Going with the Flow

Charles Fergus
May 05, 2008

It's a concept both elegantly simple and mind-stretching: Animals move across the earth-running, swimming, flying-in the same basic manner as rivers, winds, and ocean currents.

In the 1990s, Adrian Bejan, a mechanical engineer at Duke, developed what he termed "constructal theory," an analytical approach to motion based on principles of thermodynamics. According to Bejan, "Animal locomotion is no different from other flows," including inanimate ones, since they all optimize the ability of material to travel the greatest distance while expending the least amount of energy.

Working independently from Bejan, Penn State biologist James Marden had been putting weights on birds spanning the scale from hummingbirds to pigeons, on bats ranging from tiny ones to big fruit bats, and on insects as small as damselflies and as large as giant tropical moths. "The animals could all lift approximately the same amount of weight in relation to the size of their flight muscles," he says. "The size of the wings didn't matter, or how they were put together, or whether the creatures were birds, mammals, or insects. The mass of the flight muscles mattered." When one of Marden's undergraduate students plugged in data for F-15 jet engines, "It turned out that the engines worked the same basic way," Marden says. "All of the motors used by humans and animals for transportation have a common upper limit of mass-specific net force output that is independent of materials and mechanisms."

In 2002, Marden and his student, Lee Allen, published a report on their results in the Proceedings of the National Academy of Sciences. When Duke engineer Bejan heard Marden presenting the findings at a conference, he realized they might dovetail with Bejan's own constructal theory, which explains basic characteristics of locomotion for all types of flow. Could the theory also apply to animal locomotion-how fast they get from one place to another, and how rapidly and forcefully they must step, flap, or paddle in relation to their mass?

Bejan and Marden conspired to extend constructal theory from flying to running. To maintain a constant speed, they noted, both fliers and runners must expend energy sufficient to overcome the energy lost at each jump or landing, or with each rise and fall in the air, as well as energy lost to friction against hard and soft surfaces, and air drag. Ultimately they derived simple physics equations that closely predict the velocities of animals running over various terrains, as well as the wingbeat frequencies of fliers. Bejan refined the equations; says Marden, "I added the biological interpretation and did some ground-truthing, basically asking, 'Does this make sense for the organisms inhabiting Earth?'"

Next, the researchers looked at fish locomotion. Fish are neutrally buoyant so that they neither sink nor rise. Because of this neutrality, scientists have long believed that gravity doesn't affect fish. But Bejan and Marden observed that a swimming fish exhibits the same body-mass scaling as a running antelope or a flying falcon.

Although fish are indeed neutrally buoyant, they still have to push water out of the way to move forward. Bejan suggested that this displaced water raises the surface of a water body, although such movement likely would be imperceptible, spread as it is across a lake or stream or even an entire ocean. Bejan postulated that the water can only go up because the bottom and sides of any body of water are rigid. Therefore, fish must work against gravity to lift an amount of water equal to their own mass for each body length they move forward. "That put fish in the same physical realm as runners and fliers," Marden says.

"In animals, constructal theory not only predicts maximum-range speeds," notes Marden, "but it also predicts stride and stroke frequencies and net force output." In a 2006 article in American Scientist, Bejan and Marden write that constructal theory "does not maintain that animals must act or be designed in a predictable fashion, only that over large size ranges and diverse species, predictable central tendencies should emerge."

Many scientists argue that evolution has been driven by innumerable chance events, both genetic and environmental. Stephen Jay Gould, the late paleontologist and evolutionary biologist, suggested that if we could somehow "rewind the tape" of evolution and run it again, the resulting animals on Earth would look a lot different than the ones we know now. Likely so, agree Marden and Bejan, but general design rules govern the form those animals would assume-design rules that fall within the parameters set out by constructal theory. "Different lineages would likely proliferate," Marden says. "But there are design targets that animals recurrently hit."

Constructal theory may improve our understanding of how and why convergent evolution has taken place, in which animals in one part of the globe-marsupials in Australia, for example-have evolved to move and function like completely unrelated mammals in Europe and North America. You can also use constructal theory to look backward in time. Says Marden, "It would be fairly simple to plug in dinosaurs'; dimensions and mass and predict the velocity and stride pattern of, say, a Tyrannosaurus rex."

How has constructal theory been received by evolutionary biologists-and physicists, for that matter? Marden laughs. "Scientists don';t trust ';theories of everything.' But so far, nobody's seriously disputed our conclusions, including the most surprising one linking fish locomotion to other kinds of animal movement.

"Remember, this is a theory rather than a model. It's predictive, and contains no fitting constants. Our figures work within an order of magnitude. Constructal theory is meant to get people's mental wheels spinning. We believe it's done that."

James Marden, Ph.D. is professor of biology in the Eberly College of Science, jhm10@psu.edu. Adrian Bejan, Ph.D., is J. A. Jones Distinguished Professor of Mechanical Engineering at Duke University. The research described above was funded by the National Science Foundation.

Last Updated May 05, 2008