortex-lattice theory as given in R. & M. 2596, Tables 37 and 38 (Falkner, 1948), using respectively 6 and 8 simultaneous equations, viz., solutions 33 and 34 of which the latter involves an auxiliary function P to allow for discontinuities at the median section. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2819.pdf 403. Two-dimensional aerofoil design in compressible flow L. C. Woods This paper deals with the following two-dimensional problem:-- 'The design of an aerofoil to give a specified velocity against chord curve at a given free-stream Mach number.' A 'relaxation' method is adopted, based on the differential equations for incompressible and compressible flow. An essential feature of the method is that the calculations are carried out in the (φ, ψ) or w-plane, in which the aerofoil is represented by a slit along ψ = 0. The square mesh in this plane is formed by the streamlines (ψ = constant), and equipotentials (φ = constant) for incompressible flow about the aerofoil. The method is developed for a symmetrical aerofoil at zero incidence, but the modifications necessary for the more general case are indicated. A worked example is given, from which some idea of the accuracy of the method can be gained. The compressible velocity distribution about a known aerofoil was taken as the initial data. This aerofoil was actually 12 per cent thick at 30 per cent of the chord distance from the leading edge. Using a mesh giving only fourteen mesh points on the aerofoil, we find that the calculations yield a 12.06 per cent aerofoil at 28.2 per cent of the chord distance from the leading edge. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2731.pdf 404. Wind-tunnel tests on a 12-ft diameter helicopter rotor H. B. Squire, R. A. Fail and R. C. W. Eyre Measurements of the thrust, torque and flapping angle for a 12-ft diameter rotor over a range of blade angle, shaft inclination and tip-speed ratio have been made to give information on the validity of the standard rotor theory and of the effect of stalling on the retreating blade. Good agreement with the theory was obtained over the normal operating range, using aerofoil characteristics determined from the measurements in the static thrust condition. Stalling was found to be progressive in character showing first by an increase in torque and flapping angle and later by a fall in thrust, as compared with the calculated values. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2695.pdf 405. A new relaxational treatment of the compressible two-dimensional flow about an aerofoil with circulation L. C. Woods, and A. Thom The incompressible two-dimensional flow about an aerofoil with circulation is calculated using relaxation on the square mesh formed by the incompressible velocity equipotentials (φ = constant) and the streamlines (ψ = constant). Log (l/q0) and θo, where (qo, θo) is the incompressible velocity vector on polar co-ordinates, are harmonic functions in the (φ, ψ)-plane, and can be found by well-known relaxation or squaring methods. Boundary conditions are specified in the (x, y) or physical plane, but starting from an assumption for the surface velocity, approximate boundary conditions can be found for the (φ, ψ)-plane, which then enable a more accurate value of the surface velocity to be calculated, and so on. The circulation is imposed on the field by having a smaller number of equipotential lines of the mesh cutting the lower surface of the aerofoil than cutting the upper surface. Non-linear compressible flow equations involving log (l/q) and θ, where (q, θ) is the compressible flow vector, are solved by relaxation on the (φ, ψ) grid. The results for a worked example are compared with experimental curves provided by the National Physical Laboratory for the same aerofoil at approximately the same angle of incidence. There is reasonable agreement. Supersonic patches were experienced and are not difficult to treat by relaxation, although the difference equations become poorly conditioned. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2727.pdf 406. A note on the dynamic stability of aircraft at high-subsonic speeds when considering unsteady flow W. J. G. Pinsker The effect of an increase in speed relative to the speed of sound on the unsteady flow round a harmonically oscillating aerofoil, is to increase the lag of the aerodynamic forces and moments behind the deflection when the frequency is small. It is shown theoretically that this will result in a serious deterioration of the damping of both the lateral oscillation and the high frequency longitudinal oscillation with high Mach numbers. Use is made of derivatives calculated for flutter purposes to estimate the unsteady derivatives at aircraft oscillation frequencies. Illustrative examples are presented. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2904.pdf 407. A survey of performance reduction, with particular reference to turbo-propeller aircraft K. J. Lush Performance reduction methods will soon be required for routine tests of turbopropeller aircraft. A survey of the types of methods available has therefore been made to find which type seemed likely to be most useful. The purpose of performance reduction is briefly examined. Methods in use are classified into experimental methods, which require no advance numerical data, and analytical methods, which require such data. The latter class is sub-divided into methods based on small corrections and methods based on performance analyses. The suitability of each class of method is discussed. Experimental methods are only practicable if any engine control linkage scheme is such as to impose dimensionally correct relations between the linked variables. They are convenient if data are required over a range of all variables or if, of the non-dimensional groups which result from dimensional analysis, all or most are susceptible to precise control. If such methods are practicable and reasonably convenient they are very attractive and probably the best to use on turbo-propeller aircraft, particularly at high altitude or Mach number, because of the lack of knowledge, as yet, of aircraft and engine characteristics under these conditions. If experimental methods are impracticable or very inconvenient, analytical methods based on performance analyses are probably the best substitute, at least for tests at high altitude or high Mach number, until such time as numerical data on engine and airframe kehaviour are available and can be easily used. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2757.pdf 408. A wind-tunnel technique for flutter investigations on swept wings with body freedoms P. F. Jordan and F. Smith In the past it has been usual to ignore the body freedoms of aircraft in making wing-flutter investigations. This practice is no longer justified for modern designs with swept wings, and especially for tailless aircraft. In this report a technique is described which has been developed for wind-tunnel tests on wing-flutter models with the body freedoms. A half-span wing model is used, attached to a rigid body; longitudinal stability is ensured, and the body-mass parameters are reduced to small values, by an appropriate arrangement of supporting springs. The ease of parameter variations makes the wind-tunnel rig suitable for systematic investigations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2893.pdf 409. Aerodynamic forces on rectangular wings oscillating in a supersonic air stream W. E. A. Acum The aerodynamic forces on rectangular wings of various aspect ratios describing simple harmonic oscillations of small amplitude in a supersonic air stream are determined. Linearized theory is used and numerical solutions are derived by the method of 'Relaxation'. The problem is formulated in section 4 and in section 6 it is reduced to one of finding a series of conical flow solutions. Only a few terms of this series need be determined since the process converges quickly for the range of values of the frequency parameter considered. This range is believed to cover most of the practical supersonic flutter values. Moment coefficients for a range of Mach numbers and various frequency parameter values were calculated and they are tabulated and plotted at the end of the report. The coefficients are referred to tile leading-edge axis position but can be referred to any other axis by the usual formulae. For a range of Mach numbers in two-dimensional flow, the aerodynamic damping for pitching oscillation can be negative for certain positions of the axis of pitch oscillation and this implies instability (R. & M. 2140 and 2194). The results of this report show that aspect ratio has a stabilizing effect for axes less. than about 0.7 of the chord downstream of the leading edge, but has the opposite effect for axes nearer than this to the trailing edge. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2763.pdf 410. An approximate method of estimating the effect of elastic deformability of the aircraft structure on the manoeuvre point. Parts 1 and 2 H. Fingado, and A. S. Taylor This report, which is presented in two parts, develops an approximate method of estimating the effect of structural deformability on the manoeuvre point of an aircraft. The introduction outlines the scope of the complete work in relation to the work of Lyon and Ripley (R. & M. 2331 and 2415). Part I opens with a detailed discussion of the structural deformability of wings, unswept and swept, and proceeds on the basis of certain aerodynamic and structural approximations to derive relatively simple formulae for the calculation of the shift of manoeuvre point due to elastic camber, elastic wash-out (wing torsion and bending, and the effect of fuselage interference) and the direct effect of wing bending (which changes moment arms) on pitching moment. A summary and discussion of some comparative calculations of the effect of elastic wash-out, using the present method and that proposed by Lyon (R. & M. 2331) are included. They demonstrate the dangerously large shifts of manoeuvre point which may arise from elastic wash-out with swept wings and show that while the present method is somewhat less accurate than that of Lyon, it has the important advantage of being far less laborious in application. Part I1 examines the effects of fuselage and tailplane deformability, and at the same time investigates the effect of wing deformability (including root-region deformability) on the fuselage and tailplane contributions to manoeuvring stability. Bending of the fuselage, torsion of the (unswept) tailplane and deformability of the tailplane attachment are the main fuselage and tailplane effects considered, and among the subsidiary effects examined is that of engine nacelles situated in the wing. A simple procedure for numerical calculation of the fuselage and tailplane contributions to manoeuvre-point shift is set out and illustrated by a worked example, which demonstrates how elastic attachments of wing and tailplane may be used to augment the effect of the tailplane in counteracting the destabilizing effect of wing and fuselage. A simple description of the method of analysis used in Part 11, together with typical resuIts obtained from it, is given in section 12. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3019.pdf 411. An experimental investigation of a thick-aerofoil nozzle cascade S. J. Andrews and N. W. Schofield The cascade tests on a thick-aerofoil turbine nozzle bla~te suitable for a cooled turbine show that it has a good performance over a wide incidence range up to M = 0.8. Above this value the loss coefficient rises and does not fall again as M = 1 is approached. Several methods of indication of the transition point have been tried and results show that the method depending on the evaporation of crystals gives a position inconsistent with three other methods, i.e., lamp-black deposit, surface total-head measurement and stethoscope search tube. The effect of the thick trailing edge on loss coefficient is almost that predicted assuming zero velocity behind the blade trailing edge. The heat-transfer increase due to transition is probably not large, and is no worse than that on a conventional turbine section. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2883.pdf 412. An experimental investigation of the effect of engine loads on wing structures J. L. Reddaway Three cellulose-nitrate model wings, identical except I0r rib flexibility, have been tested under conditions reproducing typical engine loads. Stress distributions have been found experimentally by means of electrical resistance strain-gauges. The distribution due to an abrupt change of torsion has been compared with a theory by Williams, and that due to an abrupt change of shear with a theory by Taylor. Local stresses at the engine nacelle are found to be appreciably higher in practice than would have been predicted by either of these theories. The discrepancies, moreover, are found to increase with rib flexibility. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3062.pdf 413. An Investigation of High-Altitude Clear-Air Turbulence over Europe using Mosquito Aircraft G. S. Hislop, and D. M. Davies The British European Airways Clear-Air Gust Research Unit was formed, with the financial support of the Ministry of Supply, to investigate the problem of clear-air turbulence at high altitude over Europe. The aircraft were based at Cranfield, Bedfordshire, and flights were made of roughly 1,000 miles radius from that base. In the two years of its existence, the two PR 34 Mosquito aircraft employed for the purpose covered 92,300 miles of research flying between the selected limits of 15,000 ft and 37,000 ft. Statistically speaking this is a very small sample and must be borne in mind when considering the results. Some twenty areas of turbulence (defined as giving, vertical acceleration increments greater than ±0.2g) were actually investigated, the greatest vertical gust velocity encountered being + 26 ft/sec E.A.S. The results were examined from the passenger comfort and structural aspect, and from the meteorological aspect. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2737.pdf 414. An investigation of the disturbances caused by a reflection plate in the working-section of a supersonic wind tunnel A. O. Ormerod An investigation has been made of the disturbances caused by a reflection plate, mounted clear of the boundary layer in a supersonic tunnel. Static traverses were made, mainly at a Mach number of 1.4 above four reflection plates having different plan forms, with various conditions in the passage between the plate and the tunnel wall. In the region above the plate two main disturbances were found ; there was a small disturbance from the leading edge and a disturbance further downstream which had originated beneath the plate. Between the two there was a region of approximately constant pressure in which a model could be located. The forward disturbance seemed unavoidable. Increasing the area of the passage beneath the plate by a recess in the tunnel wall, was the most effective way of moving back and reducing the magnitude of the disturbance at the rear. With the best arrangement, at a Mach number, of 1.4, it was found possible to obtain a region of approximately constant pressure, extending downstream from the apex of the plate for a distance of about 0.66 times the height of the tunnel. A plate spanning the tunnel was found to be unsuitable because of disturbances originating at the extremities of the leading edge, in or near the tunnel boundary layer Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2799.pdf 415. An investigation of the use of an auxiliary slot to re-establish laminar flow on low-drag aerofoils R. W. Cumming, N. Gregory, and W. S. Walker Summary.--The use of an auxiliary slot on a laminar-flow aerofoil has been investigated to check whether laminar flow can be re-established by suction at the rear of the region of deposited dirt, flies, etc. Results indicate that in the absence of unfavourable pressure gradients, it is possible to re-establish a laminar boundary layer by removing a little more than the whole turbulent layer reaching the slot, and preliminary estimates suggest that with efficient ducting it should be possible to achieve a reduction in overall effective drag coefficient by this means. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2742.pdf 416. Calculation of the effect of camber and twist on the pressure distribution and drag on some curved plates at supersonic speeds G. M. Roper So far, little is known of the effect of camber or twist on the pressure distribution and drag of a wing flying at supersonic speeds, but with subsonic leading edges. According to the linear theory, for a subsonic leading edge, there is a singularity in the perturbation velocity component normal to the edge. Associated with this singularity is an infinite (or very large) suction over the sharp leading edge, as in subsonic flow. The present investigation was undertaken with a view to finding the shape of a curved wing, such that the thrust loading on the leading edges, particularly near the wing tips, is removed or modified. The shapes of two groups of such wings have been found :- (1) For the first group, when the wings are at design incidence, there are no leading-edge pressure singularities, and therefore no leading-edge thrust. The pressure difference is finite and positive everywhere on the wing, and decreases to zero on the leading edges. (2) For wings of the second group, the leading-edge singularity is modified so that its strength increases along the edge from zero at the apex to a maximum, and then decreases to zero, after which it would become negative: The effect of additional incidence is to increase the local lift everywhere and to move the positions of maximum and zero singularity strength further downstream. In this report, it is also shown how the shapes of wings of the second group can be determined to satisfy certain requirements with respect to camber and twist, or the magnitude of aerodynamic characteristics. The lift, the induced drag, and the pitching-moment coefficients for some wings of triangular plan form have been calculated, and the results are shown graphically. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2794.pdf 417. Chemical solids as diffusible coating films for visual indications of boundary-layer transition in air and water J. D. Main-Smith Experimental investigations have been made on various chemical solids as diffusible coating films for visual indicatien of boundary-layer transition in air and water. Originally, the method was applicable only at low speeds in wind tunnels and water tanks, and the indications were somewhat transient. More durable coating materials have now been made available, admitting of use at subsonic and supersonic wind-tunnel speeds from 30 to 1350 m.p.h., and at ship-hull speeds from 26 to 20 kt. The method has also proved capable of extension to aircraft in flight at speeds from 100 to 445 m.p.h, at temperatures down to -- 22 deg C and at altitudes up to 20,000 ft. The diffusible solid-coating method, with its advantages of autographic indication and simplicity and rapidity of operation, has thus become a versatiie technique in investigations on fluid flow in aerodynamics and hydrodynamics. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2755.pdf 418. Control-surface flutter with the stick free H. Templeton The determination of the stick-free flutter characteristics of a control system when the inertia of the stick is allowed for is considered. A method of solution is proposed which corresponds to impedance matching between circuit and control surface in the flutter condition. The method is applied, by way of illustration, to two typical cases, an elevator system and a servo-tab system, and the effect of variations in stick inertia and circuit stiffness demonstrated, Conclusions drawn from these two cases are listed separately, but it is concluded generally that stickfree flutter can occur in the absence of stick-fixed flutter, and that the stickqree flutter characteristics may be quite different from those for the circuit-cut condition. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2824.pdf 419. Criteria for the prevention of flutter of tab systems H. Wittmeyer and H. Templeton An investigation has been made into the flutter characteristics of an idealised tab system in which the three degrees of freedom normal translation of the lifting surface, rotation of the control surface, and rotation of the tab are represented. Specific cases of this idealised system represent similar idealised forms of the standard trimming, spring, servo, and geared tab systems. From a consideration of tile relationships existing between the systems, criteria for flutter prevention have been developed from the criteria evolved earlier for trimming tabs. As initially derived, the criteria are applicable to the stick-fixed condition (in the case of spring and servo-tabs), to the case with no aerodynamic balance on either control surface or tab, and to tile case where the control surface is statically balanced about its hinge. Comparison is made between the criteria for spring-tabs and the existing Collar-Sharpe criteria. Design implications are deduced from the criteria for spring-tabs, and the general application of the criteria to actual systems is considered in some detail. A comprehensive survey of the results is given in section 11. Points of major importance are as follows:-- (a) The criteria are liberally provided with generalised constants whose values can if necessary be adjusted in the light of practical experience. (b) The backward limit set to the tab centre of gravity will normally be less severe than in the case of the Collar- Sharpe criterion. (c) Satisfying the criteria of this report is likely to be most difficult with elevators carrying a tab on one side only, and from a flutter point of view such systems should be avoided if possible. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2825.pdf 420. Design and calibration tests of a 5.5 in. square supersonic wind tunnel J. Lukasiewicz The main design features of the wind tunnel are described and results are given of the investigations carried out to determine:- (i) the minimum pressure ratio required to operate the wind tunnel at Mach numbers up to 3.5, and (ii) the uniformity of the velocity distribution in the working section at Mach numbers of 1.57, 1.88, 2.48, 2.85, 3.25 and 3.5. It was found that the tunnel pressure recovery can be appreciably increased by means of a contraction ('second throat') located between the working section and subsonic diffuser. All nozzles tested were designed with short throats and expansion profiles with the maximum angles of expansion for the given exit Mach number. The axial variation of Mach number over selected intervals of working section (not smaller than 5 in.) was found to be of the order of ± 1.0 per cent. It was found that condensation in the wind tunnel nozzle (run with atmospheric air), has a detrimental effect on the velocity distribution in the working section, particularly at small Mach numbers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2745.pdf 421. Design and use of counting accelerometers J. Taylor The fundamental principles underlying acceleration recording by means of a counting accelerometer are analysed. The essential design requirements for a counting accelerometer are presented. A design that has been specially made to meet these requirements is described. Both mechanical and electrical counting are considered, but mechanical counting is found to be superior. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2812.pdf 422. Detailed observations made at high incidences and at high-subsonic mach numbers on goldstein 1442/1547 aerofoil H. H. Pearcey, and M. E. Faber Detailed measurements, including surface-pressure distributions, shock-wave photographs and observations of boundary-layer separation, have been made over a wide range of incidence in the National Physical Laboratory 20-in. x 8-in. High-Speed Wind Tunnel on the Goldstein 1442/1547 aerofoil NPL 177, previously tested at lower incidences in this tunnel. The tests have shown that with standard models of 5-in. chord the stall can be covered for Mach nmnbers up to nearly 0.8 unless it is delayed beyond the usual incidence range, as for Mach numbers above 0.7 for the present section. For these cases, however, it should still be possible to cover the useful range of CL which is often limited by other considerations, e.g., pitching-moment coefficients. The observations enable the effects of compressibility on CL max and on the nature of the stall to be studied in detail for the two-dimensional case. The pitching-moment coefficients, also, can be integrated from the pressure distributions. Since the main purpose of experiments of this type is to provide qualitative explanations of the compressibility effects, the limitations on the accuracy of the results due to tunnel interference and the fairly low Reynolds numbers (1.0 to 1.8 x 10power6) are not likely to detract seriously from their value. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2849.pdf 423. Determination of reversal speed of a wing with a partial-span flap and inset aileron W. G. Molyneux and E. G. Broadbent Control reversal due to deformation of a wing with a partial-span flap and inset aileron is considered theoretically for the particular case of a flap held at the root end. The semi-rigid method is used. An investigation is made for a particular aircraft. The calculated reversal speed is found to be considerably lower than for the straight-forward wing-aileron case. The effect of variation of the degrees of wing and flap constraint is also considered. It is concluded that an increase in reversal speed is best obtained by an increase in flap root stiffness. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2793.pdf 424. Enthalpy charts: for dissociating gas mixtures in the temperature range 600 deg to 4000 deg K H. Reichert Enthalpy charts have been constructed to facilitate dealing with the thermodynamic problems of combustion and flow of dissociating gases within the temperature range of 600 deg to 4,000 deg K. By means of a quantity called 'reaction enthalpy' (which is defined in this note), it is possible without previous knowledge of the composition of the mixture of gases to work out dissociation processes occurring at equilibrium. Also, if required, the composition of the mixture can be obtained from the charts. The charts are confined to the C,H,O-system, but their extension to include N in the system is quite simple. 28 charts with the total pressure p and the molar ratio nC/nH as parameters have been constructed in the first place for the four pressures p = 0.1, 1.0, 10.0 and 100.0 kg/sq cm, and for the seven molar ratios nC/nH = 0, 0.2, 0.4, 0.6, 0.8, 1.0 and ∞. The four charts (reduced in scale) for the molar ratio nC/nH = 0.4 are attached as examples. Full scale charts will be supplied on request. The present note describes work that had to be laid aside in 1947, and has now been resumed. The work done up to that date has been already described by Lutz. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3015.pdf 425. Experiments on conical diffusers H. B. Squire No systematic measurements of the efficiency of conical diffusers have been made since Gibson's tests in 1910. The present investigation was made to check this early work, and to study the variation of efficiency with Reynolds number and the changes in flow with change of cone angle. The experiments of Part I were made with cones of angles between 4 and 10 deg, of area ratio 4 between entry and exit, and with uniform flow at the entry. These showed no striking effect due to variation in cone angle and gave no sign of flow separation. The experiments of Part II were made with diffusers of area ratio 16 between entry and exit and with pipe flow at the entry, and consisted of measurements of the velocity distribution at a number of stations. The object of these later tests was to find out whether, under these different conditions from Part I, flow separation occurred at the larger cone angles, thereby giving a practical limit to the cone angle which could be used in the return circuits of wind tunnels and in other ducts. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2751.pdf 426. Experiments on the Flow past a Porous Circular Cylinder fitted with a Thwaites Flap R. C. Pankhurst, B. Thwaites, W. S. Walker This paper describes wind-tunnel experiments on a porous circular cylinder of 3 in. diameter fitted with a Thwaites Flap. Measurements were made Of the pressure distribution at mid-span, together with a number of wake traverses, over a,range of suction quantity, flap size, wind speed and flap setting. The distributed suction effectively prevented boundary-layer separation and enabled a close approximation to potential flow to be achieved. The flap was essential to the attainment of steady flow conditions with suction; without a flap the pressure recovery at the rear Of the cylinder was incomplete and the pressure distribution fluctuated. In view of this unsteadiness in the flow without a flap, the circulation could scarcely be expected to remain, as had previously been conjectured, when the flap was withdrawn. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2787.pdf 427. Experiments with static tubes in a supersonic airstream -- parts 1 and 2 D. W. Holder, R. J. North and A. Chinneck PART I. Systematic.tests have been made at a Mach number of 1.6 on a family of static tubes. The variables which have been investigated are the shape of the nose, the distance of the holes downstream, and the inclination of the tube to the flow. Pressure measurements have also been made in the vicinity of a shock wave and close to a wall. PART II. A family of flat-nosed pitot-tubes has been tested at Mach numbers of 1.6 and 1.8. At both Mach numbers it was found that no change of reading could be detected when the ratio of the external diameter to the bore was varied from 2 to 16. The Mach number calculated from the pitot pressure on the assumption that the bow wave ahead of the pressure hole was normal to the stream is, to within about ±½ per cent, equal to that calculated from the reading of a static tube. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2782.pdf 428. Flight trails of a rocket-propelled transonic research model: The R.A.E.-Vickers rocket model. Parts I to IV The Staff of the Supersonic Division, Flight Section, Royal Aircraft Establishment The development of the gas turbine which provided large thrusts from comparatively small front areas, and at the same time retained its thrust efficiency at high speeds, introduced the possibility of building a supersonic aeroplane. Existing aeroplanes displayed marked longitudinal trim changes at high subsonic speeds, and to pursue these problems into the transonic field, problems which must be solved before the supersonic aeroplane can fly, the Royal Aircraft Establishment in 1945 embarked upon a programme of research using air-launched rocket-propelled models. From the first conception of a simple model the research vehicle grew to a complex model aeroplane complete with auto-pilot, liquid-fuel rocket motor and radio telemetering equipment, aft-launched at 36,000 ft over a ground radar station. The first model, complete with prototype equipment was lost in turbulent air. On the second model launched the rocket motor failed to ignite. There was a period of 12 months further development of the rocket motor and ignition system, followed by the launch in October, 1948 of the third complete model. This model flew satisfactorily and the flight is analysed in this report. The model reached a maximum speed of M = 1.38. The static-pressure variations on the nose pitot-static-tube agree with available information, when allowance is made for the altitude change during flight. There is substantial agreement between measured thrust, longitudinal acceleration and drag, and the latter is in reasonable agreement with that predicted from wind-tunnel tests. The recorded tailplane angle agrees with that calculated from the instructions given to the auto-pilot, and with the predictions from wind-tunnel tests. The main body of the report contains a historical review of the project, brief descr{ptions of the test vehicle and experimental techniques, and the detailed analysis of the final successful flight trial. In a concluding section the project is discussed critically ; it is considered that the work done has shown the experimental method to be an exceedingly difficult one, and that the results it gives do not justify the effort it demands. No further developments are proposed, as alternative transonic research techniques have in the meantime been developed. In a series of appendices are given detailed descriptions of the test vehicle and its ancillary equipment, of the development work leading up to the final trial and of the experimental equipment and techniques. These detailed appendices will be of interest only to the specialist. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2835.pdf 429. Flow patterns in the wake of an oscillating aerofoil J. B. Bratt Part I of the report gives an account of experiments made with the National Physical Laboratory smoke generator to obtain smoke patterns in the wake of an aerofoil performing a rolling oscillation in a wind stream. Calculations are given in Part II relating to the smoke patterns produced by a nozzle in uniform motion relative to (a) an infinite row of equally spaced two-dimensional discrete vortices of alternate sign and (b) an infinite two dimensional vortex sheet with sinusoidal distribution of strength. Comparison with certain of the smoke patterns discussed in Part I suggests that the wake vorticity can be treated very closely as a system of discrete vortices, and this is supported by the consideration that the elements of a continuous vortex sheet would in general be subject to normal induced velocities, which would tend to break the sheet up. The tendency for this to occur would be greater for the higher values of ω, wince the variation of vorticity with distance along the wake would be greater. The induced velocities for a uniform infinite vortex sheet would be zero. On the assumption that the theoretical infinite vortex sheet in the wake 0f an oscillating aerofoil breaks up into discrete vortices, the size of the vortex cores is calculated by satisfying the energy equation relating the two systems. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2773.pdf 430. Flutter and divergence of swept-back and swept-forward wings A. W. Babister In this note, the equations of the flexural-torsional flutter of a swept wing are established, assuming the wing to be semi-rigid and fixed at the root. The general effects of sweep-back, wing stiffness and position of the inertia axis are determined. The critical speeds for flutter and for wing divergence are determined (i) for incompressible flow (ii) for compressible flow, applying the Glauert correction. The critical flutter speed is in general higher for a swept-back wing having the same wing stiffness as the unswept wing; for a swept-forward wing, divergence will occur before flutter. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2761.pdf 431. Four studies in the theory of stress concentration (Parts 1-4) H. L. Cox PART I - The Effect of Holes on the Strength of Materials under Compiex Stress Systems. In a plane test piece pierced by a cylindrical hole the greatest stress is set up at some point in the periphery of the hole. This stress is a principal stress and both the other principal stresses, that normal to the contour of the hole and that parallel to the axis of the hole and normal to the free surface of the test piece, are zero. Therefore, failure of such a test piece under any system of applied loading depends almost entirely on the shape of the hole and on the properties of the material only in respect of a possible difference between its strengths in tension and in compression. On this basis criteria are developed for the failure of test pieces containing circular and elliptical cylindrical holes under systems of complex stress. The results are applicable to tests on pieces pierced by oil holes drilled either perpendicularly to the axis of the test piece or obliquely. The resulting criterion for circular holes perpendicular to the plane of stress is compared with some experimental results of tests under combined alternating bending and torsion. Criteria are also developed for elliptical holes oriented at random, and it is shown that these criteria do not in themselves accord with the results of tests on the majority of materials. It is concluded that internal flaws are unlikely to account for the mechanical properties of engineering materials. PART II - Stress Concentration due to Holes and Grooves other than Elliptical in Form. In order critically to compare the results of fatigue tests on pieces containing sharp V-notches and other abrupt changes of section with tile theoretical values of stress concentration factors, a need was apparent for detailed theoretical investigation of the effect of the form of the discontinuity of section. Following generally established methods of stress analysis the stress distributions round holes and grooves of a wide range of forms have been examined both under plane direct stress and under shear stress. These analyses have been applied to several particular cases and the results have been compared with approximate formulae based on the stress distribution round elliptical contours. From the results it appears that the approximate formulae based on elliptical holes afford a reasonably accurate estimate of the maximum stress at any hole or groove under plane direct stress, but that the stress concentration under shear is influenced to a much greater extent by the general form of the hole or groove. Under both types of stress system, certain cases of anomaly arising from application of the approximate formulae are examined, and it is shown that all these anomalies are resolved by the more accurate formulae here derived. Incidentally, in this examination it is demonstrated that abrupt changes of curvature of the contour of a hole or groove cause no concentration of stress. PART III - The Effect of Surface Irregularities on Fatigue Strength. It is perhaps not generally recognized that the approximate formulae 1 + ~/(a/e) and 1 + 2~/(a/e) for the stress concentrations under shear and under direct stress due to a groove of depth a and root radius 5 are applicable not only when the ratio ale is large but equally when it is small; indeed the accuracy of these approximate formulae improves as ale decreases. This is demonstrated by computation by exact theory of the stress concentration due to a continuous nearly sinusoidal undulation of the surface of a test piece, and it is shown incidentally that when a and e are both negative, so that the groove is inverted into a protrusion, the 'de-concentration' of stress is represented very closely by the approximate formulae 1 -- ~/(a/e) and 1 -- 2~/(a/Q). It is shown further that these factors applied as corrections to computed stress factors under torsion for an approximation to a square shaft with rounded corners suffice to reconcile these results to the established solution for a square shaft under torsion. PART IV - Stress Concentration in Twisted Shafts. straightforward method for computing the stress distribution in a twisted shaft of specified cross-section is developed, and the method is illustrated by application to a round shaft with a single flat on one side and to a six-splined shaft. In these applications use is made of the process of correction for local irregularities described in Part III, and some general comments are made on the means to represent complex boundaries by analytical forms, which supplement the techniques described in Part II. An approximate formula for the concentration of shear stress in the fillet at the root of the spline of a splined shaft under torsion is proposed and the accuracy of this formula is tested by three examples. One example of a hollow shaft with a lobed external contour and a wide variation of wall thickness is worked out; and it is shown that over the smooth inner boundary the shear stress is very nearly inversely proportional to the wall thickness, whereas at the lobed outer boundary marked concentration of stress occurs at the grooves between the lobes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2704.pdf 432. Helicopter control to trim in forward flight W. Stewart A theoretical estimation of the flapping and feathering (cyclic pitch) to trim the helicopter rotor in forward flight is given and the equivalence of the two systems is shown. The feathering amplitudes to trim the complete helicopter are then estimated and compared with experimental flight values obtained on the Sikorsky R-4B and S-51 helicopters. The effects of centre of gravity position, fuselage pitching moment, etc., are considered and the delta-3 hinge effect is dealt with in an appendix. The effect of slipstream curvature on lateral control is included. Satisfactory agreement of the theoretical and experimental results is obtained. In the iongitudinal trim, the fuselage pitching moment in the presence of the rotor slipstream is a most important contribution. In the lateral trim, the induced velocity distribution and the tail rotor behaviour have a large influence and must be taken into account. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2733.pdf 433. Low-speed wind-tunnel tests on the characteristics of leading-edge air intakes in swept wings J. Seddon and D. J. Kettle Low-speed wind-tunnel tests have been made to determine the external and internal characteristics of leading-edge air intakes in swept wings, under flight conditions. Tests on a delta model show that leading-edge intakes in the wing root give an advantage in effective sweepback and critical Mach number (estimated from the low-speed pressure distribution) compared with nacelle-type intakes adjacent to the body. The internal loss in level flight for a 52° sweptback entry is 4~/o ram worse than when the entry is square to the direction of flight. The explanation of this loss is found in the nature of the pre-entry retardation for level-flight velocity ratios. A boundary-layer bypass leading from a slot inside the intake removes most of the additional loss. Tests on a swept-wing model with a simplified intake give the effects of duct diffusion, of boundary layer from an adjacent body, and of boundary-layer removal through a slot or porous wall. A general formula for intake loss is applied to show the dependence of the loss on entry shape and on the value of the design velocity ratio. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3353.pdf 434. Measurement and suppression of tension waves in arresting gear rope systems J. M. N. Willis, S. W. Chisman and N. I. Bullen Experiments were carried out in order to measure the effect of the tension waves which are induced in an arresting gear rope system after engagement, and to try out means of suppressing these waves with a view to application to projected arresting gears suitable, for entry speeds of up to 120 and 150 knots. Rope tensions were recorded for a series of tests covering a range of entry speeds up to 117 knots with a test vehicle weight of 5,400 lb. and up to 151 knots at a weight of 2,450 lb. It is shown that the amplitude of the tension waves becomes relatively greater with increase of entry speed and reaches very serious proportions at the maximum speeds obtained. The use of resilient rope anchorages has resulted in the suppression of the tension waves to a large extent, reductions in peak tensions of up to 30 per cent under some conditions having been achieved. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2981.pdf 435. Methods for calculating the lift distribution of wings subsonic lifting-surface theory H. Multhopp This report contains some fairly simple and economic methods for calculating the load distribution on wings of any plan form based on the conceptions of lifting-surface theory. The computer work required is only a small fraction of that of existing methods with comparable accuracy. This is achieved by a very careful choice of the positions of pivotal points, by plotting once for all those parts of the downwash integral which occur frequently and by a consequent application of approximate integration methods similar to those devised by the author for lifting-line problems. The basis of the method is to calculate the local lift and pitching moment at a number of chordwise sections from a set of linear equations satisfying the downwash conditions at two pivotal points in each section. Interpolation functions of trigonometrical form are used for spanwise integration both in setting up the downwash equations and in getting the resultant forces on the wing from the local forces. The preliminary chordwise integrations for the downwash are predigested in a series of charts (Figs. 1 to 6) ; it is these which make the method a practical computing proposition. The theory is outlined in sections 2 to 5 ; section 6 deals with the solution of the linear equation and section 7 with the resultant forces on the wing. Some examples are worked out in section 8 to compare with other methods; one solution is given in full detail in Tables 8 to 30 as a guide for computers. Appendices I to VI discuss more carefully some salient points of the mathematical theory, and AppendLx VII is intended to instruct the computer how to carry out the steps of the calculation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2884.pdf 436. Multiple-jet white-smoke generators C. Salter Descriptions are given of equipment devised for the generation of fairly large quantities of an optically dense white smoke and special attention has been paid to the need for delivering this through long ducts or against an appreciable back-pressure. The smoke consists of very small particles of condensed paraffin vapour and is obtained by directing jets of cool air on to high-speed jets of the vapour issuing from very small orifices. The optimum outputs are about 6 cu ft (170 litres) and 8 cu ft (230 litres) per minute from No. 1 and No. 2 generators, respectively, but considerably larger quantities can be delivered with a slight loss of opacity. Under normal operating conditions the rate of use of paraffin is rather less than 2 cu in. (33 c.c.) (No. 1) and 3 cu in. (49 c.c.) (No. 2) per minute. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2657.pdf 437. Natural frequencies and modes of a model delta aircraft D. R. Gaukroger Resonance tests on a model delta wing are described. Consideration is given to the effect of inertia distribution on the first three normal symmetric modes of vibration. The mean centre of gravity position, fuselage pitching moment of inertia and wing inertia axis have been independently varied, and the effect of concentrated tip masses has been examined. Results are given which are intended as a general guide in flutter calculations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2762.pdf 438. Neutral holes in plane sheet reinforced holes which are elastically equivalent to the uncut sheet E. H. Mansfield It is shown that, in a plane sheet under any particular loading system, certain reinforced holes may be made which do not alter the stress distribution in the main body of the sheet. These reinforced holes (hereafter called neutral holes) necessarily have exactly the same stiffness and at least the same strength as the portion of the sheet that has been cut out. The weight of the reinforcement is usually greater than the weight of the sheet that has been cut out, though there are cases where it is less. The Airy stress function is used throughout because it admits of great generality and because the properties of a neutral hole can be expressed simply in terms of the function and its derivatives. Indeed, the stress function assumes a new and special significance in determining the shape of a neutral hole. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2815.pdf 439. Note on aerodynamic camber H. C. Garner The following note has been written at the suggestion of the Chairman of the Stability and Control Sub-Committee. It is intended to explain the theoretical significance of camber derivatives, and to assess the various available methods of making experimental measurements with particular reference to the use of a curved-flow tunnel. The note amplifies the arguments put forward by the writer in Ref. 1 (1950), that there is particular need for sytematic information about the influence of curvature of flow on control hinge-moments as a step towards the understanding of three-dimensional viscous flow. After a definition of aerodynamic camber and a historical account of the development of the idea and its importance, the present state of knowledge of its aerodynamic derivatives is described. Camber derivatives are required for evaluating tunnel interference corrections and are useful for stimating corrections for aspect ratio and scale effect, in so far as the flow at a section of a finite wing can be represented as an equivalent two-dimensional flow. This quasi two-dimensional approach to the problem of control surfaces should be combined with experimental checks on the aerodynamic derivatives of various wings with flaps and also with a study of three-dimensional boundary layers. Formulae for the camber derivatives of lift and pitching moment need confirmation. The derivatives of lift at the stall and of hinge moments over the whole range of incidence are virtually unknown and in consequence the determination of (CL)max and CH is seriously limited. The significance of these two-dimensional camber derivatives is illustrated by the quantitative uncertainties that may arise. It is suggested that these might be removed by establishing formulae for the unknown derivatives from a series of tests of uneambered aerofoils with a range of flaps in the curved-flow tunnel at the Langley Aeronautical Laboratory, U.S.A., by simulating a uniform rate of change of pitch. The uncertain characteristics of the curved flow would make necessary a check between results so obtained and those deduced from tests in a straight tunnel of aerofoils with various amounts of parabolic camber. There appears to be no other satisfactory technique for measuring camber derivatives. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2820.pdf 440. Note on the effect of variable wall temperature on heat transfer H. B. Squire Two recent papers have investigated the effect of variable surface temperature on heat transfer. It seems therefore worth while to record the extension of the method given in R. & M. 1986 to the case of variable surface temperature. Using the same notation as in R. & M. 1986, T1 the surface temperature is now assumed to be a function of x, the distance along the surface from the front stagnation point. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2753.pdf 441. Note on the use of the three-dimensional shockwave recorder for studying interference in a supersonic wind tunnel A. O. Ormerod A description is given of the three-dimensional shock-wave recorder which has been used to investigate wind-tunnel interference on a sting-mounted wing having 50 deg of sweepback. Diagrams of the shock-wave patterns round the wing are given for the following conditions of Mach number and incidence:- M = 1.4 Incidence = 4 deg, M = 1.6 Incidence = 4 deg, M = 1.8 Incidence = 0 deg. From these diagrams it can he inferred that the outboard portion of the particular wing tested suffers interference from the tunnel Walls at M = 1.4. At the higher Math numbers the model behaves effectively as if it were in free air. In order to use the three-dimensional shock-wave recorder, the wind-tunnel working-section requires a window whose length is at least three times the tunnel width and which extends equal distances ahead of and behind the model. This is a very serious drawback to the general use of the method. The analysis of the photographic records is straightforward, though rather tedious. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2798.pdf 442. On the application of oblique co-ordinates to problems of plane elasticity and swept-back wing structures W. S. Hemp Summary.--The object of this report is two-fold. On the mathematical side it seeks to illustrate the use of oblique co-ordinates in applications to Elasticity and Structure Theory. On the practical side it seeks to provide methods by which designers can solve problems of stress distribution and deflection for the case of swept-back wing structures, whose ribs lie parallel to the direction of flight. The report is divided into three parts. In Part I the mathematical basis is developed. Formulae are derived which express the fundamental concepts and relations of Geometry, Kinematics, Statics and Plane Elasticity in terms of vector components in oblique co-ordinates. In Part II, the results obtained in Part I are applied to a uniform, symmetrical, rectangular section, swept-back box. A complete theory of stress distribution and deflections is obtained for the case of loading by \'normal\' forces and couples (forces whose directions and couples whose planes are normal to the plane of sweep-back) applied to the ends of the box. Some consideration is also given to problems of constraint against warping. In Part III the main results of Part II are generalised to cover the case of a more representative wing structure. This represents an extension of the usual Engineer\'s Theory of Bending and Torsion to cover the case of swept-back wings with ribs parallel to the flight direction. Practical procedures based upon this extension are laid down for stress distribution and deflection calculations. These will have the same validity for swept-back wings, as the usual design approximations have for the unswept case. An appendix reproduces tables and graphs of certain functions useful in the application of the theory, from a paper by S. R. Lewis. