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

An investigation of deterministic Lanchester-type equations of warfare

M.S.Joseph Kro

Discrete Deterministic Modelling of Autonomous Missiles Salvos

The paper deals with mathematical models of sequent salvos battle, of autonomous flight missiles (AFM) organized in the groups of combatants. Tactical integration of AFM system distance-controlled weapon is considered by performances of simultaneous approaches on targets, and continual battle models of guerilla and direct fire, are redesigned to the discrete-continual mixed model, for checking missiles sudden, and further salvos, attack effects. Superiority parameters, as well as losses and strengths of full, or the part of salvo battle, for the missiles groups as technology sub-systems combatants’, is expressed by mathematical and simulation examples. Targets engagements capacities of the missiles battle unit, is conducted through designed scenarios and mathematically derived in the research. Model orientated on answers about employment of rapid reaction defending tactics, by distance missiles attacks.Defence Science Journal, Vol. 64, No. 5, September 2014, pp.471-476, DOI:http://dx.doi.org/10.14429/dsj.64.579

Modeling and Analysis of Resolve and Morale for the `Long War\u27

In The Art of War, Sun Tzu begins by stating: War is a matter of vital importance to the State; the province of life or death; the road to survival or ruin. It is mandatory that it be thoroughly studied. Sun Tzu follow\u27s this opening by stating five fundamental factors a commander must master to be successful in combat. The first of these factors is moral influence which Sun Tzu defines as that which causes the people to be in harmony with their leaders, so they will accompany them in life and death without fear of mortal peril. In the face of the instant communication provided by satellites, 24 hour news media coverage, and other technological advances, this factor is even more relevant today. This research provides an analytic framework, based on the principles of fourth generation operations, capturing the effects of will and resolve of the combatant and population. The strategic level model investigates the long term impacts of asymmetric conflict. These results are primarily measured in the socio-political arena rather than the military battlefield. The model developed in this dissertation remains a model of conflict and combat. However, some of the impacts from the political, economic, and informational instruments of power are represented in the model through the dynamic adaptation of public resolve and combat spirit. To paraphrase Sun Tzu, war is vitally important and must be studied. Therefore, this dissertation puts forth a means to model key aspects of conflict in the `long war\u27

A Methodological Framework for Parametric Combat Analysis

This work presents a taxonomic structure for understanding the tension between certain factors of stability for game-theoretic outcomes such as Nash optimality, Pareto optimality, and balance optimality and then applies such game-theoretic concepts to the advancement of strategic thought on spacepower. This work successfully adapts and applies combat modeling theory to the evaluation of cislunar space conflict. This work provides evidence that the reliability characteristics of small spacecraft share similarities to the reliability characteristics of large spacecraft. Using these novel foundational concepts, this dissertation develops and presents a parametric methodological framework capable of analyzing the efficacy of heterogeneous force compositions in the context of space warfare. This framework is shown to be capable of predicting a stochastic distribution of numerical outcomes associated with various modes of conflict and parameter values. Furthermore, this work demonstrates a general alignment in results between the game-theoretic concepts of the framework and Media Interaction Warfare Theory in terms of evaluating force efficacy, providing strong evidence for the validity of the methodological framework presented in this dissertation

Effects of lethality on naval combat models

In the context of both discrete time salvo models and continuous time Lanchester models we examine the effect on naval combat of lethality: that is, the relative balance between the offensive and defensive attributes of the units involved. We define three distinct levels of lethality and describe the distinguishing features of combat for each level. We discuss the implications of these characteristics for naval decision-makers; in particular, we show that the usefulness of the intuitive concept "more is better" varies greatly depending on the lethality level.Natural Sciences & Engineering Research Council (NSERC) Discovery Gran

Deterministic Mathematical Modelling of Platform Performance Degradation in Cyclic Operation Regimes

This paper considers the modelling of extreme-capability working platforms that are operated in periodic cycles, each cycle having a pre-defined number of operations that affect the working surfaces. A novel hypothesis is introduced about the platform-degrading effects that cause an equivalent decrease in the successful operations after repeated cycles. Deterministic modelling, based on the basic equations of Lanchester and Dinner, is generalized here to include coupling between parameters. The newly developed mathematical model of performance degradation is in good agreement with both experimental measurements and numerical simulations. It is assumed that the new variables and their correlations link the Gaussian distribution and the observed performances of the testing platforms. Relative probability dispersions of affected surfaces are derived, as a new indirect referencing figure of merit, to describe simulations and compare them to experimental test data. The model proves a hypothesis that the degrading effects are a function of the platform capacity, frequency of operations and the number of available cycles. Degradation effects are taken into account through an equivalent decrease of effective operation capacities, reflected on the properties of the affected operating surfaces. The obtained estimations of degradation could be used in the planning of platform capacity as well as in the selection of real affected surfaces in various machining systems and for a wide range of different materials