Analytical Solution to the Wave-Drag Minimization Problem for an Axisymmetric Fore-Body Using Local Linearization

Abstract

The problem of constructing an axisymmetric forebody with minimal wave drag with given constraints on volume and dimensions has been solved within the framework of the local linearization of the relationship between the geometric parameters and the gas-dynamic functions. The optimal fore-body has been determined by varying the shape of the cone with equivalent elongation, for which the approximation for the objective function (wave drag related with volume) has been determined on the basis of the known exact values of the flow parameters. Characteristic features of the optimal shape are bluntness of the nose across the front face and a smooth conjugation with closing cylinder for bodies with sufficiently large volume, the latter exceeding the value depending on the elongation and the Mach number. Comparison with the results of direct numerical optimization in the framework of Euler’s model has shown that the proposed analytical solution provides a near-minimum wave drag.