Portland, Ore. - After an exhaustive study of all varieties of locomotion in both living and mechanical systems, two researchers have concluded this month that the same set of engineering principles applies to all systems capable of independent motion.
The study, which was carried out by engineering professor Adrian Bejan of Duke University and professor James Marden, a biologist at Penn State University, builds on a 1996 theory proposed by Bejan.
Bejan's "constructal theory" states that "For a finite-size system to persist in time [to live], it must evolve in such a way that it provides easier access to the imposed currents that flow through it." For example, the current that flows through an IC package is heat. If the package does not provide an efficient structure for dissipating that heat, the system will overheat and cease to function. In another example, in the circulatory system of the body, blood flow must be optimized by the geometric configuration of blood vessels and capillaries and arteries.
The theory aims to be as fundamental as thermodynamics, providing basic design principles rooted in physical laws. Constructal principles apply across virtually any functioning system-biological or man-made.
In 2004, Bejan began cooperating with Marden to extend the theory from its origins in comparing airplanes and the flight of birds, moving to comparisons of the gaits of animals and robots.
This month Bejan and Marden reported that all forms of locomotion obey the same ratios between the energy destroyed at each step or flap and the energy lost to friction against the ground or air. Even swimmers obey the same body-mass scaling principles as runners or fliers, whether they're living or robotic.
The theory begins with the premise that all systems that exist in the real world are imperfect, but as they evolve, they seek to distribute imperfections in the most energy-efficient way. Bejan claims that it is in fact a more fundamental principle than evolution via natural selection.
"Our findings may also have implications for understanding animal evolution," Marden said. "If you started evolution over on Earth, or it happened on another planet-with a given gravity and density of their tissues, the same basic patterns of their design would evolve again."
"A walking/running machine will move most efficiently-with the smallest-power battery-if its limbs do the optimized rhythm that we predicted/discovered for all walking animals," said Bejan. "Animal locomotion is no different than other flows, animate and inanimate. They all optimize the flow of material."
Marden elaborated, "It doesn't matter whether the animal has eight legs, four legs, two-even if it swims with no legs. Animals move such that they travel the greatest distance while expending the least amount of energy. It's simple physics, based only on gravity, density and mass."
In thermodynamics, living systems are characterized as "nonequilibrium" systems that change as energy flows through them. Such man-made systems as computers, robots and automobiles attempt to mimic functions found in nature and are, therefore, subject to the same laws. The constructal approach is to view all such systems as "flow structures" that evolve to optimize the nonequilibrium thermodynamics of the system.
Constructal theory has grown from the seeds of such "conservation of energy" principles in thermodynamics into a comprehensive field that has solved problems in a surprising variety of systems. From the way heat is exhausted from an electronics system to the way river basins are carved to the way sap flows in a leaf-all processes follow constructal laws, according to Bejan and Marden.
The researchers cast all forms of locomotion into a common description by virtue of a single physical theory-namely, that flows of all kinds naturally strive to consume the minimum amount of useful energy, whether that energy is in the form of electricity or food. By understanding this natural optimization process, engineers can construct systems that last longer, need less maintenance and consume the absolute minimum amount of energy required for an application.
An optimal balance exists between the vertical loss of potential energy-as when one falls forward when taking a step or raising a wing before flapping-and the horizontal loss caused by the friction of "feet" against the ground or wing against the air. "To run or fly at optimal speed is to strike a balance between the vertical and horizontal loss of energy," Bejan said. "Even fish have to push water out of the way to move forward."
The researchers claim all such systems strive to optimize intermittent movement. For instance, there is a preferred ratio of speed to body mass and a universal relationship between stride size and frequency.
Bejan and Marden also claim that animals in motion follow the same engineering principles as piston engines, electric motors and jet engines. Motors used by humans for transportation and muscles used by animals for locomotion obey a common upper limit of mass-specific net force output, which is independent of materials and gait mechanisms.
This research was funded by the National Science Foundation. Learn more about constructal theory by visiting www.constructal.org.
- Additional reporting by Chappell Brown