News Excerpt:
Three scientists from Roskilde University in Denmark have made a groundbreaking discovery: a universal equation that accurately predicts the flapping frequency of wings in almost all flying animals and many swimming creatures.
More about the findings:
Their findings reveal that the frequency at which wings or fins beat is determined by a simple formula, which relates the flapping frequency to the animal's mass and the size of its wings or fins.
The Formula:
- f ∝ √m/A. (∝ stands for ‘is proportional to’).
- f is flapping frequency,
- m is the mass of the airborne animal, and
- A is the area of the wings
When the researchers calculated √m/A number of various animals, birds, and insects and plotted it on the x-axis and their respective frequencies on the y-axis, they found a nearly straight line as shown in the figure. The black line follows the model based on the formula as predicted.
Application to Swimming Animals
- Interestingly, the researchers found that their equation also applies to swimming animals like whales and penguins.
- For positively buoyant diving animals that need to continuously move water to stay submerged, the same principle holds.
- The equation needs minor adjustments for swimming animals, replacing air density with water density and adjusting mass for buoyancy. However, this does not apply to fish with a swim bladder.
Validation and Limitations:
- The researchers validated their equation using data from older studies, encompassing 176 insect species (including bees, moths, dragonflies, beetles, and mosquitoes), 212 bird species (from hummingbirds to swans), and 25 bat species.
- They noted that the equation assumes certain physical conditions, such as the Reynolds number (Re), which affects fluid flow characteristics.
- At high Re, density matters more than viscosity, which fits the conditions for flying animals. The equation needs modification for low Re, where viscosity becomes more significant.
Significance of the findings:
- This universal equation offers a powerful tool for understanding the mechanics of flight and swimming across a wide range of species.
- It not only explains current wingbeat frequencies but also provides insights into the evolution of future flying or swimming animals and the design of winged robots.
- The discovery marks a significant advancement in our understanding of biomechanics and the principles governing animal locomotion.
