Some applications of the lamé function solutions of the linearised supersonic flow equations. Part I. Finite swept-back wings with symmetrical sections and rounded leading edges. Part II. Cambered and twisted wings

Abstract

Some general solutions of the linearised equations of supersonic flow, in terms of Lamé functions, were obtained by G. M. Roper, using the methods of Robinson and Squire. The results were applied to calculate : (a) the pressure distribution over some swept-back wings at zero lift, having symmetrical sections with rounded leading edges; (b) the effect of camber and twist on the pressure distribution and drag on some wings of negligible thickness. The solutions are only valid for surfaces lying wholly within the Mach cone of the apex. In the present paper, some further special solutions are found. In Part I, some of these solutions are combined.with solutions already found to give : (A) the pressure distribution and wave drag, at zero lift, on some finite unyawed swept-back wings having symmetrical sections with rounded leading edges and wing tips perpendicular to the wind direction ; (B) the change in pressure distribution and wave drag at zero lift on the surface of a Squire wing, when the local thickness/chord ratio is modified. The shapes of some curved wings, with swept-back subsonic leading edges were found by Roper, such that the thrust loading on the leading edges, at supersonic speeds, is removed or modified. In Part II of this paper, the effect of a change of Mach number on the aerodynamic characteristics of such a wing, designed for a given Mach number, is calculated. Some additional solutions of the linearised supersonic flow equations, applicable to cambered and twisted wings, have also been calculated, and the results are given in Appendices III and IV of Part II.