Gray's paradox

Gray's Paradox is a paradox posed in 1936 by British zoologist Sir James Gray. The paradox was to figure out how dolphins can obtain such high speeds and accelerations with what appears to be a small muscle mass. Gray made an estimate of the power a dolphin could exert based on its physiology, and concluded the power was insufficient to overcome the drag forces in water. He hypothesized that Dolphin's skin must have special anti-drag properties.^[1]

In 2008, researchers from Rensselaer Polytechnic Institute, West Chester University and the University of California, Santa Cruz used digital particle image velocimetry to prove that Gray's assumptions oversimplified the relationship between muscle power and drag force.^[2]

Timothy Wei, professor and acting dean of Rensselaer's School of Engineering, videotaped two bottlenose dolphins, Primo and Puka, as they swam through a section of water populated with hundreds of thousands of tiny air bubbles. Computer software and force measurement tools developed for aerospace were then used to study the particle-image velocimetry which was captured at 1,000 frames per second (fps). This allowed the team to measure the force exerted by a dolphin. Results showed the dolphin to exert approximately 200 lb of force every time it thrust its tail – 10 times more than Gray hypothesized – and at peak force can exert between 300 and 400 lb.^[2]

Wei also used this technique to film dolphins as they were doing tail-stands, a trick where the dolphins “walk” on water by holding most of their bodies vertical above the water while supporting themselves with short, powerful thrusts of their tails.

In 2009, researchers from the National Chung Hsing University in Taiwan introduced new concepts of “kidnapped airfoils” and “circulating horsepower” to explain the swimming capabilities of the swordfish. Swordfish swim at even higher speeds and accelerations than dolphins. The researchers claim their analysis also "solves the perplexity of dolphin’s Gray paradox".^[3]