Minimum drag surfaces of given lift which support two-dimensional supersonic flow fields

Abstract

The two-dimensional surface giving minimum pressure drag for given lift coefficient in supersonic flow is considered. The method adopted is a small perturbation of a plane surface; the pressure is expressed as a power series in the perturbed slope and third order terms are neglected. The shape of the optimum surface is found to be a double wedge surface, with a single discontinuity in the surface slope. The compression surface is concave at the discontinuity for Mach numbers below about 1.4 and above 3, and between these it can be slightly convex. The performance in the case γ = 1.4 is compared with that of the plane wedge, and the improvement is found to be very small, except at hypersonic speeds when improvements greater than 1 per cent are obtained. Similar results hold for waveriders (three-dimensional wing shapes) based on two-dimensional flow fields.