Attrition equations have military use and are also used in biological and economic modelling. We model the aggregation of attrition in a battle to explain the strong support in historical data for the log law, which conventionally is thought to apply mainly to losses through accident or illness. Support for the log law has been found in many studies of battle data and this has yet to be explained. Several historical studies found support for a mixture of attrition laws, suggesting that different laws could apply to different parts of the battle. We hypothesise that the log law could be supported through aggregation effects when other laws apply on a micro scale. We assume that all laws work at skirmish level and show that aggregation effects will only support the log law if the individual skirmishes being aggregated are themselves modelled by the log law. We argue that the extreme support for the log law in the Kursk dataset is due to an overwhelming support for that law at the level of individual skirmishes, and that the conventional use of square and linear law for skirmishes is incorrect. These results suggest that theoretical changes to attrition equations should be based on studies of small unit attrition as aggregation effects do not cause cross over from square or linear laws to log law. References J. F. Dunnigan, How to make war, Fourth edition, Quill, 2003. R. D. Fricker, Attrition models of the Ardennes campaign, Naval Research Logistics, 45, 1998, 1--22. R. Helmbold, Operations Research. , 1964. W. J. Bauman. Kursk operation simulation and validation exercise---phase II. US Army Concepts Analysis Agency, 1998. T. W. Lucas and J. A. Dinges, The effect of battle circumstances on fitting Lanchester Equations to the Battle of Kursk, Military Operations Research, 492, 2003, 147--180. doi:10.1017/S0022112003005512 T. W. Lucas and T. Turkes, Fitting Lanchester equations to the Battles of Kursk and Ardennes, Navel Research Logistics, 51, 2004, 95--116. doi:10.1002/nav.10101 M. Osipov. The influence of the numerical strength of engaged forces in their casualties. Voennyi Sbornik, 1915, no. 6 (June) 59--74, no. 7 (July) 25--26, no. 8 (Aug)31--40, no. 9 (Sep) 25--37, no. 10 (Oct) 93--96. Translated by R. L. Helmbold and A. S. Rehm. Naval Research Logistics, 42, 1995,435--490. R. H. Peterson, On the `logarithmic law' of attrition and its application to tank combat, Operations Research, 15, 1967, 557--558. A. H. Pincombe, B. M. Pincombe and C. E. M. Pearce, Putting the art before the force, EMAC2009, 2009. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/2584 A. H. Pincombe and B. M. Pincombe, Markov modelling on the effectiveness of sanctions: A case study of the Falklands War, ANZIAM Journal, 48, 2007, C527--C541. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/80 A. H. Pincombe and B. M. Pincombe, Tractable approximations to multistage decisions in air defence scenarios, ANZIAM Journal, 49, 2008, C273--C288. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/349 L. R. Speight. Lanchester's equations and the structure of the operational campaign: between campaign effects. Military Operations Research, 7, 2002, 15--43. S. Wrigge, A. Fransen and L. Wigg. The Lanchester theory of combat and some related subjects: a bibliography 1900--1993. Rapport-D-95-00153-1.1,1-SE. National Defence Research Establishment, Department of Defence Analysis, 1995.
@article{2585,
title = {A simple battle model with explanatory power.},
journal = {ANZIAM Journal},
volume = {51},
year = {2010},
doi = {10.21914/anziamj.v51i0.2585},
language = {EN},
url = {http://dml.mathdoc.fr/item/2585}
}
Pincombe, Adrian Hall; Pincombe, Brandon; Pearce, Charles. A simple battle model with explanatory power.. ANZIAM Journal, Tome 51 (2010) . doi : 10.21914/anziamj.v51i0.2585. http://gdmltest.u-ga.fr/item/2585/