At first glance, a galloping stallion, a soaring eagle and a tuna swimming don't look much alike, but a new study on animal locomotion suggests that when it comes to getting from place to place, these and all animals appear to have everything in common.
All animals, whether they run, fly, or swim, follow the newly proposed "constructal theory," the idea that the basic characteristics of locomotion for each animal — how rapidly and forcefully it steps, flaps or paddles itself forward — is related to its mass.
"From simple physics, based only on gravity, density and mass, you can explain within an order of magnitude many features of flying, swimming, and running," said James Marden of Pennsylvania State University. "It doesn't matter whether the animal has eight legs, four legs, two, even if it swims with no legs."
The constructal theory is based on the basic principle that systems evolve to minimize imperfections — such as energy lost to friction or other forms of resistance — and making use of the greatest amount of energy possible.
The theory applies to virtually everything that moves in nature, such as traffic flow, falling snowflakes and river currents, Bejan said. And despite glaring differences across the board, the physics of locomotion shows striking similarities from species to species.
"Running, swimming and flying occur in vastly different physical environments, and likewise, involve quite different body mechanics," Bejan said. "Nonetheless, there are strong convergences in certain functional characteristics of runners, swimmers and fliers."
For example, a running dog's stride frequency bears the same relationship to its mass as does the rate at which a blue jay flaps its wings in flight. A flying bird must compensate for loss in the vertical direction due to gravity as well as friction as it moves forward on the horizontal.
"The animal cannot eliminate both of these losses individually, but it can balance them. Equal losses are most economical, and therefore optimal," Bejan said. "They flap their wings to reposition themselves on the vertical and maintain horizontal movement."
The same applies for a dog running on the ground.
However, applying these universal similarities to swimming animals proved difficult, even though data showed that swimmers show the same locomotion-to-body mass scaling as runners and fliers.
Locomotion on the ground and in the air is governed largely by gravity, but fish are neutrally buoyant — or nearly so — in water.
This means that their tendency to float counteracts the force of gravity and they neither sink or rise, and scientists had considered fish to move as though unaffected by gravity.
But fish still have to push water out of the way to move forward, Bejan said, and the only way to do this is to move the water over the fish.
This raises the water's surface — albeit an imperceptible amount spread across a lake — and increases the force of gravity on the fish.
Because fish have to work against gravity to lift an amount of water equal to their own mass for each body length they move forward, they are subject to the same physical constraints that a bird experiences in one flap or a runner experiences in one stride.
"The fact that the same proportionalities rule optimal running, flying, and swimming is not a coincidence; rather it is an illustration of the fact that a universal principle is involved," Bejan said. "We no longer have to worry why there are patterns in nature."
This research is detailed in the January issue of The Journal of Experimental Biology.
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