Theoretical considerations on maximum running speeds for large and small animals

Mechanical equations for fast running speeds are presented and analyzed. One of the equations and its associated model predict that animals tend to experience larger mechanical stresses in their limbs (muscles, tendons and bones) as a result of larger stride lengths, suggesting a structural restriction entailing the existence of an absolute maximum possible stride length. The consequence for big animals is that an increasingly larger body mass implies decreasing maximal speeds, given that the stride frequency generally decreases for increasingly larger animals. Another restriction, acting on small animals, is discussed only in preliminary terms, but it seems safe to assume from previous studies that for a given range of body masses of small animals, those which are bigger are faster. The difference between speed scaling trends for large and small animals implies the existence of a range of intermediate body masses corresponding to the fastest animals.