| Description |
A system of differential equations that was developed by F. W. Lanchester during the First World War has formed the foundation for much of the subsequent work that has been done in the area of mathematical combat modeling. An exposition of some of Lanchester's work, which has become difficult to find in its original form, is provided in this paper. This treatment includes such topics as the "N-square law" (together with the system of linear differential equations from which it was derived), the principle of concentration, and combat conditions at long range. In addition, various illustrations of Lanchester's laws are provided, as is an examination of several possible extensions of the basic equations. These variations relate to mixed conventional/guerrilla warfare, troop reinforcement rates, the division of a force into several smaller groups, and the specialization of tactical and strategic units. Finally, the paper discusses certain limitations of the models, such as their deterministic nature and their failure to take into account relative movement between forces, and mentions alternative approaches to combat modeling that deal specifically with these problems. Much of the paper should be accessible to the general reader, although a knowledge of calculus and some familiarity with differential equations are required for most of the math. The undergraduate math student, in particular, should find this paper to be a fairly readable introduction to mathematical modeling using differential equations. |
