Several authors have considered the lifting characteristics of various simple shapes at hypersonic speeds. Non-weiler has dealt with shapes derived from wedge flows, and Townend has considered a class of two-dimensional shapes with concave undersurfaces. Cole and Aroesty and Pike have both considered two-dimensional shapes which are perturbations of simple wedge flow. They show that slightly higher values of the lift-to-drag ratio than that of the wedge are obtainable. Cole and Aroesty apply hypersonic small disturbance theory, under the constraint of constant lift, and suggest that the optimum shape is a “multi-wedge”. They show further that the optimum of a more restricted class of shapes having undersurfaces made of two plane surfaces, has a slightly concave surface. Pike has applied a more accurate (second-order) perturbation theory to a class of shapes which consist of small deviations from a wedge. He finds that the optimum undersurface consists of two plane surfaces, and confirms Cole and Aroesty's result that it must be slightly concave, except perhaps at low Mach numbers below the hypersonic range. It must be remembered that these results depend upon the assumed constraint of constant lift.