Calculation of the effect of camber and twist on the pressure distribution and drag on some curved plates at supersonic speeds

Abstract

So far, little is known of the effect of camber or twist on the pressure distribution and drag of a wing flying at supersonic speeds, but with subsonic leading edges. According to the linear theory, for a subsonic leading edge, there is a singularity in the perturbation velocity component normal to the edge. Associated with this singularity is an infinite (or very large) suction over the sharp leading edge, as in subsonic flow. The present investigation was undertaken with a view to finding the shape of a curved wing, such that the thrust loading on the leading edges, particularly near the wing tips, is removed or modified. The shapes of two groups of such wings have been found :- (1) For the first group, when the wings are at design incidence, there are no leading-edge pressure singularities, and therefore no leading-edge thrust. The pressure difference is finite and positive everywhere on the wing, and decreases to zero on the leading edges. (2) For wings of the second group, the leading-edge singularity is modified so that its strength increases along the edge from zero at the apex to a maximum, and then decreases to zero, after which it would become negative: The effect of additional incidence is to increase the local lift everywhere and to move the positions of maximum and zero singularity strength further downstream. In this report, it is also shown how the shapes of wings of the second group can be determined to satisfy certain requirements with respect to camber and twist, or the magnitude of aerodynamic characteristics. The lift, the induced drag, and the pitching-moment coefficients for some wings of triangular plan form have been calculated, and the results are shown graphically.