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2754.pdf 443. Optical considerations and limitations of the Schlieren method G. S. Speak and D. J. Walters The elementary principles of the schlieren method are first described, with reference to an ideal basic system. Various developments from this basic system are then considered with particular reference to their advantages and disadvantages from the optical point of view. The experimental procedure in setting up the system is also covered from the same aspect. The general optical theory of the schlieren method is worked out, firstly in terms of the deflection of a ray which passes through a medium of varying refractive index, secondly in terms of the change in illumination caused by this deflection, which is calculated from diffraction theory. Some typical examples are worked out in the latter case. It is concluded that the schlieren method may be used qualitatively at extremely high sensitivities with satisfactory results, but is not suitable for quantitative work where small pressure or density changes are involved. A secondary conclusion is that the twin-mirror system is in general the best for overall ease of interpretation of results, though local considerations may modify this choice. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2859.pdf 444. Permissible design values and variability test factors R. J. Atkinson For the design of structural elements it is postulated that:- (a) not more than 10 per cent to any given design should have strength below the design value (b) not more than 0.1 per cent should have strength below 90 per cent of the design value. This rule forms a working basis for the interpretation of tests on statistical lines. On the basis of a fixed probability, Part I deduces:- (i) expressions for the derivation of permissible design values from a given number of test results (ii) the number of test results required, on specimens chosen at random, so that the estimates of permissible design values can be regarded as sufficiently accurate (iii) the factor which shouId be applied to the results of tests on any number of similar components designed to meet a specified requirement. The effects of different probabilities and of different acceptable proportions of weak specimens are investigated in Part II. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2877.pdf 445. Resonant vibration of helicopter rotor blades J. Morris The blades of the operative rotors of helicopters are usually hinged both in the lift and rotational planes and it is because of this articulation that the blades in the course of rotation are akin dynamically to 'pendulum vibration dampers'. If the fundamental frequency of this species of pendulum vibration is numerically equal to nN where n is the number of blades and N is the frequency of rotation of the rotor then serious resonant forced vibration may ensue and it would appear that this is quite likely to occur in practical cases with the blades in vibration in the plane of rotation of the rotor. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2801.pdf 446. Some additional notes on the derivation of airworthiness performance climb standards A. K. Weaver After the publication of a report (R. & M. 2631) on the derivation of airworthiness performance climb standards, various subsidiary points raised in the course of discussions were examined. Some of these have been collected together in the present note. They are in the nature of elaborations of the original method and include a refined method of deriving the take-off climb standard, a method of treating interdependence of engine failure and a method for including the effect of sideslip in the margin allowed for pilotage errors. The main principles set forth in the earlier report remain unaffected. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2769.pdf 447. Some investigations on thin nose-suction aerofoils part 1 a comparison of the stalling properties of some thin nose-suction aerofoils part 2 a theoretical investigation on thin high-lift aerofoils specially designed for nose-slot suction J. Williams Summary.--The stalling properties of some thin nose-suction aerofoils already tested have been examined, and further theoretical investigations have been carried out on thin aerofoils specially designed to give high lift with nose-slot suction. In Part I, the experimental results from stalling tests on thin nose-suction aerofoils are compared and the design features of the tested aerofoils are analysed. The aero foils include the 8 per cent thick Lighthill and Glauert sections specially designed for nose-slot suction, the 8 per cent thick H.S.A. V section with distributed suction through a porous nose, and some conventional sections of moderate thickness tested in Germany with slot suction at various positions on the nose. The Lighthill and Glauert aerofoils proved quite good without suction, but the increments in CL max due to suction were rather disappointing. The H.S.A. V aerofoil with distributed suction promises to be more economical as regards suction quantities for delaying the stall at full-scale Reynolds numbers, but this needs further confirmation. Part II describes a theoretical exploration of possible thin nose-slot aerofoils specially designed to have an abrupt fall in velocity where suction is to be applied on the upper surface of the nose. In an attempt to obtain better sections as regards a late stall at practical suction quantities, various symmetrical and cambered shapes were designed by a simple approximate method and the effect of sink action was also estimated. Low-speed stalling tests are to be made on one of the new cambered sections (D.2/4) in order to determine whether the considerable improvements expected are in fact achieved. The effect of the unusual nose shape on the high-speed performance of the section will also need to be examined. The theoretical formulae required for the calculation of the velocity distribution and lift of an aerofoil with a sink on its surface, and some detailed notes on the design of the Glauert nose-slot aerofoil, are given in the Appendices. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2693.pdf 448. Some preliminary model experiments on the whirling of shafts E. Downham Experimental work is now being done to establish a basis for the solution of whirling problems on turbine and contra-rotating shaft systems in the design stage. This report is concerned primarily with the degree of accuracy to be expected from experiments on models. In experiments here described results are obtained for a simple cantilever system which are in close agreement with theory. With more complicated systems the error is somewhat greater owing to practical effects not covered by theory, though still acceptable for most design purposes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2768.pdf 449. Summary of the theoretical work done on the stability of thin plates 1939 to 1946 D. M. A. Leggett Most of the work done during the war on the stability of thin plates has been written up and published in reports (Refs. 1 to 8). These reports do not however form a connected series, and the object of this summary is to draw attention to the more important stability problems which were requiring solution at the beginning of the war, and to indicate the progress made towards their solution during the subsequent seven years. In 1939 there were three main problems, or types of problem, for which existing solutions were inadequate: (A) the critical buckling load of a flat rectanguiar plate when the edges are not all simply supported, with special reference to a plate under shear, (B) the post-buckling behaviour of a long flat plate under shear, (C) the initial and post-buckling behaviour of a curved plate under various combinations of shear, compression, and normal pressure. Of these three classes of problem (A) and (B) are primarily important in the design of plate web spars, while (C) is clearly of much wider application. For in any aeroplane of predominantly stressed-skin construction, the surface of the wings and fuselage consists very largely of thin and slightly curved plates. Moreover, in addition to the general and ever-present problem of making aircraft structures lighter, aerodynamic developments during the war presented the aircraft designer with the further task of constructing wings that would remain sufficiently smooth to provide laminar flow over a considerable portion of the wing surface (R. & M. 2193). As the degree of smoothness required is incompatible with buckling, this gave added importance to knowledge of the loads at which flat and slightly curved plates begin buckling. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2784.pdf 450. Symmetric flutter characteristics of a hypothetical delta wing D. L. Woodcock This report considers the flutter characteristics of a hypothetical Delta wing. It details the results of quaternary calculations showing the effect on the reduced critical speed of the shapes and relative natural frequencies of the first two normal modes of the aircraft. From these results the stiffnesses necessary to avoid flutter are deduced for two forms of wing structure. The aerodynamic forces have been obtained by using two-dimensional derivatives multiplied by the cosine of the quarter-chord sweepback in conjunction with strip theory applied to fore-and-aft strips. This procedure is of doubtful validity for the low aspect-ratio wing considered. With this reservation, however, the results confirm the adequacy of the present Ministry of Supply wing-stiffness requirement. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2839.pdf 451. Tests on a swept-back wing and body in the compressed air tunnel C. Salter, C. J. W. Miles and H. M. Lee The model consisted of a swept-back wing of symmetrical section and a long cylindrical body. The aspect ratio was 3.29, the taper ratio 2.75, the sweep of the quarter-chord line 42.5 deg, the maximum thickness/chord ratio at the root 8.6 per cent and at the tip 10 per cent. It has been tested over a range of Reynolds numbers of 0.5 x 10power66 to 13 x 10power6 and results are given of lift, drag and pitching moment for angles of incidence up to 30 deg. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2738.pdf 452. The critical whirling speeds and natural vibrations of a shaft carrying a symmetrical rotor E. Downham The experiments described in this report are part of a programme of model experiments designed to establish an accurate method for calculating the critical whirling speeds of complex systems. The critical whirling speeds and natural vibrations of a single shaft flexibly supported and carrying a flexible rotor of appreciable moment of inertia have been investigated and good agreement has been obtained between experimental and calculated results for the rotating system. There is some discrepancy between calculated and experimental results for the vibration of the non-rotating system, which is thought to be due to the operational characteristics of the flexible bearing. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2854.pdf 453. The design and testing of supersonic nozzles R. Harrop, P. I. F. Bright, J. Salmon and M. T. Caiger The theory of the flow through a throat near sonic velocity is developed, and is followed by a discussion of the conventional method of designing supersonic nozzles using the method of characteristics. A method of improving the Mach number distribution of the nozzle using the experimental results is developed. The nozzles designed were tested in a 3-in. square wind tunnel in which the Mach number distribution was obtained by shaping the top wall of the working-section. The Mach number distribution along the bottom wall was determined from the pressures measured by a series of static pressure holes along the wall. Considerable difficulty was found in improving the distribution; this was considered to be due to the discontinuity in curvature at the point of inflexion and the influence on the boundary layer of the sudden relaxation of the pressure gradient along the wall. An alternative method of design was developed which avoided this discontinuity in curvature, and considerably better results were obtained when attempts were made to improve the experimental Mach number distribution. The flow through the throat of the liners was determined experimentally and compared with the theory. The agreement was good on the whole, although there were differences in the subsonic entry region because the bottom wall only became flat a short distance before the throat. In addition, tests were made which showed that the assumption of two-dimensional flow through the throat was justified. The method developed to improve the distribution in the nozzle was extended to derive liner shapes for Mach numbers differing by 0.10 from the design Mach number. It was found that changes of this order could be made fairly successfully but further modification was necessary to reach the standard required for tunnel use. The necessity for a smooth and accurately constructed liner surface is stressed. The limitations of the methods used for designing supersonic nozzles are discussed and several problems are mentioned which it is thought will need further consideration. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2712.pdf 454. The effect of sweepback on the fundamental derivative coefficient for flexural motion J. B. Bratt, and K. C. Wight Measurements have been made with new equipment designed for derivative tests in a 9 x 7 ft tunnel, to determine the effect of sweepback on the derivatives for a rectangular aerofoil of aspect ratio 6. Some difficulty was experienced in the interpretation of the measurements on the swept aerofoil due to distortion of the model during oscillation. The effect is examined in detail in an appendix and a method of correction devised. A comparison between measurements for the unswept aerofoil and earlier measurements made with the same model by the method of decaying oscillations gives satisfactory agreement. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2774.pdf 455. The evaluation of downwash at large spanwise distances from a vortex lattice H. C. Garner This note explains an improved numerical method of evaluating the contributions to the downwash at moderate or large spanwise distances from a vortex lattice. By allowing freedom of choice of ihe chordwise positions of the discrete vortices of the lattice, it is possible to select three definite chordwise positions and strengths of vortices at, each of these positions dependent on the chordwise pressure distribution, so as to determine the downwash with good accuracy for three particular pressure distributions proportional to cot ½θ, sin θ and sin 2θ. The corresponding chordwise loading factors have also been evaluated for deflected flaps. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2808.pdf 456. The flutter of swept and unswept wings with fixed-root conditions Part 1 wind-tunnel experiments Part 2 comparison of experiment and theory Part 3 wing torsional stiffness criterion W. G. Molyneux The 'fixed-root' flexure-torsion flutter characteristics of four model wings of different taper ratios have been investigated in the wind tunnel. The wing inertia axis and the angle of sweepback have been varied on each wing over the ranges 0.4c to 0.5c and 0 deg to 50 deg respectively. The results show that :- (i) The flutter speed at any angle of sweepback (including the unswept case) varies approximately linearly with inertia axis position increasing as the inertia axis is moved forward aud approximately linearly with wing taper ratio increasing as the taper is increased. (ii) The flutter speed decreases slightly for small angles of sweepback and then increases rapidly as sweepback increases. The results of one theoretical treatment gave good agreement with experiment for variation of flutter speed with sweepback and inertia axis. The experimental results support the present wing torsional stiffness criterion. Simple amendment to the criterion are put forward for the effects of sweepback. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2796.pdf 457. The flutter properties of a simple aero-isoclinic wing system N. C. Lambourne and A. Chinneck The work dealt with in this report is of an exploratory nature primarily intended to provide some understanding of the flutter characteristics of a Hill aero-isoclinic wing. Essentially, this is a swept-back wing elastically designed so that the lifting loads do not affect the aerodynamic incidence. The aero-isoclinic property is dependent on the change of incidence due to torsion of the wing being neutralised by that produced by wing bending. The simple aero-isoclinic system used in the tests consisted of a rigid aerodynamic lifting surface having the two essential freedoms, rotation about a swept-back axis, and rotation about a perpendicular axis at the root. Flutter critical speeds and frequencies were measured over a range of the ratio of the bending and torsion frequencies; the results show that the aero-isoclinic condition is not sufficient to prevent flutter, and further that the critical speed for flutter may be low. As usual, forward mass-loading of the wing raises the critical speed. A subsidiary part of the report deals with a method of flutter-speed calculation in which the aerodynamic terms are restricted to static derivatives only. No damping terms whatever are present in the equations of motion. The solution yields a boundary between constant amplitude and growing oscillations, which is regarded as the flutter critical condition. The method gives critical flutter speeds that agree surprisingly well with the experiments. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2869.pdf 458. The frequency response of the ordinary rotor blade, the Hiller servo-blade, and the Young-Bell stabiliser G. J. Sissingh The present report deals with the frequency response of pivoted gyratory systems, and in particular, with the response of the ordinary rotor blade, the Hiller servo-blade, and the Young-Bell stabiliser to sinusoidal disturbances caused by pitching oscillations with constant amplitude. Physically, the problem corresponds to a single degree of freedom system excited by beats. The resulting forced oscillations are characterised by the two following phase angles :- (a) a phase angle in the plane of rotation (b) a phase angle of the oscillation of the tip-path plane, where the tip-path plane may be considered as a solid body. The latter, which is the controlling consideration, depends on the specific damping of the system and the frequency ratio. In general, the tip-path plane of the systems mentioned above oscillates in two directions, longitudinal, and lateral, where both modes of oscillation can be split up into components in phase with the attitude and in phase with the rate of change of attitude. For each individual system explicit formulae are given and the effect of the frequency ratio on the control characteristics of the Bell stabiliser and Hiller servo-blade is shown by vector loci. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2860.pdf 459. The induced velocity field of a rotor K. W. Mangler and H. B. Squire A short account and the results of a theoretical investigation (cf. Ref. 1 and 2) of the velocity field induced by a lifting rotor is given. The computation is based on the assumptions that the rotor is lightly loaded and that it has an infinite number of blades. This is applied to calculate the induced velocity distribution for disc incidences of 0, 15, 30, 45 and 90 deg. For the downwash at the rotor itself (the normal component of the induced velocity) the Fourier coefficients are given, as they are needed for the calculation of the blade motion. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2642.pdf 460. The influence of rolling moments on spin recovery as observed in model-spinning tests D. J. Harper Several aspects of model-spinning test technique have been brought into prominence by recent full-cale developments. Correlation between model and full-scale recoveries has been poor in some cases, and it appears from model tests of some new aircraft that full-scale recovery may depend on other means in addition to the normal use of rudder and elevator. Analysis of model data shows the effects of applied rolling moments and of aileron deflections on both spin and recovery to be closely related to the distribution of loading in the aircraft. The ordinary model-test result can be considerably in error in either direction due to the neglect of probable scale effects on rolling moments. Deflection of the ailerons can be of great assistance to model recovery and flight confirmation of this effect is required. Information on the scale effects on rolling moments for delta aircraft is also urgently needed, as these models show much greater sensitivity than conventional models to the application of rolling moments. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2831.pdf 461. The rolling power of an elastic swept wing E. G. Broadbent An iterative method of solution is given for the problem of loss in rolling power due to wing deformation. The method is applicable at subsonic or supersonic speeds, and compressibility effects are allowed for, provided the variation of the aerodynamic derivatives with Mach number is known. The numerical labour involved in the solution is not great and the accuracy is considerably greater than can be achieved by the semi-rigid method. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2857.pdf 462. The stress distribution in a swept-back box-beam with perpendicular ribs P. B. Hovell A solution is obtained for the distribution of internal load in a swept-back box-beam of rectangular cross-section under any system of external loading. The theory, based upon strain energy, is considered exact when the ribs are perpendicular to the spars and when the spanwise bending loads are taken by the spar booms. The general solution for encastre root conditions is given. Extensions of the method to cover root flexibility and cut-outs in the top or bottom skins are discussed. A numerical example of a simple two-spar box is investigated for a range of sweepback angle of 0 deg. to 40 deg. for an encastre root condition. The analysis shows that appreciable redistributions of load in the box, compared with the unswept box, are obtained when either torque or bending moment is applied to the beam. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2837.pdf 463. The theoretical pressure distributions around some conventional T. J. Hargest By means of Relf's analogy between aerodynamic streamline flow and electric potential flow, the theoretical pressure distributions around a series of conventional turbine blades in cascade have been determined over a range of incidence covered in some previously reported aerodynamic tests. The theoretical pressure distributions and their variation with incidence provide the basis of an explanation of the observed aerodynamic performance. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2765.pdf 464. The two-dimensional subsonic flow of an inviscid fluid about an aerofoil of arbitrary shape. Parts I to IV L. C. Woods The paper describes and applies exact methods of calculating the incompressible flow about thick aerofoils of general shape in a free stream, and about symmetrical aerofoils between channel walls. One of these methods is extended to an approximate treatment of subsonic compressible flow by making use of yon Karman's transformation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2811.pdf 465. Theoretical requirements of tunnel experiments for determining stability derivatives in oscillatory longitudinal disturbances S. Neumark and A. W. Thorpe The need of using stability derivatives of unsteady.(oscillatory) motion is explained, and requirements of tunnel experiments for determining them are established. These are based on simple theoretical considerations, valid for both incompressible and compressible (sub- and supersonic) flow. Two alternative schemes of experimental tests are critically examined. Non-dimensional derivatives are defined and applied in modified stability equations, referred to fixed or moving systems of co-ordinate axes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2903.pdf 466. Theoretical supersonic drag of non-lifting infinite-span wings swept behind the Mach lines T. Nonweiler The drag of a non-lifting swept wing of infinite span is investigated for supersonic flow when the Mach lines from the wing apex lie ahead of the wing leading-edge. The wing section is assumed to be arbitrary but identical over the entire wing-span. The drag is found according to the linear equations of supersonic flow by considering the flow due to a system of superposed source planes. The drag of such a wing is found to be finite and the effect of the speed of flight independent of the section shape assumed. The variation of drag with the section shape is shown to be proportional to the integral over the chord of the product of the local wing thickness and the value of the excess pressure existing in incompressible flow at the same position. The drag of wing-sections given by certain types of formula is evaluated in general terms, and some numerical results are given : the drag of sections with bluff noses and finite trailing-edge angles is generally between 0 and 15 per cent greater than the drag of a wing of the same sweep and thickness having a biconvex section. Finally, methods of reducing the drag by changing the section shape are considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2795.pdf 467. Thermodynamic charts for the combustion products of nitric acid and kerosene W. H. Williams Thermodynamic charts giving enthalpy, entropy, temperature, pressure and specific volume, have been constructed for the products of combustion of a hydrocarbon fuel (85 per cent C, 15 per cent H by weight) with nitric acid (98 per cent by weight). The charts have been drawn for the following mixture ratios of the propellants: (a) stoichiometric proportion (b) 10 per cent by weight excess of fuel (c) 50 per cent by weight excess of fuel (d) 10 per cent by weight excess of oxidant. Graphs of combustion temperature and specific impulse against mixture ratio are also shown. The procedure for calculating the initial enthalpy of the separate propellants (before combustion) and that of the propellant mixture is described. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2982.pdf 468. Towing-tank tests on a large six-engine flying boat seaplane, to specification 10/46 (Princess) Part 2 porpoising stability, spray and air drag tests, with improved step fairing, afterbody design and aerodynamic modifications A. G. Smith, D. F. Wright and T. B. Owen Further model tests were made on the Princess flying boat to: (a) improve the main-step fairing in order to reduce air drag while retaining satisfactory porpoising stability at high water speeds, (b) reduce the mid-planing porpoising instability found with the hull lines tested in Part I of this report (R. & M. 2641), (c) test the effect of increased wing and tailplane areas, (d) predict more accurately the full-scale performance of the final hull form by representing more closely the anticipated full-scale conditions of lift, slipstream and damping in pitch. The tank tests were made in sheltered water conditions in the Seaplane Towing Tank, Royal Aircraft Establishment, Farnborough, on a dynamic model, and parallel tunnel tests on the step-fairing design were made in the Saro Wind Tunnel at Osborne. The final hull form evolved is used for the first production aircraft. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2834.pdf 469. Two-dimensional control characteristics L. W. Bryant, A. S. Halliday and A. S. Batson The design of lifting surfaces for aeroplanes depends fundamentally on two-dimensional data for the aerofoil sections, with flaps where necessary for control. Data of this kind are required for the use of designers, and for the development of methods of calculating control characteristics and stability derivatives for finite wings. Researches on the lift, pitching moments, and hinge moments of aerofoils with plain flaps have been carried out at the National Physical Laboratory at a Reynolds number of about 10 6. The results of the experiments have been presented in a generalised form, which shows promise of being applicable over a wide field. The generalised curves have been tested as far as possible from other sources, including some tests made on one of the National Physical Laboratory sections in a Royal Aircraft Establishment Tunnel at Reynolds numbers up to nearly 10 7. It appears that a suggestion due to Preston that the ratio of experimental lift slope to the theoretical value, corresponding to the Joukowsky condition of flow past the trailing edge, provides a criterion giving the combined effects of Reynolds number, transition points, and aerofoil shape, and is a very usefnl starting point for the estimation of control characteristics. The generalised charts in this report are intended for the estimation of hinge-moment and pitching-moment derivatives from the flap/chord ratio, E after al/(a~)T has been determined from a special figure. The latter figure (Fig. 14) is a key to the whole process, and it would appear to be very desirable to improve its accuracy and usefulness by further experiments on two-dimensional lift slopes of thin wings at high Reynolds numbers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2730.pdf 470. Two-dimensional wind-tunnel interference L. G. Whitehead Exact solutions are given for the inviscid flow past two cylindrical profiles in tile centre of a stream of limited depth. The first of these relates to a nearly circular cylinder and the second to a thin section giving a constant pressure drop over the greater part of its surface. The stream has either parallel walls, constant pressure wails, or the boundaries may be partly parallel and partly of the constant pressure type. For the thin profiles the changes of thickness ratio required to give the same pressure distribution as in an unlimited flow are found. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2802.pdf 471. Velocity distribution on thin bodies of revolution at zero incidence in incompressible flow S. Neumark A new method of determining velocity distribution on slender bodies of revolution in axial flow is expounded, analogous to the linear perturbation method widely used for slender symmetrical profiles in two dimensions. The proposed method leads to simple approximate formulae for velocity distribution on a body, once the equation of the meridian line is given, either in the form of a polynomial, or a square root of one. The new method avoids many inconveniences of the older procedures, and is much more rapid. Although theoretically applicable to bodies of small thickness only, it works with satisfactory accuracy up to quite considerable thickness ratios. It has been further improved by taking into account not only axial but also radial velocity components, following a suggestion of Lighthill's supersonic theory. It may be easily applied to compressible subsonic flow. The method has been used for computing velocity distributions on twelve different bodies, of seven different thickness ratios (0.04-0.28) each, so as to exhibit the most characteristic features in typical cases, and especially to show some unexpected effects of thickness changes. Several practical conclusions have been derived from the examination and comparison of these results. The method may find useful applications in the design of fuselages, nacelles and wing junctions, and especially in determining critical Mach numbers for such bodies. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2814.pdf 472. Water and air performance of seaplane hulls as affected by fairing and fineness ratio A. G. Smith, and J. E. Allen An analysis is made of data on the variation of hull air drag with length/beam ratio and degree of local fairing, and of the maximum beam loading permitted for reasonable hydrodynamic performance. The effect of length/beam ratio on hull structure weight is also very briefly discussed. Considerable reduction of surface-area drag coefficient is shown to be possible by extending the length/beam ratio above that in normal use, keeping the height and waterborne load constant. The length/beam ratio can usefully be defined in terms of the forebody-length/beam ratio. If this be increased from 3.5 to 7 the surface drag coefficient with an unfaired two step hull decreases from 1.6 to 1.35 times that of a body of revolution of the same length and maximum cross sectional area. With a transverse step faired with a 10 : 1 straight fairing in elevation the reduction is from the order of 1.15 to 1.10 and with a step faired in plan-form and elevation from the order of 1.20 to 1.15. The usefulness of the last step form is high because no applied ventilation is required to make it operationally acceptable. Also its drag could be further reduced if applied ventilation were permitted. A similar order of total drag reduction is also possible if the forebody-length/beam ratio be increased so as to keep constant the product of the beam and the square of the forebody length. Under these conditions there is negligible increase of overall surface area, and the water performance for a given water load and hull height is reasonably constant as beam loading is increased. The limit to which the length/beam ratio can be increased will probably be determined by the minimum hull volmne or width required for stowage purposes since this decreases fairly quickly, or seating width in passenger aircraft. Hull weight is probably decreased a little with increase of length/beam ratio when the product of the beam and the square of the forebody length is kept constant. Charts are given to help in the selection of the best hull form for any given design conditions. From these may be estimated dimensions, air drag, and tile maximum beam loading to give a reasonable standard of water performance. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2896.pdf 473. Wind-tunnel flutter tests on a model delta wing under fixed and free root conditions D. R. Gaukroger, E. W. Chapple and A. Milln Wind-tunnel tests on a model wing of delta plan form are described. Tests have heen made with the wing root fixed and also with the root free in pitch and vertical translation. Critical flutter speed and frequency are given for a wide range of variation of wing and fuselage inertia parameters. The results show that, under root-free conditions, body freedom flutter occurs at low values of fuselage pitching moment of inertia, but that at higher values the flutter is similar to that obtained with root-fixed conditions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2826.pdf 474. Wind-tunnel interference effects on measurements of aerodynamic coefficients for oscillating aerofoils W. P. Jones A theory is developed for estimating the effect of wind-tunnel walls on measured values of aerodynamic coefficients for two-dimensional aerofoils oscillating in an incompressible fluid. The case of an aerofoil describing translational and pitching oscillations in a wind tunnel of rectangular cross-section is considered, and it is shown in Table 1 and Figs. 3 and 4 that the damping derivatives associated with the pitching degree of freedom are very sensitive to wall effects when the frequency parameter for the motion is small, and when the axis of oscillation is not at, or near, quarter chord. When the axis is at quarter chord, the pitching-moment damping-derivative is hardly affected by the presence of the tunnel walls. The values of the derivatives given in Table 1 refer to an axis of oscillation at mid-chord and correspond to a ratio of tunnel height to aerofoil chord of 4.75. They are used to determine the pitching-moment derivatives for an axis of oscillation at 0.445c for comparison with values obtained by J. B. Bratt from measurements on a 2-in. chord aerofoil in a 9½-in. square wind tunnel. The theoretical values corresponding to free-stream conditions differ considerably from the experimental results, but, as shown in Figs. 4 and 5, better agreement is obtained when an allowance for tunnel-wall interference is made. The remaining difference between theory and experiment may he attributed to the influence of aerofoil thickness and to boundary-layer effects. By the use of the method developed in (R. & M. 2654), these effects can also be taken into account and incorporated in the theory presented for estimating pure interference corrections for the aerodynamic derivatives. When this is done, the results given in Table 2, and plotted in Figs. 4 and 5, are obtained. A comparison of theory and experiment then shows satisfactory agreement. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2786.pdf 475. Wind-tunnel tests on the prevention of boundary-layer separation by distributed suction at the rear of a thick aerofoil (NPL 153) N. Gregory, R. C. Pankhurst, and W. S. Walker Tests of a preliminary nature have been carried out on a 33 per cent thick symmetrical aerofoil (NPL 153) with suction through a porous surface from 0- 80 chord to the trailing edge, which was rounded and fitted with a Thwaites flap. The distributed suction was found to prevent separation and to reduce the wake drag to zero. The overall effective drag (including an allowance for the power required for the suction) was reduced slightly, but still remains fairly high. No hysteresis was observed in the change of drag with suction quantity. The flap was essential to stabilise the flow : without it, the flow with suction was unsteady and the wake drag was appreciable. When the flap was deflected 20 deg there was no increase in the suction quantity required to prevent separation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2788.pdf 476. Wind-tunnel tests on two-dimensional supersonic aerofoils at M = 1.86 and M = 2.48 D. Beastall and R. J. Pallant Wind-tunnel tests, at Mach numbers 1.86 and 2.48, have been carried out on two-dimensional unswept double-wedge and circular-arc aerofoils to study the viscous effects which are not accounted for in the linearised and shock-expansion aerofoil theories. The aerofoil characteristics derived from the measured surface pressures are compared with the theoretical values. Schlieren observation was employed to examine the flow and, in particular, the separation near the trailing edges of the aerofoils. In an appendix the results obtained from experiments on breakaway caused by a step on a flat plate are applied to the aerofoil tests as a method of assessing the pressures in the dead-water regions formed by the flow separation, and comparison is made with the measured pressures. Disturbing the boundary layer by means of wires caused a delay in separation; pitot-tube traverses through the boundary layers with and without wires illustrated the change in velocity profile between the two cases. The position of separation was briefly examined also by the use of oil; the point of separation as indicated by this method was in fair agreement with that given by pressure measurements, for cases of considerable separation only. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2800.pdf 477. A direct iteration method for the calculation of the velocity distribution of bodies of revolution and symmetrical profiles F. Vandrey An integral equation is derived for the velocity on the surface of a given body of revolution or a given symmetrical profile in longitudinal flow, using the generation of a body by a vortex layer on its surface. The equation can be solved by the usual iteration method for linear integral equations of the second kind. The method of generating a body by a vortex layer leads to formulae expressing the components of the velocity outside the body by means of its pressure distribution. In general, the numerical work is greater for this method than for the indirect methods which use essentially a generation of the body by a distribution of sources and sinks on its axis. On the other hand, the method is not restricted to the case in which the analytic continuetion of the flow into the interior of the body does not meet singularities outside the axis. The only requirement is that the shape of the body must have a continuous tangent, whereas its curvature may have isolated discontinuities. Numerical examples are given for the two-dimensional case of a semi-infinite plate of constant thickness with a semi-circular leading edge, and for the three-dimensional case of a semi-infinite cylinder with three different heads (hemispherical, 2 caliber ogival and ¼ caliber rounded). The calculation is in good agreement with experimental results. Some numerical tables are given in order to facilitate the calculation of the kernel of the integral equation which forms the major part of the numerical work. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3374.pdf 478. A frost-point hygrometer for supersonic wind tunnels D. Beastall and A. Winyard This report describes a frost-point hygrometer suitable for measuring the water-vapour content of the air in supersonic wind tunnels at any stagnation pressure within their present range of operatiom It uses CO2 as a coolant and is economical in construction and operation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3112.pdf 479. A method of performance estimation for axial-flow turbines D. G. Ainley, G. C. R. Mathieson A method for calculation of the performance of conventional axial-flow turbines is presented. It makes use of data derived from the analysis of a large number of turbine tests and other associated test work reported elsewhere. The method enables the performance of a turbine to be calculated over a wide part of its full operating range. It is estimated that the tolerance on the absolute values of gas mass flow and peak efficiency will be in the region of Â±2.0 per cent for efficiency and Â±3 per cent for gas mass flow on present day types of turbine. The method is illustrated by a worked example. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2974.pdf 480. A simplified treatment of a fixed-root swept wing built on Hill's isoclinic principle D. Williams This note shows how the Hill Aero-isoclinic Principle works out in practice for a swept wing, fixed at the root and having straight flexural and inertia axes. The conditions assumed are readily represented in a wind-tunnel model and experiments by Lambourne show good agreement with theory. The further aft the flexural axis from the quarter-chord position, the smaller is the sacrifice of wing torsional stiffness entailed in making a swept wing isoclinic, and previous work has on that account taken a far-aft position as a reasonable basic assumption, with the result that, to avoid aero-elastic instability, a well-forward position for the inertia axis is arrived at. It is shown here, however, that by still further sacrifice of torsional stiffness (whether practicable or not) it is possible to reduce the gap between the two axes very considerably and so simplify one aspect of the constructional problem. It is expected that this conclusion should still hold, qualitatively at least, for the more representative conditions in which body freedoms are included, as in tile earlier work referred to above. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2870.pdf 481. A theoretical treatment of noise and non-linearities in a beam-riding system E. G. C. Burt The effectiveness of a beam-riding missile is greatly influenced by the mutual effect of noise and nonlinearities. The former is mostly due to radar jitter, while the principal non-linearity is that introduced by limiting the lateral acceleration of the missile to a safe value. For the beam-riding system discussed in this paper the degree of saturation is such that the linear analysis is inadequate, and account must be taken of the non-linearity. With certain assumptions, the system can be described analytically: further approximations lead to optimum values of the disposable parameters for obtaining the minimum miss distance. The analysis shows that, while optimum values of the parameters can be specified for a restricted class of target trajectories, a more detailed study of likely target manoeuvres is necessary before an overall optimum can be defined. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3417.pdf 482. Abstracts of papers published externally
CONTENTS. Repeated Loading and Fatigue Tests on a D.H.104 (Dove) Wing and Fin. Shock-wave and Boundaiy-layer Phenomena near a Flat Surface. Jet Flow and its Effects on Aircraft. A Shielded Hot-wire Anemometer for Low Speeds. The Economic Value of Increase of Modulus of Elasticity in Aluminium Alloys. Notes on the Opening Behaviour and the Opening Forces of Parachutes. The Application of Mellin Transforms to the Summation of Slowly Convergent Series. A Note on the Time required to make a Level Speed Measurement with a Turbine-Jet Aircraft. A Note on Repeated Loading Tests on Components and Complete Structures. Longitudinal Stability, Speed and Height. Some Developments of Expansion Methods for Solving the Flutter Equations. The Reheat Factor in Turbines and Turbo-compressors. The Steady Circulatory Flow about a Circular Cylinder with Uniformly Distributed Suction at the Surface. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2722.pdf 483. Aerodynamic coefficients for an oscillating delta wing Doris E. Lehrian Under review Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2841.pdf 484. Aerodynamic Forces on Biconvex Aerofoils Oscillating in a Supersonic Airstream + Effect of Thickness on the Aerodynamic Forces on Biconvex Aerofoils Oscillating in a Supersonic Airstream, and Calculation of Forces for Aerofoil with Flap W. P. Jones and Sylvia W. Skan A method for the calculation of the aerodynamic forces on an oscillating aerofoil which allows for the effect of thickness is developed. The steady flow regime for zero or mean incidence is first determhaed for isentropic, irrotational and inviscid flow conditions. A small disturbance is then assumed and the non-linear equation defining the subsequent motion is reduced to a linear equation for the velocity potential of the disturbance. This is expressed in difference form and solved numerically by a step-by-step process. The results obtained show good agreement with the known solutions for a thick aerofoil at incidence in steady flow, and for the case of an oscillating flat plate. Consequently, it is believed that the results derived for an oscillating biconvex aerofoil are reasonably accurate. Aerodynamic lift and pitching moment derivatives for a 5 per cent thick, symmetrical, circular-arc aerofoil at Mach numbers M = 1.4, 1.5 and 2.0 are given for a range of frequencies and compared with values obtained on the basis of the flat plate theory. The effect of thickness appears to be important at the lower values of M, and the results indicate that the flat plate theory is not sufficiently accurate. + The lift distribution and the aerodynamic force coefficients are calculated for a 7.5 per cent thick symmetrical circular-arc aerofoil at Mach numbers Mo = 2.0, 1.7, 1.5 for a range of frequencies. These results are compared wffh those given in an earlier report (Ref. 1) for a 5 per cent thick aerofoil, and with the values derived on the basis of flat plate theory. A limited comparison is also made between the calculated results and those obtained experimentally. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2749.pdf 485. Air-cooling methods for gas-turbine combustion systems F. J. Bayley This paper presents an account of the whole of the work which has been done at the National Gas Turbine Establishment on the problem of air cooling gas-turbine combustion systems. Each of the different methods, of wall cooling is discussed separately and the theory and mechanism of the cooling process is developed from first principles. Certain of the methods have been the subjects of experimental investigations and in such cases a brief description of the test arrangements is given and the results are analysed arid discussed. Sufficient information is given to enable any of the various methods to be applied to practical wall-cooling problems and, in a conclusion to the report, their relative advantages and disadvantages for different gas-turbine applications are considered. It is shown that 'sweat', or effusion-cooling, is by far the most effective and efficient method, while the use of 'louvred' surfaces represents the nearest practical approach to this ideal which is possible while suitable porous materials remain unavailable. The remaining methods (convective cooling by external airflow, localised air injection to form a protective blanket of coolant, and a combination of these two), are all less effective, but provide means whereby conventional combustion systems may be conveniently cooled without the need for porous materials or the weight increases associated with louvred walls. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3110.pdf 486. Alternating pressures and blade stresses in an axial-flow compressor J. R. Forshaw, H. Taylor, and R. Chaplin The majority of blade failures in axial-flow compressors have occurred in the rotor blades of the lower pressure stages. These have been caused mainly by fatigue in the fundamental flexural mode of vibration in the presence of the steady centrifugal and gas bending stresses. An investigation has been made into the origin of the forces exciting vibration in an axial-flow compressor, and their magnitude relative to the calculated gas bending loads. The blade stresses resulting from these forces were measured, and a value obtained for the energy input to a blade when vibrating in the predominant modes under running conditions. The experimental data were obtained from pressure elements and strain-gauges fitted to the inlet guide vanes and first four stator-blade rows of an early compressor. The oscillating pressure reached peak values when the forcing frequencies in a stage coincided with the blade natural frequencies of that stage or of adjacent stages, and was predominant for modes approximating to the fundamental flexural mode of vibration. This indicated that vibrations of any one stage â€˜modulatedâ€™ the stream, the pressure waves extending upstream and downstream. The magnitude of the alternating pressure was 40 per cent and 5 per cent of the stage pressure rise at 4,000 and 8,000 r.p.m. respectively. The ratio of the major harmonic components of the alternating stress to the calculated gas bending stress was 2:1.3 : 0.6 at rotor speeds of 4,000, 6,000 and 8,000 r.p.m. Values of input energy and kinetic energy obtained for resonances approximating to the fundamental flexural mode showed that the damping present in. a stator blade was high. Contributing factors to this high damping were the light root platform and loose fit of some blades. The prominence of blade vibration resulting from modulation of the air stream by the vibration of blades in adjacent stages is attributed to the high damping present. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2846.pdf 487. An analysis of available data on the local aerodynamic centres of aerofoils in two- and three-dimensional flow A. S. Taylor This report reviews existing information regarding the behaviour of the local aerodynamic centres of aerofoils, with a view to exposing the more important gaps in our knowledge, and, indicating the lines along which future research might most profitably be directed. Starting with the two-dimensional aerofoil in incompressible, viscous flow, for which aerodynamic centre position may be correlated with lift slope, the report passes on to examine the behaviour of the two-dimensional aerodynamic centre in compressible flow. Experimental data which have been analysed (relating to the subsonic and lower transonic regimes) are not in agreement with the predictions of potential flow theory; this suggests that the Reynolds number and transition position effects, associated with viscous flow, exert a powerful influence on the aerodsalamic centre. Considering next the locus of aerodynamic centres for wings of finite aspect ratio, the report discusses the various incompressible potential flow theories and their extension to the subsonic and transonic regimes of compressible flow, and collects in a series of figures, the published results of calculations by various investigators. A brief mention is made of supersonic theory. A further set of figures presents experimental data. No prescription can be given for determining exactly the behaviour of the local aerodynamic centres of a given wing, but in the concluding section of the report it is suggested how the reader may use the assembled data to make a reasonable guess. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3000.pdf 488. An approximation to the slow mode of longitudinally disturbed motion of an aircraft in level flight A. W. Thorpe This report develops an approximate theory of longitudinal response which applies to the slow mode of motion after a disturbance. This theory is complementary to that for the quick-period motion given by Gates and Lyon. It predicts the slow motions which occur after the quick-period motions have died out. The approximate equations given are of second order only and can therefore be solved algebraically. This has been done and the general solutions are given in Tables 1 and 2. Some numerical examples have been computed to indicate the accuracy which can be expected. The agreement with the first approximation is quite good and in some components it can be improved by the use of a further correction term. