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.

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