TDI Friday Read: The Lanchester Equations

Frederick W. Lanchester (1868-1946), British engineer and author of the Lanchester combat attrition equations. []

Today’s edition of TDI Friday Read addresses the Lanchester equations and their use in U.S. combat models and simulations. In 1916, British engineer Frederick W. Lanchester published a set of calculations he had derived for determining the results of attrition in combat. Lanchester intended them to be applied as an abstract conceptualization of aerial combat, stating that he did not believe they were applicable to ground combat.

Due to their elegant simplicity, U.S. military operations researchers nevertheless began incorporating the Lanchester equations into their land warfare computer combat models and simulations in the 1950s and 60s. The equations are the basis for many models and simulations used throughout the U.S. defense community today.

The problem with using Lanchester’s equations is that, despite numerous efforts, no one has been able to demonstrate that they accurately represent real-world combat.

Lanchester equations have been weighed….


Trevor Dupuy was critical of combat models based on the Lanchester equations because they cannot account for the role behavioral and moral (i.e. human) factors play in combat.

Human Factors In Warfare: Interaction Of Variable Factors

He was also critical of models and simulations that had not been tested to see whether they could reliably represent real-world combat experience. In the modeling and simulation community, this sort of testing is known as validation.

Military History and Validation of Combat Models

The use of unvalidated concepts, like the Lanchester equations, and unvalidated combat models and simulations persists. Critics have dubbed this the “base of sand” problem, and it continues to affect not only models and simulations, but all abstract theories of combat, including those represented in military doctrine.

Wargaming Multi-Domain Battle: The Base Of Sand Problem

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  1. Pingback: Beyond Lanchester | Mystics & Statistics

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