The theoretical treatment of slowly oscillating part-span control surfaces in subsonic flow

Abstract

To first order in frequency, subsonic lifting-surface theory is applied to arbitrary configurations of a thin wing and a trailing-edge control. The discontinuities in flow direction at the hinge line and part-span boundaries are surmounted by independent consideration of smooth equiva!enl slopes in the chordwise and spanwise directions; the combined equivalent incidences depend on the aerodynamic quantities to be evaluated. The present method yields satisfactory values for lift, pitching and rolling moments, hinge moment and the associated spanwise distributions, but does not determine the complete load distribution due to an oscillating control. Illustrative examples cover four planforms, namely, rectangular and cropped delta wings for which there are experimental data on hinge moment, an untapered swept wing that has been studied by electrical analogue, and a tapered swept wing to be the subject of future experiments. The solutions for each planform are tabulated and plotted as functions of control chord, control span or Mach number and are examined from the standpoint of numerical convergence with respect to the number of chordwise collocalion points. Consideration is given to the transformed aerodynamic problem on the reversed wing by application of the reverse-flow theorem, and these alternative numerical results strengthen confidence in the present method and give some indication of the likely accuracy. The optimum central rounding of swept edges is discussed together with many other refinements of numerical technique. A broad conclusion is that significant wing forces can be calculated to at least two-figure accuracy. The approximations in the method are such that the true theoretical values of hinge moment are likely to be within 2 per cent of the calculated stiffness derivative and within 10 per cent of the calculated damping, provided that there is due attention to the choice of equivalent incidences. Comparisons with wind-tunnel data tend to show larger discrepancies, which can be reconciled with rough predictions from charts based on two-dimensional static tests. A simple empirical correction to the theoretical hinge-moment damping is suggested, which reproduces the available experimental data within ± 10 per cent.