Some simple victory-prediction conditions for lanchester-type combat between two homogeneous forces with supporting fires

This paper develops new “simple” victory-prediction conditions for a linear Lanchester-type model of combat between two homogeneous forces with superimposed effects of supporting fires not subject to attrition. These simple victory-prediction conditions involve only the initial conditions of battle and certain assumptions about the nature of temporal variations in the attrition-rate coefficients. They are developed for a fixed-force-ratio-breakpoint battle by studying the force-ratio equation for the linear combat model. An important consideration is shown to be required for developing such simple victory-prediction conditions: victory is not guaranteed in a fixed-force-ratio-breakpoint battle even when the force ratio is always changing to the advantage of one of the combatants. One must specify additional conditions to hold for the cumulative fire effectivenesses of the primary weapon systems in order to develop correct victory-prediction conditions. The inadequacy of previous victory-prediction results is explained by examining (for the linear combat model without the supporting fires) new “exact” victory-prediction conditions, which show that even the range of possible battle outcomes may be significantly different for variable-coefficient and constant-coefficients models.