Results are presented of the numerical solution of the problem of a triangular wing of given volume having maximum aerodynamic efficiency in hypersonic flow. In calculating the aerodynamic characteristics of lifting bodies in hypersonic viscous gas flow it is often assumed that the pressure coefficient on the surface of the body is given by the Newton law [1, 2], while the friction coefficient is constant. These assumptions make i t possible to formulate the variational problem of bodies with optimal characteristics as the problem of the extremal value of a functional which can be expressed explicitly. However, even for simple problems the Euler equations will be nonlinear partial differential equations whose solution can be obtained only in certain particular cases. Therefore the additional assumption is usually made that the wing is slender, which makes it possible to solve certain simple variational problems with the aid of the analytic methods. But this assumption restricts severely the class of permissible wing forms and does not permit obtaining a complete picture of the dependence of the aerodynamic characteristics of the optimal bodies on the various parameters. The numerical method of local variations [3], used in the following, makes it possible to solve certain variational problems without imposing any limitations on the relative dimensions of the wings. Let us assume that the pressure coefficient Cp on the ~,ing surface (Fig. 1) is given by the Newton law with a modifying factor N(M co), the friction Coefficient cj = const and the upper and lower surfaces of the wing are given by the respective functions Yi Y* (x, z) and Y2 = Y2( x, z). We use the dimensionless variables ~ = x/b0, = y /V • z = 2 z / l . Here b0, l, and V are, respectively, the width span, and volume of the wing. Then the wing drag and lift coefficients and the wing volume are given by the functions (bars over letters are dropped)
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