Dependence of the parity-condition parameter on the combat-intensity parameter for Lanchester-type equations of modern warfare

Abstract

This paper studies the parametric dependence of battle outcome (in particular, force annihilation) for combat between two homogeneous forces modelled by Lanchester-type equations of modern warfare with time-dependent attrition-rate coefficients. Force-annihilation prediction has been shown to depend on a so-called parity-condition parameter, which depends on only the attrition-rate coefficients. New important results are given on how the parity-condition parameter depends on the intensity of combat and the relative fire effectiveness of the combatants. Previous analytical results of the author are shown to apply to a much wider class of attrition-rate coefficients. These new results allow a wide class of Lanchester-type equations of modern warfare with temporal variations in fire effectiveness to be studied almost as easily as Lanchester's classic constant-coefficient model.