ABSOLUTELY OPTIMAL CONFIGURATIONS WITH MAXIMUM LIFT-TO-DRAG RATIO AT HIGH SUPERSONIC

Abstract. The problem on the configuration with maximum lift-to-drag ratio in supersonic gas flow is discussed. It is assumed that pressure on the body surface is defined by a local method and friction coefficient is constant. Corresponding variational problem is stated and solved without isoperimetric conditions and also with given shape and area of the body base section. It is shown that the variational problem extremals are the following: conical surface with very small cone angle (by the order of the friction coefficient), planes perpendicular to the cone surface normal, and planes parallel to Z-axis that form the windward surface of the optimal body. If isoperimetric conditions are not prescribed, absolutely optimal body is two-dimensional wedge. If base area is given then optimal body base shape is a polygon formed by line segments. Optimal parameters are found for bodies with triangular base. The solution is found analytically and using the numerical technique of local variations. 1