REVISITING ENGEL’S VERIFICATION OF LANCHESTER'S SQUARE LAW USING BATTLE OF IWO JIMA DATA

Abstract

Since Engel’s 1954 verification of Lanchester's square law using Battle of Iwo Jima data, the homogenous Lanchester square law has been widely used as the default to approximate aggregate-level attrition in large modern battles. While this may work in some cases (particularly when forces are concentrated), there has been a death of efforts to assess the applicability of using other equations to fit the time-phased Iwo Jima battle data (for example the linear and log laws). Not all battles conform to a square law exponential attrition curve. Some battles (due to the nature or nuance of the scenario, battlefield, or engagement type) may lend themselves to being fitted better to linear, logarithmic, or several other equations. A better fit may lead to an improved understanding of future scenarios, which can help decision makers assign allocations for budgeting and deployment sizes and locations with better analytical support for approval of those decisions. This analysis revisits and replicates Engel's approach to fitting Lanchester’s square law equation, extends it to other models, and finds/compares best fits. Using the attrition data from the Battle of Iwo Jima, we test the fitness (using R-squared values) of various Lanchester equations. Among many other discoveries, we find that Engel’s model (and many other models) fits the data very well.