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2907.pdf 489. An assessment of the probable causes of variation of the speed-correction coefficient of aircraft thermometers D. D. Clark In M.R.P. 527 Shellard has summarised the evidence indicating that a variation takes place in the speed-correction coefficient of aircraft thermometers both with altitude and, in One particular case, with air speed. He also mentions some possible reasons for the variations. In what follows, an attempt has been made to list all factors which couid possibly affect the speed-correction coefficient and to examine each thoroughly in turn. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3127.pdf 490. An examination of the flow and pressure losses in blade rows of axial-flow turbines D. G. Ainley and G. C. R. Mathieson The design of axial-flow turbines has been hampered in the past by a lack of comprehensive data regarding pressure losses and gas deflections through rows of turbine blades. In the present report much of the available information relating to this subject is studied and analysed to determine magnitudes of gas pressure losses and deflections in a wide variety of blade rows and also to determine the separate influences of variables such as blade shape, blade spacing, gas Mach number, Reynolds number, incidence, etc. Of particular importance are the effects of secondary flows on the aerodynamic performance of a blade row and special attention is paid to 'secondary losses', which form the difference between the total losses occurring in an actual turbine blade row and the smaller two-dimensional flow losses which are usually measured in a blade cascade tunnel. Effects of blade tip clearance are also studied. Resulting from this analysis a number of empirical guiding rules and charts have been derived from which approximate values of the overall pressure losses and gas deflections in a range of blade rows can be deduced. A particularly significant feature brought to light is that the secondary losses can in many instances be large, the loss being generally found to be great when the blading has low reaction. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2891.pdf 491. An experimental investigation of the boundary layer on a porous circular cylinder D. G. Hurley and B. Thwaites The report describes an experimental investigation of the boundary laver on the surface of a porous circular cylinder at which there is a normal inward velocity. The primary object of the experiments was to test the approximate theory of Ref. 1 for calculating the development of a laminar boundary layer under conditions of continuous suction. The formula given in that reference for calculating the momentum thickness of the layer gave results in accord with the experimental determinations. Owing to practical difficulties in the exploration of the very thin boundary layers and in the determination of the velocity gradient around the surface, other comparisons with the theory (such as the progressive development of the boundary-layer velocity distribution and of the prediction of the separation point) were difficult. Nevertheless reasonable agreement between the theoretical and experimental velocity distributions was obtained particularly for the lower wind speed of the experiment, but no adequate test of the prediction of the separation point was found possible. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2829.pdf 492. An extension of Multhopp's method of calculating the spanwise loading of wing-fuselage combinations J. Weber, D. A. Kirby and D. J. Kettle A simple method is described for calculating the spanwise loading over wing-fuselage combinations. It is based on Multhopp's method, which is extended here to cover wings of finite thickness, large root chords compared with the body diameter and also swept wings. The method is restricted to wings of moderate and large aspect ratios (above about 2). The effect of different junction shapes above and below the wing in off-centre positions of the wing cannot yet be calculated. The calculation can be performed in about one computer-day, and comparisons with experimental results show good agreement in the symmetrical case. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2872.pdf 493. Boundary-layer control for high lift by suction at the leading edge of a 40 deg swept-back wing E. D. Poppleton Wind-tunnel tests have been made on a 40 deg swept-back wing, 10 per cent thick with constant chord and an aspect ratio of 4.6. Boundary-layer control was applied along the whole leading edge, and a comparison was made between the effects of distributed suction and suction through a slot. A 45 per cent Fowler flap was used in some tests. The overall effect of the two systems was similar, giving an increase in CL max by increasing the stalling incidence and making the wing statically stable up to the stall, when there was a severe loss of lift. At R = 1.29 x 10power6, a gain in CLmax of O.5 was obtained when CQ = 0.0023 with distributed suction over the first 2.5 per cent chord, while a CQ of 0.0074 was needed to obtain the same increment with a slot (0.18 per cent chord wide at 2.5 per cent chord). A maximum value of CL max of 1.95 was obtained by both methods with flaps down at α = 25 deg. For full-scale application, the suction required for distributed suction (8.2 lb/sq in.) is much higher than for the slot, but it may be possible to reduce this by grading the porosity in a chordwise direction or by dividing the leading edge into a number of separate spanwise compartments. With the slot, the quantity required is higher but the overall power is about the same. A reduction in power may be possible in this case, by improving the shape of the slot. As a means of producing high maximum lift on swept wings, both these methods have the disadvantage of requiring variable-incidence wings, if the full gain in CL max is to be used.: Either method can be used as a means of preventing tip stalling as an alternative to nose flaps or leading-edge slots. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2897.pdf 494. Calculation of the pressure distribution over a wing at sonic speeds K. W. Mangler A method is developed for the calculation of the pressure distribution and the aerodynamic forces and moments acting on a wing at incidence, a wing in (steady) roll and a wing in (steady) pitch. The calculation is based on the assumption of an inviscid potential flow and is restricted to small incidence and thickness ratio, so that quadratic terms in the perturbation velocities are neglected. The results are valid, if |1 - M²|.A² is small compared to 1, i.e., either for any Mach number M for wings of a small aspect ratio A, or for any aspect ratio for sonic speeds (M ≉ 1). The aerodynamic coefficients and stability derivatives l~ and m~ for a wing family which is described by the parameters aspect ratio A, taper ratio λ, and sweep ratio α (Fig. 8), are given in the form of charts. The calculation indicates, that the plan-form of the wing is of similar importance as regards the pressure distribution at sonic speeds as the chordwise section of a wing at subsonic speeds for wings of larger aspect ratios. Although the calculation is based on the assumption of an inviscid flbw without shock-waves, the results are thought to be useful for showing the main trends of the behaviour of a wing near the speed of sound. Plan-forms, which show rapid variations of the aerodynamic properties near Mach number M = 1 according to the potential theory, will have to be abandoned in favour of other planforms with more favourable characteristics. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2888.pdf 495. Control effectiveness tests at transonic speeds on an EC.1250 section with 0.25 chord concave control T. Lawrence Control effectiveness tests, using the ground-launched rocket-boosted model technique, have been made on rectangular wings of aspect ratio 4, EC.1250 section, and fitted with a 25 per cent chord concave control flap. Tests were done from M=0.73 to M=1.5, and at R=3.5 x10power6 and 7x10power6 at M=1. There is a sudden and large reversal in control effectiveness at M=0.9, but the measured effectiveness below M=0.8 and above M= 1.1 is in good agreement with theory. These tests confirm and extend to higher Reynolds numbers and Mach numbers previous tunnel tests on the same section, which are reported in R. & M. 2436. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2809.pdf 496. Control testing in wind tunnels L. W. Bryant, and H. C. Garner If ad hoc wind-tunnel work on controls is to be of value it is essential that the same precautions should be taken as are necessary for fundamental research. For the model there must be careful selection of material and accurate finish. Attention must be paid during the experiments to the observation and control of transition in the boundary layer; a suitable technique for doing this is outlined. Control power may be measured on complete models of reasonable size, but usually hinge moments can only be measured satisfactorily on partial models, which provide control surfaces large enough for accurate reproduction of contours and detailed features. The great care and time involved in the construction of models and testing of controls for design purposes are frequently not justified when the only purpose is to determine the effects of balance, gaps, or small changes of shape. On the model scale the main object of tests should be to determine the properties of the basic control shape chosen by the designer, recognising that there will in general be differences of detail in the actual aircraft for which a margin must be allowed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2881.pdf 497. Determination of the stress distribution in reinforced monocoque structures Part 1 A theory of flat-sided structures L. S. D. Morley This paper is concerned with the formation of basic differential equations for the determination of the stress distribution in reinforced monocoque flat-sided structures, such as rectangular or polygonal fuselages and wing boxes. The general scheme of the analysis is to develop the fundamental equations which govern the stresses, strains and displacements separately in the skin-stringer combination and rib flanges. Then, by identifying displacements along their intersections, the differential equations of compatibility are formed. The solution of these equations yields the stress distribution. It is intended that further papers will be devoted to the detailed solution and application of these equations to particular problems together with experimental verification for each type of problem. A simple application of the theory is demonstrated in an appendix. A three-bay flat structure, containing a rectangular cut-out in the centre bay, under uniformly distributed tension loading is investigated. The calculated results for the longitudinal direct stress resultants in the skin-stringer combination compare favourably with those of experiment. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2879.pdf 498. Estimation of the change in performance characteristics of a turbine resulting from changes in the gas thermodynamic properties D. G. Ainley Frequently turbines are tested in a laboratory with coot air which has thermodynamic properties different from those of the hot gas for which the turbine is designed. This note presents methods for correcting such tests to allow for a difference in gas thermodynamic properties. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2973.pdf 499. Evaporation from the Surface of a Body in an Airstream (With Particular Reference to the Chemical Method of Indicating Boundary-layer Transition) P. R. Owen and A. O. Ormerod The problem of predicting the rate of transport of a gas from or into the surface of a two-dimensional body in an airstream is discussed. The principal object of the investigation is to provide a means of estimating the time required to. obtain an experimental record of boundary-layer transition when a chemical technique is used. The methods evolved should, however, find an application to other forced diffusion phenomena. The general approach is based on the analogy between mass transfer, heat transfer and skin friction, and the analysis is applied to both a laminar and a turbulent boundary-layer on the surface of the body; it also includes the problem of diffusion commencing in an established boundary-layer. For this problem, an approximate, alternative solution to that Of O. G. Sutton, for a turbulent boundary layer, is given. Particular attention is paid to a description of the boundary condition at the surface of the body, and it is concluded that, for evaporation, the usual assumption that the air is saturated with the diffusing substance is, in general, satisfactory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2875.pdf 500. Experiments on the flow into a swept leading-edge intake at zero forward speed with notes on the wider uses of a slotted intake J. Seddon and W. J. G. Trebble The flow into a swept intake at zero forward speed (ground running conditions) is shown to be analogous to the flow round a sharp corner in a duct. Tests have been made on a model of a swept-wing leading-edge intake to measure the losses involved. It is found that the distribution inside the duct can be improved by the use of straight guide vanes, alternatively by means of a special intake slot, or further by a combination of both. Guide vanes increase the mean loss, but the intake slot improves (i.e., reduces) this also. The slot would require to be sealed, under flight conditions. It is suggested that this form of slotted intake may have wider applications in the future. Using the results of the experiments and an analogy with the slotted wing, conclusions are drawn regarding the main points of design of the intake slot. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2909.pdf 501. Experiments with slotted and perforated walls in a two-dimensional high-speed tunnel D. W. Holder, R. J. North and A. Chinneck Under review Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2955.pdf 502. Flutter and resonance characteristics of a model cantilever wing carrying localised masses N. C. Lambourne Resonance tests on a model cantilever wing carrying concentrated masses were made in conjunction with the flutter tests of R. & M. 2533. Measurements were made with masses up to approximately five times the mass of the bare wing added at the following positions in the section 0.3 span from the root of the wing: (i) Externally 0.28c ahead of leading edge (ii) Internally 0.3c behind leading edge. The flutter and resonance characteristics are placed in juxtaposition, and an attempt is made to correlate the two sets of phenomena by means of the Kussner criterion. The distortion modes of flutter are analysed into normal mode components, and the results suggest that for a wing rigidly fixed at the root and carrying a single concentrated mass the first three normal modes are sufficient to define the flutter mode. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2866.pdf 503. Force and moment measurements on a conical body and a rectangular wing, separately and in combination, at Mach number 1.94 J. R. Anderson and D. Treadgold Results are given of wind-tunnel measurements at M = 1.94 of lift, drag and pitching moment at small angles of incidence on two cones, three rectangular wings and on the six derived cone-wing combinations. A description of the tests and a comparison with theory are also included. The agreement between theory and experiment for the lift of the isolated cones and wings is good; however, for the drag and centre of pressure, agreement is a little less satisfactory. The measured lift of the cone-wing combinations exceeded that estimated, whereas the measured centre-of-pressure position agreed remarkably well with the estimated position. Agreement between measurement and theory for the lowest aspect ratio wing was improved when a correction was applied for the influence on the cone of the downwash generated by the wings. An unsuccessful attempt was made to measure the forces and moments on each component of the cone-wing combination independently, whilst under the influence of the flow field of the other. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2864.pdf 504. Helicopter behaviour in the vortex-ring conditions W. Stewart A region of roughness, associated with the airflow conditions of the vortex-ring state, occurs when a helicopter is operating in vertical or near vertical descents in the range of about 500 and 1,500 ft/min. The turbulent circulating air and the rapid changes in local velocities in this flow pattern can cause serious helicopter handling difficulties. This could cause concern in a slow steep approach, particularly under instrument-flying conditions. This report describes flight experience in the vortex-ring conditions with the Sikorsky R-4B, R-6 and S-51, Bell 47 and Bristol 171 helicopters. It is shown that the helicopter behaviour varies from a mild wallowing on the best type to a complete loss of control on the worst case. These effects are due to the turbulent-flow changes in the vortex ring and the loss of control is thought to be caused by large changes in pitching moments on the fuselage with small displacements of the helicopter relative to the unusual flow pattern. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3117.pdf 505. Helicopter rotor behaviour after engine failure in forward flight W. Stewart and M. F. Burle Calculations have been made to find the changes in rotor speed following engine failure in forward flight. Several particular examples were investigated, based on the parameters of the S-81 helicopter. The effect of pilot's control movement was included. A rapid loss of rotational speed occurs with practically no change in forward speed of the helicopter, thus the tip-speed ratio increases rapidly. This may lead to stalling of the retreating blade and/or interference of the blades with the droop stops, either of which are dangerous conditions. The time available to the pilot to reduce the collective pitch after engine failure is very short throughout the speed range and engine failure constitutes a danger to safety on this type of helicopter. Some form of automatic pitch reduction or power failure warning system is necessary. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2861.pdf 506. Low-Speed Tests on 45-deg Swept-back Wings Parts I and II J. Weber, G. G. Brebner, D. Kuchemann PART I - Pressure Measurements on Wings of Aspect Ratio 5. This report contains the results of pressure measurements on three 45-deg swept-back wings with constant chord and aspect ratio 5, over an incidence range up to 10 deg. Chordwise and spanwise lift distributions are given, mostly near the centre where, on two of the wings, modifications had been made to the section shape. It was found that altering the thickness distribution in the centre did not affect the loading but that approximately straight isobars could be obtained at values of CL below about 0.1. By the incorporation of twist and camber in the central part the distortion of the lift distribution in the centre could be avoided at one particular incidence, and thus the same chordwise distribution obtained over most of the span. Twist and camber alone do not improve the isobar pattern and therefore a thickness modification would be needed to give the desired lift distribution and isobar pattern at one particular incidence. PART II - Balance and Pressure Measurements on Wings of Different Aspect Ratios. This Part contains the results of balance and pressure measurements on constant-chord wings of 45-deg sweepback. Together with wing A of Part I they provide data for aspect ratios 2, 3, 5 and infinity. The results at low CL are analysed and used to verify assumptions made in the calculation method of Refs. 2 and 3. The growth of the boundary layer and its influence on the lift, drag and pitching moment are discussed. The effect of tip vortices on lift and drag is also discussed. The stall is investigated on the wing of aspect ratio 3. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2882.pdf 507. Low-speed tunnel model tests on tailplane rolling moments in sideslip A. Spence, J. W. Leathers and D. A. Kirby To provide data for stressing purposes, measurements have been made of the effect of sideslip on the rolling moment on a 41.5-deg swept-back tailplane mounted at three heights on the fin of a one fifth scale model of a single jet aircraft with a 4O-deg swept-back wing. Incidence and tailplane setting were varied, and the effects of rudder deflection were obtained with the tailplane at the top of the fin. Brief results on a delta aircraft model with a delta tailplane at the top of the fin are also included. (a) At zero tailplane lift, for tail heights, 0.31, 0.62 and 0.99 times the fin height external to the body, the values of (-lv tail) are 0.111, 0.172 and 0.199 respectively. These values are increased slightly by increase of incidence. (b) The variation with tailplane lift is as estimated for the tailplane alone. (c) Deflecting the rudder changes the rolling moment on the high tailplane in proportion to the change of side force on the fin and rudder. A smaller effect would be expected on lower tailplanes where the flow round the body contributes more to the rolling moment. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2941.pdf 508. Model tests on the asymmetry of airflow occurring in twin-intake systems at subsonic speeds J. Seddon and W. J. G. Trebble In twin air-intake systems (i.e., a pair of intakes discharging into a common duct or chamber) in which the losses are affected by external boundary layers; asymmetry of flow between the two ducts occurs below a certain critical value of the flow coefficient (entry velocity + free-stream velocity). The effects of this asymmetry on intake efficiency, and more particularly on flow distribution at the compressor, may be important. If, as seems possible, the flow oscillates between the two sides, this may give rise to vibration of the aircraft. Wind-tunnel model tests have been made on a-pair of wing-root leading-edge intakes and on various arrangements of body-side submerged intakes. In all cases a region of flow asymmetry was observed. The appropriate flow coefficients are outside the main working range of the intakes, but are such as might be encountered in a dive, or on suddenly throttling back in level flight. The main factors determining the extent of the asymmetry are analysed briefly. A theory of intake loss is adapted to provide a method of predicting the critical flow coefficient. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2910.pdf 509. Model tests on the effects of slipstream on the flow at various tailplane positions on a four-engined aircraft. Part 1 tests with contra-rotating propellers. Part 2 tests with single rotating propellers D. E. Hartley, A. Spence, and D. A. Kirby Systematic wind-tunnel tests have been made to investigate the effects of slipstream on the flow near the tailplane of a typical civil transport with four contra-rotating propellers. Tailplane height has been varied for each of several wing-body arrangements ; only one tailplane and one propeller position have been used. This report presents the main results in the form of changes in mean downwash angle, and velocity at the tailplane, as functions of tailplane position, lift coefficient, and propeller thrust. It is shown that the regions of increased downwash and velocity each extend for a range of tailplane height of about one propeller diameter whilst the region of increased downwash is displaced upwards a quarter of a diameter relative to the region of increased velocity. A comparison of this work with flight results (R. & M. 2701), in which the propellers were single rotating, show an apparent difference in the spread of the slipstream between single rotating and contra-rotating propellers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2747.pdf 510. Oscillating wings in compressible subsonic flow W. P. Jones The problem of estimating flutter and stability derivatives for wings of finite span describing simple harmonic oscillations in compressible flow is considered. It is shown that the problem can be reduced to a similar one for an equivalent wing in incompressible flow. The lateral dimensions of the equivalent wing are ~/(1 - M²) times those of the original wing and the frequency of oscillation is increased by the factor (1 - M²) -1 where M denotes the Mach number of the compressible flow. The mode of oscillation is different but related to that of the original wing and leads to a more complicated condition for tangential flow. It is suggested, however, that sufficient accuracy might be obtained by representing the boundary condition to first-order accuracy in the frequency and then solving quite generally the integral equation which determines the velocity potential at the surface of the wing. The comparisons made in Table 1 and Figs. 2a to 2d indicate that the above procedure is reasonably satisfactory in the two-dimensional case. For M = 0.7, the values of the derivatives given by the formulae derived in this report show fair agreement with the 'exact' results of Refs. 1 and 2 over a wide range of frequency parameter values. Since flutter derivatives for wings of finite span are not usually very sensitive to variations in frequency parameter, the scheme of calculation suggested should be sufficiently accurate for all practical purposes when the combined effects of thickness and viscosity are negligible. It does, however, require a reliable method for calculating derivatives for low aspect ratio wings in incompressible flow, since the aspect ratio of the equivalent wing is ~/(1 - M²) times that of the original wing and becomes small for the higher values of M. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2855.pdf 511. Part I The Effect on Transition of Isolated Surface Excrescences in the Boundary Layer. Part II Brief Flight Tests on a Vampire I Aircraft to Determine the Effect of Isolated Surface Pimples on Transition N. Gregory, W. S. Walker and D. Johnson Part I. The effect of isolated surface excrescences in a laminar boundary layer in producing disturbances which may lead to turbulent flow has been examined experimentally by several methods. Photographs of some of the flow patterns visualised by smoke and china-clay techniques are given. The critical heights of pimple which just give rise to spreading wedges of turbulent flow have been measured on a flat plate and on two aerofoils at several angles of incidence. The results are analysed and are presented in a form which enables approximate estimates to be made of the protuberances permissible on laminar-flow surfaces at full-scale flight Reynolds numbers. The estimates suggest that at an altitude of 30,000 It the critical pimple height is 0.004 in. for a speed of 850 m.p.h., whilst 0.002 in. may be permissible at all subsonic speeds. At sea-level, however, the tolerances are approximately halved. Part II. A method is given by Gregory and Walker in Part I for estimating the height of isolated surface excrescences that are just sufficient to cause a turbulent wedge in a laminar boundary layer. It is an empirical method based on wind-tunnel tests made at the National Physical Laboratory at wind speeds up to 200 ft/sec and aerofoils of 30-in. and 60-in. chord (maximum Reynolds number of approximately 3 x 10power6). To provide information at flight Reynolds numbers, two flights have been made on a Vampire aircraft indicating the effect of tiny paint pimples on the laminar boundary layer at a Reynolds number, based on wing chord, of 25 x l0 G near sea-level. It was found that the critical pimple height at 0.03-chord was 0.001 in. increasing to 0.003 in. at 0.20-chord, values which are within experimental error of those estimated by the method of Ref. 1. Although the pimples were of no specific shape, e.g., cylindrical or conical, it is suggested that, in view of the close agreement between estimated and observed results, no further flight tests are necessary. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2779.pdf 512. Some applications of the lamÃ© function solutions of the linearised supersonic flow equations. Part I. Finite swept-back wings with symmetrical sections and rounded leading edges. Part II. Cambered and twisted wings G. M. Roper Some general solutions of the linearised equations of supersonic flow, in terms of Lamé functions, were obtained by G. M. Roper, using the methods of Robinson and Squire. The results were applied to calculate : (a) the pressure distribution over some swept-back wings at zero lift, having symmetrical sections with rounded leading edges; (b) the effect of camber and twist on the pressure distribution and drag on some wings of negligible thickness. The solutions are only valid for surfaces lying wholly within the Mach cone of the apex. In the present paper, some further special solutions are found. In Part I, some of these solutions are combined.with solutions already found to give : (A) the pressure distribution and wave drag, at zero lift, on some finite unyawed swept-back wings having symmetrical sections with rounded leading edges and wing tips perpendicular to the wind direction ; (B) the change in pressure distribution and wave drag at zero lift on the surface of a Squire wing, when the local thickness/chord ratio is modified. The shapes of some curved wings, with swept-back subsonic leading edges were found by Roper, such that the thrust loading on the leading edges, at supersonic speeds, is removed or modified. In Part II of this paper, the effect of a change of Mach number on the aerodynamic characteristics of such a wing, designed for a given Mach number, is calculated. Some additional solutions of the linearised supersonic flow equations, applicable to cambered and twisted wings, have also been calculated, and the results are given in Appendices III and IV of Part II. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2865.pdf 513. Some experiments on the resistance of metals to fatigue under combined stresses H. J. Gough, H. V. Pollard and W. J. Clenshaw The basic object of the investigation was an experimental study of the fatigue resistance of metals to combined flexural and torsional stresses to which many engineering components; particularly crankshafts, are subjected in practice. Four independent variables have been employed; reversed bending stresses, reversed torsional stresses, static bending stresses and static torsional stresses superimposed on these cyclic stresses. Supplementary static, impact and simple fatigue tests, with chemical analysis and metallurgical examination, have been made on all the test materials. The investigation falls naturally into two parts, in which form it is reported. Part I of the report describes a comprehensive research into the fatigue behaviour of a selection of engineering steels and two alloy cast irons under combined bending and torsional stresses alternating in phase, the mean stress of both types of stress cycle being zero in every case; thus, two cyclic variables only have been explored in this part of the investigation. A special form of highspeed testing machine, referred to as the No. 1 Combined Stress Fatigue Testing Machine, was developed for this part of the research and is described in detail. Part II of the report describes a research into the resistance of a Ni. Cr. Mo. Va. aircraft steel to combined fatigue stresses in which the four independent variables (see above) have been investigated. A second new type of machine, referred to as the No. 2 Combined Stress Fatigue Testing Machine, was specially designed for this purpose and is described in detail. The test material, to British Standards Specification S.65A, was investigated in the hardened and tempered condition, having a tensile strength of 65 t/in.L The programme of combined stress fatigue tests consisted essentially of (a) tests on solid specimens of circular cross section, and (b) tests on three forms of hollow specimen each containing one type of discontinuity unavoidably associated with practical crankshafts ; a radial oil-hole, a transition tillet of small radius, a splined shaft having six splines; the external diameters, at the test section, of the solid specimen, the specimen with an oil-hole and the specimen with small fillet, was 0.500 in. in each case; the splined-shaft specimens measured 0.4913 in. over the crest diameter. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2522.pdf 514. Stress concentrations at a cut-out in a swept wing E. H. Mansfield The stress concentrations are determined for a panel, bounded by main load-carrying members and an oblique edge, such as might occur at a cut-out in a swept wing. The solutions given are exact and cover the effects of a member along the oblique edge and of closely-spaced stringers attached to the panel. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2823.pdf 515. Technique for flutter tests using ground-launched rockets, with results for unswept wings W. G. Molyneux, F. Ruddlesden, and P. J. Cutt A technique for the investigation of wing flutter by means of ground-launched rockets is described. An important feature of the technique is that it can be used at high speeds, including the transonic range. Model wings are attached to a solid-fuel rocket which has a miniature telemetry set housed in a detachable nose fairing. A vibration pick-up and break wires are fitted in the flutter model and these modulate the output of the telemetry set to transmit flutter information to a ground station. The rocket is fired over an open artillery range and its velocity-time curve is obtained by radio reflection Doppler equipment. Results are given of tests on flutter models of unswept, untapered wings in the range of Mach number from 0.4 to 1.0. The effects of longitudinal acceleration on the flutter are shown to be negligible for the range of acceleration and Mach number investigated, and the effect of compressibility is to reduce the margin of the measured speed above the speed calculated on the basis of incompressible flow theory from + 50 per cent at M = 0.4 to - 25 per cent at M = 0.9. A wing torsional stiffness criterion is shown to give a fair approximation to the test results. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2944.pdf 516. Tests at high subsonic speeds on a 10 per cent thick pressure-plotting aerofoil of RAE 104 section E. W. E. Rogers, C. J. Berry and R. F. Cash 1. Summary and Introduction.--A series of tests has been made in the National Physical Laboratory 20-in. × 8-in. High Speed Wind Tunnel on a two-dimensional pressure-plotting aerofoil of five inches chord and RAE 104 section. The work included : (a) A comparison of the results obtained with and without spanwise bulges on the aerofoil surface (Ref. 1). (b) A comparison (to show the effects of a change in Reynolds number at high speeds) with measurements made in tile same tunnel on a pressure-plotting aerofoil of similar profile but having a chord of two inches (Ref. 2). (c) An investigation of the pressure distribution and flow around the aerofoil at high incidences for various Mach numbers. (d) A determination of the force coefficients, surface pressures and flow patterns for the aerofoil through a range of Mach number at incidences up to 8 deg. The present report is concerned with this last item. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2863.pdf 517. Tests concerning novel designs of blades for axial compressors Part 1 blades designed for increased work at root and tip Part 2 blades designed to operate in a parabolic axial velocity distribution S. J. Andrews, R. A. Jeffs and E. L. Hartley Investigation of the flow between the blade rows in a research compressor with conventional Half-Vortex blades have shown a rapid stage-to,stage build-up of the annulus boundary layer. The axial velocity distribution under these conditions bears no resemblance to the straight-line distribution which is usually assumed in design so the incidence angles at both root and tip probably give rise to considerable secondary losses. Two sets of blades were designed therefore, with the object of minimising these effects. The first set was designed with an increased work input at the root and tip of the blades in order to re-energise the boundary layer and prevent axial-velocity profile deterioration. The second set was designed using as a design assumption a mathematical approximation to the axial-velocity profiles found experimentally at various stages in a conventional compressor. The results obtained from low-speed tests of the first set of blades show that although the boundary-layer thickness was considerably reduced, this was achieved only at the expense of 2 per cent in maximum efficiency as compared with conventional blades. The drop in efficiency is attributed to the stator blade rows which stall at incidences well below the design value, but the effect is probably not uniquely associated with variable work done. The blades designed for a variable axial-velocity profile also failed to give an improved performance. The maximum efficiency was 3 per cent below that of the equivalent conventional blades and the axial-velocity profile instead of remaining approximately:as assumed, deteriorated still further. It is considered that designing for a poor axial-velocity profile is probably wrong in principle. The Variable Work Done blades, however, would almost certainly have succeeded in producing an axial velocity substantially constant over the greater part of the annulus if the work had been symmetrically distributed about the mean radius with a ratio of mean to minimum work of about 1.1. Under these circumstances it is likely that there would have been a reduction in secondary losses and an increase in efficiency. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2929.pdf 518. The aerodynamic derivatives with respect to a rate of yaw for a delta wing with dihedral and at incidence at supersonic speeds J. H. Hunter-Tod Expressions are developed on the basis of an unsteady flow analysis for the yawing derivatives for a delta wing with small dihedral at small incidence flying at supersonic speeds. The assumptions of the linearised theory of flow are made throughout; only first-order terms in the rate of turn are considered. The terms dependent on the dihedral alone are continuous and decrease numerically with rising Mach number. The remaining terms are discontinuous at a Mach number at which a leading edge becomes supersonic; in particular the rolling-moment component due to incidence changes sign; the other derivatives may do likewise in certain circumstances. The approximate theory developed in the paper breaks down as a leading edge nears the Mach wave from the vertex of the wing. The yawing amplitude for which the results quoted present reasonable approximations decreases rapidly as this condition is approached; in particular the contributions of the leading-edge suction become undefined. Earlier results based on strip theory are greater numerically than those derived in the present paper by significant amounts that increase with Mach number and aspect ratio. The two theories agree for vanishingly small aspect ratios. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2887.pdf 519. The geared elevator tab and tail-unit stiffness requirements T. Niblett The effect of a flexible, geared, elevator tab upon the validity of the stiffness criteria for tail-units and rear fuselages is examined. To this end, the distortions of a hypothetical, semi-rigid tail-unit under the air loads induced when the elevator is displaced are calculated for various arrangements of tab and forward aerodynamic balance of the elevator. Notice is also taken of the loss of control effectiyeness and change in elevator hinge moment resulting from these distortions. It is found that a geared elevator tab covering only a fraction of the elevator span may lead to large tip distortions and appreciable reduction of control effectiveness of the elevator if it is placed near the inboard end. From consideration of the distortions of the tab and the effect upon elevator hinge moment, a torsional-stiffness criterion for tabs is proposed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2848.pdf 520. The performance after power failure of a helicopter with blade pitch control Parts I and II F. O'Hara and H. A. Mather In Part I a review is made of helicopter performance after engine failure. The transition from powered operation to autorotation is discussed and a theoretical analysis of the motion is given for a single-rotor helicopter with blade-pitch control. The technique of landing from a steady autorotative glide is dealt with briefly; the possibility is indicated of making a safe landing before the transition to steady autorotation has been completed. Reference is also made to the case of engine failure so near the ground that a safe landing may be made by increasing the blade pitch to make immediate use of the rotor energy. In Part II, tests made to investigate the performance of a Hoverfly I in the transition to autorotation following power cut in level flight are described; particular attention is given to the minimum rotor speed attained and to the height lost during the transition. Tests were made to investigate the performance for immediate reduction of pitch only; the need for quick pitch reduction however is stressed because of the rapid fall-off in rotor speed following powercut at high pitch. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2797.pdf 521. The R.A.E. 4-ft x 3-ft experimental low-turbulence wind tunnel. Part II measurements of turbulence intensity and noise in the working-section H. Schuh and K. G. Winter Measurements are given of the turbulence in the working-section together with measurements of the noise. With all the screens fitted in the tunnel, the intensities of lateral components are of the same order as the longitudinal component and range from about 0Â·01 per cent to 0Â·03 per cent of the mean speed. Frequency analyses have shown the longitudinal components to consist of fan frequencies and a low-frequency contribution at about 5 to 10 c.p.s. The lateral components consist almost entirely of a similar low-frequency contribution. With all the screens in the tunnel the low level of turbulence is confined to a restricted area near the centre of the tunnel with flashes of high-intensity turbulence spreading a considerable distance from the walls. Noise measurements with the hot-wire microphone in the middle of the working-section showed that above a tunnel speed of 150 ft/sec the longitudinal component consisted mainly of noise. Some measurements were also made with the hot-wire microphone in the turbulent boundary layer on the walls. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2905.pdf 522. The reduction to standard conditions of take-off measurements on turbo-jet aircraft G. Jackson, K. J. Lush Summary.--A reduction method intended for routine use is derived whereby the take-off distance required for a turbo-jet aircraft to clear a 50-ft screen under a specified set of standard conditions of air temperature and pressure, wind speed, aircraft weight and engine speed can be deduced from the distance measured in an arbitrary set of conditions. The method is basically similar to that used for piston-engined aircraft and the only information required in addition to that which can be observed is a numerical constant for the engine type. The method is shown to be not inconsistent with available experimental data. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2890.pdf 523. The theoretical wave drag of some bodies of revolution L. E. Fraenkel This report investigates the wave drag of bodies of revolution with pointed or open-nose forebodies and pointed or truncated afterbodies. The 'quasi-cylinder' and 'slender-body' theories are reviewed, a reversibility theorem is established, and the concept of the interference effect of a forebody on an afterbody is introduced. The theories are applied to bodies whose profiles are either straight or parabolic arcs, formulae and curves being given for forebody and afterbody drag, and for the interference drag. The results of the two theories are compared and are seen to agree well in the region of geometries where both theories are applicable. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2842.pdf 524. The theory of torsional vibrations of a four-boom thin-walled cylinder of rectangular cross-section E. H. Mansfield The,torsional vibrations of a four-boom cylinder of doubiy symmetrical rectangular cross-section are considered and the differential equation of motion is derived on the assumption that the ribs maintain the section shape but do not themselves resist any warping out of their plane and that the walls of the cylinder are effective only in shear. Frequency equations are derived for a length of cylinder, free at both ends and prevented from rotating at the mid-section. The complete behaviour of the cylinder is determined by two non-dimensional parameters and curves are given from which the frequencies for any such cylinder may be determined. It is shown that the higher frequencies in particular may be underestimated by between 40 to 80 per cent if warping constraint effects are ignored. An approximate method is given for estimating the torsional frequencies of a cylinder with non-uniform characteristics. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2867.pdf 525. Treatment of the stagnation point in arithmetical methods A. Thom In using any of the Relaxation Techniques near a stagnation point difficulties arise if the variable is log 1/q. This tends to infinity and the difference equation no longer represents adequately the differential equation without special modification. Methods are given whereby larger squares can be used than had been previously practicable. As little variation as possible has been introduced into the procedure so that if an electronic calculator is used, the alterations to the circuits would be reduced to a minimum. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2807.pdf 526. Tunnel-wall effect on an aerofoil at subsonic speeds A. Thom and Laura Klanfer This is a detailed study of the effect of the presence of walls on the flow past a symmetrical aerofoil at zero incidence. The low-speed case is considered first, followed by solutions at a Mach number of 0.7. The methods used are essentially arithmetical, but a new approach is used for the compressible case. The manner in which the walls affect the pressure distribution is clearly shown. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2851.pdf 527. Velocity distribution on thin tapered wings with fore-and-aft symmetry and spanwise constant thickness ratio at zero incidence S. Neumark and J. Collingbourne This report is a continuation of three earlier ones by the present authors (1947-9) and contains a theoretical investigation of subsonic flow past thin tapered unswept wings (of full or cropped-rhombus plan form), at zero incidence. Only the case of spanwise constant thickness ratio is considered in this first attempt although alternative cases also merit attention. The first order method of linear perturbation based on continuous systems of sources and sinks is shown to be still applicable to tapered wings, although mathematical difficulties are greatly increased. These have been overcome, at least in the simple case of the biconvex parabolic profile, so as to give general solutions and computable formulae for the velocity distribution over the entire wing area. Complete detailed solutions for the mid-chord line have been worked out numerically and two examples of complete numerical solutions, with corresponding isobar patterns, for the entire wing area are presented. These results are sufficient to illustrate the effect of uniform taper on the velocity field of unswept wings, and lead to a number of general conclusions. The most important of these is that, although taper brings about noticeable decrease of supervelocities at the centre, higher values are encountered further outboard so that, for cropped plan forms, two symmetrically placed maximum suction areas arise inside the two half-wings. These are relevant for determining critical Mach numbers, and the effect of taper may be, according to choice of geometrical parameters, either beneficial or detrimental as to the values of Motet, but practically never very considerable. The method wilt still be applicable to the more general, and more important, case of tapered swept-back wings, especially for delta wings, and a general solution for the velocity distribution in the central sections of such wings is given in Appendix I and shown to be consistent with the earlier solution for untapered swept wings. However, for applying the method successfully (up to detailed numerical investigation) to the more general case, automatic high-speed integrating machinery seems indispensable--to replace classical methods of transforming integrals and manual computing, as used in the past and in the present report. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2858.pdf 528. A full-scale investigation into the hydrodynamic behaviour of a highly faired flying-boat hull J. A. Hamilton This report describes an investigation into the hydrodynamic qualities of a Sunderland flying-boat hull, weight 50,000 lb, fitted with a main-step fairing of fairing ratio 17 : 1. The fairing was equipped with ventilating ducts, drawing air at atmospheric pressure through ports on the hull side, and discharging it through exit vents on the afterbody planing bottom. No pumping apparatus was fitted, the airflow being induced by the sub-atmospheric pressures on the fairing. The main conclusions of the investigation may be summarised in this manner: (a) A highly faired hull of this kind is hydrodynamically satisfactory, with a ventilating area equivalent to 0.042 (beam) 2 placed immediately behind the main-step line. (b) For satisfactory hydrodynamic behaviour, the step line, i.e., the junction between forebody and afterbody must be kept sharp, but only an angular discontinuity in the vertical plane is necessary. (c) Without ventilation, the highly faired hull exhibits severe hydrodynamic instability during take-off and alighting, and the resistance is about 30 per cent higher than the ventilated hull. (d) Pressure measuremenfs on the afterbody indicate that skipping instability is caused by the presence of a region of sub-atmospheric pressure, covering almost the whole afterbody during skipping, and having maximum suctions of up to 4 lb/sq in. occurring at about 0.4 beam lengths aft of the step line. The general conclusion of the investigation is that successful hulls may be designed without conventional steps, provided that sufficient internal ventilation is provided. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2899.pdf 529. A method of calculating the short-period longitudinal stability derivatives of a wing in linearised unsteady compressible flow K. W. Mangler A method is developed for the circulation of the pressure distribution and the aerodynamic forces and moments on a wing performing harmonic pitching and heaving oscillations. The calculation is based on the assumption of inviscid potential flow without shock waves and is restricted to small incidence, so that the linearized theory is valid. In contrast to other work in the field the theory applies to all Mach numbers. It is restricted to small values of the reduced frequency and should be valid for the usual range of short periods occurring at present in flight. The formal solution yields two integral equations for the parts of the load, which are in phase and go out of phase with the oscillation; these are of the same form as the corresponding equation in steady flow. The way is thus opened for solutions over the whole Mach number range at small frequencies, if the corresponding steady solutions can be found. The calculation is in fact easiest for M = 1 and has been done here for Delta wings to supplement a previous supersonic calculation made on different frequency assumptions, which broke down near M = 1. It appears from the two sets of results that the short-period oscillation will be unstable near M = 1, if the apex angle of the Delta wing is greater than about 60 deg. This confirms a now generally recognised trend. Such results near M = 1 must of course be invalidated to an unknown extent by thickness viscosity and shock waves at their maximum effect. Nevertheless it is unlikely that these factors will remove the critical nature of the transonic damping as calculated by this method. With all its obvious limitations this method, when extended to other planforms, should provide a useful tool in studying the effect of geometrical parameters on the stability of an aircraft at transonic speeds. