A Stochastic Model for Predicting the Velocity Distribution of Warhead Fragments

It has been the practice of those who study the velocity of fragments from a warhead to average the velocity of the fragment over its path rather than to examine in greater detail the underlying stochastic process. In this paper we present a more careful analysis of the pertinent statistical process by taking into account the correlations that exist along the trajectory of the fragment. One assumes that the fragments generally tumble uniformly and that drag coefficient depends only on presented area. This seems to be a good approximation in the supersonic regime (from Mach 3 to Mach 6, for example). A brief discussion of the case when drag, lift, and gravity effects are all assumed to be present is given. Also, we present a new family of “multivariate uniform distributions” geared to the physics of the problem.