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.
General
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