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The Dynamics Of "sprint" Running

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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 M v . 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, M v = F t . Now t , the time occupied in producing or checking a movement, is proportional to l/v , while M is proportional to l 3 , so that, again neglecting constants, l 3 = F l / v .