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Mathematical Research in Destroyer-Submarine Encounters

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Final rept. 1970-1971,

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The report describes the results of mathematical research into destroyer-submarine encounters. The work concentrated principally on a submarines approach and penetration into a destroyer screen. In our report, a statistical model is developed, the utility of such a model for analyzing sea exercises demonstrated, and the relative success of penetration evaluated for different patrol patterns, speeds, barrier geometries and so forth. The approach and penetration model uses an instantaneous sonar detection rate or db. -min. model. Its advantages over the so-called cookie-cutter detection model are demonstrated. The results of an investigation comparing the db.-min. model with another detection model are also discussed. Procedures for fitting the instantaneous detection rate model to observed exercise data are provided. Positioning models were also developed and are described. As a submarine approaches a barrier it is faced with a choice between delaying penetration to possibly gain a more favorable position or initiating penetration to reduce exposure and risk of detection. Where the submarine receives information about destroyer locations, this report models the situation as a stopping rule problem. Where it does not, the situation is modeled with dynamic programming. Finally, results are obtained about the distribution of a transit point into a barrier under specific assumptions about the destroyers patrol pattern and the submarines choice of a transit point. It is shown that the distribution is triangular or approximately triangular in each gap between the destroyers of the screen.

Subject Categories:

  • Operations Research
  • Undersea and Antisubmarine Warfare

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