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