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Birds of different feathers fly to the same beat

  • June 18, 2024
  • Posted by: OptimizeIAS Team
  • Category: DPN Topics
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Birds of different feathers fly to the same beat

Sub: Science and tech

Sec: Msc

Universal Formula for Flapping Frequencies in Animals:

  • Almost all animals that fly through the air and many that swim through water have evolved to flap their wings (or fins) at a frequency given by a simple formula, three scientists at Roskilde University in Denmark have found.
  • Discovery: A simple formula relating the flapping frequency of wings or fins to the mass and wing area of the animal.

  • f here is the wingbeat frequency, m the mass of the animal, ⍴air the atmosphere’s density, and A the size of the wing. Et voila.

Formula Verification:

  • Applicability: Validated across a wide range of species including insects, birds, bats, penguins, whales, and a robotic bird (ornithopter).
  • Method: Plotting calculated values against actual frequencies showed a nearly straight line, confirming the formula’s accuracy.

Derivation Process:

  • Starting Point: Newton’s second law F=ma applied to airborne animals.
  • Considerations:
    • Force (F) is generated by flapping wings to counteract gravity.
    • Momentum of air pushed by wing strokes.
    • Airflow velocity and atmospheric density.
  • Result: A theoretical equation was derived and empirically validated.

Proportionality Constant (C):

  • Importance: Represents dimensionless quantities related to wing shapes and flapping angles.
  • Implications: Can provide deeper insights into the efficiency of flight and potential limitations for heavier birds.

Application to Swimming Animals:

  • Extension: The formula also applies to swimming animals needing continuous motion to stay submerged.
  • Modification: Replace air density with water density and adjust for buoyancy.

Empirical Testing:

  • Data Used:
    • 176 insect data points (bees, moths, dragonflies, beetles, mosquitoes).
    • 212 bird data points (hummingbirds to swans).
    • 25 bat data points.
  • Limitations: Formula assumes high Reynolds number (Re) conditions where fluid density is more critical than viscosity.

Future Work:

  • Low Reynolds Number: Adjustments needed for animals operating in low Re conditions where viscosity is more significant.
  • Density Variations: Simplification of the formula is constrained unless density varies significantly by an order of magnitude.

Source: TH

Birds of different feathers fly to the same beat Science and tech

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