Theoretical calculation of generalised forces and load distribution on wings oscillating at general frequency in a subsonic stream

Abstract

The theoretical method presented here gives improved accuracy and economy of operation, because it is modelled on a very satisfactory method for steady subsonic flow and is programmed in an efficient machine code for the KDF9 computer. There is no restriction on planform, provided that any cranks are rounded to give smooth leading and trailing edges with continuous curvature. The method is programmed in two parts, illustrated by flow diagrams and an example. An appendix describes various operative schemes for obtaining generalised forces and chordwise loadings in phase and in quadrature with arbitrary wing motion in rigid or elastic modes. Restrictions on size of solution are discussed, and the usable range of chordwise and spanwise parameters should serve most needs. The method is applied to elliptical, rectangular and tapered swept wings of small and large aspect ratio at Mach numbers up to 0.8 and over a wide range of frequency parameter. Accuracy is established by direct comparison with steady flow, by independent desk calculation, by reverse-flow relationships, by asymptotic expansion for small frequency, and by studies of convergence. Results and computing times compare favourably with those of other collocation methods in current use.