A new study published in PLOS ONE on June 5 reveals a universal equation that can predict the frequency of wingbeats and fin strokes in birds, insects, bats, and whales. Researchers from Roskilde University in Denmark found that the frequency at which animals flap their wings or fins is proportional to the square root of their body mass divided by their wing area. This relationship holds true across a wide range of flying and diving animals, from bees and moths to penguins and whales.
The ability to fly has independently evolved in various animal groups, and to minimize energy consumption during flight, the frequency of wingbeats is crucial. By using dimensional analysis, the researchers were able to develop a simple equation that accurately describes the relationship between body mass, wing area, and wingbeat frequency. This equation was validated by comparing it to published data on wingbeat frequencies for different animal species.
The study also includes predictions for extinct animals, such as the pterosaur Quetzalcoatlus northropi, which was estimated to beat its wings at a frequency of 0.7 hertz. Despite the vast differences in body size and evolutionary history, animals like butterflies and bats exhibit a relatively constant relationship between body mass, wing area, and wingbeat frequency.
The implications of this research extend beyond the animal kingdom, potentially impacting the design of future technologies like flying nanobots. This groundbreaking study highlights the fundamental principles governing flight across diverse species and underscores the simplicity and accuracy of the universal equation for predicting wing and fin beats
