A Universal Mathematical Law
In the animal kingdom, both in the air and in the water, wing and fin movements follow a strikingly similar mathematical pattern. Researchers at Roskilde University in Denmark have discovered a mathematical formula that predicts the frequency of wing or fin movement in a wide range of animals, from insects and birds to mammals and marine creatures. This formula reveals that the relationship between body mass, wing or fin area and flapping frequency follows a universal law, regardless of biological differences between species.
The Mathematical Formula
The relationship between body mass, wing/fin area and flapping frequency follows a universal law. This relationship is represented by an animal’s flapping frequency over the square root of body mass divided by wing/fin area, resulting in a common curve for all species studied, including swimming species. The study analysed data from 414 species, showing that body mass and wing/fin area are the decisive factors in determining flapping frequency in flying and diving animals.
Validation and Applications
The researchers validated the accuracy of the equation by comparing its predictions with published data on flapping frequencies of various species, from bees and moths to penguins and whales. This discovery not only demonstrates the simplicity underlying the diversity of life, but could also have practical applications in the design of biologically inspired aerial and aquatic vehicles, improving our understanding of the biomechanics of flight and swimming.
Implications on Animal Diversity
Despite enormous physical differences, from butterflies to bats, animals have evolved a relatively constant relationship between body mass, wing area, and flapping frequency. This consistency could even allow the reconstruction of the flapping frequency of extinct pterosaurs. Furthermore, this finding also applies to the aquatic kingdom, demonstrating that swimming animals follow the same mathematical law, with some specific considerations for the aquatic environment.
Reference
The study, titled ‘Universal wing-and fin-beat frequency scaling’, was published in PLOS ONE on June 5, 2024, and can be consulted through the following link: https://doi.org/10.1371/journal.pone .0303834
