“simple‐approximate” battle‐outcome‐prediction conditions for variable‐coefficient lanchester‐type equations of modern warfare

This article considers combat between two homogeneous forces modeled by variable‐ coefficient Lanchester‐type equations of modern warfare and develops new “simple‐approximate” battle‐outcome‐prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed‐force‐level‐breakpoint battles and fixed‐force‐ratio‐breakpoint battles). These battle‐outcome‐prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force‐level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition‐rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable‐coefficient Lanchester‐type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.