The measured relationship
Size sets the rhythm
The sample runs from 0.01 kg to 260 kg, a ratio of 26,000 to 1 and more than four orders of magnitude. Frequency falls predictably across that enormous span.
The observed exponent, −0.22, sits close to −3/16, or −0.19 when rounded, which the authors derive from the balance between drop inertia and surface tension. The relationship describes a strong trend, while each animal's anatomy accounts for deviations around it.
The adult mouse in the table shakes about 6.4 times as fast as Labrador 2. One cycle lasts 34 ms in the mouse and 222 ms in the Labrador.
The mechanism
The drop leaves when inertia beats capillarity
Water wets hair and gathers between fibres. Surface tension holds each drop like an elastic film. A rapid change of direction gives the drop an outward apparent force.
Values in the table range from 12 to 72 times gravitational acceleration. The authors summarise the useful domain as roughly 10–70 × g, surprisingly narrow for such different animals.
If the adult mouse copied a dog's rhythm and stopped at 4 Hz, the calculation gives about 1 × g. Water would remain attached to the fur.
The anatomical amplifier
Loose skin turns the torso into a whip
A Labrador keeps its paws on the ground while skin slides far beyond the skeleton's movement. A drop at the end of a hair therefore receives speed that the spine's rotation alone could not produce.
Skin motion reaches about three times the amplitude of vertebral movement. The force associated with speed grows with the square of amplitude, giving the factor of nine.
The payoff
One second of effort saves a great deal of heat
Wet fur can retain a mass of water that is expensive to evaporate. Shaking ejects the mechanically removable part and leaves a thin film for evaporation.
The authors' energy model estimates that shaking uses between one ten-thousandth and one thousandth of the energy required to evaporate the removable water. In percentage terms, that is 0.01%–0.1%.
A few points from the table
The same outcome through very different rhythms
The goat, pig and sheep sit far from neighbours of similar mass. Body shape, fur and shaking style matter, while the scaling relationship remains clear across all 25 points.
Where the rule stops
A strong fit still has blurred edges
Most species are represented by a single animal. The squirrel's and both bears' mass and radius were estimated from published literature; the lion's and tiger's radius was estimated from similarly sized adults.
Very large animals gradually depart from the scaling relationship. They retain heat better, have different skin layers and may carry less hair. The authors also observed that hairless guinea pigs shivered instead of performing the full shake.
The study explains the mechanics of drying after the gesture begins. The sensory circuit that triggers the movement lies outside this demonstration.
How it was measured
Fast cameras, fur markers and a simulator with wet brushes
The researchers filmed animals immediately after wetting, tracked markers fixed to fur and measured mass, torso radius, frequency and acceleration. A laboratory device spun fur samples and wet brushes to test when drops detached.
The relationship between mass and frequency was fitted with one representative point for each species or breed, apart from the separately measured Labradors. Comparisons on this page use the published values, with rounding repeated after calculation.