Marine scientists have long suspected that humpback whales' incredible agility comes from the bumps on the leading edges of their flippers. Now Harvard University researchers have come up with a mathematical model that helps explain this hydrodynamic edge. The work gives theoretical weight to a growing body of empirical evidence that similar bumps could lead to more-stable airplane designs, submarines with greater agility, and turbine blades that can capture more energy from the wind and water.
"We were surprised that we were able to replicate a lot of the findings coming out of wind tunnels and water tunnels using relatively simple theory," says Ernst van Nierop, a PhD candidate at the School of Engineering and Applied Sciences at Harvard. He coauthored the study with mathematics professor Michael Brenner and researcher Silas Alben.
The advantage of the humpback-whale flipper seems to be the angle of attack it's capable of--the angle between the flow of water and the face of the flipper. When the angle of attack of a whale flipper--or an airplane wing--becomes too steep, the result is something called stall. In aviation, stall means that there isn't enough air flowing over the top surface of the wing. This causes a combination of increased drag and lost lift, a potentially dangerous situation that can result in a sudden loss of altitude. Previous experiments have shown, however, that the angle of attack of a humpback-whale flipper can be up to 40 percent steeper than that of a smooth flipper before stall occurs.
In a paper recently published in Physical Review Letters and highlighted in the journal Nature, the Harvard research team showed that the bumps on the humpback flipper, known as tubercles, change the distribution of pressure on the flipper so that some parts of it stall before others. Since different parts of the flipper stall at different angles of attack, abrupt stalling is easier to avoid. This effect also gives the whale more freedom to attack at higher angles and the ability to better predict its hydrodynamic limitations.
The researchers also found that the amplitude of the bumps plays a greater role than the number of bumps along a flipper's leading edge. "The idea is, you could make an aircraft that's much harder to stall and easier to control," says van Nierop. For example, fighter jets could be designed to be more acrobatic without risk of stall-induced crashes. In the water, naval submarines could be made more nimble.
The Harvard research validates the first controlled wind-tunnel tests of model flippers, conducted five years ago at the U.S. Naval Academy, in Annapolis, MD, where it was shown that stall typically occurring at a 12-degree angle of attack is delayed until the angle reaches 18 degrees. In these tests, drag was reduced by 32 percent and lift improved by 8 percent.
That research was detailed in a 2004 study in collaboration with West Chester University and Duke University. "This [Harvard work] basically shows that theory and empirical measurements are close, and adds greater weight to our original assertion on the function of the tubercles," says Frank Fish, a biology professor at West Chester and a lead author of the original study.