A study of airfoil optimization, using the equations of hypersonic gas dynamics to explore the "Newtonian chine strip" theory that airfoil concavity enhances the lift-to-drag ratio for a fixed drag penalty. The flow behind concave and convex exponential shock waves is investigated, and the corresponding airfoil surfaces are determined. The calculations show that the optimum lifting surface for fixed drag is only slightly more concave than a flat plate and that the improvement in performance is small. A limit line is shown to exist in the flow field behind convex exponential shock waves, so that it is not possible to construct a convex airfoil that supports an exponential shock wave over its entire length if the nose curvature is too large. 53 pp. Refs.