Optimization of the shape of a body with respect to two criteria: Radiation heat flux and wave drag

The numerical solution of the two-criteria variational problem of the body contour with minimum radiation heat flux and wave drag is obtained in the class of axisymmetric and plane slender bodies in hypersonic flow. Solutions obtained using the Pareto, ideal point and minimax methods are compared. It is shown that in the class of axisymmetric slender bodies the optimum body gives a decrease in the radiation heat flux as compared with a cone of up to 15% for the Pareto method, up to 13% for the ideal point method, and up to 5% for the minimax method. A solution is also obtained in the subclass of power-law slender bodies and it is shown that the optimum power-law bodies are inferior, as compared with the optimum bodies from the general class of such bodies, in reducing both radiation heating and resistance.