Lanchester’s Laws can be used to calculate the relative strength of opposing military forces to predict which side will win in a battle. Featuring Tom Rocks Maths intern Dan Hunt.

Lanchester’s Linear Law (part 1) looks at the situation when combat takes place with a fixed front line – for example with troops advancing through a valley. This is perhaps most relevant to historic battles between infantry.

Lanchester’s Square Law (part 2) develops the model further to include the situation where all soldiers are able to fight at once. This was developed by Frederick Lanchester during World War 1 where ranged rifle combat became the norm, but can just as easily be applied to archers as shown in the video.

Produced by Dan Hunt with assistance from Dr Tom Crawford at the University of Oxford.