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

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

Potential uses of Numerical Simulation for the Modelling of Civil Conflict

This paper explores ways in which civil conflict can be simulated using numerical methods. A general two-party model of conflict is developed by extending an approach proposed by [Christia, F., (2012), Alliance Formation in Civil Wars, Cambridge University Press, New York], which is based on a metric of the 'relative power' that exists between the state and a rebel group. Various definitions of relative power are considered and one of these is chosen to illustrate different types of two-sided armed conflict, namely direct-fire, guerrilla and asymmetric warfare. The additional suggestion of Christia that random or stochastic events can lead to unexpected conflict outcomes is also further extended in this paper. The inclusion in the model of terms describing concurrent rebel recruitment of civilians and state deployment of troops are then described. Examples are presented for various hypothetical cases. It is demonstrated that numerical simulation techniques have great potential for modelling civil war. The Christia approach is shown to provide an excellent basis from which numerical models of civil conflict can be built and from which the progress of a conflict can usefully be visualised graphically

Targeting, deployment and loss-tolerance in Lanchester engagements

Existing Lanchester combat models focus on two force parameters: numbers (force size) and per-capita effectiveness (attrition rate). While these two parameters are central in projecting a battle’s outcome, there are other important factors that affect the battlefield: (1) targeting capability, the capacity to identify live enemy units and not dissipate fire on non-targets; (2) tactical restrictions preventing full deployment of forces; and (3) morale and tolerance of losses, the capacity to endure casualties. In the spirit of Lanchester theory, we derive, for the first time, force-parity equations for various combinations of these effects, and obtain general implications and trade-offs. We show that more units and better weapons (higher attrition rate) are preferred over improved targeting capability and relaxed deployment restrictions unless these are poor. However, when facing aimed fire and unable to deploy more than half one’s force it is better to be able to deploy more existing units than to have either additional reserve units or the same increase in attrition effectiveness. Likewise more relaxed deployment constraints are preferred over enhanced loss-tolerance when initial reserves are greater than the force level at which withdrawal occurs

Modeling insurgency attrition and population influence in irregular warfare

We develop a model that is a combination of Lanchester and Deitchman attrition models and population epidemic models. Based on different attrition, recruitment, and transition rules we study the relationships between dynamic population flow and insurgency success or failure. The goal of our work is to provide an analytical framework for these situations and to analyze the effect of different initial conditions and interactions on the success or failure of an insurgency. The models developed herein are descriptive, not predictive, and are designed to give decision makers an insight into a complex insurgency process.http://archive.org/details/modelinginsurgen109453418US Army (USA) author.Approved for public release; distribution is unlimited

The salvo combat model with area fire

This paper analyzes versions of the salvo model of missile combat where area fire is used by one or both sides in a battle. While these models share some properties with the area fire Lanchester model and the aimed fire salvo model, they also display some interesting differences, especially over the course of several salvos. Whereas the relative size of each force is important with aimed fire, with area fire it is the absolute size that matters. Similarly, while aimed fire exhibits square law behavior, area fire shows approximately linear behavior. When one side uses area and the other uses aimed fire, the model displays a mix of square and linear law behavior

Nation-Building Modeling and Resource Allocation Via Dynamic Programming

Dynamic programming is used in many military and industrial applications to solve sequential decision making problems. This research proposes the development of a model and approach to address the application of dynamic programming in nation-building modeling. Through the creation of component indices to capture the state of operational variables: Political, Military, Economic, Social, Infrastructure, and Information (PMESII), a functional form of a system of differential equations is developed to account for the interactions between the state indices and instruments of national power: Diplomatic, Informational, Military, and Economic (DIME). Solving this problem with dynamic programming provides an improved sequence which describes the application of DIME in a manner that minimizes an objective (i.e. cost, time) and allows the model to account for external factors such as an insurgent reaction to US policy. An application of the model is derived for Iraq to demonstrate the utility of the model and explore various aspects of the solution space. This modeling approach offers a potential significant capability when analyzing and planning for nation-building operations

Small arms combat modeling: a superior way to evaluate marksmanship data

Purpose – Marksmanship data is a staple of military and law enforcement evaluations. This ubiquitous nature creates a critical need to use all relevant information and to convey outcomes in a meaningful way for the end users. The purpose of this study is to demonstrate how simple simulation techniques can improve interpretations of marksmanship data. Design/methodology/approach – This study uses three simulations to demonstrate the advantages of small arms combat modeling, including (1) the benefits of incorporating a Markov Chain into Monte Carlo shooting simulations; (2) how small arms combat modeling is superior to point-based evaluations; and (3) why continuous-time chains better capture performance than discrete-time chains. Findings – The proposed method reduces ambiguity in low-accuracy scenarios while also incorporating a more holistic view of performance as outcomes simultaneously incorporate speed and accuracy rather than holding one constant. Practical implications – This process determines the probability of winning an engagement against a given opponent while circumventing arbitrary discussions of speed and accuracy trade-offs. Someone wins 70% of combat engagements against a given opponent rather than scoring 15 more points. Moreover, risk exposure is quantified by determining the likely casualties suffered to achieve victory. This combination makes the practical consequences of human performance differences tangible to the end users. Taken together, this approach advances the operations research analyses of squad-level combat engagements. Originality/value – For more than a century, marksmanship evaluations have used point-based systems to classify shooters. However, these scoring methods were developed for competitive integrity rather than lethality as points do not adequately capture combat capabilities. The proposed method thus represents a major shift in the marksmanship scoring paradigm