Modelling the mobile land battle: Lanchester's equations, mini-battle formation and the acquisition of targets

Since its formulation more than 70 years ago, Lanchester attrition theory has had a pervasive influence in military OR. It has helped to fashion beliefs concerning the likely effects of the concentration of force, and variants of the theory's mathematical equations are incorporated in many battle models. This study focuses on two features of the tactical battle which may impact on the validity of Lanchester theory: the acquisition of targets, and the tendency of mobile engagements to be fragmented into a network of mini-battles. An appendix sets out a scheme for modelling these two phenomena, and incorporates them in a simulation of a mobile engagement. In the paper proper this simulation is used to estimate the way that casualties may vary as a function of starting odds, detectability of targets and weapon lethality. Conclusions are then drawn as to the bounds which should be placed on the validity of Lanchester theory, and on the form of mathematical equation likely to be of most practical utility.