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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. 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 5. 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 12° and 18°, 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 6. 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 7. 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 8. 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 9. 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 10. 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 11. 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 12. 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 13. 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 14. 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 15. 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 16. 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 17. 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 18. 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 19. 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 20. 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 21. 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 2·93 in. and 5·89 in. respectively have been determined from measurements of velocity taken at distances of about 0·0025 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 5·89 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 22. 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 23. 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 24. 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 25. 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 26. 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 27. 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 28. 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 29. The Calculation of the Profile Drag of Aerofoils H. B. Quire; 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 30. 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 31. 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 3½°, 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 32. 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 33. 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 34. 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 35. 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 36. 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. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1993.pdf 37. 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 38. 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 39. 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 0° to ±15° ; Range of incidence -4° to 8°. (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 0°, 4° and 8°. Control angles ±10° and ±15°. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1936.pdf 40. 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 41. 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 42. 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 43. 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 44. 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 45. 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 46. 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 47. 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 48. 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 49. 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 50. 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 (tc), or of a power loss coeeficient (such as (pc2) is calculated for a definite series of values of the radius (rc = 0.3, 0.45, 0.6, 0.7, 0.8, 0.9, 0.95, 0.975). These values are then plotted against rc2, 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. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2043.pdf 51. 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 52. 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 53. 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 54. 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 ±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 55. 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 56. 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 57. 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 58. 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 ½ 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 59. 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 60. 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 61. 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 62. 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 63. 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 64. 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 65. 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 66. A Résumé 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 67. 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 68. 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 69. 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 70. 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 71. 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 72. 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 73. 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 74. 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 75. 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. × 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 76. 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 77. 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 78. 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 79. 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 CL = 0.24 and CL = 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 80. 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 81. 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 82. 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 83. 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 84. 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 85. 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 86. 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 87. 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 88. 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. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2063.pdf 89. 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 90. 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. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/1997.pdf 91. 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 92. 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 93. 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 94. 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 95. 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 ½ 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 ½ 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 96. 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 97. 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 × 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 × 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. × 9 ft. wind tunnel at Reynolds numbers up to 5 × 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 98. 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 99. 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 100. 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. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2048.pdf 101. 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 102. 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 103. 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 104. 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 105. 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 106. 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 107. 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 108. 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 109. 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 110. 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 §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 §9. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2034.pdf 111. 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 112. 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 113. 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 114. 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 115. 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 116. 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 117. 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 118. 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 119. 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 120. 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 121. 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 122. 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 123. 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 124. 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 125. 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 126. 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 127. 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 128. 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 129. 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 130. 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 131. 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 132. 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 133. 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 134. 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 135. 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 136. 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 137. 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 138. 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 139. 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 § 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 140. 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 141. 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 142. 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 143. 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 144. 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 145. 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. Available from: http://naca.central.cranfield.ac.uk/reports/arc/rm/2042.pdf 146. 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 147. 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 148. 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 149. 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 150. 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 151. 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 152. 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 153. 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 154. 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 155. 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 156. 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 157. 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 158. 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 159. 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 160. 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 161. 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 162. 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 163. 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 164. 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 165. 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 166. 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 167. 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 168. 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 169. 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 170. 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 171. 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 172. 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 173. 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 174. 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 175. 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 occurs·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 176. 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 177. 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 178. 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 179. 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 180. 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 181. 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 182. 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 × 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 × 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 183. 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 184. 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 185. 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 186. 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 187. 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 188. 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 189. 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 190. 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 191. 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 192. 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 193. 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 194. 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 195. 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 196. 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 197. 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 198. 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 199. 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 200. 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 × 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 201. 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 202. 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 × 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 203. 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 204. 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 205. 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 206. 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 207. 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 208. 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 209. 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 210. 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 211. 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 212. 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 213. 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 214. 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 215. 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 216. 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 217. 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 218. 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 219. 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 220. 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 221. 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 222. 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 223. 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 224. 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 225. 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 226. 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 227. 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 228. 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 229. 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 230. 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 231. 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 232. 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 233. 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 234. 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 235. 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 236. 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 237. 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 238. 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 239. 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 240. 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 241. 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 242. 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 243. 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 244. 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 245. 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 246. 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 247. 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 248. 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 249. 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 250. 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 251. 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 252. 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 253. 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 254. 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 255. 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 256. 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 257. 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 258. 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 259. 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 260. 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 261. 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 262. 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 263. 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 264. 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 265. 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 266. 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 267. 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 268. 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 269. 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 270. 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 271. 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 272. 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 273. 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 274. 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 275. 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 276. 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 277. 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 278. 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 279. 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 280. 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 281. 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 282. 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 283. 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 284. 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 285. 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 286. 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 287. 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 288. 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 289. 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 290. 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 291. 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 292. 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 293. 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 294. 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 295. 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 296. 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 297. 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 298. 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 299. 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 300. 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 301. 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 302. 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 303. 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 304. 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 305. 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 306. 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 307. 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 308. 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 309. 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 310. 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 311. 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 312. 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 313. 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 314. 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 315. 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 316. 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 317. 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 318. 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 319. 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 320. 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 321. 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 322. 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 323. 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 324. 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 325. 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 326. 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 327. 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 328. 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 329. 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 330. 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 331. 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 332. 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 333. 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 334. 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 335. 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 336. 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 337. 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 338. 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 339. 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 340. 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 341. 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 342. 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 343. 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 344. 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 345. 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 346. 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 347. 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 348. 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 349. 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 350. 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 351. 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 352. 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 353. 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 354. 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 355. 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 356. 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 357. 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 358. 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 359. 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 360. 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 361. 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 362. 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 363. 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 364. 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 365. 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 366. 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 367. 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 368. 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 369. 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 370. 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 371. 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 372. 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 373. 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 374. 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 375. 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 376. 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 377. 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 378. 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 379. 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 380. 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 381. 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 382. 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 383. 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 384. 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 |