Optimum lifting body shapes in hypersonic flow at high angles of attack

A variational procedure for the determination of lifting body configurations having a maximum lift-to-drag ratio K _max in hypersonic flight at high angles of attack , is proposed. It is based on an analytical solution to the problem for three-dimensional hypersonic flow over small aspect ratio wings using thin shock-layer theory. This reduces the variational problem of finding K _max, and the corresponding optimized wing shape, to the minimization of a linear functional subject to various constraints. The contributions of nonequilibrium thermochemical effects and laminar or turbulent viscous drag effects are also included in the problem formulation. The solution shows that optimized wings have an unbent forward part and a concave lower surface. Due to bifurcation in the optimization process, the planform may have either a sharp apex or a straight nose cut. Corresponding values of K _max() significantly exceed the limiting value K _N=cot for a flat wing. Real thermochemical effects and air viscosity are shown to cause a decrease in K _max and sometimes to influence the optimized wing geometry; however, the relative increment of K _max to K _N is still retained.