Lanchester's laws

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Idealized simulation of two forces damaging each other neglecting all other circumstances than the 1) Size of army 2) Rate of damaging. The picture illustrates the principle of Lanchester's square law.

Lanchester's Laws are a set of mathematical formulas used to model the outcome of military conflicts, particularly focusing on the relative strengths of opposing forces. These laws were formulated by British engineer Frederick W. Lanchester in the early 20th century. Lanchester's Laws have been applied to various fields beyond military strategy, including business competition and biology, due to their insights into the dynamics of competing groups.

Lanchester's Linear Law

The first of Lanchester's Laws is known as the Linear Law, applicable to ancient and medieval warfare where combatants engage in one-to-one battles, such as in a phalanx or line formation. The Linear Law can be expressed mathematically as:

\[ N = R \times T \]

where \(N\) is the number of combatants a force can bring down, \(R\) is the rate at which they can inflict casualties, and \(T\) is the time engaged in combat. This law implies that the combat power of a force in such scenarios is directly proportional to the number of its combatants.

Lanchester's Square Law

The second, more widely known of Lanchester's Laws, is the Square Law, which applies to modern warfare where long-range weapons allow many combatants to target a single opponent simultaneously. The Square Law is represented by the formula:

\[ N^2 = R \times T \times F^2 \]

where \(N\) is the number of combatants a force can bring down, \(R\) is the rate at which they can inflict casualties, \(T\) is the time engaged in combat, and \(F\) is the force's firepower. According to the Square Law, the combat effectiveness of a force grows with the square of the number of its units, making numerical superiority exponentially more significant.

Applications and Limitations

While Lanchester's Laws provide a theoretical framework for understanding the dynamics of conflict, their application in real-world scenarios is limited by numerous factors. These include the quality of troops, terrain, morale, technology, and the element of surprise. Moreover, modern asymmetric warfare, where conventional military forces face non-traditional combatants, poses challenges to the direct application of Lanchester's Laws.

See Also

• Military strategy
• Frederick W. Lanchester
• Warfare