On the Optimal Shapes of Waveriders Constructed on Plane Shocks

Abstract

Formulations of variational problems on maximum lift-drag ratio lifting shapes are considered for different sets of isoperimetric conditions. The problem with a differential constraint setting a lower limit on the local slope of the leading edge of the waverider and simulating either the maximum heat flux to the leading edge or the contribution of the force acting on the leading edge to a particular component of the aerodynamic force is considered. Solutions of the problem of the optimal shape of a waverider constructed on plane shocks are derived for given lift coefficient and specific volume, both with and without constraints on the waverider dimensions.