Approximate Circular and Noncircular Offset Probabilities of Hitting

For equal or unequal delivery errors and an offset point of aim, the chance that the burst point of a warhead occurs within a given distance of a selected point of the target is approximated by reference to weighted noncentral chi-square distributions. Offset circular and noncircular probabilities of hitting for the two and three dimensional cases may thus be approximated with a single, straight-forward and rather simple technique by the use of an approximate central chi-square distribution with fractional number of degrees of freedom or a transformation to approximate normality. Computations of probabilities of hitting are illustrated by examples. The approximations recommended appear to be of sufficient accuracy for many weapon systems evaluation problems. We do not claim originality for the various parts of theory involved, but rather our purpose is to provide the weapon systems analyst with a reasonable and useful analytical procedure.