{Reference Type}: Journal Article
{Title}: Universal wing- and fin-beat frequency scaling.
{Author}: Jensen JH;Dyre JC;Hecksher T;
{Journal}: PLoS One
{Volume}: 19
{Issue}: 6
{Year}: 2024
{Factor}: 3.752
{DOI}: 10.1371/journal.pone.0303834
{Abstract}: 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.