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Applications of Historical Analyses in Combat Modelling.

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Abstract

While Lanchester’s equations are commonly used as the basis for force-on-force combat models, it is important to remember that Lanchester’s Equations are not a model of combat, only a model for combat attrition. There have been numerous attempts to compare historical combat data with the behaviour expected from Lanchester's Equations. The present work extends this comparison between historical battle data with behaviour expected from a battle where attrition is described by Lanchester’s Equations. It examines how analyses of historical battles can contribute to the development of models of combat and hence our understanding of combat in addition to the processes used in the creation of databases of historical battle results. The historical data is compared against the expectations of both the deterministic and stochastic forms of Lanchester’s Square Law.

Executive Summary

Lanchester’s equations are commonly used as the basis for force-on-force combat models, even if only as a metamodel for a more complex combat model. It is important to remember that Lanchester’s Equations are not a model of combat, only a model for combat attrition. The equations alone, therefore, cannot be expected to capture other effects such as the movement of engaged forces. There have been numerous attempts to compare historical combat data with the behaviour expected from combat models. To validate differential models of attrition, force and casualty numbers for both sides intermediate to the starting and finishing values are required. That level of detail is rarely available and often does not exist. An alternate approach using only the initial and final values of engaged force’s strength has been tried previously. However, Lanchester’s Equations describe the behaviour of a single system in time while the historical databases contain information about an ensemble of battles, each potentially with different values of attrition rate coefficients. The issue of why the results from such an ensemble follow the behaviour expected from Lanchester’s Equations has never been adequately explored or explained.; The present work extends this comparison between historical battle data with behaviour expected from a battle where attrition is described by Lanchester’s Equations. It examines how analyses of historical battles can contribute to the development of models of combat and hence our understanding of combat in addition to consideration of the processes that are used in the creation of databases of historical battle results. The implications of those processes on the limitations of this form of analysis, the constraints they impose and the resulting inherent biases are discussed, as well as methods that can be used to quantify and mitigate their effects.; The historical data is compared against the expectations of both the deterministic and stochastic forms of Lanchester’s Square Law. However, it should be noted that examination of Lanchester’s stochastic differential equation was not intended to be comprehensive or rigorous. Both have been covered extensively elsewhere, including by the author, and the present work contains numerous references to more authoritative works on these subjects for the interested reader.; Finally, evidence for considering battle as a particular type of complex adaptive system, one that involves co-evolution and scale free behaviours, is examined. It is proposed that this may be responsible for the unexpected observation that the behaviour of several parameters used to characterise combat is the same for both an ensemble of different battles and for the evolution of a single battle.

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