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2924.pdf 530. A simple method for calculating the span and chordwise loading on straight and swept wings of any given aspect ratio at subsonic speeds D. Küchemann The methods of classical aerofoil theory are used to derive a general theory for wings of any given plan form. Accordingly, the general downwash equation is split into two parts : one, the effective incidence, being due to the downwash induced by the vorticity component along the span; and the other, the induced incidence, which is due to the downwash induced by the streamwise vorticity component. The latter is related to the downwash in the Trefftz plane, and a downwash factor is introduced to include both the limiting cases of very small aspect ratio (Jones) and of very large aspect ratio (Prandtl). The downwash resulting from the spanwise vortices is approximated by a simple relation, the accuracy of which is proved to be satisfactory for practical purposes, and an exact solution of this equation is given for wings of very large aspect ratio, swept or unswept. For wings of moderate or small aspect ratios, the solution given fulfills the approximate downwash equation only in the mean over the whole chord, i.e., the downwash is correct not at a few discrete points but on the average. Again, the limiting cases of Jones and Prandtl are included in the present solution. Thus, the load over the whole surface of a given wing can be calculated at a given subcritical Mach number, and the procedure is as simple and rapid as that of the classical aerofoil theory. The calculated results are confirmed by experiment. With this method, the effects of wing thickness and of the boundary layer can easily be taken into account, as well as aero-elastic effects. Non-linearity of the lift due to tip vortices is also treated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2935.pdf 531. Aerofoil design in two-dimensional subsonic compressible flow L. C. Woods In Part I of this paper the method of two-dimensional aerofoil design in incompressible flow due to Lighthill (1945) is extended to compressible subsonic flow. Lighthill's equations are derived as special cases of more general equations due to tile author, and some advances are made in tile application of these equations to aerofoil design. It is shown, for example, how the designer can control the nose radius of curvature. The method of Ref. 1 requires that the velocity distribution be prescribed analytically, whereas this paper deals with distributions defined numerically, a development especially important for compressible flow design. The compressible flow theory is based on an approximation to the equation of flow not unlike, and with at least the same accuracy, as the Kabrman - Tsien approximation for calculating the flow about a given aerofoil. A method of estimating the effects of a modification to the designed aerofoil shape, on the velocity distribution is also given. In Part 2 five examples have been calculated. Aerofoil I is symmetrical, with a 'roof-top' distribution at a given angle of incidence, showing how a given nose radius can be achieved; Aerofoil II is symmetrical, designed for M∞ = 0, and α = 0 (M∞being the Mach number at infinity, and α the absolute angle of incidence),while Aerofoil III has been designed for the same distribution but at M∞ = 0.7. A comparison is made between Aerofoil III and that obtained from Aerofoil II by linear pertubation theory. It is shown, as would be expected, that this theory underestimates the reduction in thickness necessary to produce a compressible flow aerofoil from one designed for incompressible flow and the same velocity distribution. Aerofoils IV and V are asymmetric aerofoils designed for M∞ = 0.7, the former being designed to have a given distribution over each surface at incidence, while the latter is designed so that the upper surface has a given distribution at incidence and the lower surface has a given distribution at zero incidence. The design of an asymmetric aerofoil by the author's method is about two days' work for one computer. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2845.pdf 532. An experimental investigation of stress diffusion in non-buckling plates L. H. Mitchell The purpose of this report is to provide experimental resuKs for comparison with theoretical analyses of stress diffusion problems. The structures considered consist of plane reinforced sheet which has been assumed not to buckle. Symmetrical loads are applied to the edge booms connected to the sheet by continuous no-slip joints. Attention is concentrated on the stress distribution near the ends of the parallel strips of plate. An outline of the existing theoretical work which is applicable to this type of problem is given. The stringer-sheet theory, the only one capable of dealing adequately with unreinforced sheet, is compared with the photoelastic results. It is shown that the stringer-sheet theory overestimates the peak shear stresses near the corners of the strips and consequently also the rate of diffusion of load from boom to sheet. It is also shown that the experimental shear stresses are in reasonable agreement with those predicted by a more exact plane-stress theory. This theory predicts that the peak shear stress in the plate is 2/π times the direct stress in the boom at the end of the panel. However, with the type of joint considered here, the maximum shear stress is likely to be much higher than the value given by this prediction. Some attention is also given to transverse end stiffeners and it would seem that these normally have very little effect on the shear stresses. The photoelastic models were made from the Allylstrene plastic called C.R.39. The no-slip joints were obtained by gluing the stiffeners to the plates. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2878.pdf 533. Analysis of reynolds number effects in fluid flow through two-dimensional cascades D. J. K. Stuart This report describes an investigation into the effects of Reynolds number on the flow through two dimensional cascades of the diffusing type. Particular emphasis has been. placed on the causes of high loss especially at very low Reynolds numbers. Separation of both the laminar and turbulent boundary layers are verified as sources of low efficiency in this particular type of flow and these phenomena have, consequently, been studied in considerable detail. The main work consists of approximate mathematical analysis of representative flows but this theoretical work has been carried out in conjunction with, and is supported by, results drawn from an extensive programme of tests made in the low-speed wind tunnel at the Cambridge University Engineering Laboratory. These tests are fully described in Ref. 1. Mach number effects were specifically avoided in the experimental work although a wide range of Reynolds number was covered; the effects of compressibility have not, therefore, been considered in the main analysis. The transition to turbulent flow in the boundary layer is shown to be of vital importance in determining the pattern of flow, especially at low Reynolds numbers where laminar breakaway is likely to occur, and the need for a theoretical or semi-empirical method of predicting transition is stressed. In the theoretical work tile generally accepted approach has been followed in ttlat the potential flow pattern has been used as a basis for further calculation. The close agreement of the analysis with the experimental results has justified the use of the approximate methods of boundaw-layer calculation which were selected, i.e., Thwaites' method for the laminar layer and Hewson's method for the turbulent layer. In conclusion it is shown that design methods can be modified to ensure improved performance at a specified Reynolds number or over a range of Reynolds number. In the course of the report the importance of assessing wind-tunnel results in relation to secondary effects such as the contraction of the air stream in the plane perpendicular to that considered is well illustrated, and methods of correction to enable more universal application of particular results are outlined. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2920.pdf 534. Analysis of short-period longitudinal oscillations of an aircraft--interpretation of flight tests S. Neumark A method is presented of analysing experimental curves obtained in flight when an aircraft is disturbed longitudinally by a suitable elevator input and performs mainly short-period oscillations. Determination of frequency, damping factor, amplitude ratios and phase angles of various oscillatory curves leads to formulae for evaluating stability derivatives. Cases of elevator fixed or oscillating, for tailed and tailless aircraft, are considered and illustrated by numerical examples. The main results of the investigation are listed in section 6. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2940.pdf 535. Determination of the stress distribution in reinforced monocoque structures Part III A theory of swept wings where the ribs are in the line of flight L. S. D. Morley This paper gives and applies a method of estimating the stresses caused by root constraint in a two-spar swept wing of reinforced monocoque construction where the ribs are parallel to the line of flight. The general scheme of the analysis develops the fundamental equations that govern the stresses, strains and displacements in the separate components~ Then, by comparison of displacements along their inter-sections, equations of compatibility are formed. The solution of these equations yields the stress distribution and the distorted shape. In deriving the fundamental equations for the skin-stringer combination, use is made of an oblique system of co-ordinates and stresses. A suggested numerical procedure is given for the evaluation of the stress distribution and distorted shape. It is found convenient to use matrices and the procedure has been so planned that the elements of a matrix are obtained by simple operations on the dements of preceding matrices. A wing loading condition is also derived which produces zero rib warping, i.e., there is no redistribution of stress at the root of the wing. Tests on a cellulose-nitrate model have provided good qualitative confirmation of the theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2967.pdf 536. Downwash tables for the calculation of aerodynamic forces on oscillating wings
Tables prepared at the National Physical Laboratory for the Aerodynamics Division by the Mathematics Division Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2956.pdf 537. Effects of reynolds number on the flow of air through a cascade of compressor blades H. G. Rhoden The experimental work consisted of the separate testing of three cascades of axial-flow compressor blades of camber angles 20 deg, 30 deg and 40 deg respectively. Measurements were made of the distribution of static pressure over the central cross-section of the middle blade of each cascade, together with traverses of static pressure, total head and angle of flow at inlet and outlet to each cascade in the plane of the central cross-section. The tests covered a range of actual Reynolds number from 3 x 10power4 to 5 x 10power5, based on the inlet air velocity and the blade chord, and also a range of inlet air angle α1, from 35 deg to 60 deg. In the tests there were numerous cases of laminar boundary-layer separation at low Reynolds numbers and a few cases of turbulent separation at higher Reynolds numbers. These occurred on the convex surfaces of the blades. There were also a few cases of laminar separation from the concave surfaces of the blades. The results show the effect of Reynolds number, blade camber, and inlet air angle on cascade performance. The type of pressure distribution likely to give good performance over a wide range of Reynolds number is discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2919.pdf 538. Flight tests at transonic speeds on freely falling models. Parts I to V C. Kell In the past decade the problems associated with high-speed flight have increasingly occupied the minds of many workers in aerodynamics and aircraft structures. The possibility of achieving supersonic flight has introduced a number of new problems not the least of which has been that of obtaining aerodynamic information throughout the transonic range of speeds. This report deals with one of the early test techniques developed for this purpose. Basic bodies carrying the aerofoils to be tested were released from an aircraft flying at height, and accelerated under the influence of gravity through the transonic speed range. Radar recorded the flight path and telemetering equipment carried within the body transmitted information to a ground station during the free fall. The work on this method of test which was started in 1943 was brought to a close in 1949. The main reason for abandoning the experiments was the limiting accuracy of the telemetering equipment although other contributing causes were present. Part I of this report is a historical precis of the Work and Part II a description of the models and the technique itself. In Part III the drag measurements on nine wings are presented and in Part IV the application of the technique to flutter tests is considered. Part V discusses the accuracy of the technique. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2902.pdf 539. High-speed wind-tunnel tests on six wings of 40-deg sweepback, with various section shapes L. N. Holmes and A. B. Haines Tests have been made in the Royal Aircraft Establishment High-Speed Wind Tunnel on six wings, all of the same plan form (aspect ratio 3.5, taper ratio 0.4, quarter-chord sweep 40 deg) and thickness/chord ratio (10 per cent) but of different section shapes. Four of the wings had symmetrical sections, one was cambered and one was twisted with camber varying from root to tip. Of the symmetrical wings, the one with RAE 101 section had a much better performance than the other three (RAE 104, NACA 66A-010 and HSA I). The steep drag rise with Mach number occurred at a Mach number about 0.02 higher on the RAE 101 wing than on the next best wing (MD for CL = 0.2 was 0.91). The RAE 101 wing also had a higher lift-curve slope and more regular pitching-moment characteristics. The HSA I wing, which has a large leading-edge radius, appeared to give unsatisfactory pitching moments at a low CL and high Mach number. The wing with constant camber gave disappointing results, but the twisted, cambered wing had a very good performance. Compared with the symmetrical RAE 101 wing, it had higher values of MD and lower values of drag for all values of CL above 0.2. It is thought that, for wings of constant section, and having the plan form and thickness/chord ratio used for these tests, the RAE 101 section is close to the optimum. However it should be possible to obtain further improvements by varying the section shape from the root to the tip. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2930.pdf 540. Improvements in the fatigue strength of joints by the use of interference fits W. A. P. Fisher and W. J. Winkworth A study is made of the effect of interference fit in loaded holes on the fatigue strength of the associated part. Fatigue-test results are given for aluminium alloy fiat bars with a single hole loaded by a pin in double shear. Two series of tests were made. In one series the pin was fitted directly in the hole with various degrees of interference fit up to 0.003 in. excess diameter. The other series had a mild steel bush interposed with similar degrees of interference in the bar, but with a push fit between pin and bush. Both sets showed a great increase in fatigue strength for interference fits above a critical value. The application of these results for raising the fatigue strength of aircraft structural joints is considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2874.pdf 541. Investigations of the Behaviour of Aircraft When Making a Forced Landing on Water (Ditching) A. G. Smith, C. H. E. Warren and D. F. Wright This investigation reviews the work done up to 1948 on the behaviour of aircraft when making a forced lending on water. It is confined in detail to the tests made on hydrodynamic and structural performance in the Free Launching Tank at the Royal Aircraft Establishment and the Controlled Launching Tank at the Marine Aircraft Experimental Establishment, and includes an analysis of the air-sea rescue questionnaires sent in by air crews who have experienced actual ditchings. Reference is also made to parallel work in the U.S.A. and Germany. The work done is primarily concerned with the contributions made to the Air-Sea Rescue Organisation in the 1939-45 war period and the determination of the ditching characteristics and requirements for post-war civil and military aircraft. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2917.pdf 542. Low-speed tunnel tests of some split flap arrangements on a 48-deg delta wing Parts 1 and 2 J. F. Holford, and J. W. Leathers A series of low-speed wind-tunnel tests have been made to investigate the behaviour of split flaps on one or both surfaces of a delta wing. The investigation is split into two parts described separately in the body of the report. Part I deals mainly with the estimation of the drag of such flaps with special reference to their use as air brakes on aircraft. Part II deals with an investigation into the phenomena of flow re-attachment behind the flaps and its effect on the flap characteristics. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2996.pdf 543. Low-speed wind-tunnel measurements of longitudinal oscillatory derivatives on three wing plan-forms G. F. Moss Tests have been made on a 90-deg apex delta wing, a 60-deg swept-back wing and a 40-deg swept-back wing to obtain values of longitudinal oscillatory derivatives for various frequencies, amplitudes and Reynolds numbers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3009.pdf 544. Low-speed wind-tunnel tests on two thin cranked wings with 60-deg sweepback inboard C. J. Mansell Low-speed wind-tunnel tests have been made on two thin wings of aspect ratio 3 with 60-deg leading-edge sweep at the root. Both wings show large forward movements of the aerodynamic centre at moderate lift coefficient (CL = 0.5 to 0.7). This forward movement can be delayed to CL = 1.0 by full-span Kruger-type leading-edge flaps. The normal type of split flap with hinge-line parallel to the wing trailing edge gave a decrease in usable CL and better results were obtained with flaps with their hinge-line skewed to the wing trailing edge at a smaller angle of sweepback. With skewed split flaps and full-span nose flaps CL = 1.2 at α = 17½ deg was reached on both wings with only small movements of the aerodynamic centre. Abrupt changes in lv and nv with change of incidence occurred in the region of flow breakdown on the wing without flaps. These abrupt changes were postponed to CL > 1 by nose flaps and skewed trailing-edge flaps. Ailerons with unswept hinge-line produced greater rolling moments than ailerons with swept hinge-lines or all-moving tip ailerons. The Reynolds number of the tests was about 2.3 Ã— 10power6 and the Mach number 0.18. Some favourable scale effects would be expected at higher R, but the general nature of the breakdown of flow will probably be similar on a full-scale aeroplane. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2995.pdf 545. Measurement of lift, pitching moment and hinge moment on a two-dimensional cambered aerofoil to assist the estimation of camber derivatives H. C. Garner, and A. S. Batson Aerodynamic camber derivatives are used in predicting three-dimensional control characteristics, in estimating wind-tunnel interference and in applying model data to full scale. Knowledge of these derivatives has been discussed in R. & M. 2820 (1950), from which it was apparent that experiments were needed to confirm empirical formulae for the derivatives of lift and pitching moment and to check widely differing formulae for the hinge-moment derivative. A two-dimensional RAE 102 aerofoil with a 4 per cent parabolic centre-line and plain control surfaces of chord ratios 0.2 and 0.4 has been tested at a low speed and Reynolds number 0.95 x 10power6. Particular attention is given to the effect of bmmdary-layer transition. Aerodynamic coefficients are obtained from measured forces and moments and from the pressure distribution at one section. The measured pressures compare fairly well with calculated distributions when the experimental circulation is used. Most of the coefficients from the integrated pressures are consistent with the balance measurements. The empirical formulae for the camber derivatives of lift and pitching moment are consistent within about 6 per cent. A new formula for the hinge-moment derivative is suggested, which, though at times 25 per cent different from experiment, is believed to correspond to an aerodynamic camber as it normally operates on a lifting surface in incompressible viscous flow. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2946.pdf 546. Measurements of the direct pitching-moment derivatives for four wing planforms at transonic speeds J. B. Bratt, W. G. Raymer and J. E. G. Townsend Measurements of the direct pitching-moment derivatives m and m at transonic speeds for two delta and two swept wing planforms are discussed. The tests were made in the N.P.L. 9Â½ in. high-speed wind tunnel using slotted liners, a Mach number range from M = 0.695 to M = 1.07 being attained. These measurements extend earlier subsonic results obtained with solid tunnel liners into the transonic range. Comparison with theory is made for one of the delta wings and the effect of a body on the other was examined. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3435.pdf 547. Measurements of two-dimensional derivatives on a wing-aileron-tab system with a 1541 section aerofoil. Part 1 direct aileron derivatives K. C. Wight Measurements have been made of the direct two-dimensional damping and stiffness derivatives for a 20 per cent aileron on an aerofoil with a 1541 section in incompressible flow. Corrections arising from the apparatus are discussed and reference is made to an attempt to measure the direct tab derivatives. The effects are shown of frequency parameter, amplitude of osciliation, Reynolds number, aileron angle and position of transition on the wing. Variation with frequency parameter is substantially the same as for vortex-sheet theory and variation of amplitude produces little change in both derivatives. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2934.pdf 548. Multhopp's subsonic lifting-surface theory of wings in slow pitching oscillations H. C. Garner A draft of this theory was completed by H. Multhopp during 1950, before he left the Ministry of Supply. It has been edited by the writer, who is responsible for the calculated examples. This report is an extension of Multhopp's subsonic lifting-surface theory (Ref. 1) from steady flow to harmonic pitching oscillations of low frequency. The method is applicable to wings of arbitrary plan-form. The basis of the method is to calculate the local lift and pitching momenf at a number of chordwise sections from a set of linear equations satisfying the downwash conditions at two points of each section. By neglecting terms of second order in frequency, the oscillatory problem is related to the corresponding steady one with changed boundary conditions. The evaluation of these conditions involves chordwise integrations, which require two new influence functions. Complete tables of these functions as well as the original functions i and j, occurring in steady motion (Ref. 1), are obtainable from the Aerodynamics Division, National Physical Laboratory (Ref. 11). With the aid of these tables the derivatives of lift and pitching moment become calculable by a straightforward routine. The limitations imposed by assuming only two terms in the chordwise loading cannot be evaluated at this stage. The theory is easily generalized to include any number of ehordwise terms, but each additional term introduces two further influence functions. The theory is outlined in sections 2 to 5. Section 6 describes calculations of pitching derivatives for circular, arrowhead and a family of delta wings; promising comparisons are obtained, when the number of spanwise terms is varied. In sections 7 and 8 these results are compared with other theories; a development of vortex-lattice theory (Ref. 5) is shown to give satisfactory agreement, and the deficiencies of a purely steady theory are evaluated. The available wind-tunnel data for oscillating wings of the selected plan-forms are discussed in section 9. The theory is remarkably consistent with the pitching derivatives measured at low speeds and predicts fairly well the effect of compressibility up to a Mach number of about 0.9. Appendix II gives instructions for the computer. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2885.pdf 549. Note on the lift slope, and some other properties, of delta and swept-back wings E. F. Relf In studying anct comparing various theories for the determination of the distribution of loading on wings, Garner has given values for the lift slope of several families of swept-back and delta wings deduced from several different lifting-surface theories. In Fig. 8 of Ref. 1, Garner has plotted these lift slopes as functions of the aspect ratio A, for different values of the angle of sweep. It occurred to the writer to try plotting the ratio of the lift slope to that for elliptic loading instead of the lift slope itself, and when this was done it was noticed that the above ratio was very nearly independent of aspect ratio A, and gave a unique curve for all the available results when plotted against sweepback angle, A. The curve is shown in Fig. 2 and it will be seen that none of the points is more than 3 per cent from the mean curve and most are much closer than this. The cases given by Garner cover an aspect-ratio range from 2 to 8 and a sweep range from 20 to 70 deg, as will be seen from Fig. 1, reproduced from his report. The value of the twodimensional lift slope used in deducing that for elliptic loading at any given aspect ratio was, of course, 2pi, since comparison is with potential calculations on wings of zero thickness. In using the mean curve to predict a lift slope for practical purposes it might be more logical to use the most probable value of the two-dimensional lift slope for the case in question rather than the value for an ideal fluid and zero aerofoil thickness. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3111.pdf 550. Observations of the flow round a two-dimensional aerofoil oscillating in a high-speed air stream A. Chinneck, D. W. Holder, and C. J. Berry Photographs have been taken of the flow round a 10 per cent thick RAE 104 aerofoil performing pitching oscillations at low values of the frequency parameter (ω < 0.1) in subsonic and supersonic air streams. Apart from a difference of phase, the general flow patterns appeared to be similar to those observed in steady motion, the pattern for a particular instantaneous incidence of the oscillation resembling that for steady motion at a different incidence. It is suggested that, for the range of frequency parameter covered, the observed phase lag of the flow pattern corresponds to the lag in the circulation. The phase lag of the flow pattern (as indicated in most cases by the positions of the regions where transition from laminar to turbulent flow occurs in the boundary layer) has been determined for various conditions of frequency, amplitude and Mach number, and for two positions of the axis of oscillation. For one axis position direct measurements of the pitching-moment derivatives had been made previously, and the phase lag of the flow pattern found in the present experiment is approximately the same as that in the pitching moment. At the supersonic speed (M = 1.6) used in the present tests any phase difference that was present was too small to be detected in a photograph. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2931.pdf 551. On the post-buckling behaviour of stiffened plane sheet under shear E. H. Mansfield The post-buckling behaviour of a flat plate reinforced by stringers and frames is considered theoretically, attention being concentrated on the case of pure shear loading. Formulae and graphs are presented for the rapid determination of the shear stiffness, shear strain and induced compressive stresses in stringers and frames. The analysis is an extension of work by Kromm and Marguerre. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3073.pdf 552. Pressure and boundary-layer measurements on a two-dimensional wing at low speed G. G. Brebner, and J. A. Bagley Results are given of pressure measurements and boundary-layer traverses on a two-dimensional wing with 10 per cent RAE 101 section at Reynolds numbers of 1.6 x 10power6 and 3.2 x 10power6. These results, which have been integrated to give lift, drag and aerodynamic-centre characteristics, are used to check some calculation methods for the growth of the turbulent boundary layer and for the effect of a known boundary layer on the pressure distribution. It is concluded that the calculation of the boundary layer still needs a little refinement before it is accurate enough to predict viscosity effects on pressure distribution, lift, drag and aerodynamic centre; but that these effects can be calculated if the actual boundary-layer characteristics are known. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2886.pdf 553. R.A.E. high-speed wind-tunnel tests of the trailing-edge controls on a delta wing with 52-deg sweepback K. W. Newby Tests have been made in the Royal Aircraft Establishment 10-ft x 7-ft High-Speed Wind Tunnel to determine the effectiveness of trailing-edge controls on a delta wing, of 52 deg leading-edge sweep and NACA 0010 section (trailing-edge angle 12 deg) using the half-model technique. Three plain controls were tested-an inboard control, an outboard control, and the two combined. For a trimmed CL of 0.2 to 0.3, there is no appreciable reduction of effectiveness on any control below M = 0.87. For M = 0.94, all controls have at least 50 per cent. of their low-speed effectiveness in pitch and roll. At higher incidence, reductions in effectiveness occur, particularly near M = 0.87, but are mostly associated with the effects of control deflection on tip stalling. The tests were made at R = 1.8 X 10power6 (based on mean chord) and hence the results may give a pessimistic idea of the behaviour at high Reynolds number. The pitching-moment characteristics show that cropping the pointed wing tip alleviates the tip stalling, as expected. For the cropped wing, the backward shift, with Mach number, of the aerodynamic centre at CL = 0.2 is less than 0.04c up to M = 0.93 Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2999.pdf 554. Rolling power measurements and comparative calculations for a flexible model wing constructed from xylonite N. C. Lambourne et al Partly to gain experience of aero-elastic models constructed from Xylonite, and partly to provide information regarding loss of rolling power due to wing distortion, a tip-to-tip model of the wings of a Spitfire aircraft was constructed. It was mounted on a longitudinal axis in a wind tunnel so that it could roll continuously. Rates of rolling were measured for a range of air speeds and the results are compared with those of calculations. The variation of rolling power with air speed was calculated by : (a) the Collar and Broadbent method (R. & M. 2186) which is based on strip theory, (b) a method developed by H. C. Garner based on lifting-line theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2895.pdf 555. Second harmonic control on the helicopter rotor W. Stewart The application of second harmonic control on a helicopter rotor causes a redistribution of the loading over the disc. This can be utilised to postpone the forward speed limitations imposed by stalling of the retreating blade. This report develops the theory for second harmonic control. The resultant flapping motion and subsequent incidence distribution depend mainly on blade inertia number. A practical check on the flapping with a full-scale rotor on a testing tower gave excellent agreement with the theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2997.pdf 556. Some actuator-disc theories for the flow of air through an axial turbo-machine J. H. Horlock Using actuator-disc theory, simplified methods are given for the solution of the direct problem of the incompressible flow of air through an axial-flow turbo-machine. Calculations based on these methods are compared with other approximate solutions to the flow through a model compressor stage. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3030.pdf 557. Some remarks on Multhopp's lifting-surface theory K. W. Mangler and B. F. R. Spencer This note contaiias an alternative method to that proposed by Multhopp in his subsonic lifting-surface theory for dealing with the spanwise integration of the downwash. The method consists of arranging the series form of the infhmnce function near the inducing section so that the logarithmic term may be integrated, instead of introducing an artificial correction function as Multhopp does. Multhopp's scheme for the solution of the system of linear equations is retained, and there is no increase in the amount of computor work involved. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2926.pdf 558. Supersonic flow past slender bodies of elliptic cross-section L. E. Fraenkel The theories of supersonic flow past slender, smooth, pointed bodies of arbitrary cross-sectional shape, due to Ward, and of the flow past slender bodies of revolution with discontinuities in profile slope, due to Lighthill, are applied and extended to calculate first approximations for the aerodynamic forces on bodies of elliptic cross-section with discontinuities in profile slope. Open-nose bodies are included in this class, but only the external forces are considered. The investigation is restricted to bodies the major axes of whose cross-sections are co-planar and whose cross-sections have constant eccentricity. General expressions are deduced for the wave drag, lift, induced drag, and pitching moments of such bodies. The drag formula bears a marked resemblance to that for the equivalent body of revolution (i.e., the body of revolution with the same axial distribution of cross-sectional area), but the discontinuities introduce a slight difference in one term. The lift formula is identical with that already deduced by Ward for a particular case of the present problem. The general theory is applied to elliptic cones, and a comparison is made with Squire's solution of this problems. Numerical results for the wave drag of bodies of revolution having straight and parabolic profiles are also extended to bodies of elliptic cross-section. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2954.pdf 559. Tests in the R.A.E. 10-ft x 7-ft high speed wind tunnel on drop tanks fitted to two swept-back wings Part 1 Comparison of under-wing and wing-tip installations Part 2 Comparison of various under-wing drop-tank arrangements D. E. Hartley and A. B. Haines The report describes tests made in the Royal Aircraft Establishment 10-ft Ã— 7-ft High Speed Wind Tunnel on drop tanks, fitted to two wings, having the same plan-form with a sweepback of 40 deg and an aspect ratio of 3.5, but differing in thickness/chord ratio, being 10 per cent and 8.5 per cent thick respectively. Part I compares the results obtained with the drop tanks mounted in two alternative positions on the 10 per cent thick wing : under the wing at about mid-semi-span, supported by an 8.5 per cent thick strut or alternatively, at the wing tip in a mid-wing position. Part II compares the results obtained with several different types of under-wing installation, e.g., with different designs of strut or alternatively dispensing with the strut and fitting the tanks directly on to the lower surface of the wing. The latter are referred to as 'nacelle-type' tanks. Most of the tanks had a fineness ratio of 8 : 1. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2951.pdf 560. Tests on a typical whittle compressor A. Simons and C. K. Roberts Tests have been carried out to determine the performance of a typical Whittle compressor (produced in 1944) as used in the W2/700 series of engines. At 1,500 ft/sec tip speed the overall pressure ratio (total head) was 4.27 and the adiabatic efficiency was 75.6 per cent at a mass flow of 36.3 lb/sec. The overall efficiency fails rapidly from 79.6 per cent at 1,400 ft/sec to 75.6 per cent at 1,500 ft/sec due to choking of the outer half of the impeller eye. The maximum diffuser efficiency is approximately 80 per cent at a tip speed of 1,500 ft/sec. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2913.pdf 561. The aerodynamic effects of aspect ratio on flutter of unswept wings W. G. Molyneux, and E. W. Chapple The report describes a method for the direct measurement of the aerodynamic effects of aspect ratio on wing flutter. The method requires the use of stiff (virtually rigid) wings flexibly mounted at the root. Details are given of tests on untapered, unswept wings with freedoms in modes of linear flexure and uniform pitch. A comparison is made between measured values of the flutter characteristics and the values calculated using an aerodynamic theory for oscillating wings of finite aspect ratio, and reasonable agreement for flutter speeds and frequencies is obtained. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2942.pdf 562. The determination of the pressure distribution over an aerofoil surface by means of an electrical potential analyser S. C. Redshaw The potential flow, both with and without circulation, around several thin aeroplane wings has been studied by means of a three-dimensional potential analyser. It is shown that, by using the normal assumptions made in the exercise of the linear perturbation theory, it is possible to obtain the pressure distribution for small angles of incidence, as well as the slope of the lift-incidence curve, easily and rapidly. Experiments are also described in which it was attempted to remove the effect of boundary restraint in a manner analogous to that used in a flexible-walled wind tunnel. Suggestions are made for producing a potential analyser of increased scope together with the possibility of extending the work to curved and twisted thin wings. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2915.pdf 563. The effect of a spike protruding in front of a bluff body at supersonic speeds D. Beastall and J. Turner Wind-tunnel tests at M = 1.5, 1.6 and 1.8 are described in which the effect of mounting a stem, with different nose pieces, on the forward face of a bluff-nosed body is studied. The drag on the front face of the body was derived from pressure measurements for different projections of the stem. Schlieren equipment was used and several interesting phenomena observed in the flow are discussed, in particular a flow oscillation resembling that which sometimes occurs with centre-body intakes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3007.pdf 564. The effect of diameter ratio on the performance of a low-stagger axial-compressor stage R. A. Jeffs and R. G. Adams Low-speed tests have been carried out on a family of three single-stage compressors of different diameter ratios. The simple blade design tested showed considerable variations of performance as the diameter ratio was decreased from 0.65 to 0.35 but most of these variations are predictable by simple means and it is expected that they may be partially avoided by appropriate design methods. It is recommended that low-stagger constant ... stages of low diameter ratio should be designed on the basis of radial equilibrium after the inlet guide blades. In the interests of minimizing the loss of working range at low diameter ratios, at least the outer half of the blades should be designed as far below nominal conditions as other considerations allow. The performance of such stages is fairly well estimated by integration of the strip performances of the various sections of the blade, though further information is necessary to fully define the work-done characteristic. Evidence is shown that the establishment of radial equilibrium demands an axial distance which increases considerably with decreasing diameter ratio, and it is suggested that conditions upstream of a stator-blade row are influenced by conditions required for radial equilibrium downstream of that row. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3151.pdf 565. The effect of tight clamping on the fatigue strength of joints W. A. P. Fisher and W. J. Winkworth The effect of clamping on the fatigue strength of joints in aluminium alloy is investigated experimentally. Tests on Z-section stringers connected to long, slotted cleats give an endurance for tightly clamped joints about nine times that for unclamped joints. Tests of bolted joints in aluminium alloy sheet material show still greater improvement for very tight clamping. In both series of tests, the clamping tends to cancel the weakness in fatigue of a loaded hole. Tight clamping is considered to have many applications in design of aircraft joints from the standpoint of fatigue strength. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2873.pdf 566. The flow at the mouth of a stanton pitot A. Thom An arithmetical calculation is made of the flow at the mouth of a Stanton Pitot as the Reynolds number tends to zero. A stationary eddy is found under the lip of the Pitot. A figure is found for the height of the effective centre of the Pitot rather greater than the experimental value determined by Sir Geoffrey Taylor. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2984.pdf 567. The full-scale hydrodynamic performance of a large four-engined flying boat at overload in calm water and swell J. A. Hamilton and R. V. Gigg Tests have been made on a large four-engined flying boat (Solent Mk. 3), to determine the hydrodynamic performance in sheltered water and in open-sea swells. The sheltered water characteristics were investigated over a range of weights between 72,000 and 84,000 lb. The performance in swell covered weights up to 82,000 lb, and swell heights up to 5 feet. The latter tests were made at Gibraltar in February, 1951. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2898.pdf 568. The manoeuvrability of aircraft in circling flight H. L. Price An investigation is made into the manoeuvre of an aeroplane in the entry into and recovery from a true banked horizontal turn executed without sideslip or loss-of height, and the proper continuous co-ordination of aileron, elevator and rudder is deduced for all stages of the manoeuvre. It is shown that the roiling motion is practically unaffected by the other modes of motion, enabling the kinematics of the rolling.mode to be solved in terms solely of the applied aileron movement or stick force. The aileron is regarded as the prnne initiator of the turn, operated in some pre-chosen manner, and the elevator and rudder loads are expressed as functions of the determinable rolling velocity and acceleration. The loads to trim in the final steady turn are found as a particular case. Several different forms of aileron operation are examined, including a family in which the maximum value of the rolling velocity (or helix-angle in roll) is stipulated beforehand. The co-ordinating elevator load may, in adverse cases, attain peak values considerably in excess of the final load to trim, and the dependence of such peaks on the manner of aileron control operation is examined. It is shown that rapid entries into a turn demanding large rolling velocities at high altitudes are likely to require a large pull back of the stick, followed by a hasty push forward. In order to ensure that the elevator co-ordination should consist of a steady one-way movement of the stick, it is necessary that the aileron be applied in such a way that maximum rolling velocity be obtained when the angle of bank is small. Two manoenvrability criteria are suggested for the entry into the turn, the first relating the final elevator load to the amount of g generated, and the second relating maximum aileron toad to the maximum required rolling velocity and final angle of bank. Extensive information regarding this roiling aspect of the manoeuvre is presented in a set of charts using non-dimensional parameters. The mathematical analysis is contained in appendices. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2838.pdf 569. The R.A.E. hollerith punched-card installation (1945-1952) R. A. Fairthorne, G. J. Griffith and M. F. C. Woollett This report sketches the scope and working of the punched-card installation in Mathematical Services Department, Royal Aircraft Establishment, during the period from 1945 to 1952. Types of work for which the equipment is best suited are indicated, and some representative computing problems that have been handled by the equipment discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3084.pdf 570. The secondary flow in curved pipes H. G. Cuming The Navier-Stokes equations for the flow of a viscous incompressible fluid through curved pipes of different sections are solved in power series of the curvature of the pipe. The solution is given as far as the first power of the curvature for the case of an elliptic section and a discussion given of the effect of the aspect ratio of the pipe on the intensity of the secondary flow. It is shown that the axial velocity is modified by two curvature terms of opposite effect. For values of the aspect ratio near unity the first of these predominates and the resultant effect is an increase of velocity in the outer half of the bend and a decrease in the inner: for large values of the aspect ratio the second term is numerically much greater and there is a resultant decrease in axial velocity in the outer half of the bend and an increase in the inner half. The solution is also given to the first power of the curvature for the case of a square section. This shows that the intensity of the secondary flow in a pipe of square section is greater than that in a pipe of circular section. Finally the solution is given as far as the second power of the curvature for the case of flow through a curved pipe of circular section when suction proportional to the curvature is applied at the walls. The result shows that with the particular distribution of suction considered the diminution in flux through a curved pipe may be almost entirely eliminated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2880.pdf 571. The spinning of model aircraft and the prediction of full-scale spin and recovery characteristics G. E. Pringle and D. J. Harper The report discusses some technical aspects of a long series of tests made with dynamic scale model aircraft in the Royal Aircraft Establishment Vertical Tunnel for the purpose of studying their spinning characteristics. Data accumulated up to the end of 1947 are included, and mention is made, where appropriate, of any further work done up to the end of 1949. The central problem is that of drawing valid conclusions regarding the full-scale spin and recovery; with this in mind there is some discussion of the sensitivity of the spinning model to applied forces including those that upset the spin to produce recovery and those that alternatively generate a new spin. The difference between model- and full-scale spins is analysed with a view to correcting the model data, and some attention is given to power-on spins. A chapter is given to special aspects of the spin of tailless aircraft, and another to safety devices. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2906.pdf 572. Theoretical load distribution on a wing with a cylindrical body at one end J. Weber A method is derived for calculating the spanwise load distribution over a lifting wing having a long circular-cylindrical body at one end. The solution is derived for arrangements giving constant induced downwash, but can be generalised to obtain approximate results for other plan-forms including those with sweepback. Charts are given for the case in which the sectional lift slope is constant along the span. The lift distribution over both wing and body can be determined quickly, or the overall load obtained directly. The results are applicable to the determination of side forces on a fin in combination with the rear fuselage of an aircraft, or of the lift loading on a wing with a weapon or fuel tank at one tip. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2889.pdf 573. V-g records from Vampire aircraft (March 1951-October 1951) E. Marjorie Owen and J. R. Heath-Smith Four hundred and sixty-one V-g records covering 923 flying hours were taken from Vampire aircraft operating in England and Germany during the period March to October, 1951. V-g boundaries expected to be exceeded once in 30, 100 and 300 hours are estimated, special consideration being given to aircraft engaged on ground-attack duties. The results confirm the general belief that more severe accelerations and higher speeds may be expected when aircraft are on ground attack duties than when they are on other duties. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2963.pdf 574. Wind-tunnel observations of boundary-layer transition on a wing at various angles of sweepback A. Anscombe and L. N. Illingworth Visual observations have been made of boundary-layer transition on a wind-tunnel model of constant chord at zero lift over a range of sweepback angles from zero to 50 deg. At each angle above 25 deg, a critical speed could be found within the speed range of the tunnel (400 ft/sec) at which striations appeared within the laminar boundary layer, while the transition line itself lay at 50 per cent to 60 per cent chord. As the speed wffs further increased, transition started to move forward, finally occurring close to the leading edge. The wind speed at which the striations appeared and the forward movement of transition started, decreased with increasing angle of sweepback. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2968.pdf 575. Wind-tunnel tests on the NACA 63A009 aerofoil with distributed suction over the nose N. Gregory, and W. S. Walker Preliminary wind-tunnel investigations into the effectiveness of distributed suction over the nose of a thin aerofoil in delaying the stall, and in increasing the maximum lift coefficient have been carried out in this country by Pankhurst, Raymer and Devereux (1948) on HSA V (NPL 308) aerofoil and in America by Nuber and Needham (1948) on NACA 64A212 aerofoil. The present experiments were undertaken to add to the available knowledge by testing another section. In particular, information was sought on scale effect on suction quantity, on the effect of distributed suction on a flapped aerofoil and on the influence of the shape of the nose of the section on the maximum lift coefficient obtainable with suction. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2900.pdf 576. Wind-tunnel tests on the NPL 434 nose-slot suction aerofoil J. Williams, R. C. Pankhurst and Edna M. Love Stalling tests were made on the 8 per cent thick section NPL 434, which has been specially designed for nose-slot suction. At the higher suction quantities, the maximum lift of the aerofoil was considerably greater than for the Lighthill and Glauert sections previously tested when due allowance was made for the difference in camber. At low suction quantities, there was no improvement. Tests with various slot widths showed that the velocity into the slot as well as the suction quantity was important in relation to high maximum lift, and that the values of CLMAX achieved with suction were determined more nearly uniquely by the momentmn coefficient rather than by the quantity coefficient. Static pressure measurements made in the slot and ducting indicated that the suction head required at the stall was high, being at least equal to the dynamic head in the slot throat, but that some reduction could be expected from improvements in the slot entry shape. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2876.pdf 577. A detailed experimental comparison of axial compressor blades designed for free vortex flow and equivalent untwisted and twisted constant section blades S. J. Andrews and H. Ogden As a contribution to the knowledge of the performance of potentially cheap compressor blades, six stages of both twisted and untwisted constant section or' strip ' blades were tested at a low speed in the 106 compressor. The performance is compared with that of six stages of equivalent free vortex blades, and interstage flow traverses provide the more detailed flow information. In terms of maximum stage efficiency, the twisted constant section blades are half a per cent better than the free vortex blades and the untwisted blades are one and a half per cent worse. Both twisted and untwisted 'strip' blades have a higher surge flow than the free vortex blades, but there is very little difference in the temperature rise characteristics. At values of flow coefficient greater than the design flow, the performance of the three sets of blades becomes almost identical and the application of 'strip' blades at a diameter ratio of 0.75 involves no sacrifice in performance. Incidental tests on the relation between pressure coefficient and Reynolds number show that the maximum pressure coefficient falls to about half its original value for a change in Re from 1.3 x 10power5 to 0.023 x 10power5 and this is accompanied by a reduction in the surge point flow coefficient. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2928.pdf 578. A survey and correlation of data on heat transfer by forced convection at supersonic speeds R. J. Monaghan This report surveys and, wherever possible, correlates experimental data available in the united Kingdom up to January 1953 on heat transfer by forced convection to bodies moving through the air at supersonic speeds (or the corresponding wind-tunnel problem). The main aim of the investigation was to seek possible explanations for the occasional apparent inconsistencies between wind-tunnel results from different sources, between wind-tunnel and flight results and between either type of experimental results and the predictions of theory. The main topics covered are kinetic temperature rise, heat-transfer coefficients and transition from laminar to turbulent flow. Conclusions are reached concerning the reliability of the data for design purposes and suggestions are made concerning the most useful fields of study for future experimental work. Additional note to Summary. October, 1956. A considerable amount of further evidence has become available in the years since 1953 and in places it is necessary to amend some of the statements made in this report. This has been done by adding footnotes prefixed by the date 1956. