Lanchester's laws

Lanchester's laws are mathematical formulas 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.[1][2]

In 1915 and 1916 during World War I, M. Osipov[3]: vii–viii  and Frederick Lanchester independently devised a series of differential equations to demonstrate the power relationships between opposing forces.[4] 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,[5] 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.[6]

  1. ^ Lanchester F.W., Mathematics in Warfare in The World of Mathematics, Vol. 4 (1956) Ed. Newman, J.R., Simon and Schuster, 2138–2157; anthologised from Aircraft in Warfare (1916)
  2. ^ Davis, Paul K. (1995). "Lanchester Equations and Scoring Systems". Aggregation, Disaggregation, and the 3:1 Rules in Ground Combat. Rand Corporation. doi:10.7249/MR638.
  3. ^ Osipov, M. (1991) [1915]. "The Influence of the Numerical Strength of Engaged Forces on Their Casualties" Влияние Численности Сражающихся Сторонъ На Ихъ Потери (PDF). Tsarist Russian Journal Military Collection Военный Сборник. Translated by Helmbold, Robert; Rehm, Allan. US Army Concepts Analysis Agency. Archived (PDF) from the original on 4 November 2021. Retrieved 23 January 2022.
  4. ^ Wrigge, Staffan; Fransen, Ame; Wigg, Lars (September 1995). "The Lanchester Theory of Combat and Some Related Subjects" (PDF). FORSVARETS FORSKNINGSANSTALT.
  5. ^ Christian, MAJ Joshua T. (23 May 2019). An Examination of Force Ratios (PDF). Fort Leavenworth, KS: US Army Command and General Staff College.Public Domain This article incorporates public domain material from websites or documents of the United States Army.
  6. ^ David A. Shlapak, and Michael W. Johnson, Reinforcing Deterrence on NATO’s Eastern Flank (Santa Monica, CA: RAND Corporation, 2016)

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