On optimal configurations in supersonic flow

Analytical solutions for variational problems on configurations of threedimensional (3D) bodies with the maximal lift-to-drag ratio at a given base area or a planform area are found within the limits of a localised interaction between the supersonic flow and the body surface. Functionals of considered variational problems depend on derivatives of the desired function with respect to independent variables only, and this simplifies the solution and allows studying the structure of the extremal surface. It is shown that the lower surface of optimal bodies is planar. If a base area is given, the upper surface is cylindrical with the generating line parallel to the oncoming flow velocity vector. If a planform area is given, the optimal body is a flat plate with the highest possible value of the liftto-drag ratio at a prescribed Mach number and friction coefficient. The optimal body with a planar upper surface is a wedge. These results are valid if the base pressure is taken into account and also for zero base pressure