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3033.pdf 579. Aerodynamic flutter coefficients for subsonic, sonic and supersonic flow (linear two-dimensional theory) P. F. Jordan The solution is derived, in a convenient form for numerical evaluation, for a two-dimensional aerofoil oscillating with arbitrary downwash at sonic speed, and is shown to be the limit of both the subsonic and the supersonic solutions as the Mach number tends to unity. Linear theory is shown to be applicable at sonic speed for an oscillating aerofoil of zero thickness, but at near-sonic speeds consideration of the lift distribution shows that linearization is not permissible. Hence for near-sonic speeds the sonic solution gives a better approximation to the non-linear solution than does the linear solution for the actual speed. It is shown that interpolation of the force coefficients is more justifiable in the subsonic range than in the supersonic range. The physical validity of the linear solution is discussed ; certain singularities which occur in the transition to sonic speed are shown to have no physical significance. The four main aerodynamic force coefficients for an oscillating two-dimensional wing are presented in the form of tables and isometric graphs over the ranges 0 to 2 of Mach number and 0 to 1.4 of frequency parameter based on the wing chord; the present sonic solution and existing subsonic and supersonic solutions have been supplemented by interpolated values for Mach numbers between 0.7 and unity. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2932.pdf 580. Aileron control of small-aspect-ratio aircraft; in particular, delta aircraft W. J. G. Pinsker The aerodynamic and inertia characteristics associated with small-aspect-ratio wings are shown to affect aileron control, causing a tendency towards excessive aileron power combined with poor initial response. Simple formulae are given for the determination of the critical parameters and the effects of these on some aileron manoeuvres are analysed. Touchiness of lateral trimming is also expected to add to the handling difficulties of such aircraft. Finally, design criteria are discussed for the attainment of optimum aileron control. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3188.pdf 581. All-moving wing-tip controls at subsonic, sonic and supersonic speeds a discussion of available theoretical methods and their application to a delta wing with half-delta controls H. H. B. M. Thomas and K. W. Mangler Methods are now available to calculate throughout the speed range the performance of all-moving wing-tip controls on flat-plate wings in inviscid flow, neglecting the shock waves in the transonic regime. The theory, with all its limitations, seems likely to predict in broad outline the main features of this type of control, and should therefore be useful to designers who have hesitated to consider its adoption because of the lack on the one hand of experimental data and on the other of a reasonable analytical approach to the aerodynamics of the problem. In this report, therefore, the theory has been developed and assembled in such a way as to be directly applicable to plan-forms, the spanwise sections of which consist of one segment only, and the case of half-delta controls on the tips of delta wings has been studied in some detail. Much of the theory applies also to plan-forms the spanwise sections of which consist, in part, of two or more segments, such as the swallow tail. A numerical illustration for half-delta controls on a 60-deg delta wing has been used to compare with free-flight transonic measurements of rolling moment and hinge moment. The agreement is as good as could be expected. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3086.pdf 582. An analysis of steady straight flight with inclined thrust S. B. Gates and A. W. Thorpe Griffith's proposal to achieve vertical take-off and landing at the usual attitude demands sea-level thrust considerably greater than the weight and continuously rotatable through 90 deg. A study of the steady states of such a system is necessary as a preliminary to work on the flying techniques involved in the project. In this survey a vectorial method of analysis has proved useful in displaying the special features of the performance of such aircraft at both high and low speed. The main conclusions are: (a) The high-speed performance is sensibly a maximum when the thrust is along the axis of minimum drag. Hence inclining the thrust is useless except in the grounding operations. (b) When the thrust exceeds the weight by a Substantial margin, steady flight is confined to very high speed in a very small incidence range. In this regime there are two flight-path angles for every incidence. (c) Handling may therefore be difficult until, with increase of height, the thrust has fallen below the-weight. If this proves to be so, it is suggested that the full thrust should be used to climb out of the 'excess thrust' region as quickly as possibly. The aerodynamic dividends in increased height and speed of economic cruise are obvious, but no attempt is made at a project assessment. (d) At very low speed, the attitude corresponding to any given inclination of the thrust is almost constant, and a large range of low speeds and flight-path angles is possible. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3096.pdf 583. An experimental investigation of the effects of deformation on the aerodynamic characteristics of a swept-back wing Joseph Black A wind-tunnel investigation of the effects of structural deformation on the pressure distributions round a tapered wing, with 44-deg leading-edge sweepback, has been carried out over a range of deformations at a Reynolds number of 0.6 x 10power6. A technique for constructing a model and deforming it into any desired deformation has been successfully developed. The model is made of Perspex which becomes plastic at 100 deg C.; after being boiled in a water bath the model can be deformed into any desired deformation, and on cooling, it sets hard with the deformation 'frozen' in. When the model is boiled again it reverts to its undeformed shape and a new deformation can then be applied while it is in its plastic state. The cycle can be repeated any number of times with the same model, to cover a range of deformations. From the modes investigated the appropriate deformations required to produce an almost elliptic span loading at a selected moderate overall lift, or to delay tip stalling at high incidence, were established. The most important feature is to have a maximum wash-out at about 0.7 semi-span, with a decrease of wash-out from there to the tip, and not a continuously increasing wash-out right to the tip. The Weissinger method for theoretical prediction of airloads was found to be reasonably satisfactory for the effect of deformation at low incidence. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2938.pdf 584. An unconventional type of fatigue-testing machine F. Aughtie, and H. L. Cox When any elastic system is subj ected to a range of load, the energy stored in the system fluctuates between two values corresponding to the maximum and minimum loads of the cycle. Since the driving unit usually supplies energy at a constant rate (corresponding to losses in the machine), the energy given out by the specimen during one quarter cycle must be stored in some manner and then returned during the following quarter cycle. In existing types of fatigue-testing machine this energy is stored in a rotating mass (flywheel) and gives rise to cyclic variations in its speed. The object of this note is to indicate that the energy can be better stored in an oscillating mass which is, ideally, attached directly to the specimen. When this is done the full specimen load is transmitted through a direct (solid) connection and does not travel through the linkwork to the operating mechanism of the machine. As a consequence the operating mechanism can be made much lighter, the driving power required is considerably reduced and the machine can be run at a much higher speed (if desired). The dual problem of starting the machine and also ensuring stable operation can be solved by the use of a 'slipping clutch' already employed successfully in another connection. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2833.pdf 585. Balance and pressure measurements at high subsonic speeds on a model of a swept-wing aircraft (Hawker P.1052) and some comparisons with flight data J. R. Collingbourne and A. C. S. Pindar Basic results are given of measurements in the Royal Affcraft Establishment 10-ft Ã— 7-ft Subsonic Wind Tunnel over a range of lift coefficient at Mach numbers up to 0.93, the Reynolds number being 1.75 million. Though a really full analysis has not been possible, the data are discussed briefly and are compared with flight results on two aircraft of the type. The tunnel-flight comparisons show reasonable agreement as regards the onset of longitudinal instability and the general characteristics of the pressure distributions on the wing. Full comparisons are not possible because of the absence of comprehensive and accurate flight measurements of pressure distribution. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3165.pdf 586. Calculation of stability derivatives for oscillating wings Doris E. Lehrian A method of calculating stability derivatives for wings oscillating at low frequencies is developed from the modified vortex-lattice method outlined in R. & M. 2470. Derivatives are obtained for the following wings describing plunging (vertical translational) and pitching oscillations: (i) Delta wings of aspect ratio A, = 1.2, 2 and 3 with a taper ratio 1/7. (ii) Arrowhead wing of aspect ratio 1.32 with a taper ratio 7/18 and angle of sweep of 63.4 deg at quarter chord. (iii) Circular plate. Comparison is made with measured values of the derivatives for the delta wing of aspect ratio 1.2 and the arrowhead wing oscillating in incompressible flow. Satisfactory agreement is obtained with experiment, and also with values calculated by the Multhopp-Garner method 4. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2922.pdf 587. Calculation of the pressure distribution over the surface of two-dimensional and swept wings with symmetrical aerofoil sections J. Weber A simple method is described for calculating the pressure distribution on the surface of a thick two-dimensional aerofoil section, at any incidence, in incompressible potential flow. The method has been proposed by F. Riegels and H. Wittich, Refs. 1 and 2. It is particuIarly suitable for practical applications, since knowledge of the section ordinates only is required. This paper gives a complete derivation of the theory including a detailed discussion of the approximations made and their effect on the accuracy of the results. The pressure distributions calculated by the present method are identical withthe exact values for aerofoils of elliptic cross-section, and the numerical values for Joukowsky aerofoils agree well with the exact solutions. Calculations for a typicM practical aerofoil show good agreement with the results from S. Goldstein's method, approximation III, Refs. 3 and 4. The method is extended to sheared wings of infinite span and to the centre-section of swept wings, using tile solution for zero lift from Ref. 16 and the solution for the thin wing with lift from Refs. 10 and 17. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2918.pdf 588. Calculations of the pressure distributions and boundary-layer development on a body of revolution with various parabolic afterbodies at supersonic speeds L. E. Fraenkel Detailed calculations are made of the flow over a series of bodies at Mach numbers of 1.2, 1.4 and 1.6 and Reynolds numbers of 48 to 72 millions. The bodies consist of a basic forebody and parallel portion to which are added truncated parabolic afterbodies of three different thickness ratios. The calculations are in three main parts : (i) Calculation of the inviscid flow over the bodies, mainly by the method of characteristics. (ii) Calculation of the boundary-layer properties by what is essentially an extension to compressible flows of the method of Squire and Young. (iii) Calculation of the pressure distribution on the 'modified' afterbodies which result from adding the displacement thicknesses to the original profiles, by Ferri's method of linearized characteristics. The results indicate that the slender body' and quasi-cylinder theories predict the flow over afterbodies with only very limited accuracy for the thickness ratios and Mach numbers occurring in practice, but that the linearized similarity law remains a useful means of generalizing the particular results of exact inviscid-flow calculations. The boundary layers are seen to thicken very rapidly towards the rear of the afterbodies and this causes pressure changes of as much as 12 percent of the peaksuction. The skin-friction results agree extremely well with those for the equivalent flat plate. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2966.pdf 589. Control surfaces restrained by viscous friction as a means of damping aircraft oscillations W. J. G. Pinsker A method is described of controlling the phase of the free motion of control surfaces by viscous friction and geared masses. Substantial improvements in the damping of aircraft oscillations can be achieved if such devices are applied to existing or additional control surfaces or to tabs attached to such controls. The merits of various arrangements are discussed and formulae for the determination of optimum conditions are derived. The conclusions are illustrated by numerical examples. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2962.pdf 590. Flow instability of centre-body diffusers at supersonic speeds D. Beastall This note offers explanations for certain types of flow instability which occur with centre-body diffusers at supersonic speeds. These instabilities manifest themselves as oscillations of the shock pattern ahead of the diffuser and the flow through the diffuser for certain conditions of operation and are likely to affect seriously the performance. Two main types of oscillation have been distinguished : a violent oscillation which occurs when the flow through the diffuser is throttled below a certain value ; a less severe oscillation which occurs when the vortex sheet from the intersection of the shock waves ahead of the diffuser or a separated boundary layer strikes the cowl. The explanations of the oscillations are substantiated by schliere'n photographs of two- and three-dimensional model diffuser tests in a wind tunnel. It seems possible, in the light of the explanation given in this note, to be able to predict the range of instability of any centre-body diffuser configuration by fairly simple model tests. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2933.pdf 591. Gust alleviation factor. Parts I, II and III J. K. Zbrozek Part I. The report presents the theoretical calculations of gust alleviation factor made for rigid aircraft and with one degree of freedom only (i.e., vertical motion). It is shown that for average gust lengths and for orthodox (tailed) aircraft the influence of thesecond degree of freedom (i.e., pitching) on the value of the gust alleviation factor is negligibly small, providing the pitching moment of inertia and damping are not unduly small. The influence of aspect ratio, the importance of the mass parameter and the gust shape on the values of the gust alleviation factor are shown. The large influence of the gust shape on the value of the alleviation factor makes the gust analysis by simple measurements of maximum aircraft acceleration inadequate, and the full records of the time-history of the aircraft are necessary. An alternative, more direct method of gust measurements is suggested. The inadequacy of the present gust alleviation curve in Air Publication 970 is pointed out and a suggestion for replacement of this curve by the curves calculated in this report is made. Part II. Theoretical calculations of the gust alleviation factor for a range of Mach numbers show an appreciable decrease in its value with increasing Mach number. The reduction in the value of the gust factor at M = 0.7 is about 10 per cent. for sharp-edged gusts and lightly loaded aircraft (μg = 20) and decreases to about 5 per cent. for gust length of 10 chords and heavy aircraft (μg = 100). The analysis of existing flight records indicates that the gust loads at high Mach numbers can be estimated satisfactorily if the gust factor and the lift slope are corrected for compressibility. Part III. The gust loads on swept wing aircraft can be split up into two parts, (a) gust load neglecting pitching motion and (b) correction to gust load due to pitching. Gust loads neglecting pitching can be estimated using the gust alleviation factor of Part I, taking the appropriate aircraft mass parameter and wing aspect ratio and replacing the actual gust length H in wing chords, by an effective gust length Ho~ = H eff + β, where β is the sweep of wing tip expressed in chords. The gust loads computed by this method give satisfactory agreement with gust-tunnel results. For an aeroplane with high wing loading and small aspect ratio the overall effect of wing sweep on gust loads is small. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2970.pdf 592. Hinge-moment derivatives for an oscillating control C. S. Sinnott The semi-empirical 'equivalent profile' method of W. P. Jones (1948) is extended to the case of an aerofoil with an oscillating control. The oscillatory hinge-moment derivatives for such an aerofoil-control combination in a low-speed wind tunnel are estimated, an allowance for tunnel wall interference effects being included. A comparison with measured values of the control derivatives is made for two values of the control chord ratio, representing an aileron and a tab. The method of this report gives results in much better agreement with experiment than those obtained by vortex-sheet theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2923.pdf 593. Interference corrections for asymmetrically loaded wings in closed rectangular wind tunnels H. C. Garner, and W. E. A. Acum The problem of tunnel interference on a complete lifting wing fitted with ailerons is considered in relation to aerodynamic measurements on a six-component balance. Asymmetric loading introduces corrections to the incidence of the wing, the drag and the rolling, pitching and yawing moments. The basic theory of wall interference in closed rectangular tunnels is outlined in sections 3 to 5. In section 6, the tunnel-induced upwash is expressed in terms of the loading on the wing and four quantities dependent on the shape of tunnel. These quantities are evaluated for a duplex tunnel in Tables 4 to 7 and may be computed for a general rectangular shape with the aid of Tables 1 to 3. Section 7 describes how the evaluation of tunnel interference is conveniently linked with Multhopp's lifting-surface theory to determine corrections to incidence, pitching moment and rolling moment. A worked example in the case of antisymmetrical loading is given in Appendix II, which concludes with an approximate procedure, suggested as a possible substitute for the lifting-surface method. The corrections to drag and yawing moment are discussed in detail in section 8. All the corrections are summarized in section 9 and expressed as products of experimental aerodynamic coefficients and theoretically determined quantities, which are evaluated in Table 8 for an arrowhead wing (Fig. 4) with various ailerons in a duplex tunnel. The corrections to incidence due to symmetrical loading are equivalent to corrections to lift of the opposite signs these vary from - 11 to - 5Â½ per cent depending on the type of loading. The corresponding corrections to rolling moment due to antisymmetrical loading are about - 2 per cent. Corrections to drag are very roughly + 20 per cent. When the spanwise loading is asymmetrical, there arises an induced yawing moment, which may require an interference correction of the order + 25 per cent. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2948.pdf 594. Measurements of the aerodynamic derivatives for swept wings of low aspect ration describing pitching and plunging oscillations in incompressible flow C. Scruton, L. Woodgate, and A. J. Alexander The aerodynamic lift and moment derivatives for pitching oscillations in incompressible flow have been measured for two axis positions on (i) a clipped delta wing of aspect ratio 1.2, (ii) a complete delta wing of aspect ratio 1.6, and (iii) an arrowhead wing of aspect ratio 1.32. The results for the arrowhead wing and the dipped delta wing are compared with values predicted by the vortex-lattice and the Multhopp-Garner methods of calculation. The results for the complete delta wing are compared with values calculated by Garner and by Lawrence and Gerber. In each of the comparisons a satisfactory measure of agreement was found between the theoretical and experimental values of the derivatives. Calculated values for the clipped delta wing based on very low aspect ratio theory did not accord with those found by experiment. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2925.pdf 595. Measurements of the direct pitching-moment derivatives for three wing planforms at high subsonic speeds J. B. Bratt, W. G. Raymer and J. E. G. Townsend Measurements of the direct pitching damping and stiffness derivatives for a delta and two swept wing planforms made in the N.P.L. 9Â½ in. High Speed Tunnel are discussed, and results for the delta are compared with theory. Experiments to investigate the cause of loss of damping at low frequencies obtained in earlier tests are also described, and the effect on derivative measurements of random oscillatory flow disturbances is examined. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3419.pdf 596. Model testing technique employed in the R.A.E. seaplane tank T. B. Owen, A. G. Kurn and A. G. Smith A description is given of the various techniques evolved in recent years to provide model data as a basis for predicting the full-scale behaviour of a seaplane. The seaplane tank and associated equipment is described in detail, together with the routine methods of operation. The factors affecting the choice of model scale are discussed and the methods of model construction described. A description is given of a typical test programme on a new design to determine the longitudinal and lateral stability on the water, spray and rough water behaviour and water drag. This description is illustrated with typical results for a modem conventional hull of length : beam ratio of about 7. Finally, the design factors affecting the longitudinal stability and spray formation are discussed in Appendices. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2976.pdf 597. Preliminary report on a gust alleviator investigation on a Lancaster aircraft J. Zbrozek, K. W. Smith and D. White The investigation of gust alleviator effectiveness is limited to an analysis of statistical measurements of c.g. accelerations. The measured alleviation is much smaller than was initially expected and in some cases is even negative. Theoretical analysis, supported by experiment, indicates that the loss of gust alleviator effectiveness is mainly due to the large pitching moment contributed by the ailerons. The aircraft with gust alleviator in operation suffers a considerable loss of stability and calculations show that with increasing gust length alleviator effectiveness decreases and eventually becomes negative. Airframe flexibility also has some detrimental effect. The effectiveness of the alleviator in terms of wing-root bending stress alleviation is considered to be more favourable, but no experimental data are yet available. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2972.pdf 598. Problems of longitudinal stability below minimum drag speed, and theory of stability under constraint S. Neumark Practical difficulties in cruising below minimum drag speed have long been known but not fully explained. The reasoning proposed by Painleve in 1910 purported that flight below minimum drag speed should be fundamentally unstable, so that any speed error would lead to a divergence. This reasoning is shown to be invalid on the ground of the general theory of dynamic stability in uncontrolled flight, Painleve's criterion being a grossly inadequate approximation to the condition of phugoid stability. However, the criterion may be fully vindicated for the case of flight controlled by the elevator in such a way as to maintain constant height. In this form, the criterion seems not only to explain qualitatively the troubles encountered in slow cruising, but also to lead to a good quantitative estimate of speed variation following an initial disturbance. The criterion also applies to the problem of ultimate height response to an elevator deflection. The concept of stability of partially controlled flight is further developed, leading to a general theory of 'stability with constraint', i.e., when a control (elevator, throttle, etc.) is used to suppress one component of the disturbance. The theory may be useful as giving approximate solutions of problems in which the pilot moves his control so as to keep one component of the disturbance always as small as possible. The principles of the theory are set out in section 4.1, and several examples given in sections 4.2, 4.3 and 4.4. Flight tests are needed to explore further the validity of this method of approximation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2983.pdf 599. Some flutter tests on swept-back wings using ground-launched rockets W. G. Molyneux and F. Ruddlesden This report gives the results of tests on flutter models of untapered wings with 20 deg, 40 deg and 60 deg sweepback. Tests have been made up to a Mach number of 1.4. A comparison is made between the measured flutter speeds and the speeds estimated using a flutter speed formula. Modifications to the formula are proposed which include a compressibility correction of the form (1.0 - 0.166M cos A), 0 < M cos A < 1.6, where A is the angle of sweepback. A comparison is also made between measured flutter speeds and those calculated using two-dimensional incompressible flow theory. This shows that the calculated speeds are lower than the measured speeds except in the transonic region, where they are in some cases slightly higher. The calculated flutter frequencies are on the average some 20 per cent higher than the measured values. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2949.pdf 600. Tests on a single-stage turbine comparing the performance of twisted with untwisted rotor blades I. H. Johnston and L. R. Knight An experimental single-stage turbine designed for the testing of a variety of blade forms with cold air is described together with the instrumentation provided for test measurements. Performance results obtained on this unit from two rotor blade designs are presented and it is shown that for the incidence range covered by the tests an untwisted constant-section blade of about 10 per cent reaction possesses characteristics of pressure loss and deflection nearly identical to those of a conventional rotor blade twisted along its length to conform to the requirements of radial equilibrium, the mean diameter sections of the two blade designs being identical. It should be noted that the rotor blade section used in these tests provides a gas outlet angle and degree of reaction which, although lower than those employed in current aircraft engine practice, may well become typical for designs requiring a higher volumetric flow per unit turbine frontal area, e.g., a high temperature cooled turbine. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2927.pdf 601. The buckling shear stress of simply-supported, infinitely-long plates with transverse stiffeners P. W. Kleeman This report is an extension of previous theoretical investigations of the elastic buckling in shear of flat plates reinforced by transverse stiffeners. The plates are treated as infinitely long and simply-supported along the long sides. Stiffeners are spaced at regular intervals, dividing the plate into a nuraber of panels of uniform size. The effect of bending and torsional stiffnesses of the sLiffeners upon the buckling shear stress is calculated for the complete range of stiffnesses, for panels with ratios of width to stiffener spacing of 1, 2 and 5. The results are presented in tabular and graphical forms. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2971.pdf 602. The Calculation of the Loading and Pressure Distribution on Cranked Wings G. G. Brebner Using distributions of vortices and sources over the aerofoil surface, approximate formulae are developed for finding the spanwise and chordwise loadings of cranked wings (i.e., wings with discontinuous changes of sweep), and the chordwise pressure distribution at the crank, in incompressible flow. The method can be extended to subcritical compressible flow by considering the 'analogous wing.' Calculations by the present method are compared with experimental results on two wings and with calculations by another method for wings of M, W and A plan-form. Agreement with experiment is good. Comparison with the other method shows satisfactory agreement between the spanwise loadings, but the present method yields more information about chordwise distributions, and is quicker. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2947.pdf 603. The component pressure losses in combustion chambers H. A. Knight and R. B. Walker This Report summarises the available knowledge of the component losses in a combustion chamber. The information given in this Report should enable the pressure drops through swirlers, primary baffles, cooling systems, etc., to be calculated. Most of the data were abstracted and collected from the various reports listed in the bibliography. In certain cases (e.g.,mixing losses) the information is incomplete and in these circumstances the limited experimental results available are supplemented by hypotheses which require proof. A specimen calculation of the pressure drop and airflow distribution of a typical chamber is given in Appendix U. The calculated and measured values of pressure drop (cold) agreed within 4 per cent. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2987.pdf 604. The design and testing of an axial compressor having a mean stage temperature rise of 30 deg C A. D. S. Carter, S. J. Andrews and E. A. Fielder This report describes a compressor which was designed to give a mean stage temperature rise of 30 deg C. It has six stages so that the overall pressure ratio at the design point is 4.5 : 1. Full details of the factors which led to the form adopted and of the design itself are given in the report. The test results fully substantiated the design assumptions. In particular, using standard design data, it is possible to achieve temperature rises of about 30 deg C without sacrificing unduly any desirable performance features. Such temperature rises were considerably above those being used at the time this work was carried out, and are in fact substantially above the mean value used in present-clay designs. Details of the stage characteristics and the matching of the compressor have been given in the report, together with some other points of special interest. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2985.pdf 605. The estimation of shock pressure recovery and external drag of conical centre-body intakes at supersonic speeds E. L. Goldsmith and C. F. Griggs Methods of predicting shock pressure recovery and external drag at all mass flows have been developed for conical centre-body intakes at supersonic speeds. Comparison with wind-tunnel measurements shows that the method for predicting the shock pressure recovery gives the correct variation for the shock losses as the shock configuration changes with mass-flow ratio. Agreement near full mass flow is not so good when the losses other than shock losses are probably changing rapidly and the shock configuration remains unchanged. Results of drag tests show that reasonable agreement with theory is obtained for the rise in drag which occurs when the intake is spilling and for the drag at full mass flow. Curves are included to assist in the calculation of the drag rise and the associated reduction in pressure recovery. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3035.pdf 606. The forward take-off of a helicopter F. O'Hara A theoretical analysis is given of the accelerated motion of a single-rotor helicopter for estimation of the forward take-off performance. The motion is considered in stages during which either the disc attitude to the horizontal or the flight speed is constant. Equations are derived for the motion along and normal to the flight path and solutions are given assuming constant mean values for the aerodynamic forces on the rotor and fuselage. The equations of motion for constant disc attitude have a simple solution for motion from rest (and for special initial conditions) giving a straight flight path, and a general solution giving a curved flight path. The performance at constant speed is considered for a general climb away case and also for climb away approaching steady flight conditions with the thrust approximately equal to the aircraft weight. For application of the theory, charts of the various solutions are given covering a representative range of the variables. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2937.pdf 607. The harmonically oscillating wing with finite vortex trail P. F. Jordan The wing of infinite span oscillating harmonically in incompressible flow but having a vortex trail of finite length Sc is discussed theoretically. The 'incomplete circulation functions' Cs which arises in this case is tabulated. As an example, the damping moment due to slow pitching oscillations is shown for several values of S. The result is of interest as a wind-tunnel correction, in particular in that range of small frequencies which occurs in flight stability oscillations. Agreement with an experiment in an open-jet wind tunnel is obtained. A contradiction between different experiments in closed-jet wind tunnels is mentioned. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3038.pdf 608. The oscillating aerofoil in subsonic flow W. P. Jones A relatively simple method for calculating the aerodynamic forces on an oscillating aerofoil is developed and used to derive the aerodynamic coefficients for M = 0.7, 0.8 and 0.9 for a range of frequency parameter values. The two-dimensional aerofoiI is represented by a flat plate and the usual assumptions of linearized theory for unsteady flow are made. The problem is reduced to one of finding the solution of an integral equation for the velocity potential of the disturbed flow. This is solved by the use of the known solution of a related problem in incompressible flow in which the aerofoil oscillates at a frequency increased by the factor (1 - M²)-1 and for which the condition for tangential flow is suitably modified. By successive approximation to this modified boundary condition, it is possible to obtain solutions to any desired accuracy. Formulae for the aerodynamic coefficients may also be derived for each approximation. Those given by the first approximation are of sufficient accuracy for use in stability calculations when the frequency parameters involved are low. For higher values, more complicated formulae corresponding to higher-order approximations could be derived if required. The results obtained confirm that values given in Ref. 6 which were derived by Dietze's method for M = 0.7 and by Schade for M = 0.8 are substantially correct. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2921.pdf 609. The R.A.E. 4-ft x 3-ft experimental low-turbulence wind tunnel. Part IV. Further turbulence measurements H. Schuh Further measurements of turbulence in the working section are given with 2 and 3 screens in the bulge. The extended region of high intensity turbulence near the walls of the working section, which was observed with 9 screens in the bulge, disappeared when the number of screens was reduced from 9 to 2 or 3. The longitudinal component of turbulence is approximately independent of the nmnber of screens ; the lateral component does not change, if the number of screens is reduced from 9 to 3, but increases by a factor 2.5 to 3, if the number of screens is further reduced from 3 to 2. In order to explain the origin of the turbulence in the working section, further turbulence measurements have been made at the end of the second diffuser, before the rapid expansion and in the bulge. The intensities of turbulence are about 12 per cent of mean speed at the end of the second diffuser and drop to about 4 to 6 per cent before the rapid expansion. However, this turbulence seems to be reduced by the screens in the rapid expansion and in the bulge below the level of disturbances set up by inhomogeneities of the last screen. These disturbances are the origin of the lateral components of turbulence in the working section. The extended region of high intensity turbulence near the walls of the working section is connected with the existence of a return flow in the bulge, but several possible explanations exist as to how this produces the region of high intensity turbulence in the working section. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3261.pdf 610. The R.A.E. electronic simulator for flutter investigations in six degrees of freedom or less F. Smith, and W. D. T. Hicks This report describes, the design and construction of an electronic simulator for flutter investigations in any number of degrees of freedom not exceeding six. Tile principles of the simulation are discussed, and the actual circuits of the machine are described in some detail for those wishing to build similar machines. The advantages and limitations of this method of solving flutter equations are considered, and other developments and applications are discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3101.pdf 611. The subsonic flow past swept wings at zero lift without and with body D. Kï¿½uchemann and J. Weber Note.--This memorandum is a summary of the material contained in a number of earlier Royal Aircraft Establishment Reports by the authors and Was prepared at the request of the Aeronautical Research Council for publication as an R. & M. A review is given of the effects associated with the subsonic inviscid flow past swept wings at zero lift with the aim of providing the information needed for an understanding of the flow phenomena, methods of obtaining the full benefit of sweep are described. Detailed solutions for incompressible flow are given for three basic cases : (a) the sheared wing of infinite span (b) the centre-section of a swept wing of infinite span (c) the flow in the curved intersection line between wing and body. These solutions are used to find approximate solutions for any given wing of finite aspect ratio. The Prandtl-Glauert procedure is extended and applied to derive approximations for the compressible flow in the subcritical region. The special cases treated in detail are : the flow in the tip regions of wings ; tapered wings ; wing-fuselage interference for symmetrical arrangements; and modifications to the wing or to the body shape, for instance to restore sheared-wing conditions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2908.pdf 612. Theory of aerofoil spoilers L. C. Woods A mathematical theory of aerofoil spoilers in two-dimensional subsonic flow is presented. Equations are given for load distributions, lift, drag, moments and hinge moments pro.duced by spoiler-flap combinations. The theory is developed for a spoiler in a general position but the trailing-edge spoiler receives special attention. For this important case the theory gives good agreement with experiment, but in the more general case, because of uncertainty about the pressure distribution on the aerofoil to the rear of the spoiler, the agreement is not as good. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2969.pdf 613. Theory of Aerofoils on which occur bubbles of stationary air L. C. Woods Spoilers, split flaps and sometimes (with thin aerofoils) incidence alone cause the flow to separate from the aerofoil surface. This flow often reattaches to form a closed bubble of virtually stationary air at a fairly constant pressure. The paper sets out a mathematical theory of the subsonic inviscid flow external to the bubble whose position is assumed. The influence of the bubble on the lift and moment coefficients is calculated and some comments are made about the stalling of thin aerofoils. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3049.pdf 614. Wind-tunnel flutter tests on a delta wing with an all-moving tip control surface D. R. Gaukroger Wind-tunnel tests on a half-span model delta wing, fitted with an all-moving tip control surface, are described. The model, which is flexible, has a leading-edge sweepback of 45 deg; and the control surface, which is rigid, has an area 9.3 per cent of the gross wing area. The control surface is hinged at 47.4 per cent of its root chord. Provision is made for varying the circuit stiffness and the position of the centre of gravity of the control surface and its pitching moment of inertia. The tests show that certain combinations of control-surface inertia and circuit stiffness produce very low flutter speeds. The effect of reducing the control-surface area by cropping the tip is examined, and in general is found to be beneficial. It is shown that the most favourable conditions for avoiding low flutter speeds exist when the control surface centre of gravity is well forward of the hinge-line and the control-surface natural frequency is well removed from the natural frequency of the wing in its fundamental flexural mode. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2978.pdf 615. Wind-Tunnel Tests on the Effect of a Localised Mass on the Flutter of a Swept-back Wing with Fixed Root D. R. Gaukroger Wind-tunnel tests to determine the flutter characteristics of a model wing, carrying a localised mass, are described. The investigation covers the effects of wing sweepback, and of the magnitude and position of the localised mass. Consideration is also given to the effects of pitching radius of gyration and aerodynamic shape. The mass values. used vary from 0.13 to 1.17 times the wing mass. The test results indicate that the parameters that have the greatest effect on critical flutter speed are mass value, spanwise and chordwise position of the localised mass, and wing sweepback. Radius of gyration and aerodynamic shape of the localised mass are found to be secondary in their effects. It was found that the flutter speed of a wing could be considerably increased or decreased by attaching a localised mass; under certain conditions the flutter speed could be more than doubled. A number of different forms of flutter were obtained in the tests, and the values of the parameters at the transition from one form of flutter to another provide the main guide to the flutter characteristics of a wing carrying a localised mass. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3141.pdf 616. Wind-tunnel tests on the symmetric and antisymmetric flutter of swept-back wings D. R. Gaukroger Wind-tunnel tests to determine the symmetric and antisymmetric flutter characteristics of a swept-back wing are described. The investigation covers the separate experimental treatment of the symmetric and antisymmetric body freedorns over a range of wing sweepback angles. Consideration is also given to the effect on critical flutter speed and frequency of variations in overall centre of gravity position, fuselage pitching moment of inertia, fuselage roiling moment of inertia, fuselage mass and tailplane volume coefficient. The test results indicate that flutter speeds lower than the flutter speed of the wing with the root rigidly fixed may be obtained for a tailless aircraft with slight sweepback under unfavourable inertia conditions of the fuselage; for other sweepback and inertia conditions the flutter speeds are likely to be equal to, or higher than, the fixed root speeds. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2911.pdf 617. Wind-tunnel wall interference effects on oscillating aerofoils in subsonic flow W. P. Jones A theory is developed for estimating the effect of wind-tunnel walls on the air forces acting on an aerofoil oscillating in a subsonic airstream. It can only be applied for a range of frequencies well below the frequency at which transverse vibrations of the air stream may be induced. The possibility of resonance occurring for certain combinations of tunnel height, frequency of oscillation of aerofoil, wind speed and Mach number was first pointed out by Runyan and Watkins, and the present paper confirms their conclusions. The method is applied to calculate aerodynamic derivatives for an oscillating flat plate in a wind tunnel of height equal to 4.75 aerofoil chord and a Mach number M = 0-7. Results obtained are tabulated for comparison with the known theoretical free-stream values. It is shown that the influence of the walls is considerable even at frequencies of oscillation well below that of resonance. Measurements of the pitching-moment damping coefficient for the RAE 104 aerofoil of 2-in. chord in:the 9.5-in. x 9.5-in. Wind Tunnel have been made by Bratt and his results for M = 0.7 differ appreciably from the corresponding estimated values given in this note. However, by the use of the equivalent profile method much better agreement may be obtained. This method is used to estimate the pitching-moment damping for a range of Much numbers and low-frequency parameter values corresponding to those used in the tests. Fairly good agreement between estimated and measured values is obtained up to M = 0.8, and the calculations indicate, in accordance with experiment, a loss of damping at the highest Mach numbers considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2943.pdf 618. A case of longitudinal stick-free dynamic instability of an aircraft fitted with power-operated control, g-restrictor and spring feel S. Neumark, J. Collingbourne, and H. H. B. M. Thomas Following flight experience of a particular aircraft, the effect of including a bob-weight and feel spring in the circuit of a power-operated longitudinal control on the dynamic stability of the aircraft is investigated. The main findings of the investigation, which are given in the Introduction and fully set out in the discussion and conclusions at the end of the paper, can be summarised briefly as follows: (a) With such a control system, instability of the aircraft short-period oscillatory mode can result. In these circumstances damping of this oscillatory mode deteriorates progressively with increase of speed. (b) Friction in the control circuit is an important factor affecting the characteristics of the aircraft stability. (c) It is considered that by care in design, particularly as regards positioning of the bob-weight, and choice of gearing, such instability can be avoided. Each case, however, requires examination on its own merits, on the lines of the analysis given here. (d) For setting up the equations of motion, the transfer function of the power unit is required. In the present calculations a simple approximation is used, which raises the degree of the characteristic equation from a quartic to a sextic. (e) Some consideration was given to the effect of changes in the moreimportant design parameters, but it is found that apart from the gearing and position of the bob-weight mentioned above, they may have (within reasonable limits) only a mild palliative effect. The main investigation was done by means of the usual mathematical analysis, with friction represented by an equivalent viscous damping. Additional results are obtained by the use of the Nyquist presentation and of the Philbrick Electronic Analog Computor. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3094.pdf 619. A study of the aircraft arresting-hook bounce problem J. Thomlinson The kinematics of an arresting-hook unit are studied in order to determine, within the limits of the assumption of a perfectly rigid hook unit, the damper force necessary to control hook bounce. The necessity for a smooth deck and the desirability of small trail angle for the hook unit are demonstrated from several aspects. The design requirements for a hook damper unit are discussed in all their functional aspects and methods are given for determining the up-swing motion of an arresting hook unit immediately following engagement of an arresting wire. The behaviour of arresting wires after being depressed by the passage of aircraft wheels is also outlined. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2980.pdf 620. A survey of the alternating pressures exciting high frequency vibrations in gas turbines J. R. Forshaw A survey of the predominant harmonic components of the alternating pressures is made for three centrifugal compressors, three axial-flow compressors and a single-stage turbine to ascertain the forces exciting vibration in a compressor or turbine stage. The predominant harmonic components of the alternating pressures in the casing are the first-order components of the impulse from the rotor blades or impeller vanes. Harmonics up to the seventh of these impulses can be detected in parts of the speed range, The alternating pressures in a compressor annulus have components similar to those observed in the casing for the stage but in addition have components of greater magnitude excited by dissimilar flows in individual blade passages. The largest orders are those which excite the fundamental flexural mode of vibration of the blades and the corresponding blade movements amplify the alternating pressures. The amplitude of the alternating pressures is dependent on the work done in a blade or impeller vane passage, the incidence at entry to the stage, the exit conditions and the general flow conditions and there is usually a relative reduction when operating near the design point. There is a reduction in the alternating pressures with distance from the source particularly across a blade row. There are three other sources of excitation at part load : (a) Stalling flutter at high positive incidence can occur in a.,dal-flow compressors for blades of low stiffness over wide ranges of operation provided the incidence and mass flow are greater than the boundary conditions. (b) Alternating pressures can be excited gear the surge by one or more stall cells rotating at some fraction of compressor speed (c) At the stalling incidence of a stage, if a proportion of the stage stalls due to dissimilar geometry or flow and the remainder of the stage and compressor as a whole is operating at relatively high efficiency, large alternating pressures of all forcing orders can be excited. This effect is the more severe the lower the natural frequencies of the blades. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2989.pdf 621. Abstracts of Papers Published Externally [Unknown] Note: All papers discussed by the Aeronautical Research Council and recommended by them for external publication after 1st April, 1932, have been published in abstract only in the Reports and Memoranda Series. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2916.pdf 622. An analysis of the longitudinal stability and control of a single-rotor helicopter F. O'Hara The general theory of longitudinal stability and control for a single-rotor helicopter is presented in a form similar to that for fixed-wing aircraft. It is shown to be possible to establish for the helicopter in forward flight, in the same way as for fixed-wing aircraft, stick-fixed static and manoeuvre margins, on which the stability and handling qualities depend to a marked extent. If the static margin Kn > 0 the helicopter is mathematically statically stable, and the pilot requires a forward stick displacement to hold increased speed and conversely. If the manoeuvre margin Hm > 0, the helicopter is unlikely to be subject to rapid divergence in a disturbance, and the pilot requires a backward stick displacement for positive normal acceleration in a pull-out. Theoretical relations are derived for Kn and Hm in a general form covering the case of a tailplane linked to the rotor control. Relations are given also for determining Kn and Hm from measured control changes to trim. An analysis is given of the growth of acceleration in a pull-out and assessment of estimated acceleration curves in terms of the National Advisory Committee for Aeronautics 'divergence requirement' suggests that the latter may be satisfied if Hm has a small positive value. Further evidence on this point will be obtained in tests now being made on a number of helicopters to study the correlation of stability and control characteristics and pilots' impressions of the handling qualities. Extension of the theory to stick-free longitudinal stability depends on knowledge of the rotor forces on the control plane and the analysis of these forces is being considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2958.pdf 623. An empirical analysis of the planing lift characteristics of rectangular flat-plates and wedges P. Ward Brown The fluid flow about planing plates and wedges is briefly described and discussed, and on the basis of theoretical and physical considerations of this flow empirical formulae are presented for the lift developed by these planing surfaces. The formulae are mutually compatible and cover the whole range of planing of zero and finite deadrise surfaces including the chine-dry and chine-wet conditions. The lift formulae are extensively compared with experimental data, over a range of trim angles from 2 to 30 deg and deadrise angles from 0 to 40 deg, and very good agreement obtained. The analysis confirms the existence of an effective critical wetted length for all the planing surfaces studied and shows that the wave-rise about planing wedges is an irrelevant feature of the flow. The formulae are thought to be of such a nature that they may form the foundation for the lift prediction of more complex planing surfaces than are dealt with here. