The dynamics of "sprint" running

The Greatest Allowable Speed of Movement.—Consider a series of “similar animals ” of different size and let the linear dimensions of any individual of the series be chacterised by the length l. Let M be the mass of one of its limbs, and v the greatest velocity it can attain in that limb. Then the momentum of the limb is proportional to Mv. Now this momentum is created at the beginning of a movement, or destroyed at the end of a movement, by a force F acting for a time t; and we may write, neglecting constants, Mv = Ft. Now t, the time occupied in producing or checking a movement, is proportional to l/v, while M is proportional to l³, so that, again neglecting constants, l³ = Fl/v.