Universal wing- and fin-beat frequency scaling

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The discussion highlights the application of dimensional analysis in deriving an equation that relates the wing-beat frequency of flying animals and the fin-stroke frequency of diving animals, such as penguins and whales. This equation indicates that the frequency is proportional to the square root of the animal's mass divided by the wing or fin area. Notably, the constant of proportionality remains consistent across various species. The findings are particularly striking as they reveal a shared mathematical relationship between the dynamics of flight in air and swimming in dense fluids, suggesting a fundamental principle governing movement in different environments.
Filip Larsen
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Good to know the power of dimensional analysis is still able to find gold:
We derive an equation that applies for the wing-beat frequency of flying animals and to the fin-stroke frequency of diving animals like penguins and whales. The equation states that the wing/fin-beat frequency is proportional to the square root of the animal’s mass divided by the wing area. [...] the constant of proportionality is to a good approximation the same across all species
https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0303834
journal.pone.0303834.png
 
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What I find astonishing here is that flying through air and swimming through a heavy viscous fluid land on the same curve.
 
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