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2998.pdf 624. An extension of the hydrodynamic source-sink method for axisymmetric bodies A. H. Armstrong Real flow patterns are produced by formally placing a pair of conjugate complex sources at conjugate complex points on the axis of symmetry. These complex singularities are shown to be equivalent to a non-uniform distribution of real doublets on a real disc. Reciprocal relationships are formulated between these new singularities and the well-known simple source ring and vortex ring. While the latter are simpler physically, the new type of singularity is easier to handle in mathematical analysis, involving only square roots instead of elliptic integrals. Sufficient conditions are determined under which an axisymmetric body may be generated by a real distribution of sources and sinks along the axis of symmetry, and the formula for the source intensity is given when these conditions are satisfied. An example deals with the flow about all oblate spheroid. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3020.pdf 625. An investigation of the high alternating stresses in the blades of an axial-flow compressor J. R. Forshaw A vibration investigation of the 1st, 2nd and 3rd stage stator blades of an axial-flow compressor gave high values of the alternating stresses of the order of 10,000 lb/sq in. On three runs excessive values of the alternating stress of 24,000, 27,500 and 48,000 lb/sq in. were obtained, and for these and forborne of the other maximathe incidence was estimated to equal the stalling incidence. There is excitation at all speeds of low orders showing dissimilar flow in different parts of the stage and this excitation increases in a critical manner at or near stalling incidence indicating a partial stall which is localised in parts of the stage. At greater incidence the flow deteriorates, the contrast between various parts of the stage is reduced, and the level of the alternating stress falls to a value slightly higher than that at incidences lower than the partial stall. This phenomenon occurs for critical operating conditions and is different from stalling flutter. Both phenomena could occur in the same compressor, the latter would be influenced by blade stiffness and could occur over wide ranges of operation provided the incidence and mass flow are greater than the lower boundaries. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2988.pdf 626. Calculation of flutter derivatives for wings of general plan-form Doris E. Lehrian The vortex-lattice method of calculating flutter derivatives presented in this note is an extension to higher frequencies of the work on stability derivatives reported in R. & M. 2922. The method is a modified form of the scheme outlined in R. & M. 2470 and is suggested as an alternative to the latter method since it gives a simpler routine calculation for wings of general plan-form. Derivatives are calculated for the following wings, describing plunging and pitching oscillations: (a) Delta wings of aspect ratio A = 1.2 and 3 and with a taper ratio 1/7. (b) Arrowhead wing of aspect ratio 1.32 with a taper ratio 7/18 and angle of sweep of 63.4 deg at quarter-chord. The results for the delta wing A = 1.2 and the arrowhead wing are compared with values of the pitching derivatives obtained in low-speed tests; those for the delta wing A = 3 with the values calculated in R. & M. 2841. The comparison indicates that the present method gives reasonable accuracy for low-aspect-ratio wings in incompressible flow; the method may be sufficiently reliable for use with the equivalent wing theory suggested in R. & M. 2855 for the calculation of flutter derivatives in compressible subsonic flow. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2961.pdf 627. Elevator flutter involving two tabs E. G. Broadbent and Mary Clarke An account is given of a theoretical flutter investigation in connection with an accident to a Sea Venom aircraft. The investigation covers both symmetric and antisymmetric flutter of the tailplane-elevator-tab system. The main (symmetric) calculations include six degrees of freedom, comprising three structural modes and movements of elevator, spring-tab and trim-tab respectively. The parameters that are varied include elevator mass-balance, position and magnitude of mass-balance on each tab independently, structural damping and stiffness of the tab circuits, chord and mass of the trim-tab, and flexibility of the elevator mass-balance attachments. The investigation shows the symmetric flutter to be a probable cause of the accident and confirms the efficacy of the remedial measures adopted, which consisted of modifications to the tab mass-balances combined with a reduction in chord and inertia of the trim-tab. Several points of general interest are discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3210.pdf 628. Examples of the effects of shock-induced boundary-layer separation in transonic flight H. H. Pearcey, and D. W. Holder The present state of knowledge concerning the interaction between shock waves and boundary layers, and several examples of the importance of the interaction in high-speed flight were described in a previous report. It was shown that the major effects arose from, and could be explained in terms of, separation of the boundary layer at or ahead of the shock wave. The present note gives further examples of the consequences in flight of shock-induced separation of the boundary layer; these examples have been derived from data obtained in NACA and British flight tests, and from high-speed wind tunnel experiments. The variation of the pressure coefficient at the trailing edge of the wing has been used to deduce the onset of separation from the results of the flight tests. It is found that separation occurs on straight wings at approximately the same value of the local Mach number just ahead of the shock as for two-dimensional aerofoils with turbulent boundary layers. For swept wings the available data are inadequate for a detailed comparison. Various features in the "steady-flow" characteristics and buffeting behaviour of the aircraft considered are then shown to be closely associated with boundary-layer separation. These features include wing dropping, loss of control effectiveness, and the "pitch-up" instability which has been encountered with swept-back wings. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3510.pdf 629. Flight tests on a Vampire Mk. 5 with a redesigned anti-snaking rudder W. J. G. Pinsker A specially designed rudder has been fitted to a Vampire Mk. 5 to act as an aerodynamic yaw damper. Flight tests show that the damping of the lateral oscillation has been substantially increased in consequence a logarithmic decrement greater than unity being attained even at 40,000 ft altitude. This is a considerable improvement on the results obtained previously on the same aircraft, when the standard rudder was used as the damping surface. Air to air aiming is shown to have benefited from the effect of the damping rudder. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3014.pdf 630. Flow in the laminar boundary layer near separation B. S. Stratford, G. E. Gadd Summary.--A simple formula is derived for the separation of the laminar boundary layer. The method of derivation and a key test suggest that it should be reasonably accurate and of general application, including particularly the range of sharp pressure gradients and small pressure rises to separation. In addition a partially new exact solution is found for the boundary-layer equations of motion; also the pressure distribution is obtained for continuously zero skin friction, this pressure distribution being expected to attain any given pressure rise in the shortest distance possible for a given laminar boundary layer provided that there is neither transition nor boundary-layer control. The final formula of the paper is given by equation (41); equation (43) is a simpler but rather less accurate formula. The pressure distribution for continuously zero skin friction is represented by equation (39) and is shown in Fig. 3 as curve (c). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3002.pdf 631. Investigations on an experimental air-cooled turbine Part 1 general description of turbine and experimental technique Part 2 cooling characteristics of blades having a multiplicity of small diameter coolant passages D. G. Ainley, N. E. Waldren and K. Hughes Part 1. Tests on internally air-cooled turbine blades operating under realistic conditions are required to determine (a) the degree of cooling achievable and (b) the effects of cooling on the overall turbine performance. This requirement has led to the manufacture and installation of an experimental air-cooled turbine specially designed for testing internally air-cooled nozzle and rotor blades. This part of the report records a general description of the turbine, the first set of cooled blades to be tested, and the associated instrumentation. It also records some results of earlv tests made to check the cooling of the turbine structure (excluding blades). Part 2. A thorough examination in an experimental turbine has been made of the cooling characteristics of a set of internally air-cooled nozzle and rotor blades. Particular attention was paid to the rotor blade cooling characteristics and results show that a very substantial reduction in mean rotor blade temperature may be achieved with a cooling flow equal to 2 per cent of the main gas flow. The blades were not uniformly cooled, the hlade temperatures being very much higher near the leading and trailing edges than in the mid-chord sections. However, examination of the steady thermal stresses created by the non-uniformity in cooling, and the transient stresses likely to occur during 'thermal shock', suggest that the non-uniform cooling is not very detrimental. An increase in turbine inlet gas temperature of about 270 deg C above the permissible value for the same rotor blades and same life without cooling appears possible with a cooling flow ratio of 0.02. The results further indicate that when operating with a fixed cooling flow ratio the mean degree of cooling achieved on the present blades is not substantially influenced by changes in the gas flow Reynolds number or, within limits, by substantial changes in blade aerodynamic loading. The results also indicate that cascade tests to investigate cooling characteristics of hlades may not be wholly applicable to similar blades operating in an actual turbine stage. This may be due largely to the fact that the amount of heat transferred from the gas to a blade is influenced considerably by the location of the boundary-layer transition points and these in turn may be greatly influenced hy the degree and nature of the turhulence in the main gas stream. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2975.pdf 632. Local coefficients of skin friction and heat transfer for turbulent boundary layers on two-dimensional diffusers J. N. Hool This report considers the changes of local coefficients of skin friction and heat transfer for turbulent boundary layers in two-dimensional subsonic air streams under rising pressure gradients. The values of the local coefficients of skin friction and heat transfer are compared on the basis of Reynolds' Analogy, von Karman's improvement to Reynolds' Analogy, and on the basis of similar velocity and temperature boundary-layer profiles. Tests on diffusers at total angles of 4 deg and 7 deg showed that the local coefficients of heat transfer based on the measured heat transfer values, increased with increase of the strealn velocity and diffuser angle relative to the local coefficients of heat transfer, based on Reynolds' analogy and on von Karman's improvement to Reynolds' analogy. The local coefficients of heat transfer calculated on an assumed similarity of velocity and temperature distributions were unsatisfactory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2986.pdf 633. Measurements of the effect of windscreen shapes on the drag of cockpit canopies at transonic and low supersonic speeds using the free-flight-model technique C. Kell The effect of changes in the shape of the windscreen on the drag of a cockpit canopy has been measured on models in free flight. Canopies were attached to the models by means of a flexible mounting in such a way as to allow the canopy drag to be measured directly. The drag of the canopy was measured over a range of Mach numbers between 0.85 and 1.55 and the results show the improvements to be obtained by variations in the sweep of a vee windscreen and changes in the angle of a sloping windscreen. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3024.pdf 634. Measurements of the paths of the vortex cores shed from the wings of a typical guided-missile model at M = 1.57 R. H. Plascott The paths of the cores of the vortex sheets shed from the wings of a typical guided-missile model, having cruciform rectangular wings mounted on a long cone-cylinder body, have been traced in their movement downstream over a range of incidence and yaw from 5 to 20 deg and 0 to 20 deg respectively at M = 1.57. The measuremenfs have shown that: (a) the cores of the vortex sheets remain very close to the plane parallel to the free stream containing the line of the mid-chords of the wings from which the vortex sheets are shed (b) the movement of the fully rolled-up cores in this plane can, for practical purposes, be attributed entirely to the flow induced by the other wing (c) estimates of the paths of the vortex cores based on slender-body theory do not agree at all well in the regions investigated owing to the presence of strong shock waves and rapid expansions. Estimates of the paths of the vortex cores based on a semi-empirical analysis have shown reasonable agreement, however, and it is considered that approximations similar to those made in these estimates for this configuration would give reliable values for other configurations in the regions near the wings; wall downstream of this region a slender-body theory analysis would probably be satisfactory (d) slender-body theory gives a reasonable estimate of the spacing of the cores of the fully rolled-up sheets at the zero yaw condition. Estimates of the characteristics of four rear surfaces using this vortex spacing have shown satisfactory agreement with experiment (e) further tests to check these conclusions on a large range of missiles seem desirable. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3016.pdf 635. Note on the circulation in circuits which cut the streamlines in the wake of an aerofoil at right-angles J. H. Preston G. I. Taylor in an Appendix to R. & M. 989 (1924) suggested that, in the two-dimensional flow of a real fluid, the circulations in all circuits enclosing the aerofoil and cutting the streamlines in the wake at right-angles would be very nearly the same. The present writer in R. & M. 1996 (1943) gave a 'proof' that the circulations in such circuits were alI equal, and Temple (1943) gave a more rigorous proof of the same theorem. This theorem is of fundamental importance in the calculations of the lift of aerofoils allowing for the boundary layer (see Preston R. & M. 2725, 1949, and Spence, 1954) and it is re-examined in this note. The theory is developed for convenience and simplicity, for an aerofoil with a jet issuing from the trailing edge and the effect of the wake is deduced from this. Elementary considerations, which are set out below, suggest that, in the case of an aerofoil with jet, the above theorem is not true. It would also appear that it is not quite true for an aerofoil with wake, since the same arguments can be applied. However, in this case the departure of the circulation from a constant value for circuits of the type under consideration may be expected to be small, and the effect of this on the prediction of the lift should be negligible for incidences below the stall. In the case of the aerofoil with a strong jet, the existence of circulation in circuits not enclosing the aerofoil but cutting the jet twice at right-angles may have important effects on the lift. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2957.pdf 636. Notes on the analysis of stability in accelerated motion S. B. Gates and A. W. Thorpe Linear differential equations whose coefficients are functions of the independent variable are now assuming importance in aeronautics in the discussion of the motion following a small disturbance in a specified accelerated motion. In such problems the undisturbed state is often a transition motion in a limited time interval between two steady motions and we are concerned to see that the disturbed motion does not exceed tolerable bounds in a limited time. The extension of classical stability theory to such problems involves some logical difficulties and very great mathematical ones, since such equations are seldom soluble algebraically. For these reasons an indirect attack oll the problem is made here by seeking to establish upper bounds to the solution of second-order equations, which are those most commonly occurring. The subject is introduced by a study of the equation x.. + b(t)x. + c(t)x = 0. The theory is then applied to a simple problem of pitching motion in an airstream of varying velocity. Finally a system of two second-order equations involving two variables x and y is discussed from this angle. This system is not tractable in its most general form, but the special cases that yield to treatment are those which have occurred in some recent problems. This analysis should be useful in the examination of any problem to which it can be applied; the exploration of its range has hardly begun. It is, of course, open to the objection that the gap between the bound and the solution can in general only be found by numerical integration. Some surveys by numerical integration to compare with the bound analysis will be the quickest way of assessing this method as a tool for general use. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3394.pdf 637. On the statistical optimisation of guided-weapon systems E. G. C. Burt and R. W. Bain The statistical nature of the input to a guided-weapon system (target information and noise) requires that the criterion of weapon performance be itself a statistical quantity. The criterion used in this paper is the mean square miss distance, the mean being taken over a large number of engagements, such that all probable target and noise inputs are encountered, and it is shown that there exists an optimum realisable system for which this mean square miss distance is a minimum. For the derivation of the optimum system it is necessary to assume that the target and noise inputs, or appropriate functions of these inputs, may be considered to form a stationary (but not necessarily ergodic) ensemble for a short interval prior to collision. Account is taken of the fact that the system must include a missile, with its aerodynamic characteristics and limited available acceleration, and this leads to a number of optimum systems depending on these factors. The beam-riding system is shown to satisfy the main requirements of the analytical framework, so that this system may be identified with the optimum system. From this identification follows the definition of certain components of the beam-rider, and the optimisation of the latter requires the insertion of electrical networks in the ground tracker or in the missile, or both, depending on the sources of noise. Explicit formulae are derived for cases in which the noise spectral density is assumed to be constant with frequency, and the target manoeuvres to be such that their lateral accelerations form a stationary ensemble over the necessary interval. The examples give n show that a definite improvement results from the use of the optimum system, in that both the miss distance and the acceleration requirement are reduced. The realisation of networks defined by their transfer functions is discussed in Appendix IV, and examples are given of optimum networks for the beam-riding system. One such example has been the subject of simulator tests, in which it is compared with the 'phase-advance' system. It is concluded that the missile accelerations required to achieve a given miss distance are considerably less than those hitherto considered necessary, and that the results of the paper warrant a further programme of analysis, simulation and flight trials. Such work might well lead to a significant advance in the efficiency of missile design. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3418.pdf 638. One-dimensional treatment of non-uniform flow R. D. Tyler For one-dimensional flow of a perfect gas, conditions at a station of a duct are defined by any four independent properties. Standard methods exist for the calculation of any other desired property from the given four independent properties. The object of this paper is to illustrate the errors likely to arise when the simple one-dimensional flow methods are applied to a circular section duct in which a boundary layer exists. Graphical results are presented, for the case of a one-seventh power law boundary-layer velocity profile, showing the ratio of the true mean values calculated with allowance for the boundary-layer, to quantities derived from the simple one-dimensional calculation. Various boundary layer thicknesses and a range of Mach numbers are dealt with. Specifically three examples are worked out in detail, with different selections of the four independent variables, the selections being chosen to cover problems of common interest. The results of the first two examples might be applied, for instance, to the problem of the performance or design of a duct discharging adiathermally to atmosphere, from a reservoir with known stagnation conditions. The errors are usually small. Thus calculations by simple one-dimensional theory differ by less than about 21 per cent up to a 'one-dimensional' Mach number M = 1, and 5 per cent up to M = 2, from the values obtained by assuming a boundary-layer thickness at exit of 10 per cent of the duct radius. For other boundary-layer thicknesses the errors are roughly in proportion. The results of the third example indicate the errors likely to arise in the analysis of other quantities at a station, from measurements of mass flow, area, total temperature and static pressure. Here the accuracy of the one-dimensional method is within 2 per cent up to a freestream Mach number M' = 2 for any boundary-layer thickness. Total pressure is an exception, the error in this case approaching 10 per cent at M' = 2. General equations are presented for use in cases not covered by these examples. They are analogous to the onedimensional equations, and give ratios of mean flow quantities to their sonic values, as functions of Mach number and correction factors, graphically presented, which depend on the velocity distribution. As a further illustration of possible application of the theory, the correction factors may be used for the calculation of momentum fltix or kinetic energy flux from the mean velocity and mean density. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2991.pdf 639. Some notes on the flow patterns observed over various swept-back wings at low Mach numbers (in the R.A.E. 10-ft x 7-ft high speed tunnel) A. B. Haines This paper collects together the flow patterns observed by an oil film (titanium oxide) technique over ten different Swept-back wings at high incidence and low Mach number in the Royal Aircraft Establishment 10-ft X 7-ft High Speed Tunnel. The designs range from 0.04 to 0.10 in mean thickness/chord ratio and from 40 deg to 60 deg in angle of sweep. Almost all the wings suffer from a leading-edge separation and the paper discusses in general terms how the regions of flow separation, together with their associated part-span vortex sheets are affected by changes in incidence, Reynolds number and wing design. Some brief reference is made to how the flow patterns are related to the overall force and moment characteristics and how these characteristics might be improved by the use of different types of modification. It appears that some correlation may ultimately be established between the spanwise extent of the separation over a swept-back wing at a given incidence with concepts based on two-dimensional flow and the pressure distribution over the swept wing in polential flow. No correlation can be expected in terms of the chordwise extent of the separation, in view of the presence of 'part-span vortex sheets'. The need for research into the 'bursting' of 'short' separation bubbles in two-dimensional flow and into the nature and reasons for the part-span vortex sheets in three-dimensional flow is especially emphasized. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3192.pdf 640. Tests in the Royal Aircraft Establishment 10-ft x 7-ft high-speed tunnel on 50-deg swept-back wings. Part I. Three of 7.5 per cent thickness. Part II. One of 7.5 per cent thickness with stall fences and leading-edge chord extension A. B. Haines, and C. W. Rhodes Tests have been made in the Royal Aircraft Establishment 10-ft x 7-ft High-Speed Tunnel on three half-wings having a sweepback of about 50 deg on the quarter-chord line and 7.5 per cent thick sections. Two of the wings had sections of the RAE 101 shape (maximum thickness at 0.31c) and differed principally in aspect ratio (3.1 and 3.5). The third wing had an aspect ratio of about 3.1 but a different section shape with its maximum thickness further aft at 0.4c and, as shown by the results of the tests, an effectively sharper nose than for the RAE 101 shape. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3043.pdf 641. The calculation of the pressure distribution on thick wings of small aspect ratio at zero lift in subsonic flow J. Weber The method of expressing the velocity increment over aerofoils directly in terms of the section ordinates (Refs. 1 and 2) is extended to cover also straight and swept wings of finite aspect ratio. The wings considered are untapered in plan-form but may be tapered in thickness. The section can be of any given shape so that in this sense the analysis is more general than that of Refs. 3 to 6 which deal with wings of biconvex section. The coefficients required in the calculation are tabulated for the centre-section of straight and swept-back wings (φ = 0 deg, φ = 45 deg and φ = 60 deg) of aspect ratios 0.5 ; 1 ; 2 ; and 4, the wing of infinite aspect ratio having been treated in Ref. 1. The remaining calculations can be made very quickly. Since wings of very small aspect ratio can be treated also by the method of slender-body theory, the relations between linear theory, slender-body theory, and linearised slender-body theory are discussed. For the special case of ellipsoids, the results obtained from the various methods are compared with the exact solution. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2993.pdf 642. The effect of a wind gradient on the rate of climb of an aircraft W. A. Mair The behaviour of an aircraft climbing in the presence of a wind gradient is analysed by a method similar to that used in R. & M. 379, but with fewer simplifying assumptions. It is shown that the result obtained in the earlier paper is only correct if the angle of climb is small and if the true air speed is constant during the climb. With the climb techniques that are now usual, however, the true air speed is not constant during the climb; with typical subsonic aircraft the effect of this is to change the correction due to a wind gradient by about 10 per cent. For aircraft climbing at supersonic speeds the effect of acceleration may be much greater than this. Since the percentage change of rate of climb due to a given wind gradient is approximately proportional to the flight speed, the effect does not become less important as aircraft speeds increase. Moreover, wind gradients having a significant effect on the rate of climb are not confined to low altitudes. For a modern high-speed aircraft it is shown that the wind gradient may change the rate of climb by 20 per cent or more. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2953.pdf 643. The measurement of high frequency alternating pressures in gas turbines J. R. Forshaw and H. Taylor The measurement of alternating pressures in gas turbines could not be achieved by existing techniques. The pressures consisted of small-amplitude alternating pressures superimposed on pressures up to 100 lb per sq in. and at temperatures up to 250 deg C in compressors and up to 850 deg C in turbines. The frequencies of the predominant harmonic components varied from 100 to 17,000 c.p.s, and those for the smaller components up to 40,000 c.p.s. Improvements were required in the recording techniques which are reported elsewhere but the changes in amplifiers are described. The development of a capacity pressure element to record the alternating pressures at a point in a casing is described. A small diameter diaphragm was used to facilitate installation and to obtain the pressure over as small an area as possible. The diaphragm was arranged near the gas stream and the effect of temperature changes was eliminated by applying a filtered balance air supply behind the diaphragm to permit calibration during the investigation. The balance air supply permits equalisation of pressure across the diaphragm so that higher sensitivities can be used. The alternating pressures decrease sharply with distance from the source and if the alternating pressure is required at a point other than in the casing a special approach will be required. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2990.pdf 644. The reflection effect of fences at low speeds J. Weber, and J. A. Lawford This note considers the effect on the flow over a swept wing, of vertical plates of small height--commonly called 'fences'. It is shown, as might be expected, that the nature of this effect is that of a partial-reflection plate. The effect of this partial reflection on the pressure distribution over the wing on either side of the fence has been investigated theoretically and by means of pressure measurements at low speeds on an untapered 45 deg swept-back wing. An earlier physical explanation 1 of the flow changes caused by fences has been substantiated, and the proportion of full reflection effect has been determined experimentally for various shapes of fence. Methods are described for calculating the changes in pressures distribution, chordwise loading and spanwise loading. The effect of a fence in obstructing boundary-layer outflow on swept-back wings of large aspect ratio has not been considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2977.pdf 645. The strength of annealed and heat-treated glass F. G. J. Brown and J. Ellis This report develops statistical methods of choosing allowable design stresses for annealed and heat-treated glass. The results are easy to apply but additional fundamental knowledge of some properties of glass is needed before they can be used to the best advantage. The report draws attention to these gaps in existing knowledge and makes recommendations for further research. The report discusses the influence of the known causes of strength variations between nominally identical specimens in relation to two types of glass typical of those used by the aircraft industry, and shows that improved control of heat-treatment processes offers the best hope of a big increase in the useful strength of glass. Chemical protection of the glass surfaces, or changes of composition which increase the intrinsic strength and chemical stability of the glass, would increase the useful strength of both annealed and heat-treated glasses. The potential benefits for heat-treated glass are small compared with those obtainable by improved control of the heat-treatment processes but are nevertheless important. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3003.pdf 646. The stress distribution in panels bounded by constant-stress edge members E. H. Mansfield Exact solutions are given for the stress distributions in long panels bounded by constant-stress edge members. The influence of closely spaced stringers and ribs on the peak shear stresses is investigated. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2965.pdf 647. The torsional rigidity of solid cylinders of double-wedge section E. H. Mansfield The torsional rigidity of solid cylinders of double-wedge section is considered theoretically. Minimum energy methods are used to determine close upper and lower limits to the rigidity. The results are presented in graphical form. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2959.pdf 648. Theoretical load distribution on a wing with vertical plates J. Weber The spanwise load distribution is calculated for wings with plates normal to the wing and parallel to the main stream, or inclined to it at a small angle. The calculations are made for configurations having minimum induced drag. The results are used to obtain an approximation for wings of any plan-form (where the condition of minimum induced drag no longer applies), including wings with sweepback. Wings with plates of equal height on the upper and lower surfaces of the Wing, and wings with plates on the upper surface only, are considered. Charts and tables for the additional load distribution with plates of various heights, 0 < h/b < 0.3, at the spanwise positions : b1/b = 0.2, 0.4, 0.6, 0.8, 0.9, 1.0 are given. Side-force distributions on the plates, as well as integrated side-forces and the moments of the side-force, are calculated. In the Appendix, a method of calculating the load distribution on wings with a discontinuity in chord, sectional lift slope, or geometric incidence is described. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2960.pdf 649. Theoretical load distributions on fin-body-tailplane arrangements in a side-wind J. Weber and A. C. Hawk A theory has been developed for calculating the distributions of sideforce and lift on fin-fuselage-tailplane arrangements in a side-wind but with the tailplane set at zero incidence. The analysis is limited to incompressible flow and has been further simplified by assuming that the geometrical arrangement is in each case such as to give constant induced sidewash. The results, which can be extended to other arrangements and to compressible sub-critical flow, are required for stability and stressing analyses. This paper is a continuation of an earlier note by the first author (Ref. 1), where the interference between fin and fuselage was considered. The addition of the tailplane introduced into the present report brings considerable changes in the load distribution as well as in the overall forces. The actual calculation procedure is very simple and quick since the main functions needed are presented in tables and charts for representative cases. The results for other geometrical arrangements can be obtained by interpolation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2992.pdf 650. Thermodynamic data for the calculation of gas turbine performance D. Fielding and J. E. C. Topps The essential features of a practical method of determining gas turbine performance are that it shall be suitable for accurate routine calculation, and that it is capable of simple modification in order to deal with a range of fuels or with complex cycles. It is the opinion of the authors that the exactitude of the method should also be demonstrable, within the limits imposed by the scales employed, and that it should require only the use of parameters physically intelligible to the average engineer, and a sequence of operations which can be followed by a computer. The calculation should not, moreover, be onerous, involving the use of large or complex charts, or interpolation in tables. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3099.pdf 651. A comparison of the measured and predicted flutter characteristics of a series of delta wings of different aspect ratios H. Hall and E. W. Chapple The report gives the results of tests to investigate the aerodynamic effects of aspect ratio on the flutter of delta wings that are virtually rigid but are flexibly supported at the root. A function representing the aerodynamic effects of aspect ratio on wing flutter speeds is derived from the experiments. Flutter calculations are made using this function as a correction to the derivatives obtained from two-dimensional theory, and there is good agreement between measured and calculated results. Calculations are also made using derivatives obtained from three-dimensional theory, but the agreement between measured and calculated results is poor. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3071.pdf 652. A method for calculating the lifting forces on wings (unsteady subsonic and supersonic lifting-surface theory) J. R. Richardson A numerical method is given for calculating the lifting forces on oscillating wings of any plan-form. The principles and techniques of Multhopp's subsonic theory have been applied to the supersonic problem resulting in a single basic theory which embraces both subsonic and supersonic cases. One of the most important features of the method is the careful choice of the points at which the lift and downwash distributions are measured. The position of these points in the chordwise direction depend upon whether the local leading and trailing edges are subsonic or supersonic. Extensive use has been made of various interpolation functions which simplify the evaluation of the integrals required for both the downwash and the generalised forces. In the latter case it is shown that the continuous lift distribution can be replaced without loss of accuracy by a set of concentrated lift forces at the lift points. The lift distribution is expressed in terms of these discrete forces since for most purposes they are more convenient to use. It is shown that control surfaces can be dear with by using equivalent continuous deflections and downwash angles to replace the true discontinuous values. Simple expressions are given for these equivalent values, and these expressions are applicable to both subsonic and supersonic cases. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3157.pdf 653. A new standard for the prediction of full-scale spin and recovery characteristics from model tests T. H. Kerr The important features of a model, which affect the scale effect in the spin and recovery are discussed in the light of several model to full-scale comparisons and the general background. Of spinning experience. These features have been shown to be the λ of the spin, the thickness/chord ratio of the wing and the inertia ratio B/A of the model. Using these parameters, a new standard for the prediction of the full-scale spin and recovery from the model test has been presented. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3130.pdf 654. An experimental investigation of the transonic flow over an unswept wing of aspect ratio 3.5, taper ratio 0.5, with a 4 per cent biconvex section J. B. Scott-Wilson The results of force measurements and surface oil flow studies on a wing-body combination with an unswept wing of aspect ratio 3.5, taper ratio 0.5, and a 4 per cent biconvex section, are analysed. The tests were made at Mach numbers from 0.72 to 1.02, at a Reynolds number of 1.89 Ã— l0power6. At four Mach numbers, 0.70, 0.80, 0.93 and 0.96, a picture of the flow development with incidence is built up, based on the oil flow patterns on the wing, and a correlation is established between changes in overall forces, and changes in tile flow development. At other Mach numbers the flow development is inferred from the overall forces by means of this correlation, and, in this way, an attempt is made to show how transonic flow develops over the wing. At transonic Mach numbers four phases in the development of the flow with incidence are found. These are (a), no shock-induced separation, (b), shock-induced separation, with the shock roughly stationary on the wing, (c), shockinduced separation, with a rapid forward movement of the shock, and (d), leading edge separation. The aerodynamic derivatives are found to assume roughly constant values in each phase, and their variation with phase and Mach number is considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3209.pdf 655. An investigation of the velocity distribution around the nose of the aerofoil with a flap Ian H. Rettie The velocity distribution around the nose of an NACA 0015-64 aerofoil was found by experiment and that around the nose of a Piercy 15/40 aerofoil by calculation for various angles of incidence and flap deflection. It was established that at all incidences this velocity distribution is a function of the position of the stagnation point, irrespective of the flap deflection. This result is shown to be true generally, and it is suggested that use might be made of it in the design of a lift-coefficient meter, which could also be used to give warning of a stall. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3027.pdf 656. Calculated velocity distribution and force derivatives for a series of high-speed aerofoils C. S. Sinnott The Polygon method of Woods is used to calculate the velocity distribution over a number of two-dimensional aerofoils at low incidence, subcritical flows only being considered. Lift slopes and aerodynamic centres at zero lift are also calculated. Some comparisons with experimental results are made, and these show good agreement at zero incidence. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3045.pdf 657. Calculation of derivatives for a cropped delta wing with an oscillating constant-chord flap in a supersonic air stream J. Watson Summary.--The lift, pitching moment and hinge moment are derived for a delta wing with a trailing-edge flap of constant chord when tile wing is at zero incidence in a supersonic air stream and tile flap oscillates harmonically with small amplitude and low frequency. It is assumed that the wing is sufficiently thin and the amplitude of oscillation sufficiently small to permit the use of linearised theory. Expressions for the various control derivative coefficients are obtained for a particular delta wing of aspect ratio 1.8 and taper ratio 1/7. The investigation covers partial-span flaps; in each case there is a lower limit to the Mach numbers for which the theory applies, though from practical considerations this restriction is not serious. The derivatives are evaluated and tabulated for Mach numbers 1.1, 1.2, 1.4, 1-6, 2.0. The theory is shown to apply without appreciable error, provided that the frequency parameter based on mean chord does not exceed 0.4. The calculated values of hinge-moment damping are compared with preliminary experimental values obtained at the National Physical Laboratory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3059.pdf 658. Current tests on laminar boundary layer control by suction through perforations S. F. J. Butler This note describes current experiments on laminar-boundary-layer control by suction through perforations. No attempt was made to obtain full-chord laminar flow, as this had been shown previously to be a natural consequence of applying a suitable suction distribution, providing turbulent wedges did not result from oversuction. In the present tests, the main aim therefore was to determine the flow rates at which such wedges appeared for different arrangements of perforations. In order to simplify the test procedure, most of the results were obtained using one or more closely spaced rows of perforations at a single chordwise station on an otherwise plain wing. A method is given, supported by some experimental evidence, for predicting the perforation spacing which would be required in a full-chord application from the results thus obtained at a single chordwise station. With all the configurations tested, a limiting suction rate was found above which turbulent wedges appeared, causing premature transition. This limit exhibited an adverse Reynolds-number effect and also made it essential to use a uniform backing to obtain a satisfactory performance. It is suggested that flow curvature under three-dimensional conditions may further restrict the suction rates which could be used. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3040.pdf 659. Derivative measurements and flutter tests on a rectangular wing with a full-span control surface, oscillating in modes of wing roll and aileron rotation W. G. Molyneux and F. Ruddlesden Details are given of tests to measure the aerodynamic coefficients for a rectangular wing with a fullspan aileron oscillating in modes of wing roll and aileron rotation. A new technique was used in which aileron rotation was geared to wing roll so that oscillation occurred in both degrees of freedom simultaneously. The measured coefficients are compared with those derived from two-dimensional theory, and with coefficients estimated by an empirical method. The agreement with theory is poor but the estimated coefficients agree well with those measured. Flutter calculations for the system were made, using both measured and theoretical derivatives, and the results are compared with flutter test results. The calculated flutter speed using measured derivatives agrees closely with that measured, whereas using theoretical derivatives the agreement is poor. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3010.pdf 660. Effect of Yaw on the compressible laminar boundary layer J. Tinkler The equations governing the laminar compressible boundary layer on a yawed body of infinite span are transformed to give three non-dimensional equations defining two velocity components and the enthalpy. Assuming that the Prandtl number is unity and that there is zero heat transfer, a relation is obtained between the stream Mach number and the angle of yaw for flows which give the same boundary-layer equations. The further assumption of viscosity proportional to the absolute temperature is made and 'similar' solutions are found to be given by a family of surface Mach number distributions normal to the leading edge. 'Similar' solutions, obtained from a differential analyser, are presented for a range of two controlling parameters. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3005.pdf 661. Experimental and theoretical investigations of the flow of air through two single-stage compressors J. H. Horlock The development of actuator-disc theory and its application to predict the flow through axial-flow turbo-machines has been given in Ref. I. An investigation of the accuracy of these theoretical predictions of performance has been made on an axial-flow-compressor test rig in the Cambridge University Engineering Laboratories. This investigation has involved the traversing of pressure and angle measuring instruments at the trailing edge and further downstream of blade rows, and comparisons of the axial velocity profiles obtained from these pressures and yaw angles at the various stations with theoretically predicted profiles. The changes in the axial velocity profiles at the trailing edges of blade rows due to the interference effect of neighbouring rows have also been studied, both in the stalled and unstalled regions of operation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3031.pdf 662. Experiments at M = 1.41 on elliptic cones with supersonic leading edges E. W. E. Rogers and C. J. Berry Tests have been made at a Mach number of 1.41 on six elliptic cones forming two families of models. In the first, the vertex angle in the plane of the major axes of the elliptic cross-sections was maintained constant at 60 deg and the ratio between the minor and major axes varied; in the second family, the minor axis was constant and the vertex angle had values of 30 deg, 60 deg and 90 deg. Two cones from the first family were pressure-plotted at incidences up to 15 deg, the resulting pressure distributions being integrated to give the lift and pressure drag arising from the curved surfaces of the cones. Except for one of the pressure-plotting models, lift, drag and centre-of-pressure position were measured for all models on a strain-gauge balance. For the one cone on which a comparison was possible, good agreement was obtained for the lift and drag derived from the two methods. The distribution of pressure on the two pressure-plotting cones was found to be approximately conical in form (i.e., constant along the cone generators) and at 0 deg, good agreement with theory was obtained. At incidence, the agreement was worse and deteriorated when, at the higher incidences, transonic-type shock waves appeared on the upper surfaces of the cones. The'se shock waves which lay along a cone generator moved inboard with increase in incidence, and vortices, formed from flow separating from near the leading edges, also appeared, with a consequent modification of the upper-surface pressure distribution. These transonic-type shock waves were observed by using optical systems of schlieren or shadowgraph type, but with the light beam passing obliquely through the tunnel so that it was approximately parallel to the shock front; the separation vortices were detected by observing the motion of an oil film on the surface of the models. Good agreement was obtained between linear (flat-plate) theory and experiment for the lift of the family of cones having a 60 deg vertex angle; there is only a small effect on the lift-curve slope due to increasing the cone thickness (i.e., the minor axis of this family). The surface shock waves and separation vortices were responsible for a change in the rate at which the drag of the cone family increased with the lift. The comparatively slender cone of the other family had a lift curve which was markedly non-linear at the higher incidences and this effect was attributed to the presence of separation vortices. The inclination of the cone-likeshock originating at the vertices of the models and also the distribution of pressure over the bases of the cones were measured. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3042.pdf 663. Experiments on the use of suction through perforated strips of maintaining laminar flow transition and drag measurements N. Gregory, W. S. Walker Wind-tunnel tests are described in which suction is applied at perforated strips, as an alternative to porous strips or s]ots, in order to maintain a laminar boundary layer. A test was first carried out on a single row of perforations on a cambered plate, as a preliminary to the main tests which were performed on strips of multiple rows of perforations drilled through the surface of a low-drag-type aerofoil 13 per cent thick and of 5-ft chord. Up to a wind speed of 180 ft/sec it has been ascertained that suction may be safely applied to extend laminar flow provided the ratio of hole diameter to boundary-layer displacement thickness is less than 2, the ratio of hole pitch to diameter is less than 3 and there are at least three rows of holes in the strip. With less than three rows, the criteria are much more restrictive. It is possible to extend laminar flow by suction through perforations whose diameters and pitches exceed these values slightly, but only with the risk that excessive suction quantities will produce wedges of turbulent boundary layer originating at the holes. A uniform distribution of suction through the holes was necessary. This was successfully obtained by two methods, the use of cells and throttle holes, and with tapered holes. In particular, tests were carried out on some panels supplied by Handley Page, Ltd., in which the cells and tapered holes had been constructed by commercial methods, and the suction distribution proved satisfactory. The resistance of some of the cellular arrangements was measured. It was found that when the suction quantities were the minimum required to maintain laminar flow, the additional losses in total head of the sucked air due to the resistance of the throttle holes could be made small compared with the loss in total head of the sucked boundary layer. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3083.pdf 664. Flight experiments on boundary-layer control for low drag M. R. Head, D. Johnson and M. Coxon Tests have been made with distributed suction applied to a short-span sleeve fitted to the upper surface of the wing of a single-seat Vampire aircraft. Full-chord laminar flow was maintained up to Reynolds numbers in the region of 29 million and Mach numbers up to 0.70, which was very nearly the critical Mach number of the sleeve section. The suction quantities required were sufficiently small to result in overall reductions in profile drag of between 70 and 80 per cent, account being taken of the power required for suction. Difficulties were experienced due to surface roughness, and although these are believed to have resulted largely from the particular type of porous covering used in the tests, the problem of maintaining a sufficiently smooth and clean surface is evidently of crucial importance to full-scale application. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3025.pdf 665. Flight investigation of some airworthiness problems of civil boat seaplanes J. Taylor, J. E. Allen and A. G. Smith A general investigation has been made into measurement, control and performance problems associated with boat seaplane take-off and initial climb. Particular attention was paid to engine failure during take-off and initial climb, and also to the criteria to be used for defining the minimum speed for control in the air. The aircraft employed was a Solent flying-boat of weight 78,000 lb, powered by four Hercules Mark XIX engines. The general conclusion is that the present methods used for landplanes are also applicable to seaplanes, with certain modifications to meet water-stability requirements and the greater freedom of manoeuvre available with respect to heading and position on the water. