Expected Target Damage for Pattern Firing

Abstract

This paper evaluates analytically the damage function for a rectangular target from a firing pattern of n rounds by extending to a pattern distribution the method of Grubbs [ Opns. Res. 16, 1021–1026 (1968)] for a salvo of rounds. The delivery function for the pattern center and the dispersion of each round are taken to be noncircular normal, and the damage function law for each round is defined to be a noncircular exponential square falloff. The results are computationally somewhat more complex than for a salvo, since one must keep track of the coordinates of each round in computing the average chance that a round of the pattern (i.e., a pattern element) will damage a given target element. A series expansion for the fractional target damage by a pattern is obtained.