The movements of bumblebees and blue whales could not appear more different, but zoologist Graham Taylor of Oxford University finds an underlying similarity. He and his colleagues have discovered that the locomotion of most creatures that fly or swim can be characterized by a single mathematical proportion called the Strouhal number—the ratio between an animal’s cruising speed and the rate at which it flaps its wings or swishes its tail.
The Strouhal number dictates how efficiently an animal moves through air or water by predicting how its body interacts with the vortices it creates through its propulsion. Taylor and his colleagues compared published cruising speeds and wing-flapping patterns of 42 bird, bat, and insect species to search for patterns. In every case, the flying animals have a Strouhal number close to 0.3. This is the same value previous researchers had measured for tail-propelled aquatic creatures such as dolphins, sharks, and other fish.
“The amazing thing is we found a rule that applies to both swimming and flying,” says Taylor. “It’s a wonderful example of convergent evolution, with animals that have evolved independently—fish, dolphins, bats—following the same geometry.” He suggests his results are so universal that they should apply to flying or swimming life-forms on other planets, if they exist. The work has caught the attention of the U.S. and the United Kingdom militaries, which are working to create reconnaissance vehicles that propel themselves like flying insects. “This study will help us predict how fast these things will need to flap, so we can start on design specifications,” Taylor says.