Wildlife Conservation Efforts

Formula for Flapping Frequency across Flying and Swimming Animals


From UPSC perspective, the following things are important :

Prelims level: Flapping Frequency


Why in the news?

  • Researchers at Roskilde University in Denmark discovered a formula that correlates the flapping frequency of winged and swimming animals to their mass and wing/fins size.
    • The formula applies universally across a diverse range of species, from insects to birds, bats, penguins, whales, and even robotic ornithopters.

Formula for Flapping Frequency

  • The formula was derived from Newton’s second law (F= mass x acceleration) applied to animals flapping wings to stay airborne.
  • Factors considered in the derivation included air density, wing size, and the forces generated by wing movements.

Research Methodology

  • The researchers derived the formula theoretically from Newton’s second law, relating the force needed to stay airborne or submerged to the wing/fins’ motion, air/water dynamics, and animal mass.
  • They incorporated empirical observations into a constant C to account for specific shape and flight kinematics variations.

Application and Validity

  • The formula’s validity was tested across various animals:
    • 176 insect data points (e.g., bees, moths, dragonflies)
    • 212 bird data points (from hummingbirds to swans)
    • 25 bat data points

Formula Extension to Swimming Animals

  • The formula also predicts the frequency of fin/fluke movements in swimming animals.
  • Adjustments are made for water density and buoyancy effects, excluding fish with swim bladders.

Limitations and Modifications

  • The formula applies well in conditions with high Reynolds numbers (Re), where fluid flow is streamlined.
  • At low Re values, where viscosity dominates, modifications are needed.
  • The equation holds as long as animal density variations do not exceed a factor of ten.

Insights and Future Research

  • Insights from the formula include understanding flight efficiency and potential evolutionary pathways for winged animals.
  • Future research aims to explore further insights hidden within the C constant, potentially revealing deeper principles governing animal flight and swimming dynamics.


[2024] The organisms “Cicada, Froghopper and Pond skater are:

(a) Birds

(b) Fish

(c) Insects

(d) Reptiles

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