A “static” solution to a “dynamic” problem in acquisition probability

This paper reports a novel solution to a special case of a classical problem in operations research, “The probability that an acoustic homing torpedo will ‘acquire’ a submarine”. Because of uncertainties in the position of submarine relative to torpedo an exact kinematic solution to the problem is not possible, and only a probabilistic solution may be obtained. The complicated realistic problem is idealized here to a tractable model by a small number of simplifications; later the effect of removing these simplifications one at a time is examined, and it is made plausible that each has only a small influence on the acquisition probability. As an illustration of the application of the concepts developed, an example in which the submarine is assumed to move radially outward from the torpedo –‐ but otherwise incorporating reasonable assumptions about the kinematics of the torpedo and submarine –‐ is completely solved in detail. In this example the uncertain position of the submarine is given by simple frequency distributions; a more complicated case could be solved by numerical methods. The solution of this specialized problem is particularly interesting because of the immediate and unexpected operational research results which may be inferred.