This work discusses the problem of reducing the drag due to lift at high-speed flight conditions. To accelerate the optimization algorithm convergence and to study characteristic features of the optimal delta wing the procedure of the geometry parameters system selection is developed within the framework of the linear theory. It is established that the hypergeometrical directrix of the wing describes near to optimum aerodynamic shape and corresponds to a superelliptical distribution of the local angle of attack over the wing span. Differences between the results of the theoretical studying and the direct numerical optimization based on the Euler's equations are analyzed. Configuration of the high-speed flying vehicle, designed under HEXAFLY-INT project, with hypergeometrically profiled windward surface is proposed to enhance aerodynamic performance. Flow fields and aerodynamic loads numerical studying is carried out in a wide range of the Mach number.
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