Effects of planform curvature in supersonic wings

Abstract

In this thesis a method is developed for calculating supersonic wings with curved subsonic leading edges. The linearized theory is used throughout the thesis. The wing with the curved subsonic leading edges is transformed into a wing with straight subsonic leading edges by means of a transformation as used by Coene for quasi-homogeneous approximations to the solution of this problem. The Mach cone is invariant under the transformation. The solution of the transformed Prandtl-Glauert equation is expressed in terms of Fenain's solutions for the delta wing. In general the solution is an infinite sum of terms, each term related to a solution for the delta wing. However, a condition is formulated under which certain families of wings with curved leading edges possess solutions in closed form. It is shown that any boundary value problem for such wings can be solved by the superposition of these exact solutions of the Prandtl-Glauert equation. The problem is thus reduced to determining the number of terms necessary to approximate the given boundary values within satisfactory bounds, and within a satisfactory region of the wing. One family of wings with curved leading edges that has a solution in closed form is found. The flat plate with these leading edges is studied in detail. In order to find a reasonable approximation to the flat plate, in a satisfactory region of the wing, up to five solutions are superposed. It has been found that the curvature has a considerable effect on the perturbation velocity and the leading edge suction force. The leading edge suction force thus found is compared with that calculated by some other approximate methods.