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Lanchester's laws are mathematical formulae for calculating the relative strengths of a predator/prey pair. This article is concerned with 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.〔Lanchester F.W., ''Mathematics in Warfare'' in ''The World of Mathematics,'' Vol. 4 (1956) Ed. Newman, J.R., Simon and Schuster, 2138-2157〕〔(Lanchester Equations and Scoring Systems )〕 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). == Lanchester's Linear Law == For ancient combat, between phalanxes of soldiers with spears, say, one soldier could only ever fight exactly one other soldier at a time. If each soldier kills, and is killed by, exactly one other, then the number of soldiers remaining at the end of the battle is simply the difference between the larger army and the smaller, assuming identical weapons. The linear law also applies to unaimed fire into an enemy-occupied area. The rate of attrition depends on the density of the available targets in the target area as well as the number of weapons shooting. If two forces, occupying the same land area and using the same weapons, shoot randomly into the same target area, they will both suffer the same rate and number of casualties, until the smaller force is eventually eliminated: the greater probability of any one shot hitting the larger force is balanced by the greater number of shots directed at the smaller force. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lanchester's laws」の詳細全文を読む スポンサード リンク
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