Canonical Methods in the Solution of Variable-Coefficient Lanchester-Type Equations of Modern Warfare

James G. Taylor and Gerald G. Brown
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James G. Taylor: Naval Postgraduate School, Monterey, California
Gerald G. Brown: Naval Postgraduate School, Monterey, California

Operations Research, 1976, vol. 24, issue 1, 44-69

Abstract: This paper develops a mathematical theory for solving deterministic, Lanchester-type, “square-law” attrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It gives a general form for expressing the solution of such variable-coefficient combat attrition equations in terms of Lanchester functions, which are introduced here and can be readily tabulated. Different Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. We give results for two such forms: (1) effectiveness of each side's fire proportional to a power of time, and (2) effectiveness of each side's fire linear with time but with a nonconstant ratio of attrition-rate coefficients. Previous results in the literature for a nonconstant ratio of these attrition-rate coefficients only took a convenient form under rather restrictive conditions.

Date: 1976
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