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3017.pdf 666. Flight measurements of the drag of a swept-wing aircraft (hunter Mk. 1) at mach numbers up to 1.2, together with some measurements of lift-curve slope D. R. Andrews and J. E. Nethaway Flight tests have been made to determine the drag of a Hawker Hunter F Mk. I aircraft. The results show that at low Mach number the drag coefficient at zero lift is 0.0125 and the effective induced-drag factor K is 1.09, both values being corrected to a constant Reynolds number of 34 x 10power6. Above a certain C L the drag due to lift increases rapidly, the C L at which this occurs falling from 0.76 at M = 0.3 to 0.41 at M = 0.7. Some approximate measurements of K made at supersonic speeds suggest that virtually all the leading-edge suction on the wing is lost beyond M = 1.0. At C L = 0.1, the compressibility drag rise commences soon after M = 0.8, the drag rising rapidly beyond M = 0.92 and attaining a peak C D of 0.0565 at M = 1.15. The compressibility drag rise obtained from high-speed wind-tunnel tests agrees well with that obtained in flight although this agreement may be largely fortuitous in view of the low tunnel Reynolds number. Measurements of incidence show that the lift-curve slope at M = 0.3 is 3.5 rising to 4.6 at M = 0.9. The zero-lift angle remains constant with Mach number at about 0.4Â°. Agreement with wind-tunnel tests is reasonably good when allowance is made for differences in geometry and in Reynolds number. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3420.pdf 667. Flutter tests on some delta wings using ground-launched rockets W. G. Molyneux and F. Ruddlesden This report gives the results of tests on flutter models of cropped delta wings having 40, 50 and 60 deg leading-edge sweepback and a taper ratio of 1 : 7. A comparison is made between the measured flutter speeds and the speeds estimated using a flutter speed formula, and the estimated speeds are found to be within ± 15 per cent of the measured speeds. A modification to the formula is proposed to allow for the high values of stiffness ratio that are obtained for delta wings. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3231.pdf 668. Initial lift of finite aspect-ratio wings due to a sudden change of incidence Doris E. Lehrian The initial lift for wings of finite aspect ratio due to a sudden unit change of incidence is considered and, by the use of the method developed in R. & M. 21171, the ratio of the initial to the final values of the lift is determined for rectm~gular wings and cropped delta wings of taper ratio 1/7. These values indicate that the initial lift may be greater than the final lift for aspect ratios A =< 2. This result appears to be supported by the values of instantaneous lift which were measured for the delta wing of aspect ratio 1.2 as its incidence was rapidly changed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3023.pdf 669. Internal air-cooling for turbine blades a general design survey D. G. Ainley The degree of cooling that might be achieved in gas-turbine blades with simple internal air-cooling is surveyed with a view to pin-pointing the essential requirements for effective cooling with small quantities of cooling air. A shape parameter Z (defined as (SJc) *'2/(Ao/c~)) is derived which forms a useful figure of merit for comparing the relative efficiencies of various cooling passage configurations. To secure maximum economy in total cooling air in blades with a given cooling passage configuration, it is desirable that the turbine-blade rows should be designed with high pitch/chord ratios and low relative gas outlet angles (measured from axial direction). These requirements may run counter to those for high turbine-expansion efficiency and in practice some compromise must be sought to give optimum overall efficiency. It is shown that efficient blade cooling becomes progressively more difficult at lower values of turbine-flow Reynolds numbers, and cooling systems should be designed to give adequate cooling at the lowest operating Reynolds numbers since this represents the most onerous condition. The potentialities of blades with laminar-cooling and turbulent-cooling flow in the cooling passages are compared. Although laminar-cooling flow might enable better cooling at low Reynolds numbers to be achieved, turbulent cooling flow is generally to be preferred since this (a) permits more consistent cooling over a wide range of Reynolds number in a simple air-cooled engine and (b) presents a simpler blade manufacturing problem. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3013.pdf 670. Loading conditions of tailed aircraft in longitudinal manoeuvres T. Czaykowski An analysis of aircraft response and loading conditions in symmetrical manoeuvres is presented with a particular recognition of the designer's needs. The analysis is based on the theory of aircraft response to elevator induced longitudinal manoeuvres. Basic response functions have been derived for the chosen, exponential type of elevator motion, and from these, general expressions have been obtained for various derived response quantities, such as tailplane loads, elevator hinge moments, normal accelerations at the tail, etc. A computational method which reduces the calculations to a routine is given in Appendix B. The method allows the evaluation of.the complete time histories of response quantities or, alternatively their significant maxima. The simplifying assumptions underlying the analysis are critically reviewed and possible limitations of the method are discussed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3001.pdf 671. Low-speed-tunnel model tests on the flow structure behind a delta-wing aircraft and a 40 deg swept-wing aircraft at high incidences D. A. Kirby and A. Spence In view of the possibility of trimming some swept-wing aircraft at incidences above the stall, there has been a desire to visualise the whole pattern of vortex sheets and separated flow starting from the stalling wing, and to follow it back beyond the tailplane. To supplement other methods, a swivelling head has been used, giving the velocity, pitch and yaw, and results are given in this report for a 48-deg delta (Javelin) and a 40-deg swept-wing aircraft (Swift without fences). The tests showed that at incidences beyond the stall there is a large bubble of separated flow behind the wing. For the delta at 35 deg this bubble had not closed at the station of the tailplane and extended over the whole of the region behind the wing. The velocity and pressure field found in the separated flow resembles that behind a square plate at 90 deg. The vorticity pattern, measured in a plane cutting the bubble of separated flow from the stalled wings, is complicated by rotating masses of air inside the bubbles, between the strong inner vortex sheets, and the weaker tip vortices. The results have been analysed to show the effect of change of tail height. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3078.pdf 672. Measurements of two-dimensional derivatives on a wing-aileron-tab system with a 1541 section aerofoil. Part 2 direct tab and cross aileron-tab derivatives K. C. Wight Measurements have been made of the direct tab derivatives and cross aileron-tab derivatives for a 1541 section two-dimensional aerofoil (N.P.L. 282) with a 20 per cent aileron and 4 per cent (approx.) tab. In addition some measurements of the direct aileron derivatives have been made for comparison with earlier results together with a number of static derivatives for the wing and controls. The influence is shown of frequency parameter, Reynolds number, position of transition, mean tab angle and sealing of the control hinge gaps. Some tests have been made with the aileron set at minus 8 deg and the tab at plus 12 deg for which condition the hinge moment on the aileron was zero. Reasonable agreement with the values given by the 'equivalent profile' theory is shown for both direct damping derivatives and for the direct tab stiffness derivative. The direct aileron stiffness derivative shows some departure from the theoretical value when ω > 1. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3029.pdf 673. On some aspects of the use of shock tubes in aerodynamic research B. D. Henshall Interest has recently been revived in an apparatus which was first developed fifty years ago. This apparatus, which is known today as a shock tube, consists of a simple duct which may be closed or open at one end, and closed at the other end. A diaphragm divides this duct into two compartments which initially contain gases at different pressures. When the diaphragm is ruptured, an unsteady gas motion ensues. A survey of existing shock tube theory and experimental results has been conducted; particular emphasis was placed on the features of actual shock tube flow which diverged from ideal non-viscous theory. A basic ideal shock tube theory has been formulated in detail; using those parameters which have greatest practical significance, and subsequently, performance charts affording a rapid method for the aerodynamic design of shock tubes using air as the working fluid have been developed. Experimental results diverge from the simple ideal theory mentioned above, principally because viscous effects are present in actual shock tube flow. Careful analysis of available experimental data yielded a series of important parameters which should be incorporated in any modified theory of shock tube flow. A new analytical approach led to the development of a theory of shock tube flow which included the effects of boundary layer growth on the walls of the shock tube and explained severaI features of the actual flow patterns which are at variance with ideal non-viscous theory. As presented herein, the theory is restricted to shock tube flows where the shock wave is weak, and the boundary layers on the walls of the tube are laminar and incompressible. The complete Solution of shock tube flow including the effects of viscosity is a formidably difficult problem, but it is hoped that the present analysis may be a useful first step towards the full solution. As a parallel study with the above theoretical work, the design and construction of a shock tube installation was undertaken. Low cost was one of the main criteria of this design, and a shock tube made of mahogany was finally selected. (The Bristol shock tube is believed to be the first employing wooden construction.) Ancillary equipment was developed for the installation, and particular attention was given to the optical and electronic equipment. The development of the apparatus, and principally that of the electronic instrumentation, took considerable time; but a detailed calibration of the shock tube was ultimately carried out. Finally, timed photographs of the transient diffraction of a shock wave over a wedge were obtained; this illustrated one main. application of the shock tube, that is, the study of unsteady flows. In conclusion, the probable future development and uses of shock tubes in aerodynamic research is discussed in the light of recent experimental and theoretical work. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3044.pdf 674. On the integral equations of two-dimensional subsonic flutter derivative theory D. E. Williams This note gives the result of an attempt to find an analytical solution of Possio's integral equation - the equation which connects the downwash and the pressure distribution on an aerofoil oscillating in two-dimensional subsonic compressible flow. A method is given for solving this problem and for solving the corresponding problem in incompressible flow (the solution of Birnbaum's integral equation). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3057.pdf 675. On the stressing of multi-rib thin wings of low aspect ratio and rectangular plan-form L. S. D. Morley Exact theories are used to examine tile validity of certain methods of wing stressing when they are applied to thin wings of low aspect ratio. Attention is confined to thetwo spar multi-rib wing having rectangular cross-section and rectangular plan-form. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3052.pdf 676. Pressure probes selected for three-dimensional flow measurement D. W. Bryer, D. E. Walshe and H. C. Garner Seven pressure probes have been tested in a uniform stream in order to ascertain the best types for measuring velocity and flow direction. Methods of calibration are discussed in section 8 together with the effects of wind speed, flow direction and turbulence on the calibration factors (section 4). The performance of three of the probes in the turbulent boundary layer of a flat plate is analysed and their accuracies compared when they are used to estimate displacement and momentum thicknesses (section 6). The Conrad probe is proved superior to other types for boundary-layer measurements. Further research on the lines indicated in section 7 is necessary before the best type of probe for use in regions of separated flow can be ascertained. The main features of the velocity-measuring probes are listed in Table 4. For measuring static pressure in three-dimensional flow, a disc type of probe is described and shown to be insensitive to flow direction and scale effect (section 5). Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3037.pdf 677. Some effects of shock-induced separation of turbulent boundary layers in transonic flow past aerofoils H. H. Pearcey The effects of shock-induced separation of turbulent boundary layers on two-dimensional aerofoils are introduced by considering the development of the surface-pressure distribution and flow pattern as the free-stream speed is increased in the transonic range (defined as that for which regions of supersonic flow exist on the aerofoils but are limited in chordwise extent). The progressive rearward extension of the supersonic flow, as the terminating shocks move rearwards over the surfaces, is an essential feature of this development. Unless the incidence and thickness of an aerofoil at lift are both very small, the upper-surface shock, at some stage in its movement, induces a boundary-layer separation which tends to reduce the pressure rise through the shock. The consequences of this are usually not serious until the shock fails to re-establish subsonic flow immediately downstream. At that stage, however, the 'bubble' of separated flow begins to expand rapidly towards the trailing edge and beyond, and in so doing to exert a dominating influence on the development of the overall flow, i.e., on the actual and relative rates of shock movement, or flow development, on the two surfaces. This influence wanes as soon as either the lower surface shock reaches the trailing edge or a centred supersonic expansion occurs there; the bubble finally collapses when the upper-surface shock moves on to the trailing edge. The physical nature of the overall flow and the mechanism by which separation affects its development so strongly are described qualitatively. The picture presented has been made as complete as possible, even though this involves some ideas which must be regarded as speculative, in the hope that it might form a tentative basis for more rigorous treatments or for extension of the work.to swept-back and finite wings. Considerations of the flow at the trailing edge of the aerofoil and downstream along the wake figure prominently in the description, and the pressure at the trailing-edge position is used extensively. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3108.pdf 678. Some factors influencing the speed of response of hydraulic position servomechanisms C. W. Lewis A study is made of the influence of working pressure, relay torque-arm radius and other design factors on the maximum output speed and velocity constant of a single-stage hydraulic servo for guided missile use. Methods are given for determining the best relay torque-arm radius, which may be applied to valves having non-linear flow and reaction characteristics. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3089.pdf 679. Some observations of the flow over a delta-winged model with 55-deg leading-edge sweep, at Mach numbers between 0.4 and 1.8 E. P. Sutton A delta-winged model, with 54.8-deg leading-edge sweep and a 6 per cent thick RAE 101 section, has been tested in the Royal Aeronautical Establishment (Bedford) 3-ft Wind Tunnel. The results of lift and pitching moment measurements at Mach numbers from 0.70 to 1.02 and from 1.42 to 1.82 are presented and discussed with the aid of surface oil-flow observations. The Reynolds number of the tests was between 2.2 and 3.3 x 10power6. At Mach numbers up to at least 1.07 a leading-edge-separation vortex sheet formed on the wing at incidence. An interaction between the vortex sheet and the wing upper-surface shock wave at Mach numbers just below 1.0 caused unsteadiness of the forces on the model and a pitch-up. At Mach numbers from 1.42 to 1.82 the flow was attached at the leading edge, and an oblique shock lay across the upper surface of the wing. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3190.pdf 680. Subsonic wind-tunnel tests on a crescent-winged aircraft, including tests of leading-edge droop designs and several tailplane heights C. N. Hall and B. J. Prior The longitudinal characteristics of the aircraft (Aspect Ratio 4.0) were investigated on a half-model in the Royal Aircraft Establishment 10 ft Ã— 7It Wind Tunnel at a Reynolds number of 1.3 million up to a Mach number of 0.93, and at higher Reynolds numbers at low speed. The tests showed that the high-speed characteristics at low lift were satisfactory, but that at all Mach numbers a severe instability occurred at moderate lift coefficients (C~ = 0.45 to 0.6). Examination of tuft and off-flow patterns established that for Mach numbers up to M = 0.8, the tip stall began as a leading-edge separation at the outer kink; at the highest Mach numbers the flow separation was initially shock-induced. Further tests were therefore made with leading-edge droop applied over the outer wing and with wing fences near the outer kink. The 'pitch-up' at low Mach number was delayed by these means to CL = 0.8 (ΔCL = 0.25), but the stability at high Mach number was not improved. A further modification, in which the plan-form was changed to eliminate the outer kink, brought a small improvement at high Mach number, the pitch-up being delayed to CL = 0.65 at M = 0.9. Lowering the tailplane had a much more powerful effect on the aircraft's stability than these wing modifications, and with the tailplane below the wing chord plane (where wake surveys showed the downwash to be greatly reduced), the nose-up instability.was almost eliminated throughout the test range of Mach number. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3208.pdf 681. Supersonic flow past quasi-cylindrical bodies of almost circular cross-section D. G. Randall The supersonic flow over bodies for which the surface boundary condition may be satisfied on a circular cylinder is considered. The method is based on the linearised small-perturbation theory of supersonic flow. The disturbance velocity potential is obtained as a Fourier series, each term of which contains a certain basic function and the first eleven of these functions are evaluated. The pressure distribution and wave drag have been calculated for some bodies consisting of circular cylinders surmounted by canopies. An extension of the method to solve certain wing-body interference problems is also described. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3067.pdf 682. The aerodynamic effects of aspect ratio and sweepback on wing flutter W. G. Molyneux, and H. Hall The report describes tests to obtain direct measurements of the aerodynamic effects of aspect ratio and sweepback on wing flutter. The tests were made on rigid wings with root flexibilities. It is shown that measured effects of aspect ratio and sweepback on the flutter of these wings can be represented quite closely in flutter calculations based on two-dimensional flow theory by multiplying the two-dimensional aerodynamic coefficients by appropriate factors. The effect of sweepback is represented by multiplying all aerodynamic coefficients by cos A, where A is the wing leading-edge sweepback, and the effect of aspect ratio is represented by multiplying the aerodynamic damping coefficients by l/ƒ(A) and the stiffness coefficients by 1/[ƒ(A)]² where A is the aspect ratio. For the wings tested an average value for ƒ(A) is ƒ(A) = {1 + (0.8/A)}. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3011.pdf 683. The calculation of the spanwise loading of sweptback wings with flaps or all-moving tips at subsonic speeds G. G. Brebner, D. A. Lemaire The results of some electric tank tests by Duquenne and Grandjean on wings of 45 deg sweepback with trailing edge flaps have been analysed to provide the basis for a method of calculating the spanwise loading. The analysis yielded information about the effect of sweep on the equivalent incidence of a section with flap, on the downwash factor and on the spanwise loading distribution with an incidence discontinuity. Interpolation formulae are developed to extend the results to wings of any sweep and flap span, and thus a complete calculation method is presented for the spanwise loading with this type of control. The calculation method is tentatively extended to a wing with all-moving tip control, and the results compared with those of Thomas and Mangler. There is a marked discrepancy between the two calculations. Further electric tank tests to fill this, and other gaps are suggested. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3487.pdf 684. The development of slotted working-section liners for transonic operation of the R.A.E. Bedford 3-ft wind tunnel E. P. Sutton The development of removable slotted liners to extend the range of the Royal Aircraft Establishment 3-ft Supersonic Wind Tunnel at Bedford to transonic speeds is described. The liners are mounted within the existing working-section on the two sides, enclosing shallow outer chambers between their slotted surfaces and the original side walls. At all speeds there was originally a pronounced streamwise pressure gradient, associated with reversed flows in the outer chambers. It was almost eliminated by the addition of perforated screens behind the slots to suppress turbulent mixing there. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3085.pdf 685. The effect of the ground on a helicopter rotor in forward flight I. C. Cheeseman, and W. E. Bennett An approximate method of estimating the effect of the ground on the lift of a rotor at any forward speed is described. Flight tests on several different helicopters show reasonable agreement with the theory. Curves are given showing the relation between thrust, height, speed and power. The theory has been extended to include the effect of a variation in blade loading coefficient and shows that, within the range that this parameter takes on present single-rotor helicopters, the effect is small. The effect of fitting flat surfaces beneath the rotor is also considered and it is shown that the ratio of the thrust in the ground cushion to the thrust clear of the ground, at constant power, is greater for the winged helicopter, but that for the salne rotor operating at constant power, the clean helicopter will have the higher net thrust for speeds less than the stalling speeds of the attached surfaces. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3021.pdf 686. The effect of wing-tailplane aerodynamic interaction on tail flutter D. E. Williams When aerodynamic coefficients are calculated for tailplane flutter calculations it is usual to neglect the aerodynamic effect on the tailplane of the disturbance due to the wing and to assume that the tailplane oscillates in a steady stream. In this report a two-dimensional theory, which includes the effect of the wing-tailplane aerodynamic interaction, is developed for any wing and tailplane in the same horizontal plane. To represent this effect the standard derivatives are modified and additional derivatives are introduced. Calculations for a particular system show that the change in the standard derivatives is small but that the additional derivatives are comparable in size with the standard derivatives. The additional derivatives are used to investigate the effect of the wing motion on tailplane-elevator flutter, and it is shown that the aerodynamic interaction has little effect on the flutter of the binary system considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3065.pdf 687. The effects of taper on the supervelocities on three-dimensional wings at zero incidence K. W. Newby Relationships have been derived for expressing the velocities on three-dimensional tapered wings at zero incidence in terms of the velocities on untapered infinite swept wings. The theoretical investigation of the effects of taper is confined to simple wings having aerofoil sections formed by cubic or parabolic arcs ; some experimental evidence is given to show that the results of this investigation can probably be applied quantitatively to wings having conventional aerofoil sections. The results given in this report show that plan-form and thickness taper have a marked effect on the velocities near the centre of a wing, but that these effects decrease with increase of sweepback. A calculation method is outlined in section 4.2.6 of the text for applying the results obtained for wings having parabolic-arc aerofoil sections, to wings having arbitrary section shapes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3032.pdf 688. The icing of compressor blades and their protection by surface heating G. L. Shires and G. E. Munns This paper describes an investigation into the feasibility of protecting compressor blades against ice accretion by the method of surface heating. Experiments with surface-heated inlet guide vanes and stator blades were performed in the icing tunnel at the Royal Aircraft Establishment. An electrically heated blade, having almost uniform surface temperature, was developed and then used to determine the effects of air velocity and icing conditions on the minimum heat flow required to prevent the formation of ice. The theoretical method, by J. K. Hardy, of calculating this heat requirement shows reasonable agreement with the experimental results. Steel, copper and copper-plated gas-heated blades with various internal passage shapes were also tested and their heat requirement compared with those of the corresponding electrically heated blades under the same external conditions. The ratio of the latter to the former heat quantity is called the thermal efficiency and is shown to be a function of internal passage shape, blade material, conductivity and dimensions, the gas flow and the external conditions. Finally, a method of estimating the pressure drop through the gas-heated blades is suggested and a worked example is included to demonstrate the method of assessing the mass flow and pressure required to anti-ice a row of inlet guide vanes by means of a compressor bleed. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3041.pdf 689. The influence of plain bearings on shaft whirling E. Downham Experiments are described which show the effects of bearing length, bearing clearance, and lubricant viscosity on the critical whirling speeds of a single-shaft rotor system supported in plain bearings. The critical speed of a two-bearing-shaft rotor system is shown to depend upon rotor unbalance for bearings of normal clearance. When the clearance is small relative to the bearing length, unsymmetric stiffness characteristics are obtained and produce two critical speeds instead of one. The lubricant in a drip-feed bearing is shown to have a stiffening effect, with consequent increase of critical whirling speed. It is also shown that the critical whirl amplitudes with dry bearings can be appreciably larger than those obtained with lubricated bearings. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3046.pdf 690. The interaction between shock waves and boundary layers at the trailing edge of a double-wedge aerofoil at supersonic speed B. D. Henshall, and R. F. Cash A comprehensive review of the work at the National Physical Laboratory on shock-wave--boundary-layer interaction has recently been published. The experiments reported below were designed to investigate a further case of this interaction which was not considered in Ref. 1 ; namely, that occurring near the trailing edge of a double-wedge aerofoil at supersonic speed. This interaction should be similar to that where the shock is generated by a wedge attached to a flat plate; indeed, the only difference between these two cases is that the downstream solid boundary of the latter is replaced by the centre-line of the wake of the aerofoil. Experimental results confirm that these interactions are both qualitatively and quantitatively similar and further support the physical explanations of these flow patterns given in Ref. 1; moreover, the results apply generally to aerofoils with flat surfaces towards the rear. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3004.pdf 691. The representation of engine airflow in wind-tunnel model testing J. Seddon, and L. F. Nicholson The problems of engine airflow representation in wind-tunnel models are reviewed. Methods which have been used satisfactorily in low subsonic tunnels are described briefly. Special difficulties associated with testing at transonic speeds are noted. Techniques of special application to small supersonic tunnels are described in some detail. It is shown that there are reasons why the representation of jets may be more important at supersonic speeds than at subsonic speeds and a description is given of the Royal Aircraft Establishment Jet Interference Tunnel, which is designed for the study of some of the problems involved. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3079.pdf 692. The secondary flow in a cascade of turbine blades W. D. Armstrong In recent papers it has been demonstrated that the so-called secondary flow which occurs when a non-uniform stream passes through a cascade of turning vanes or blades can be calculated by a consideration of tile turning of the vorticity vectors. Whenever the upstream vorticity or the angle of turn is small the perturbation method of Squire and Winter or Hawthorne ~ may be used for the calculation of the downstream vorticity component in the stream direction between the blades. Estimation of the induced velocities however requires a knowledge of the flow which would exist in the absence of the streamwise vorticity. It has been shown that this flow is not normally two-dimensional but may be calculated by an analytical technique whereby the cascade of blades is replaced by an 'actuator plane.' In certain special cases this basic flow is two-dimensional and can be used to demonstrate the applicability of the simple perturbation secondary flow theories. Many practical examples of secondary flow involve conditions which are beyond the limits of the perturbation theories and then all initial experimental approach to the problem enables suggestions to be made for the simplification of the analytical difficulties. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2979.pdf 693. The three-dimensional boundary-layer equations and some power series solutions L. C. Squire The boundary-layer equations are derived for a very general co-ordinate system, and various theorems hitherto only proved in more restrictive systems are extended to this general system. The particular case of streamlines of zero geodesic curvature is investigated in detail and a solution of such a flow found by a power series method. Finally Howarth's stagnation-point solution is extended to second-order terms by numerical investigation. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3006.pdf 694. The use of pitot-tubes in the measurement of laminar boundary R. J. Monaghan Consideration of experimental results obtained with relatively large pitot-tubes in relatively thin laminar boundary layers on cones and flat plates in supersonic wind tunnels and then analysed using standard pitot equations, shows that the most noticeable distortion of the velocity profile is the appearance of a peak near the outer edge of the boundary layer. The displacement of the main body of the profile, familiar in incompressible-flow tests, may be small in supersonic flow and difficult to detect when making measurements with small-diameter pitot-tubes. Displacement and momentum thicknesses calculated from pitot traverses will be in error because of this distortion and displacement. The simple correction factor obtained by Davies is shown to correlate results obtained by Blue and Low and indicates that if the ratio of tube diameter to boundary-layer thickness is less than 0.2, then measured values may be less than 4 per cent above their true values. Additional profile distortion may occur if flattened pitot-tubes are used to measure boundary layers on slender bodies of revolution and Appendix II describes the method of manufacture of tapered quartz tips of circular crosssection, which have a better response rate than flattened tubes of the same internal height. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3056.pdf 695. Velocities on two-dimensional closed and semi-infinite aerofoils at zero incidence S. Neumark, and B. Thwaites An attempt is made to clarify the position as to the comparative two-dimensional velocity distributions on a thin doubly symmetrical aerofoil and on the corresponding semi-infinite body, the front part being the same in the two cases. It is shown that the approximate linear method may be used with advantage to investigate the problem. The method provides a simple general proof that the supervelocity at the mid-chord station of a closed doubly symmetrical profile of any shape is approximately halved when the rear half is replaced by a semi-infinite parallel body. No such simple relationship applies to the entire chordwise distribution on the front part. All exact solution of the velocity distribution has been obtained for one particular semi-infinite profile and several alternative examples have been studied by the linear method. It is found that the ratio of maximum supervelocities may often considerably exceed 0.5 and sometimes rise to nearly 1.0. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2994.pdf 696. Velocity distribution on thin tapered arrowhead and delta wings with spanwise constant thickness ratio at zero incidence S. Neumark, J. Collingbourne and E. J. York This report is a continuation of four earlier ones by the present authors and contains a theoretical investigation of subsonic flow past thin tapered swept-back wings at zero incidence, by the first-order method. The basic theory is followed by the results of computation carried out on the Automatic Computing Engine of the National Physical Laboratory, for several groups of plan-forms, partly of arrowhead and partly delta type, with varying sweepback, aspect ratio and taper, the profile being biconvex parabolic and thickness ratio constant spanwise. The results are illustrated by graphs of isobar patterns on 36 wings. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3008.pdf 697. Wind-tunnel tests on seaplane hulls in the R.A.E. 5-ft diameter open jet tunnel and the N.P.L. compressed air tunnel A. G. Smith Results of research work done in this country and the subject matter of Refs. 1 to 4 on the measurement and analysis of the air drag of seaplane hulls are collected together in this report. The data consist of the results of systematic tests made in the 5-ft Diameter Open Jet Tunnel of the Royal Aircraft Establishment and in the Compressed Air Tunnel of the National Physical Laboratory. These tests were conducted to find out the origin and order of the component drags of a hull and to determine in what way the hull drag differed from that of an equivalent body of revolution. Tests were made over Reynolds numbers ranging from the order of 2 to 60 x 10power6 in order to examine scale effect as far as possible, and a few tests were made to determine the possible effect of controlling boundary-layer transition. Otherwise all tests were made transition free. Subsequent to the systematic tests, tests were made on a specific hull form to investigate the form of step fairing designed for the Princess flying-boat, which form may be regarded as the best so far applied to hulls of contemporary fineness ratio and beam loading. The results show that the air drag of the hull form need not exceed 1.05 to 1.10 times that of the body of revolution which corresponds to it in length and surface area, if the drag of the body of revolution is estimated to consist only of skin friction with fully turbulent boundary layer and the pressure drag corresponding to its fineness ratio. This hull drag should be obtainable at all Reynolds numbers likely to be achieved full scale. Further work should be done in the Compressed Air Tunnel to measure the effect of using higher fineness-ratio hulls and new forms of main-step and afterbody shape. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3018.pdf 698. A general method (depending on the aid of a digital computer) for deriving the structural influence coefficients of aeroplane wings Parts 1 and 2 D. Williams A general method (requiring the aid of a digital computer) is described for deriving the influence coefficients of any type of wing, and hence for evaluating its strength and stiffness characteristics. The method allows for shear deflections, and hence implicitly takes account of effects like shear lag and warping of wing cross-sections. A rapid method accurate enough to serve as a basis for dynamical calculations is first described, and secondly a more rigorous method on which to base final stressing of the structure. In Part I a method for deriving the influence coefficients of any type of wing, and hence of deriving the deflection and stresses, was described in outline. The practical application of the method, however, raises a number of minor problems (mostly concerned with boundary values), which have all to be overcome if the method is to become popular among stressmen. Some of the more important of these problems are treated in this part. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3048.pdf 699. A method for calculating the pressure distribution over jet-flapped wings D. Kuchemann The incompressible flow past an aerofoil with a thin jet emerging from its lower surface somewhere near the trailing edge is considered. Based on unpublished work of Gates, Maskell and Spence, a simple method is described for calculating the pressure distribution over wings of non-zero thickness. The effects of finite aspect ratio and of camber are included and the method can be used for design purposes. The possible effects of sweep are briefly discussed. It is pointed out that a saddleback chordwise loading is typical for aerofoils with jets and that this is the basic reason for many of the aerodynamic advantages of the jet-flap system. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3036.pdf 700. A note on test factors N. I. Bullen The calculation of test factors is reviewed. The distribution, of the population from which the test sample is taken is assumed to be Gaussian. Three cases are discussed, in which (i) there is no prior knowledge of the mean or standard deviation (if) there is no prior knowledge of the mean but the standard deviation is a given fraction of the mean (i.e., coefficient of variation known) (iii) there is no prior knowledge of the mean but the standard deviation is known. In each case an estimate is made of the average proportion of items under strength which go into service as a result of the continued application of a given test factor. The distributions of the statistics used in the solution of cases (i) and (iii) can be found from published Tables. The corresponding distributions for case (ii) for the appropriate ranges are given in this paper. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3166.pdf 701. A Numerical Method for Calculating the Starting and Perturbation of a Two-dimensional Jet at Low Reynolds Number R. B. Payne The number of available exact solutions of the full equations of motion of an incompressible viscous fluid is remarkably few. Those that exist are mostly limited to steady flows. Where a steady state solution does exist, one may be able to obtain a little information about the corresponding unsteady flow by the method of small perturbations. However, in the interesting case of instability, this only shows how a small disturbance behaves initially. The subsequent stages of chaotic motion, as the laminar flow 'breaks up', have attracted the attention of many but still largely remain a source of fascination rather than a field for fruitful research. Only when the flow becomes completely turbulent can the theories of turbulence be applied. These theories do not discuss the origin of turbulence, still leaving the gap in the present state of knowledge between small perturbation theory and turbulence. There is, therefore, a great need for a method of attacking directly the full equations of motion of an unsteady viscous flow. Recent advances in high speed electronic computers make available a powerful device for performing the computations. The lack of some such calculating robot has no doubt discouraged earlier attempts to adopt this approach. Since with any electronic computer one has available only a finite storage space, the possibility of solving a completely three-dimensional problem is perhaps a little ambitious at present. Further, from turbulence theory it is known that large eddies have a tendency to break into smaller eddies limited only by viscosity. Hence, in order to follow numerically a turbulent flow, a large number of closely spaced mesh points would be required to include both the large scale and small scale effects. It is therefore necessary to confine the range of eddy sizes, so that a suitably low Reynolds number must be chosen. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3047.pdf 702. A subsonic lifting-surface theory for low-aspect-ratio wings C. R. Taylor A method is developed for determining the loading on low-aspect-ratio wings. By allowing for down stream effects on the flow at a station on the wing and for the trailing-edge condition, the method improves on R. T. Jones's theory for wings of very small aspect ratio. Calculations have been made for thirteen different wings and a comparison with other methods of solution is given for some cases. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3051.pdf 703. A theoretical and experimental investigation of the flow over a family of rectangular wings of biconvex section at M = 1.42 R. C. Lock An account is given of experiments made at M = 1.42 using three rectangular half-wing models having biconvex sections with thickness ratios 0.04, 0.06 and 0.08, mounted on a reflection plate. Measurements were made of the pressure on the upper surface of the wing and of pressure and flow direction in the neighbourhood of the wing. tip. Direct shadow photography and observation of surface oil patterns enabled various details of the flow to be visualised. The results are correlated with the linearised theory and with certain second-order modifications to this theory. It is found that in general the linearised theory provides a sufficient approximation to the detailed flow only for the thinnest wing at very small incidences. In most cases the suggested modifications effect a considerable improvement. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3055.pdf 704. Aerodynamic characteristics of rectangular wings of small aspect ratio I. J. Campbell, C. F. Blanks and D. A. Leaver The results of a programme of low-speed wind-tunnel measurements of the lift, drag and pitching moment on a number of model wings, each fitted with a full-span plain flap, and of a much more limited programme of hinge-moment measurements are presented. The wings differed from one another in profile but all were of rectangular plan-form and of aspect ratio 1.25. The flap chord was varied between 0.125 and 0.500 of the overall chord. Three of the profiles investigated were conventional in having zero trailing-edge thickness but the other three had large trailing-edge thickness, a feature thought to be of interest in connection with the design of torpedo fins. Theoretical values of the lift slopes, hinge moments and positions of the centre of pressure were calculated from Lawrence's theory for thin rectangular wings of various aspect ratios in inviscid flow and the results are presented in tabular and graphical form. Predicted values, combining aspect-ratio effects with largely empirical allowances for thickness and boundary-layer effects, are checked against the measured values of the required aerodynamic characteristics of the 'conventional' profiles and the agreement is fairly satisfactory. Although the aspect ratio was small, the induced drag associated with incidence and flap deflection was found to be well represented for all profiles by the usual expression derived from consideration of the elliptically loaded lifting line. A limited number of measurements suggested that the size of the gap between the control surface and the main part of the wing exercises little: influence on the lift slopes, drag and c.p. positions if the gap width is less than 0.5 per cent of the overall chord. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3142.pdf 705. An investigation of the hydrodynamic stability and spray characteristics of high length/beam ratio seaplane hulls with high beam loadings D. M. Ridland, J. K. Friswell and A. G. Kurn Tests have been made on a series of high length/beam ratio seaplane hulls with high beam loadings. The effects of varying the hull parameters, forebody warp, afterbody length and afterbody angle, together with the interaction of these effects, and of tailoring the afterbody, on the calm water hydrodynamic stability and spray characteristics of the series have been determined. To amplify this work, investigations have been made into the effects of load, moment of inertia and radius of gyration, and slipstream, together with a limited assessment of longitudinal hydrodynamic stability characteristics in waves. Dynamic models were used and tests for the main investigation consisted of assessments of longitudinal hydrodynamic stability characteristics, both undisturbed and disturbed, at two weights, of spray behaviour at these weights, and of directional hydrodynamic stability characteristics at the higher weight only. Improvements in test techniques are described and, where appropriate, reference is made to earlier work on hulls of low length/beam ratio. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3095.pdf 706. Aspect-ratio effects on compressor cascade blade flutter D. A. Kilpatrick and R. A. Burrows This report gives the results of cascade tests on blades of aspect ratio varying from 3.0 to 1.5, with particular reference to stalling flutter. It is concluded that the influence of aspect ratio on stalling flutter cannot be simply formulated but depends largely on the particular blade design. The effect on the magnitude of the flutter stresses is not critical although the curves do show a tendency to flattening at an aspect ratio about 2.0 (height/thickness: ratio of 20), indicating that the advantages of further reduction in aspect ratio are relatively small. The 'critical flutter velocity' is more complex. For the 'low' to 'moderate' stress levels the increase of critical flutter velocity, with decreasing aspect ratio, occurs quite gradually, while for the high stress levels the increase is very much greater, and is in fact itself quite critical. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3103.pdf 707. Calculating derivatives for rectangular wings oscillating in compressible subsonic flow Doris E. Lehrian Stability and flutter derivatives are obtained for rectangular wings describing plunging and pitching oscillations in subsonic flow. These are evaluated by applying the simple approximate 'equivalent' wing theory (R. & M. 2855) with the vortex-lattice method of downwash calculation. The derivatives for the wing of aspect ratio 4 at Mach number 0.866 are compared with values calculated by a method based on exact theory; at this high Mach number it is found that the present method is sufficiently accurate for only a very limited range of the frequency parameter. At very low values, the pitching-moment derivatives for this wing are in reasonable agreement with those calculated by the Multhopp-Garner method and with results from wind-tunnel tests at high subsonic Mach number. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3068.pdf 708. Calculation of derivatives for a cropped delta wing with subsonic leading edges oscillating in a supersonic air stream J. Watson Summary.--The lift, pitching moment and full-span constant-chord control hinge-moment are derived for a cropped delta wing describing harmonic plunging and pitching oscillations of small amplitude and low-frequency parameter in a supersonic air stream. It is assumed that (a) the wing has subsonic leading edges, (b) the wing is sufficiently thin and the Mach number sufficiently supersonic to permit the use of linearised theory. Expressions for the various derivative coefficients are obtained for a particular delta wing of aspect ratio 1·8 and taper ratio 1/7; these are avaluated and tabulated for Mach numbers 1·1, 1·15, 1·2, 1·3, 1·4, 1·5, 1·6 and 1·944. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3060.pdf 709. Experiments on Pitot-Tubes in Shear Flow F. A. MacMillan When a pitot-tube is used in a pipe or boundary layer, the shear and the presence of the wall may cause the pressure in the tube to differ from the true total pressure on the axis of the tube. To investigate these effects, measurements were made in a pipe of circular section, with turbulent flow, using pitot-tubes of different external diameter D. Some supporting experiments were also made in a turbulent boundary layer on a flat plate with zero pressure gradient. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3028.pdf 710. Experiments on two-dimensional base flow at M = 2.4 L. Fuller and J. Reid This report gives an account of experiments carried out on a family of two-dimensional afterbodies to determine the effect of boat-tail angle and internal flow on the base pressure, the afterbody pressure, and the velocity distribution in the wake. The afterbodies tested were of constant length with boat-tail angles of 0, 2Â½, 5, 7Â½ and 10 deg respectively. Each member of this series was mounted on a common model screwed to the upper surface of a flat plate placed at zero incidence in a uniform supersonic stream of Mach number 2.41. The inside of the model, which was hollow, was shaped in the form of a plenum chamber tapering towards the rear to a two-dimensional convergent nozzle with a parallel throat exhausting into the region behind the base. This nozzle was supplied with dry air at 20 deg C bled from the main tunnel supply. Measurements were made of the afterbody pressure distribution, the base pressure, and the velocity distribution in the wake for each member of the family over a range of internal flow extending from no flow to tpj/p∞ = 11. Further information on the base flow with the untapered afterbody was also provided by measurement of the effect of internal flow on the plate pressure distribution behind the base. In all cases these pressure measurements were supplemented by schlieren photography. In the concluding sections of the report the results are analysed and discussed in detail both from the theoretical aspect and also with regard to their practical application. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3064.pdf 711. Note on the Convergence of Numerical Solutions of the Navier-Stokes Equations A. Thom and C. J. Apelt A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local 'mesh Reynolds number', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3061.pdf 712. On flutter testing in high-speed wind tunnels N. C. Lambourne, and C. Scruton The requirements for simulating in a Wind tunnel flutter conditions appropriate to high-speed flight are discussed, and an assessment is made of the desirable features of a wind tunnel suitable for flutter testing at transonic and supersonic speeds. It is concluded that such a tunnel should have either the Mach number or the stagnation pressure variable during the tunnel run, and that it is of considerable advantage, and for some purposes essential, for high stagnation pressures to be available. The stagnation pressure required to allow flight conditions to be simulated with a flutter model is considered to range from at least 2 atmospheres for transonic speeds to about 15 atmospheres for M = 4. No attempt to simulate, kinetic heating is envisaged, although its effect on stiffness should be allowed for in the design of the model. To minimise uncertainties due to the variation of the model stiffness with temperature, it is desirable that means for controlling the stagnation temperature should be incorporated in the tunnel. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3054.pdf 713. Operational formulae for response calculations S. Neumark The paper presents systematic tables of formulae whose purpose is to facilitate the operational solution of response problems reducible to linear differential equations with constant coefficients and with simple forcing functions. The formulae enable the user to find operational equivalents of a wide class of simple functions and, inversely, to find functional equivalents of a great number of operational expressions, in the most rapid and direct manner. In such a way, it is possible to reduce to a minimum the usual heavy algebraical work involved in response calculations. The tables include only such functions whose operational equivalents are algebraic fractions, but these cover a wide field of practical applications. Operational fractions of the 1st, 2nd, 3rd and 4th order are treated in a comprehensive way, so that all possible particular cases are included. Additional tables make it possible to reduce every fraction of 5th or 6th order to a combination of fractions of lower order. The introductory text describes the method of deriving the formulae and explains how to use them in solving response problems. A number of examples are appended which show the advantages of the tables and give solutions of several typical problems. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3075.pdf 714. Pressure-plotting measurements on an 8 per cent thick aerofoil with trailing-edge flap blowing J. Williams, and A. J. Alexander Wind-tunnel experiments were carried out on all 8 per cent thick aerofoil between end plates, with Mowing from a slot in the knee of a 25 per cent chord trailing-edge flap, to improve the lifting efficiency of the flap. Both the blowing-slot width and position were varied. The sectional lift and pitching moment were derived by chordwise integration of the surface static pressures measured at the mid-span station. Tuft observations as well as surface-pressure measurements were made to determine the extent of the turbulent separation region on the trailing-edge flap and of the laminar separation bubble on the aerofoil nose. The blowing momentum required to prevent flow separation on the flap, at a given flap angle and zero wing incidence, proved much less than might have been expected from earlier two-dimensional experiments on thicker wings with blowing over the flap from the shroud. This reduction is probably associated with the low effective aspect ratio of the present quasi two-dimensional model as well as with improvements in blowing techniques. The separation bubble on the aerofoil nose began to expand markedly (with the flap deflected) when the incidence reached only a few degrees, and simultaneously the blowing momentum needed to prevent flow separation on the flap tended to increase. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3087.pdf 715. Published reports and memoranda of the Aeronautical Research Council
