Lanchester's equations and the structure of the operational campaign: Within-campaign effects

This article considers the application of Lanchester's attrition equations to operational campaigns and battles. Lanchester theory has had an influence, both on the way that attrition is represented in aggregated battle models, and on beliefs about the likely effects of the concentration of force. However, the Lanchester formulation effectively ignores the structure that may be imposed on the battle by the command process. This article considers the manner in which this structure may affect the workings of Lanchester theory. After briefly outlining the main features of Lanchester theory and outlining the scope of this investigation, the paper examines possible motives for fitting Lanchester-derived formulae to historical battle data. It suggests that the main motive is to establish the strength and form of any statistical relationship between the sizes of the opposing forces on the one hand, and the likely balance of attrition on the other. It then discusses some structural factors that may affect the workings of Lanchester theory. After some numerical and qualitative analysis of the Iwo Jima, Inchon-Seoul and Ardennes campaigns, it reviews the results in the light of the factors just alluded to. Based on this evidence it suggests that Lanchester theory is unlikely to provide a good account of the balance of attrition and its likely time profile in any but the simplest of operational campaigns. If accurate description is the aim then the analyst will have to consider: the overall objectives of the commanders; the likely orchestration demands of the campaign; the opportunities for the concentration of force (and the non-terrain factors which may facilitate such concentration); the dynamic assignment of missions and the likely adaptive reactions; loss mechanisms other than those covered by conventional attrition; and, above all, the likely effectiveness of the forces involved.