Optimum Nose Shapes for Missiles in the Superaerodynamic Region

Abstract

SUMMARY The mechanics of the kinetic theory of gases is employed to describe the drag force on the nose of a missile moving in the superaerodynamic region of the atmosphere. Three separate cases are considered—ideal specular reflection, specular-type reflection from a slightly rough surface, and surface absorption followed by random emission of the striking molecules. The calculus of varia­ tions is employed to obtain the differential equation of the nose shape which minimizes the drag force for each of the three cases. The resulting differential equations are then solved by a numerical procedure. The drag coefficients for the optimum nose shapes are likewise determined and these are compared with the drag co­ efficients given by other nose shapes. It is further shown that the drag coefficients arising when specular-t3^pe reflections occur are significantly dependent on the nose shape. When surface absorption followed by random emission occurs, the drag co­ efficient is not strongly dependent on either the missile nose shape or the fineness ratio of the nose.