New formulas for predicting the size distribution of warhead fragments

Abstract

The well-known Mott formula for predicting the size distribution of fragments from an exploding bomb or warhead has been in use for many years. The formula has the advantage of simplicity and seems to represent faithfully, in most cases, the majority of the distribution of fragment weights. However, it is generally recognized that it is quite poor in matching the smallest fragment sizes and can, for some materials, misrepresent the larger weights also. If the only concern is fitting the “center” of the distribution, there is no need for further investigation. When one is also interested in extremes, some generalization of the Mott law is needed. It is the purpose of this paper to present a reasonable systematic statistical theory for doing this. The approach used is a bit different from that of Mott, but in the same spirit. Computer results for two different types of test cylinders are presented.