Force-on-Force Attrition Modelling

viii, 160 pages. Footnotes. Illustrations. References. Annotated Short Bibliography of Lanchester-type Combat Model. Comprehensive Bibliography of the Lanchester Theory of Combat. Copyright date in 1981, Title page has date of 1980. Cover has some wear and soiling. Lanchester's laws are mathematical formulae for calculating the relative strengths of a predator-prey pair, originally devised to analyse relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time, with the function depending only on A and B. In 1916, during World War I, Frederick Lanchester devised a series of differential equations to demonstrate the power relationships between opposing forces. Among these are what is known as Lanchester's Linear Law (for ancient combat) and Lanchester's Square Law (for modern combat with long-range weapons such as firearms). Idealized simulation of two forces damaging each other neglecting all other circumstances than the 1) Size of army 2) Rate of damaging. With firearms engaging each other directly with aimed shooting from a distance, they can attack multiple targets and can receive fire from multiple directions. The rate of attrition now depends only on the number of weapons shooting. Lanchester determined that the power of such a force is proportional not to the number of units it has, but to the square of the number of units. This is known as Lanchester's square law. More precisely, the law specifies the casualties a shooting force will inflict over a period of time, relative to those inflicted by the opposing force. In its basic form, the law is only useful to predict outcomes and casualties by attrition. It does not apply to whole armies, where tactical deployment means not all troops will be engaged all the time. It only works where each unit (soldier, ship, etc.) can kill only one equivalent unit at a time. For this reason, the law does not apply to machine guns, artillery, or nuclear weapons. The law requires an assumption that casualties increase over time: it does not work in situations in which opposing troops kill each other instantly, either by shooting simultaneously or by one side getting off the first shot and inflicting multiple casualties. Note that Lanchester's square law does not apply to technological force, only numerical force; so it requires an N-squared-fold increase in quality to compensate for an N-fold increase in quantity. Lanchester's equations are related to the more recent salvo combat model equations, with two main differences. First, Lanchester's original equations form a continuous time model, whereas the basic salvo equations form a discrete time model. In a gun battle, bullets or shells are typically fired in large quantities. Each round has a relatively low chance of hitting its target, and does a relatively small amount of damage. Therefore, Lanchester's equations model gunfire as a stream of firepower that continuously weakens the enemy force over time. By comparison, cruise missiles typically are fired in relatively small quantities. Each one has a high probability of hitting its target, and carries a relatively powerful warhead. Therefore, it makes more sense to model them as a discrete pulse (or salvo) of firepower in a discrete time model. Second, Lanchester's equations include only offensive firepower, whereas the salvo equations also include defensive firepower. Given their small size and large number, it is not practical to intercept bullets and shells in a gun battle. By comparison, cruise missiles can be intercepted (shot down) by surface-to-air missiles and anti-aircraft guns. So it is important to include such active defenses in a missile combat model. Lanchester's laws have been used to model historical battles for research purposes. Examples include Pickett's Charge of Confederate infantry against Union infantry during the 1863 Battle of Gettysburg, and the 19.…