Numerical determination of the parity-condition parameter for lanchester-type equations of modern warfare

Abstract

This paper presents a simple numerical procedure for determining the parity-condition parameter for deterministic Lanchester-type combat between two homogeneous forces. Deterministic differentialequation combat models are commonly used in parametric studies for computational reasons, since they give essentially the same results for the mean course of combat as do corresponding stochastic attrition models. The combat studied in this paper is modelled by Lanchester-type equations of modern warfare with time-dependent attrition-rate coefficients. Previous research has generalized Lanchester's classic “square law” to such variable-coefficient combat. It has shown that the prediction of battle outcome (in particular, force annihilation) without having to spend the time and effort of computing force-level trajectories depends on a single parameter, the so-called parity-condition parameter, which is “the enemy force equivalent of a friendly force of unit strength” and depends on only the attrition-rate coefficients. Unfortunately, previous research did not show generally how to determine this parameter. We present general theoretical considerations for its numerical noniterative determination. This general theory is applied to an important class of attrition-rate coefficients (offset power-rate coefficients). Our results allow one to study such variable-coefficient combat models almost as easily and thoroughly as Lanchester's classic constant-coefficient model.