Determination of Optimum Non-Slender Bodies of Revolution having Minimum Drag in Free Molecular Flow

Abstract

The problem of determining the body of revolution having minimum drag has been considered in the free molecular flow region under given integral constraints and in combination with the calculus of variations. It has been shown that for a given surface area or volume, the optimum shape is sharp nosed if diameter is prescribed and it is flat nosed if the length is prescribed. When the volume and thickness are known the optimum shape has cusp at the origin whereas if surface area and diameter are given the optimum body shape is independent of the value of k, a parameter dependent upon the temperature ratio and the speed ratio.