An investigation of deterministic Lanchester-type equations of warfare

M.S.Joseph Kro

Lanchester-Type Models of Warfare, Volume I

The Twentieth Century has been characterized by innumerable attempts to use the Scientific Method as a basis for policy planning in national and international affairs. The emergence of the field of operations research (OR) out of attempts of scientists in the Western Democracies to apply the Scientific Method to military problems during World War II is well known. Since World War II there has been a dramatic growth in both the interest in and use of OR and systems-analysis techniques for such purposes within the U.S. defense establish- ment, especially since the beginning of the so-called McNamara Era of defense planning. A concomitant trend has been an equally dramatic increase in both the number and variety of mathematical models used to support these analytical activities

Modeling of combat operations

Introduction/purpose: The goal of the research in this paper is to present and evaluate the method of modeling operations by aggregating forces by simulating the battle process with Lanchester's equations. This method is the software basis of a certain number of programs used in NATO, in war simulations, and in the planning and analysis of operations. Its value is in understanding the consequences of decisions made with outcomes and results of combat actions. Methods: The case study of the well-known Operation Desert Storm gathered the necessary data on operational parameters and the way forces are used in battles. The obtained data were transformed into operational variables of the combat model using the force aggregation method, whose simulation was carried out using the method of differential Lanchester's equations (quadratic law). Results: By simulating the modeled operation, the parameters of the outcome of the conflict were obtained with numerical indicators of success, consumption of resources, etc. The results were analyzed and a certain correlation with the parameters of the real operation was determined, which enables the validation of the model. Conclusion: The partial validity of the model describing the conflict on a practical historical example from a case study was confirmed. There are objective limitations in the application of modeling of military operations and optimization of the use of forces. The value of this method is the possibility of a reliable strategic assessment of the adversary's military power at the strategic level

Inferencia bayesiana para algunas leyes de Lanchester

Lanchester (1916) introdujo una serie de ecuaciones o leyes determinísticas para modelar los números de bajas en un combate sin refuerzos. Un inconveniente de estos modelos es que no son útiles ni para la inferencia ni para la predicción, ya que el resultado de una batalla viene determinado por los parámetros del sistema y los tamaños iniciales de cada ejército. Se han propuesto varias versiones estocásticas de las ecuaciones de Lanchester. En este artículo, se resumen algunos de estos modelos y se demuestra cómo utilizar la inferencia bayesiana para estimar los parámetros importantes dada la información a priori que proviene de batallas anteriores, simulaciones, etc. y dada una muestra de datos de un combate. Finalmente, se ilustran los métodos empleados con datos reales y simulados

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

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.Lieutenant Commander, United States NavyApproved for public release. Distribution is unlimited

Refighting Pickett’s Charge: mathematical modeling of the Civil War battlefield

Objective. We model Pickett’s Charge at the Battle of Gettysburg to see whether the Confederates could have achieved victory by committing more infantry, executing a better barrage, or facing a weaker defense. Methods. Our mathematical modeling is based on Lanchester equations, calibrated using historical army strengths. We weight the Union artillery and infantry two different ways using two sources of data, and so have four versions of the model. Results. The models estimate that a successful Confederate charge would have required at least 1 to 3 additional brigades. An improved artillery barrage would have reduced these needs by about 1 brigade. A weaker Union defense could have allowed the charge to succeed as executed. Conclusions. The Confederates plausibly had enough troops to take the Union position and alter the battle’s outcome, but likely too few to further exploit such a success

HYBRID THREATS AS AN EXOGENOUS ECONOMIC SHOCK

The aim of this study is to contribute to the theory of exogenous economic shocks and their equivalents in an attempt to explain business cycle fluctuations, which still do not have a clear explanation. To this end the author has developed an econometric model based on a regression analysis. Another objective is to tackle the issue of hybrid threats, which have not yet been subjected to a cross-disciplinary research. These were reviewed in terms of their economic characteristics in order to complement research in the fields of defence and security

Facets of the ecology, behaviour and evolution of ants

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