Universal wing- and fin-beat frequency scaling

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SUMMARY

The discussion centers on a derived equation that relates the wing-beat frequency of flying animals and the fin-stroke frequency of aquatic 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 area. Remarkably, the constant of proportionality remains consistent across various species, highlighting a universal principle in biomechanics. The findings suggest that both aerial and aquatic locomotion share fundamental similarities despite differing mediums.

PREREQUISITES
  • Understanding of dimensional analysis
  • Familiarity with biomechanics principles
  • Knowledge of animal physiology related to mass and wing/fin area
  • Basic grasp of fluid dynamics
NEXT STEPS
  • Research the implications of dimensional analysis in biomechanics
  • Explore the mathematical derivation of the wing-beat frequency equation
  • Investigate the biomechanics of different species, focusing on mass and wing/fin area
  • Study fluid dynamics principles as they relate to swimming and flying
USEFUL FOR

Biologists, biomechanics researchers, and anyone interested in the comparative physiology of flying and swimming animals will benefit from this discussion.

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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