A Finger on the Pulse of the World

/ by Maggie Wittlin /

Constructal theory, once used to explain river basin shape, predicts all animal locomotion.

Adrian Bejan at work with natural patterns. Credit: Duke University Photography

Move over, Clarissa. Duke mechanical engineering professor Adrian Bejan thinks he can explain it all.

In a paper published in the January, 2006 issue of the Journal of Experimental Biology, Bejan and Penn State biology professor James Marden claim that one simple theory can quantitatively explain important characteristics of animal movement, independent of whether the animal runs, swims or flies. The method, constructal theory, is a principle Bejan developed in the late ‘90s to explain the shape of river basins. He’s already used the hypothesis to model a diverse array of natural phenomena that involve repetition or flow, from breathing, to air current paths, to bird migration routes.

“I think it is a big thing to have a principle that explains why a pattern occurs in nature,” Bejan said. “And now we have this huge body of evidence in animal locomotion supporting what this simple, intuitive-feeling physics statement predicts.”

Constructal theory says that a system not in equilibrium will, over time, generate paths that allow currents to flow with easiest access and least resistance. Essentially, systems evolve so they experience the least friction and maximize efficiency. In terms of locomotion, this means animals move in a way that minimizes energy spent.

Stunningly, by when this minimization takes place in a single two part movement—such as the up-down flap of a bird’s wings—even a freshman physics student can derive specific properties of the animal’s motion. The theory correctly predicts how an animal’s velocity, frequency of motion, and the force it applies to water, air or the earth will vary with its mass.

For example, a bird does two things during a single flap of its wings: It lifts its own weight and overcomes air drag. Therefore, the total energy used up during a flap equals the change in gravitational potential energy plus the energy lost to the friction of the air. This total energy-per-flap can be expressed in an equation containing the bird’s velocity, its mass. By minimizing energy loss with respect to velocity, the velocity can be expressed in terms of the animal’s mass and body density. Similar manipulations can find flapping frequency and the force applied to the air.

The researchers predicted from their theory that larger birds fly faster and flap their wings less frequently but with greater force.

“These predictions match all the data that people have been collecting in zoology,” Bejan said. “This theory in question has been tested voluminously and the theory predicts everything.”

It may be counterintuitive to think the same theory that applies to fliers and runners also applies to swimmers. Fish are not generally thought of as exerting a gravitational force on the ground, but, according to Bejan, coauthor Marden has shown that fish deform the shape of surface water and thereby put increasing pressure on the ocean floor.

“Ultimately the hard ground has to feel the movement of the animal that’s trying to move relative to the hard ground,” he said. “The firm spot that allows everyone to have locomotion is the Earth.”

Bejan boasted that his theory can explain patterns found in nature that are often deemed random or chaotic; he believes constructal theory shows that randomness is not a factor in natural patterns.

“What I’m telling you is totally, let’s say, the upside-down of what the proponents of chance and non-determinism have been promoting for more than a hundred years.” Bejan said. “This is—how should I say—the end of the story. The end of the argument. A law of physics that says it all, and it takes less space in a future physics book than all this debate that currently has led to things such as chaos and chance and fluctuations and turbulence and other buzz words that mean ‘I don’t know.’”

In addition to its ease of use, Bejan says constructal theory has stood up to all of its critics.

“The reason we are publishing it is because we were able to overcome opposition from, obviously, extremely famous biologists who insist that gravity has nothing to do with swimming,” he said.

“This is a theory full of blood.”

Originally published January 13, 2006

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