Scaling Laws and the Speed of Animals

In a recent issue of the American Journal of Physics, I read an interesting paper by Nicole Meyer-Vernet and Jean-Pierre Rospars examining the top speeds of organisms of varying sizes, from bacteria up to blue whales. They found that the time it takes for an animal to move its own body length is almost independent of mass, across 21 orders of magnitude. They derived a simple scaling argument and order-of-magnitude estimate for this remarkable fact. Before I elaborate further on their paper, I will give an overview of scaling arguments and their power.

There is a false dichotomy in physics, that concepts can either be explained in quasi-philosophical vague descriptive arguments, or in terms of rigorous formulae that take years of study to understand. For example, one could describe general relativity with the bowling-ball-on-a-bedsheet analogy, and when that fails, crack out the Einstein field equations. However, this sad dichotomy is actually a happy trichotomy: in between the two extremes is the powerful tool of scaling arguments.