ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
In Ballistic Research Laboratories Memorandum Report No. 530, Lotto Method of Computing Kill Probability of Large Warheads, F. G. King describes a random sampling method for determining kill probabilities of a large warhead against an airplane. To obtain the results the method requires a physical model, hand drawing of random numbers, and the use of kill probability curves for the vulnerable components of the airplane. In this report a mathematical model for the purpose of solving the problem on a high-speed digital computing machine is presented. This model is based on J. von Neumanns suggestion that the airplane be replaced by several ellipsoids resembling the fuselage, wings, and engines. The necessary formulas for computation are derived from the basic geometric model. The kill probabilities are determined by three-dimensional integrals which are evaluated either by random sampling methods or by straightforward numerical quadratures. These methods are compared from the viewpoints of accuracy, speed, and machine storage requirements. Limited comparison of the results and some remarks about applicability of more general problems are also made. The method of generation of the pseudo-random numbers used in the random sampling procedures is also described in the appendix.