Frederick Lanchester was born in London in 1868. He did not distinguish himself at school, despite the gift of a private education. He more than made up for this in later life, developing Britain’s first four-wheeled motorcar, several innovations in internal combustion engines, an epicyclic gearbox, cantilever suspension, worm-drive transmission, disc brakes, wire wheels, pressure-fed lubrication, and even early ideas toward power steering and four-wheel drive. Mr Lanchester was also a pioneer in aviation, developing a circulation theory of lift and a vortex theory explaining how wings generate lift and drag.
Yet he is perhaps best known for the mathematical laws he developed in 1916 to determine the relative strengths of armies. Mr Lanchester’s crucial insight was related to the nature of modern, mechanised warfare. He realised that while in pre-industrial warfare a single soldier could only engage one enemy combatant at a time (with his sword, spear or bow), a modern soldier (with a machine gun or aeroplane) could engage many.
Mr Lanchester was the first to understand that this meant, in pre-modern war, the relation between the size of an army and the combat power of that army followed a linear law. In other words, if you doubled the army, you got twice the combat strength: 3+3=6.
In modern combat, however, a superior force would not only would kill more of the enemy, but would lose fewer men than the enemy. Over time, this process would multiply the initial superiority, making the kills and losses even more lopsided, further accentuating the superiority. The increase in combat power would therefore have a multiplying effect (kills and losses), not a linear effect. In turn, this meant that increasing the size of an army would follow a square law: 3x3=9.
Mr Lanchester developed mathematical equations to show how this square law applied to war. Modified versions are still used by military operational planners today. They are especially useful for applying to attritional wars, because, as aforementioned, in attritional wars, the degradation of combat power is the aim in and of itself, rather than victory in a decisive battle or the capture of land or specific key points, like cities. Therefore, as one side loses power, the terrible logic of the square law takes hold: it doesn’t lose a linear amount of relative power, but the square root.....
