A Matter of Proportion: Scaling in Sports and Elsewhere

Some insects can jump remarkable distances. A flea can jump up about a foot — 100 times its height. At the rate, a person would be able to leap over tall buildings. Actually most people can't even jump up their own height and no animal about the size of a person can do much better. Why is this? When the 1968 Summer Olympics were held in Mexico City, some people were concerned that reduced air resistance at that high altitude would be an unfair advantage leading to new records. Others thought that since less oxygen would be available at that altitude, times might increase rather than improve. How much difference should the change in altitude make? The formula for the period of a pendulum is rather simple. Why is this? We want to understand why humans are such weaklings compared to fleas in jumping up. The key to studying jumping height is to look at energy. Contraction of muscles provides energy, so the amount of energy available to an organism in a short time should be roughly proportional to the mass of its muscles. This mass should be roughly proportional to the size of the animal. Thus we expect (available energy) ≈ C(body mass),