Bigger bodies tend to move faster on land, in water, and in the air. This broad trend is supported by the speed-size data collected from many sources for flying, running and swimming (Fig. 1)1. On this unifying background, outliers exist. The burst speed of the cheetah is greater than the steady speed of the elephant. The tuna can swim faster than the steady whale. There are outliers that are even more distant from the general trend, but they should not be confused with the fastest runners, swimmers and fliers. For example, there are insects (e.g., the flea) that snap and jump at speeds much greater than what their speed-mass scaling law would predict. The ant odontomachus holds this kind of speed record (of order 200 km/h) by snapping its jaws shut, in order to jump to the side, to get out of the way of danger. This is a one-shot event, not cyclical locomotion. Most of her life, this ant walks on land at ant speed, in accord with the speed-mass scaling law for animal locomotion1.

Figure 1 Animal speed-mass data (fliers, runners, swimmers) compiled from sources indicated in ref.1. Full size image

Hirt et al.2 addressed this aspect of animal locomotion with a model chosen to account for the starting (accelerating) period in the movement of the fastest animals. The model consisting of elastic fast-twitch fibers was constructed such that the speed emerges as a concave function of body size, with its peak at a body size that is not the largest size (Fig. 2). Bejan3 observed that the existence of body size for peak speed also rules the evolutionary design of jet fighter aircraft, which is the human made counterpart of the animal of prey, with a high burst speed followed by a long period of inactivity on the ground.

Figure 2 Animal speed-mass data compiled after Hirt et al.2, showing that the peak speed belongs to animals that are close to but not the biggest. The data are compiled from sources indicated in ref.2. Full size image

The following analysis is a theoretical treatment of this physics aspect of locomotion. It is a generalization of the unifying theory of animate, inanimate and vehicle movement, which includes the lifetime and life travel of animate and inanimate movement4.

Additionally, the following theory accounts for several features of the alignment of locomotion data that have not been questioned. One is the fact that the data for airplanes in Fig. 1 are not aligned with the data for animal fliers. Why are the airplane data trending above the animal speed-mass correlation? Why do the airplane data fall on a steeper line than the data for animal fliers? Moving over to Fig. 2, why does the body size for peak speed decrease in the direction from swimming to running and flying?