Annihilation Prediction for Lanchester-Type Models of Modern Warfare

This paper introduces important new functions for analytic solution of Lanchester-type equations of modem warfare for combat between two homogeneous forces modeled by power attrition-rate coefficients with “no offset.” Tabulations of these Lanchester-Clifford-Schläfli (or LCS) functions allow one to study this particular variable-coefficient model almost as easily and thoroughly as Lanchester's classic constant-coefficient one. LCS functions allow one to obtain important information (in particular, force-annihilation prediction) without having to spend the time and effort of computing force-level trajectories. The choice of these particular functions is based on theoretical considerations that apply in general to Lanchester-type equations of modern warfare and provide guidance for developing other canonical functions. Moreover, our new LCS functions also provide valuable information about related variable-coefficient models. Also, we introduce an important transformation of the battle's time scale that not only simplifies the force-level equations, but also shows that relative fire effectiveness and intensity of combat are the only two weapon-system parameters determining the course of such variable-coefficient Lanchester-type combat.