Lanchester's laws

Lanchester's laws are mathematical formulae for calculating the 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.

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In 1915 and 1916 during World War I, M. Osipov^{: vii–viii} and Frederick Lanchester independently 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).

As of 2017 modified variations of the Lanchester equations continue to form the basis of analysis in many of the US Army’s combat simulations, and in 2016 a RAND Corporation report examined by these laws the probable outcome in the event of a Russian invasion into the Baltic nations of Estonia, Latvia, and Lithuania.

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