Perfection is the enemy of evolution

Biologists have treated the view that fundamental differences exist between running, flying and swimming as evident, because the forms of locomotion and the animals are so different: limbs and wings vs body undulations, neutrally buoyant vs weighted bodies, etc. Here we show that all forms of locomotion can be described by a single physics theory. The theory is an invocation of the principle that flow systems evolve in such a way that they destroy minimum useful energy (exergy, food). This optimization approach delivers in surprisingly direct fashion the observed relations between speed and body mass (M(b)) raised to 1/6, and between frequency (stride, flapping) and M(b)(-1/6), and shows why these relations hold for running, flying and swimming. Animal locomotion is an optimized two-step intermittency: an optimal balance is achieved between the vertical loss of useful energy (lifting the body weight, which later drops), and the horizontal loss caused by friction against the surrounding medium. The theory predicts additional features of animal design: the Strouhal number constant, which holds for running as well as flying and swimming, the proportionality between force output and mass in animal motors, and the fact that undulating swimming and flapping flight occur only if the body Reynolds number exceeds approximately 30. This theory, and the general body of work known as constructal theory, together now show that animal movement (running, flying, swimming) and fluid eddy movement (turbulent structure) are both forms of optimized intermittent movement.

Here we show that constructal-law physics unifies the design of animate and inanimate movement by requiring that larger bodies move farther, and their movement on the landscape last longer. The life span of mammals must scale as the body mass (M) raised to the power 1/4, and the distance traveled during the lifetime must increase with body size. The same size effect on life span and distance traveled holds for the other flows that move mass on earth: atmospheric and oceanic jets and plumes, river basins, animals and human operated vehicles. The physics is the same for all flow systems on the landscape: the scaling rules of “design” are expressions of the natural tendency of all flow systems to generate designs that facilitate flow access. This natural tendency is the constructal law of design and evolution in nature. Larger bodies are more efficient movers of mass on the landscape.

In the present study, we show that the fastest runners and swimmers are becoming not only faster but also heavier, taller and more slender. During the past century, the world record speeds for 100 m-freestyle and 100 m-dash have increased with body mass (M) raised to the power 1/6, in accordance with the constructal scaling of animal locomotion. The world records also show that the speeds have increased in proportion with body heights (H) raised to the power 1/2, in accordance with animal locomotion scaling. If the athlete's body is modeled with two length scales (H, body width L), the (M, H) data can be used to calculate the slenderness of the body, H/L. The world records show that the body slenderness is increasing very slowly over time.