Below is given a list of the Reports and Memoranda published by the Aeronautical Research Council. The reference numbers other than the R. & M. numbers are not consecutive, as many reports are confidential to the Council and not for issue to the public. Normally every R. & M. is bound into the Annual Technical Volume bearing the same year as the date of the original report. Owing to the post-war difficulties of publication this procedure will not be aMe to be rigidly adhered to, and such R. & M. which are not available at the time of compilation of the Annual Technical Volumes will be combined together in special volumes. Those R. & M. below marked with a star will be thus dealt with. Monographs are not incorporated in Annual Technical Volumes. R. & M. No. 2600, entitled Index of all Reports and Memoranda published in the Annual Technical Reports and separately, is published by H.M.S.O. at 2s. 6d. Similar previous lists of the Council's published papers are Reports and Memoranda Nos. 650, 750, etc., to 2650. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2750.pdf 716. Some experiments with sonic throats downstream from the working-section of a slotted-wall high-speed tunnel A. Chinneck, and N. A. North Tests have been made in the National Physical Laboratory 9-in. Ã— 3-in. High-Speed Tunnel to investigate the use of sonic throats downstream from the working-section of a slotted-wall high-speed tunnel employing diffuser suction. It was found that such throats behaved at subsonic speeds in a manner similar to their behaviour in a solid-wall tunnel. The Mach number in the working-section was approximately that to be expected from the ratio of the area between walls, at the beginning of the slots, to the area at the throat. Tests were made with various configurations, including the conditions which could be expected on the 18-in. Ã— 14-in. and 36-in. Ã— 14-in. High-Speed Tunnels at the N.P.L. It was found that the throat mechanisms at present used with the subsonic liners on these tunnels should work satisfactorily, and that the power required should be of the same order as that required to run the unchoked slotted walls at unit Mach number. Information has also been obtained on the beneficial effects to be obtained from (a) an improvement in the pressure recovery downstream from the parallel slotted length of the working-section and (b) a reduction in the slope of the upstream face of the sonic throat. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3053.pdf 717. Supersonic wind-tunnel flutter tests of two rectangular wings P. R. Guyett Two rectangular wings of aspect ratio 4 were flutter tested in a supersonic wind tunnel at Mach numbers 1.6 and 2.0 using a technique in which a structural stiffness was varied to give flutter at the Mach number. The results are in reasonable agreement with calculations using theoretical three-dimensional derivatives and arbitrary wing modes, though in general the calculated critical stiffnesses are rather higher than the test values. It is shown theoretically that structural damping has an important effect upon the stiffness required to avoid flutter, and may in some circumstances be destabilising. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3080.pdf 718. The accuracy of the measurement of turbulent skin friction by means of surface pitot-tubes and the distribution of skin friction on a flat plate R. A. Dutton An experimental study has been made of two-dimensional turbulent boundary-layer flow with zero pressure gradient. The investigation was made to determine the accuracy of a method proposed by Preston for measuring the local turbulent skin friction. The general momentum equation was used in conjunction with measurements of skill friction by Preston's method, to obtain increments in momentum thickness which could be compared with the measured values. The experiments were made on a smooth flat plate, 6 ft long, which spanned the working-section of a return-circuit wind tunnel. Transition was promoted by trip wires and glass-paper strips. A constant Reynolds number of 3.9 X 10 5 per foot was maintained throughout the experiments. The results, together with certain basic arguments, indicate that Preston's method will give the correct skin friction. For the range of Reynolds numbers covered in the experiments (1500 < Ro < 4000) the skin-friction coefficients obtained for different values of Ro (the Reynolds number based on momentum thickness), were approximately 10 per cent and 6 per cent less than the corresponding Prandtl-Schlichting and Schoenherr values respectively. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3058.pdf 719. The effect of changes in the stability derivatives on the dynamic behaviour of a torpedo J. D. Lambert This report investigates the extent to which the dynamic behaviour of a torpedo is sensitive to changes in its stability derivatives. The main object in carrying out the investigation was to provide guidance on the accuracy of measurement of the stability derivatives that should be necessary for any given torpedo. The considerations of the report are, however, also pertinent to the problem of deciding the effectiveness of possible changes in the design of a torpedo, the dynamic behaviour of which is unsatisfactory. Illustrative examples are worked out in detail. The report emphasises the importance of the so-called margin of stability. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3143.pdf 720. The effect of internal contraction, initial rate of subsonic diffusion, and cowl and centrebody shape on the pressure recovery of a conical-centrebody intake at supersonic speeds E. L. Goldsmith The effect of internal contraction, cowl and subsonic diffuser shape on the pressure recovery of a 0c = 25 deg conical-centrebody intake designed for a Mach number of 2.46 has been studied experimentally at M = 2.48. Substantial gains in pressure recovery have been recorded with increase of initial angle of the cowl undersurface and the internal, contraction ratio. Small gains were also recorded by decreasing the initial rate of subsonic diffusion and correspondingly increasing the rate at lower duct velocities. Calculations have been made of the increased drag at full mass flow due to excessive internal contraction at Mach numbers below the design value. An empirical correlation of pressure recovery at full mass flow with contraction ratio and initial undersurface angle of the cowl yields results which should aid in the prediction of pressure recovery for conical-centrebody intakes. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3204.pdf 721. The effect of structural damping on binary flutter E. G. Broadbent and Margaret Williams The paper describes an investigation of the effect of structural damping in the torsion mode on wing flutter with the object of finding circumstances in which damping reduces the flutter speed. The drop in flutter speed can be considerable (25 per cent) and extend to very large values of structural damping. The effect is most apparent when the relative density (wing to air) is high, and when the wing bending mode involves a relatively large aerodynamic stiffness. The rate of decrease of flutter speed with damping in small, and for the amounts of damping normally encountered in practice the effect is unlikely to be important. Possible practical cases are, however, part-full under-wing fuel tanks, which can supplyhigh structural damping, and large tailplane amplitudes in the wing torsion mode, which can supply considerable aerodynamic damping; in both cases the effect could be appreciably adverse. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3169.pdf 722. The effect of wing torsion on aileron-tab flutter H. Hall This paper gives the results of an investigation into the effects of wing torsion in a ternary-type spring tab flutter. The results presented are for a series of calculations on an idealised system having degrees of freedom in wing pitch, rotation of the control surface and rotation of the tab; the pitching degree of freedom is spring restrained and is intended to represent wing torsion. The tab is restrained as a trim tab or pure aerodynamic servo tab, but the results are expected to apply qualitatively to a spring tab. A comparison is made between these results and those of earlier investigations into a similar problem by Wittmeyerand Wittmeyer and Templeton, where the main surface mode considered was one of vertical translation to represent wing bending. From this previous work criteria were suggested for the prevention of this type of flutter, and in an analogous manner criteria are now tentatively proposed for prevention of wing torsion-aileron-tab flutter. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3072.pdf 723. The full-scale air drag of some flying-boat seaplanes A. G. Smith An analysis has been made of the full-scale measured drag and lift performance, data available on the Sunderland, Solent, Shetland, Sealand, Saro E.6/44 and Princess boat seaplanes, which all have hulls of fairly orthodox length/beam and fineness ratios but with different degrees of aerodynamic fairing. The drag coefficient and profile drag show progressive decreases from the order of 0.033 to 0.018 and from 1.5 lb to 0.33 lb per 100 lb of all-up weight respectively, the best seaplane being the Princess. The value of the extra-to-induced drag coefficient k, at 1.1 is generally good for all the aircraft and extends up to a C~ of the order of 1.0. This drag reduction is caused by improvement in hull design, reduction of drag with change of propulsion unit from propeller reciprocating to propeller turbine and turbine jet, and also with increase of size. The hull drag is of the order of 0.22 of the total profile drag for all the aircraft but the ratio of the turbulent skin-friction drag of the idealised wing, hull and tail unit to the actual profile drag, increases to 0.73 for the Princess from 0.4 for the Sunderland. Further drag reductions would be possible if full use were made of recent methods of reducing hult air drag still further by detail fairing and increase of length-to-beam ratio. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3082.pdf 724. The matrix force method of structural analysis and some new applications J. H. Argyris and S. Kelsey Summary.--The purpose of this paper is : (a) to summarise the basic principles of the matrix force method of structural analysis given in Ref. 1 and to present also some new applications of the general theory ; (b) to establish and illustrate on simple examples the special method of cut-outs developed in Ref. 1. In this procedure the stresses in a structure with cut-outs are derived from the simpler analysis of the corresponding structure without cut-outs under the same loads and/or temperature distribution ; (c) to present a method for the determination of the stresses in a structure, some of whose components have been modified subsequent to an initial stress analysis. This procedure, not included in Ref. 1, is, in fact, a generalisation of the cut-out method (b) and gives the stresses in the modified system solely in terms of the stresses of the original system subject to the same loads and temperature distribution. The theory is illustrated on some simple examples which show clearly the extreme simplicity of the powerful techniques (b) and (c). We emphasise that the application of these methods requires only one stress analysis : that of tile continuous structure under the same external loads, as the modified structure. No additional stress analysis due to other, e.g., perturbation, loads is involved. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3034.pdf 725. The optics of the Mach-Zehnder interferometer L. H. Tanner The paper is intended to give a complete optical theory of the Mach-Zehnder interferometer, without using difficult mathematical methods or complicated three-dimensional diagrams. The topics covered include the effect of tile spectral distribution of the source, with and without dispersion. The effect on the fringe contrast of the size and shape of the source are considered. These effects are related to the fringe pattern which is produced near the usual source position if a source is placed in what is normally the emergent beam. This fringe pattern is related to the displacement of the two images of a co-ordinate system in the emergent beam, as seen through the four-mirror system. The effects of all such displacements are discussed and illustrated. The effect of mirror movements on these displacements is analysed, to show the number of fine adjustments required, and the effect of each. A section on the imperfections of the optical elements includes discussions of the effects of differences of thickness, incidence and refractive index, wedge angles, surface flatness and refractive index variation. Except for the permissible wedge angles, the limits found necessary are less strict than those usually given. Aberration of the collimating lens has practically no effect. A review of methods of adjustment of the interferometer includes descriptions of some of the well-known methods and of two which do not appear to have been described previously. Of these, one is a method for obtaining a parallelogram arrangement, which was used by K. J. Habell, and the other is an accurate method for final adjustment based on the source-plane fringe pattern. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3069.pdf 726. The sampling errors of atmospheric turbulence measurements N. I. Bullen Estimates of atmospheric turbulence from counting accelerometer records show a large scatter. The simple assumption of a random distribution of gusts is inconsistent with this scatter. A formula which takes account of the variations in gust density is given and the calculated sampling errors for 10 ft/sec gusts are found to be about four times those calculated on the basis of a random distribution. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3063.pdf 727. The theoretical determination of normal modes and frequencies of vibration I. T. Minhinnick In this paper the various methods that have been devised for the determination of the natural frequencies and normal modes of aircraft are discussed and their accuracy and the amount of work that they entail are compared. An extensive bibliography is given. The discussion is mainly from the point of view of the flutter analyst, who commonly bases his analyses on the normal modes, but the description and comparison of the various methods should be of general interest. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3039.pdf 728. Wind-tunnel tests on the effect of body freedoms on the flutter of a model wing carrying a localised mass D. R. Gaukroger and E. W. Chapple Wind-tunnel test results for the flutter of a swept-back wing carrying a localised mass, and having symmetric or antisymmetric freedoms of the root, are given. The tests were made on a model wing of 23 deg sweepback, the chordwise and spanwise positions of a localised mass being varied for two localised mass values. In most of the symmetric flutter tests the inertia conditions of the fuselage were constant, and representative of full scale. For the antisymmetric tests, the fuselage rolling moment of inertia was varied. The test results indicate that, in general, the symmetric flutter case is more critical than the antisymmetric for masses at outboard positions on the wing, but for heavy inboard masses the antisymmetric case may be the more critical. The results are too complex for any detailed use in predicting the effects of mass loading on the flutter of particular aircraft. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3081.pdf 729. A theory of the separated flow from the curved leading edge of a slender wing J. H. B. Smith The simple model used by Brown and Michael to represent the flow past a slender delta wing with leading edge separation, is extended to treat wings which have pointed apexes, curved leading edges and straight, unswept trailing edges. The vorticity of the fluid near the leading edge is represented by all isolated vortex of varying strength, which is curved in the non-conical cases considered here. A step-by-step method of calculation is used which starts from an assumed conical flow near the apex and employs the condition of zero total force on the vortex system in one cross-flow plane to obtain the configuration in the next. Numerical values of the co-ordinates and strength of the vortex, the lift coefficient and the centre-of-pressure position are found for three plan-form families at different incidences. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3116.pdf 730. Aerodynamic Characteristics in the Approach, Superfine and Negative Pitch Ranges of Two Four-Bladed Propellers with N.A.C.A. Series 16 Blade Sections. Technical Staffs of de Havilland Propellers, Limited, and Rotol, Limited. Tests were conducted on two similar full-scale propellers in tim 24-ft Wind Tunnel at the Royal Aircraft Establishment by representatives of Rotol, Ltd. and de Havilland Propellers, Ltd. to measure the aerodynamic characteristics over a blade-angle range of - 20 deg to + 40 deg, measured at the 0.7 radius, and over a range of advance ratio of 0.1 to 2.4. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3105.pdf 731. An approximate method of calculating the laminar boundary layer in two-dimensional incompressible flow M. R. Head Summary.--In the present approximate method the use of a doubly-infinite family of boundary-layer velocity profiles enables the momentum and energy integral equations of the boundary layer to be satisfied exactly, together with the first compatibility condition at the surface. The principal characteristics of the velocity profiles used have been calculated, and are presented graphically in a series of charts which enable calculations to be carried out with a minimum of labour. Several examples of boundary-layer flow have been worked out in detail by the use of the method, and agreement with known exact solutions is in most cases extremely satisfactory. No important restrictions on the application of the method have so far appeared; in particular it has been found possible to deal successfully with certain types of flow giving rise to similar profiles and with distributed suction starting either at the leading edge or at some point downstream. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3123.pdf 732. An experimental investigation of leading-edge flow separation from a 4 per cent thick two-dimensional biconvex aerofoil B. D. Henshall, and R. F. Cash The development of leading-edge flow separation as incidence is raised, for a 4 per cent thick twodimensional biconvex aerofoil, was studied experimentally for wide ranges of incidence at Mach numbers of 0.40, 0.50, 0.60 and 0.70. Pressure distributions and flow photographs are presented which illustrate the growth of the 'bubble' of separated flow. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3091.pdf 733. Approximate calculations of the laminar boundary layer with suction, with particular reference to the suction requirements for boundary-layer stability on aerofoils of different thickness/chord ratios M. R. Head 1. General Introduction.--In an earlier report an account was given of an approximate method for calculating the incompressible laminar boundary layer in two dimensions. Application of the method to the various cases for which exact (or nearly exact) solutions were available gave results which were in all cases in very satisfactory agreement with the accepted solutions. The accuracy of the method (essentially a development of one given earlier by Wieghardt), evidently resulted from satisfying both the momentum and energy integral equations of the boundary layer, together with the first compatibility condition at the surface. The doubly-infinite family of velocity profiles used in the method was obtained by a numerical procedure which gave a very much wider range of physically acceptable profiles than could be achieved by the use of simple analytic expressions (e.g., polynomials). In the present paper the approximate method just referred to has been applied to the class of problems for which it was specifically devised, namely problems where suction (or blowing) is applied through the surface. In Part I solutions are given for the following cases: (a) Flat plate with uniform suction and sinusoidal variation of external velocity (b) Flat plate with intermittent suction (c) Suction applied following the normal separation point to maintain a zero skin-friction layer for the flow U = 1 - x (d) Flat plate with uniform blowing. In Part II results are given of comprehensive calculations for a series of aerofoils with related pressure distributions. The distributions of suction required to maintain neutral stability of the boundary layer are given as functions of thickness/chord ratio and Reynolds number. The effect of Mach number is also inferred on certain simplifying assumptions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3124.pdf 734. Body freedom flutter of ground-launched rocket models at supersonic and high subsonic speeds D. R. Gaukroger A theoretical investigation of symmetric body freedom flutter of a rocket model is described. The results confirm that structural failures of models were caused by this type of flutter, and an extension of the investigation indicates the parameters that are of importance. A high ratio of body to wing mass and a well forward position of the overall centre of gravity are conditions under which flutter may occur. Increase of body pitching radius of gyration and tailplane volume are beneficial. It is concluded that this type of flutter may be significant in some aircraft designs, and that the canard has no advantage in this respect over the conventional lay-out of wing and tailplane. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3189.pdf 735. Boundary-layer measurements on 15-deg and 24.5-deg cones at small angles of incidence at M = 3.17 and 3.82 and zero heat transfer F. V. Davies and R. J. Monaghan Transition measurements on 15-deg and 24.5-deg cones at MCD = 3.17 and 3.82 showed that the transition front was extremely sensitive to incidence, a fourfold variation occurring between transition Reynolds numbers on the leeward and windward sides of the 15-deg cone at 2-deg incidence. At zero incidence the transition Reynolds number was between 2.5 and 3.0 x 10power6 and no significant variation was observed over the test range of stagnation pressures from 2 to 5 atmospheres. Pitot traverses on the top generator of the 15-deg cone at MCD = 3.17 showed that the effects of small angles of incidence (- 2 deg to + 1 deg) on the characteristics of the laminar boundary layer were nearly linear and were in excellent agreement with the theory of F. K. Moore. The same results showed that small angles of incidence altered the thicknesses of both laminar and turbulent boundary layers, but did not affect the shapes of the velocity profiles. The alteration with incidence of the displacement thickness of the laminar boundary layer was large (agreeing with Moore's theory), and in amount was more than twice that found with a turbulent boundary layer. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3133.pdf 736. Concept of complex stiffness applied to problems of oscillations with viscous and hysteretic damping S. Neumark The concept of complex stiffness in problems of oscillations with viscous, or structural (hysteretic) damping is often used in a wrong way, leading to erroneous solutions. It is shown in the Paper that correct expressions for complex stiffness are different in the cases of forced and free oscillations. All fundamental cases for a single degree of freedom are critically re-examined and compared, and fallacious solutions eliminated. The law of hysteretic damping being only known for a simple harmonic oscillation, all problems involving decaying oscillations, or more than one oscillatory mode, can only be treated tentatively at present, until the general law is found. This requires further experimental work. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3269.pdf 737. Design of warped slender wings with the attachment line along the leading edge J. Weber This report deals with the design of slender warped wings with unswept trailing edge but otherwise arbitrary planform which have, at the design lift coefficient, zero load along the leading edge and a near planar vortex sheet from the trailing edge. The wing can have an arbitrary chordwise curvature on which a spanwise curvature is superposed so that in any spanwise section the wing is straight over the inner part of the wing and curved over the portion near to the leading edges; the position of this change can vary arbitrarily in the chordwise direction. Formulae and working charts are given for determining the local load coefficient (and with it the streamwise velocity component), the spanwise velocity component, the total lift coefficient and the total drag. Numerical examples, for the gothic planform, are given to illustrate some of the effects of the various parameters on the load distribution, the section shapes and the drag. Slender-wing theory has been applied except for determining the wave drag which has been obtained from an approximate relation derived by the not-so-slender theory of Adams and Sears. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3406.pdf 738. Drag reduction of thin wings at supersonic speeds, by the use of camber and twist G. M. Roper Camber and twist is applied to the problem of reducing the drag due to incidence, of thin triangular or swept-back wings, at supersonic speeds, with subsonic leading edges and supersonic or sonic trailing edges. Two cases are considered: (i) with leading-edge suction forces ignored, (ii) with leading-edge suction forces included. It is found that twist, especially towards the wing tips, is more effective in reducing drag, for given lift, for the larger values of tan γ/tan μ, where γ is the semi-apex-angle and μ is the Mach angle, and that camber is more effective for the smaller values, though, in general, the best results are obtained by a suitable combination of camber and twist. For triangular wings, with suction ignored, the maximum percentage drag reduction varies from about 10 per cent (for sonic leading edges) to 50 per cent (for very slender plan-forms) and, if suction forces are included, from zero (for very slender plan-forms) to about 10 per cent (when the leading edges are sonic). The effect of the swept-back trailing edge is, in general, to increase the maximum percentage drag reduction for given lift if suction forces are ignored; but to decrease the maximum reduction for smaller values of tan γ/tan μ, and to increase the maximum reduction for values of tan γ/tan μ near to one, if suction forces are included. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3132.pdf 739. Experimental observation of vortices in wing-body junctions A. Stanbrook Tests have been made on various wing-body combinations to investigate the nature of the flow in the junction. It was found that vortices are formed due to separation of the boundary layer on the body in the flow towards the wing. The free edge of the resulting vortex sheet rolls up to form the vortex which then trails downstream around the wing. As incidence is increased the vortex on the suction side of the wing moves towards the wing and the vortex on the pressure side moves away from the wing. The vortices are present with both swept and unswept rounded leading edges at subsonic and supersonic speeds but were not found with sharp leading edges at zero incidence. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3114.pdf 740. Experiments with a two-dimensional aerofoil designed to be free from turbulent boundary-layer separation at small angles of incidence for all mach numbers D. W. Holder, and R. F. Cash The present investigation was designed primarily to check the validity of a simple method which had been suggested for designing an aerofoil section on which, for a limited range of incidence, turbulent boundary-layer separation is absent at all values of the free-stream Mach number. Assuming that this method proved successful, a second object was to study the transonic flow past the aerofoil, and to compare the results with previous speculations concerning the nature of the flow when separation is absent. Since separation was expected to occur when the angle of incidence was increased to a sufficiently large value, a third object was to study the flow when separation was present and, in particular, to confirm whether the effects of separation are less severe for the present section than for most previous sections. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3100.pdf 741. Flutter of an all-moving tailplane E. G. Broadbent and Margaret Williams Tailplane flutter is investigated theoretically for the following semi-rigid modes : (i) tailplane bending, frequency ω1; (ii) tailplane torsion, frequency ω2; (iii) tailplane rotation, frequency ω3; (iv) fuselage bending or torsion (according to symmetry), frequency ω4. The frequency ratios ω2/ω1 ; ω3/ω1 ; ω4/ω1, are varied and graphs of flutter speed against ω3/ω1 are given. The flutter speed drops sharply at low values of ω3/ω1 but it is probably the ratio ω3/ω4 that determines the position of the drop in flutter speed. Symmetric and antisymmetric results are included both for swept-back and unswept tailplanes. The effects of compressibility are excluded, apart from one isolated calculation, but this omission is not considered to have an important effect on the conclusions. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3284.pdf 742. Free vibrations of a stiffened cylindrical shell P. R. Miller This report presents the first stage of an investigation of the response to random noise of a stiffened cylinder, representing an aircraft fuselage, including an analysis of the lower modes of such a cylinder. Preliminary investigations suggested that assumptions and approximations which are valid for the uniform, i.e., unstiffened, shell are not necessarily valid for a shell with heavy stiffening, and this report therefore starts with a review of existing theories in which the assumptions are examined critically, and, it is hoped, somewhat rationalised. There is very little literature on stiffened shells and this review deals mainly with uniform ones, including the general analysis of strain in a thin shell and the vibrations of a uniform cylindrical shell in vacuo, but includes some comments on the effects of an acoustic medium round the shell. The energy approach is then extended to give the resonant frequencies and natural modes of a circular cylindrical shell uniformly stiffened with closely spaced longerons and frames, 'close spaced' implying that stiffener spacing is much less than the spacing of nodal lines. The effects of rotary inertia have had to be included owing to the lack of symmetry of the section about the skin, but shear deflections are still neglected. Further numerical work is required before much comment can be made on tile results, but they seem to be similar in nature to those obtained for the uniform cylinder. Finally, some indication is given of how the theory can be extended to cover higher-order modes where shear deflection and stiffener spacing become important. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3154.pdf 743. Investigations into the use of an electrical resistance analogue for the solution of certain oscillatory-flow problems P. J. Palmer, Anne R. Copson and S. C. Redshaw The use of an electrical resistance analogue, for solving the problem of a thin two-dimensional wing oscillating in an incompressible ideal fluid, is considered; wings with and without flaps are investigated. The particulars of the design and construction of a special graded analogue are given. Experimental results are obtained for flat plates, with and without flaps, oscillating harmonically with small amplitudes in a steady air stream. These experimental results are in close agreement with theory. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3121.pdf 744. Longitudinal stability and control of the single-rotor helicopter A. R. S. Bramwell The equations of motion of the helicopter are presented and reduced to non-dimensional form. The force and moment derivatives for the single-rotor helicopter (including tailplane if required) are given as simple formulae or in the form of charts. Comparisons are made with wind-tunnel and flight tests where possible and agreement is generally quite good. In the development of the theory, static and manoeuvre stabilities are introduced in a manner analogous to fixed wing aircraft practice. It is shown that the static stability of the helicopter is proportional to the coefficient E in the stability quartic whilst the manoeuvring qualities are represented by coefficient C. The N.A.C.A. 'divergence requirement' is expressed in terms of the 'short-period' motion. Calculations show that the poor damping in pitch of the single-rotor helicopter without a tailplane results in poor manoeuvring qualities, i.e., considerable time taken to reach steady acceleration following a control movement, but that the fitting of even a small tailplane provides a great improvement in stability and control. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3104.pdf 745. Low-speed experiments on the wake characteristics of flat plates normal to an air stream R. Fail, J. A. Lawford and R. C. W. Eyre Experiments on isolated fiat plates perpendicular to the wind are described. It is shown that the effects of aspect ratio on drag, base pressure and flow pattern are small up to A = 10. All of these rectangular plates shed turbulent eddies at particular frequencies; generally there are two shedding frequencies for each plate, one associated with the smaller dimension of the plate, and a lower frequency associated with the larger dimension. Large changes in the shape of low-aspect-ratio plates have very small effects on the aerodynamic characteristics but perforating the plate can eliminate the regular shedding of eddies and reduce the random low-frequency velocity fluctuations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3120.pdf 746. Low-speed wind-tunnel tests on the de havilland sea venom with blowing over the flaps S. F. J. Butler and M. B. Guyett This report contains the results of low-speed tunnel tests of longitudinal stability on a modified Sea Venom Mk. 21 fitted with blowing over the flaps. At each flap angle, a range of values of the sectional momentum coefficient was tested. As a typical example, the increase in trimmed CL at constant incidence resulting from blowing at flaps 60 deg was about 0.45, the increase in CLMAX being somewhat smaller. The equivalent reduction in approach speed of 10 to 15 kt predicted from the tunnel results was later achieved in flight. The tunnel results suggested a beneficial reduction in minimum-drag speed due to blowing, particularly at large flap angles. Trim changes were large, amounting to about 8 deg on the all-movable tail at flaps 60 deg. A comparison is made between estimated and measured effects of blowing. It is shown that, whilst the lift and pitching-moment increments resulting from flap blowing can be estimated fairly closely, the drag increments at large flap angles are much larger than would be expected, The additional drag tends to decrease the minimum-drag speed and increase the minimum drag, and may affect the take-off and landing performance appreciably. The effect will be unfavourable in the first case and favourable in the second. A flight/tunnel comparison is included of the lift increments resulting from blowing. At flaps 40 deg, agreement is good, but at larger flap angles, the lift increments measured in flight were less than those measured on the model. Possible reasons f0r this are discussed. There is a favourable Reynolds-number effect on CLMAX which is found to be somewhat larger for the blown flap than for the unblown flap. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3129.pdf 747. Measurements of the direct hinge-moment derivatives at subsonic and transonic speeds for a cropped delta wing with oscillating flap J. B. Bratt, C. J. W. Miles and R. F. Johnson Under review Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3163.pdf 748. Methods for determining the wave drag of non-lifting wing-body combinations L. M. Sheppard The area-rule, moment of area-rule and transfer-rule methods for estimating the wave drag Of wing-body combinations are discussed. It is pointed out that the moment of area rule and the transfer rule are different forms of the area rule, and that the transfer rule expresses the interference wave drag in a simple form. The existing methods of wave-drag estimation are restricted to combinations with bodies having continuous surface slope andhere an extension to combinations with bodies having discontinuous surface slope is given. This paper is concerned with the theoretical methods and their associated numerical techniques and no numerical results for particular applications are presented. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3077.pdf 749. Methods for estimating distributions and intensities of sonic bangs D. G. Randall Methods recently developed for estimating distributions and intensities of sonic bangs are described. They are applied to several interesting flight manoeuvres and the results discussed in detail. The effect on sonic-bang distributions and intensities of refraction (caused by the temperature gradient existing in the actual atmosphere) is also considered. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3113.pdf 750. Observations of the flow past a two-dimensional 4 per cent thick biconvex aerofoil at high subsonic speeds B. D. Henshall, and R. F. Cash Flow photographs and detailed pressure distributions for a 4 per cent thick circular-arc biconvex aerofoil at high subsonic speeds and high incidences have been analysed and the divergence boundary (defining the onset of separation effects) for the aerofoil determined. Emphasis was placed on the transition from leading-edge to shock-induced separation as the free-stream Mach number was raised at a fixed incidence. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3092.pdf 751. Observations of the flow patterns of two-dimensional 4 per cent thick biconvex aerofoil at Mo = 1.40 and 1.63 B. D. Henshall, and R. F. Cash Direct-shadow and schlieren photographs and pressure distributions of the flow past a two-dimensional 4 per cent thick biconvex aerofoil for a limited range of incidences at Mach numbers of 1.40 and 1.63 are presented. Shock-induced boundary-layer separation at the trailing edge of the aerofoil was present at M 0 = 1.63 with transition-free boundary layers but was absent up to 5 deg incidence at M 0 = 1.68 with transition-fixed boundary layers and up to 6 deg incidence at M 0 = 1.40 with transition-free boundary layers. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3093.pdf 752. Published reports and memoranda of the aeronautical research council
Below is given a list of the Reports and Memoranda published by the Aeronautical Research Council. The reference numbers other than the R. & M. numbers are not consecutive, as many reports are confidential to the Council and not for issue to the public. Normally every R. & M. is bound into the Annual Technical Volume bearing the same year as the date of the original report. Owing to the post-war difficulties of publication this procedure will not be able to be rigidly adhered to, and such R. & M. which are not available at the time of compilation of the Annual Technical Volumes will be combined together in special volumes. Those R. & M. below marked with a star will be thus dealt with. Monographs are not incorporated in Annual Technical Volumes. R. & M. No. 2600, entitled Index of all Reports and Memoranda published in the Annual Technical Reports and separately, is published by H.M.S.0. at 2s. 6d. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2850.pdf 753. Some exploratory jet-flap tests on a 60-deg delta wing J. Williams, and A. J. Alexander Summary.--As a preliminary investigation of the effects of high sweep and low aspect ratio on jet-flap wings, some wind-tunnel experiments were carried out on a half-model of a 60-deg delta wing, already tested with blowing to prevent flow separation over a trailing-edge flap. Much larger values of the blowing-momentum coefficient Cì\' than before were achieved by using a low tunnel speed. Balance measurements were made of lift, pitching moment and thrust for Cì\' values up to 1·5, wing incidences between - 4 deg and + 20 deg, and flap angles of 30, 60 and 90 deg. Although substantial magnification of the direct jet lift occurred, the movement of the centre of lift was appreciable and positive values of the thrust occurred only at the lowest flap angle. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3138.pdf 754. Subsonic wind-tunnel tests of various forms of air intake installed in a fighter-type aircraft B. J. Prior and C. N. Hall Tests have been made at Mach numbers up to 0.93 in the Royal Aircraft Establishment 10 ft X 7 ft High Speed Wind Tunnel to examine how the longitudinal characteristics of a fighter-type aircraft are affected by the installation of air intakes in the nose, fuselage sides, or wing roots. None of these intakes alters the lift or pitching moment characteristics significantly, but their effects on external drag vary, and only the nose intake avoids an increase. This superiority derives principally from its low area ratio, the value of which largely determines not only the critical Mach number and hence the behaviour at transonic speeds of the intake fairing but also its sensitivity to spillage and aircraft attitude. Both forms of divided intake cause an increase in profile drag of roughly 20 per cent; on the side intake this is due to the siting of the boundary-layer by-passes and on the wing-root intake to the increased wing thickness. Their high area ratios make them sensitive to changes in flow direction and lead to high suction levels over the intake fairings which are expected to cause drag increases early in the transonic range. Separation in the canopy-intake junctions of the side intake reduces the drag divergence Mach number to 0.87, compared with 0.89 for the other models. The shaping of the wing-body junction which was combined with the nose and side intake installations leads to a marked reduction in drag at transonic speed, an advantage not shared by the wing-root lay-out. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3134.pdf 755. The design and testing of an axial-flow compressor having different blade profiles in each stage A. D. S. Carter, R. C. Turner, D. W. Sparkes and R. A. Burrows The report opens with a brief survey of various blade profiles and their two-dimensional cascade performance characteristics. The requirements of the different stages of an axial compressor are then discussed. This is followed by the design details of a suitable test compressor embodying in each stage the blade profile most suited to the duty that stage has to perform. The test results for this compressor are given and discussed at some length. It is concluded that a compressor with suitable blade profiles in each stage has considerable advantages over one in which the same profile is used throughout. These advantages are : (a) The compressor will have a good surge line. (b) Its part-load efficiency will be high. (c) It will have a wide characteristic at constant speed. (d) It may have a high efficiency at high flow. (e) It will have a higher peak efficiency than some designs. (f) It should be more reliable. A possible disadvantage is that it may have a lower surge pressure ratio at the design speed than a compressor with high load blade sections throughout. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3183.pdf 756. The Development of a Variable Mach-Number Effuser J. B. McGarry A series of tests Was undertaken on a simple, two-dimensional, variable Mach-number effuser, or nozzle, designed for the range of supersonic flows up to Mach number 3.0. The performance of the nozzle was assessed from the magnitude of the percentage variation in its exit Mach-number distribution. Studies of the effect on the performance of alterations to the position of the nozzle-block pivots and other geometrical features were made. On the basis of these studies, a final build of nozzle was developed which produced flow of a uniformity sufficient for intake and engine model testing over the Mach-number range from 1.5 to 3.0. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3097.pdf 757. The effect of inlet circumferential maldistribution on an axial compressor stage R. C. Turner, J. Ritchie and C. E. Moss This report describes tests on a single compressor stage with circumferentially non-uniform inlet conditions. The stage was a model of the first stage of a typical modern aircraft-engine compressor, and the tests were planned as part of an investigation into the surge behaviour of compressors with inlet flow maldistribution. It was found that with a roughly rectangular inlet velocity distribution of amplitude Â± 25 per cent of the mean value, the surge flow instead of showing an expected increase was almost unchanged, being in fact slightly reduced. The efficiency fell greatly, with an accompanying small drop in temperature-rise coefficient. The velocity profile was distorted and its amplitude greatly decreased at the outlet of the stage. These results are important in that they suggest that the surge of the first stage is not the primary factor in determining the surge of a multi-stage compressor. It would appear that the primary effect of maldistribution is to decrease the efficiency of the first stage or stages, and thus alter the stage matching at the surge flow, which is, however, mainly determined by the later stages. The maldistribution will probably have disappeared at these later stages, which will thus exhibit their normal characteristics. These conclusions are supported by analysis of multi-stage compressor performance and by theoretical considerations. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3066.pdf 758. The effect of reynolds number on the performance of a single-stage compressor A. D. S. Carter, C. E. Moss, G. R. Green, G. G. Annear In a preliminary report a description has been given of some tests on the effect of Reynolds number on the static-pressure rise through a single-stage axial-flow compressor. The work has since been extended and the full performance data of the compressor obtained over a wide Reynolds-number range. This report presents a comprehensive review of the results obtained in the complete test series. The tests were carried out in the National Gas Turbine Establishment Variable-Density Return-Flow Rig. As description of the rig is beyond the scope of this report, a complete description of the rig and the operating technique will be issued as a separate report. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3184.pdf 759. The formation of regions of separated flow on wing surfaces Part 1 low-speed tests on a two-dimensional unswept wing with a 10 per cent thick RAE 101 section Part 2 laminar-separation bubbles and the mechanism of the leading-edge stall L. F. Crabtree Tests of a two-dimensional straight wing with a 10 per cent thick RAE 101 section have been made in a low-speed wind tunnel to check the validity of a criterion suggested by Owen and Klanfer for the type of bubble which will be formed when a laminar boundary layer separates from the surface of an aerofoil. The results confirm this hypothesis and show that if the boundary-layer Reynolds number based on displacement thickness at separation, calculated from an observed pressure distribution, is greater than 450 a short bubble is formed, and for (Rδ1)s less than 400 a long bubble is formed. For values of (Rδ1)s within the range 400 to 450 it is uncertain which type of bubble will occur. A method is given, based on these results, for predicting the type of bubble formed on a two-dimensional unswept wing of arbitary section shape for a given incidence and Reynolds number. A brief discussion of the physical structure of bubbles is given, and the more important problems yet to be solved are indicated. A hypothesis is put forward to explain the phenomenon of the 'leading-edge stall' of moderately thin aerofoil sections, and some remarks are added on the scale effect on the maximum lift attained by aerofoils which experience this type of stall. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3122.pdf 760. The influence of aerodynamic heating on the flexural rigidity of a thin wing E. H. Mansfield This report considers the loss of flexural rigidity of a thin wing due to the presence of middle-surface stresses resulting from aerodynamic heating. The spanwise properties of the wing are assumed constant but the wing section is arbitrary. The loss of flexural rigidity is comparable with the corresponding loss of torsional rigidity. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3115.pdf 761. The measurement of unsteady forces and moments on slender bodies oscillating in a wind tunnel J. F. Clarke An apparatus for the measurement of unsteady aerodynamic reactions on slender bodies is described. It is particularly stated to tests at supersonic speeds. The forces and moments on the model are detected by strain-gauges attached to the model mounting sting and by supplying their bridge circuits with properly phased A.C. of the right frequency, direct meter readings of the stiffness or damping reactions may be obtained. The results of a short series of tests on a cone-cylinder at subsonic Mach numbers and reduced frequency parameters (based on model length) up to 0.06 are given. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3170.pdf 762. The Mixing of Free Axially-Symmetrical Jets of Mach Number 1.40 N. H. Johannesen Axially-symmetrical, supersonic, fully-expanded jets of diameter about 0.75 in. and of Mach number 1.40 issuing into an atmosphere at rest were investigated by schlieren and shadow photography and by pressure traversing. The development of the jets was found to depend critically on the strength of the shock waves in the core of the jet at the nozzle exit. With strong shock waves present the jet spread very rapidly and was very unsteady. The jet did in some cases break up into large eddies of the same size as the diameter of the jet. When no disturbances were present in the core of the jet the spreading was far more gradual and the jet showed only slight unsteadiness. The turbulent mixing region of the first part of the jet with strong shock waves was investigated in detail by pitot tubes. The first inch was found to correspond to a two-dimensional half-jet. The velocity profiles were similar and well represented by the error integral. The rate of spreading was only half the value for low-speed flow. By integrations across .the mixing region the entrainment and-the loss of kinetic energy were determined. These quantities were found to agree well with the values estimated by assuming an error-integral velocity profile. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3291.pdf 763. The pressure in a two-dimensional static hole at low Reynolds numbers A. Thom and C. J. Apelt A description is given of an arithmetical method for obtaining solutions for steady incompressible viscous flow at low Reynolds numbers in the form of expansions in powers of the Reynolds numbers. The method has been used to find a solution for the flow past the mouth of a two-dimensional static hole. The pressure in the hole is determined and it is shown that the disturbance to the flow caused by the hole produces an error in the pressure recorded in the hole. The error is positive and if it is expressed in non-dimensional form, i.e., (pressure error/Â½pU2), its magnitude decreases with increasing Reynolds number for the range for which the solution is valid. The theoretical results are compared with experimental results obtained for the error in the pressure recorded by a circular static hole. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/3090.pdf 764. The shape of the centre part of a swept-back wing with a |