Historical support for a mixed law Lanchestrian Attrition Model: Helmbold's ratio.

摘要

This is the first in a series of reports on the breakthrough research in historical validation of attrition in conflict. Significant defense policy decisions, including weapons acquisition and arms reduction, are based in part on models of conflict. Most of these models are driven their attrition algorithms, usually forms of the Lanchester square and linear laws. None of these algorithms have been validated. Helmbold defined the ''activity ratio'' to be the ratio of the Lanchester coefficients in the pair of differential equations of the Lanchester square law of attrition. He derived an equivalence between this ratio and a ratio containing the initial and ending force sizes, herein called the Helmbold ratio, and demonstrated a relationship between the Helmbold ratio and the initial force ratio in a large number of historical battles. This paper reexamines the implications of this relationship and concludes that its existence, rather than being supportive of the Lanchester square law, is supportive of a mixed law lying between the Lanchester linear law and a Lanchester logarithmic law. It is shown that the Helmbold relationship can discriminate between several attrition formulations; however, while this is a necessary condition, it is not sufficient to conclude that data fitting the relationship were caused by a given attrition formulation. The conclusion is that the data are not fine enough to determine the differential form of the attrition equations but do lead to a statistical statement about the outcomes of battles. 8 refs., 51 figs., 8 tabs.