Flapping frequency of birds, bugs, bats and whales described by common equation

A single common equation can carefully approximate the frequency of wingbeats and fin strokes made by birds, bugs, bats and whales, regardless of their completely different physique sizes and wing shapes, Jens Højgaard Jensen and colleagues from Roskilde College in Denmark report in a brand new examine within the open-access journal PLOS ONE, publishing June 5.

The flexibility to fly has advanced independently in many alternative animal teams. To reduce the vitality required to fly, biologists anticipate that the frequency that animals flap their wings ought to be decided by the pure resonance frequency of the wing. Nonetheless, discovering a common mathematical description of flapping flight has proved troublesome. Researchers used dimensional evaluation to calculate an equation that describes the frequency of wingbeats of flying birds, bugs and bats, and the fin strokes of diving animals, together with penguins and whales.

They discovered that flying and diving animals beat their wings or fins at a frequency that’s proportional to the sq. root of their physique mass, divided by their wing space. They examined the accuracy of the equation by plotting its predictions towards revealed knowledge on wingbeat frequencies for bees, moths, dragonflies, beetles, mosquitos, bats, and birds ranging in measurement from hummingbirds to swans.

The researchers additionally in contrast the equation’s predictions towards revealed knowledge on fin stroke frequencies for penguins and a number of other species of whale, together with humpbacks and northern bottlenose whales. The connection between physique mass, wing space and wingbeat frequency exhibits little variation throughout flying and diving animals, regardless of large variations of their physique measurement, wing form and evolutionary historical past, they discovered. Lastly, they estimated that an extinct pterosaur (Quetzalcoatlus northropi) — the most important identified flying animal — beat its 10 meter-square wings at a frequency of 0.7 hertz.

The examine exhibits that regardless of large bodily variations, animals as distinct as butterflies and bats have advanced a comparatively fixed relationship between physique mass, wing space and wingbeat frequency. The researchers be aware that for swimming animals they did not discover publications with all of the required data; knowledge from completely different publications was pieced collectively to make comparisons, and in some instances animal density was estimated based mostly on different data. Moreover, extraordinarily small animals — smaller than any but found — would doubtless not match the equation, as a result of the physics of fluid dynamics modifications at such a small scale. This might have implications sooner or later for flying nanobots. The authors say that the equation is the only mathematical clarification that precisely describes wingbeats and fin strokes throughout the animal kingdom.

The authors add: “Differing nearly an element 10000 in wing/fin-beat frequency, knowledge for 414 animals from the blue whale to mosquitoes fall on the identical line. As physicists, we have been stunned to see how effectively our easy prediction of the wing-beat formulation works for such a various assortment of animals.”



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