Conical Bodies with Star-Shaped Transverse Contour Having the Minimum Wave Drag

The problem of constructing the transverse contour of a conical body having the minimum wave drag in the range of supersonic velocities provided that the length and the volume are preserved is considered. A cone is taken as the initial body, an assumption about locality of the relation between variations in the geometric parameters and the pressure on the surface is made, and the quadratic approximation of this relation is used. The found solution is compared with the results obtained within the framework of the Newton model. These solutions are proposed to combine being based on the assumption of the power-law relation between the radius and the derivative of radius with respect to the angular coordinate. In this case, a class of contours in which half of the cycle consists of the element with monotonic variation in the radius and arc of the circle is distinguished. These contours can be described by specifying a single geometric parameter, namely, the exponent. Using the inviscid perfect gas model, direct numerical optimization of the shape of transverse contour is carried out and the possibility of reducing the wave drag as compared to the star-shaped bodies with plane faces is demonstrated.