%0 Journal Article
%T Universal wing- and fin-beat frequency scaling.
%A Jensen JH
%A Dyre JC
%A Hecksher T
%J PLoS One
%V 19
%N 6
%D 2024
%M 38837960
%F 3.752
%R 10.1371/journal.pone.0303834
%X We derive an equation that applies for the wing-beat frequency of flying animals and to the fin-stroke frequency of diving animals like penguins and whales. The equation states that the wing/fin-beat frequency is proportional to the square root of the animal's mass divided by the wing area. Data for birds, insects, bats, and even a robotic bird-supplemented by data for whales and penguins that must swim to stay submerged-show that the constant of proportionality is to a good approximation the same across all species; thus the equation is universal. The wing/fin-beat frequency equation is derived by dimensional analysis, which is a standard method of reasoning in physics. We finally demonstrate that a mathematically even simpler expression without the animal mass does not apply.