How Important are Superior Numbers?: A Reappraisal of Lanchester's Square Law

David L. I. Kirkpatrick

doi:10.1017/9781108973458

Series: Elements in Defence Economics

How Important are Superior Numbers?

A Reappraisal of Lanchester's Square Law

Published online by Cambridge University Press: 06 February 2021

David L. I. Kirkpatrick

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David L. I. Kirkpatrick: Affiliation:
University College London

Summary

A century ago Frederick Lanchester formulated a mathematical model of combat which suggested that the combat power of a military force was proportional to the product of the individual effectiveness of the units in the force and the square of the number of units deployed. This model reinforced a long-established faith in the importance of superior numbers. However, successive historical studies failed to identify any clear relationship between the numbers and losses in opposing forces. This Element analyses American Civil War battles, and shows that the ratio of losses incurred was inversely proportional to the ratio of numbers effectively engaged. This result demonstrates that the numbers of fighting units in a military force are less important than the ability of those units to get into action and inflict losses on the enemy. This result demonstrates the limitations of the Square Law, and should prevent it from being applied indiscriminately.

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American Civil War superior numbers Lanchester’s Square Law quality versus quantity defence policy

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Type: Element
Information: Series: Elements in Defence Economics

DOI: https://doi.org/10.1017/9781108973458 [Opens in a new window]

Online ISBN: 9781108973458

Publisher: Cambridge University Press

Print publication: 04 March 2021

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