Thanks to science, we now have a pretty good answer, and, more importantly, a good explanation: Around 4 Hertz, 4.3 Hz for a Labrador retriever. Andrew Dickerson of the Georgia Institute of Technology was able to determine the 4.3 Hz figure by filming lots of dogs
whipping their hair shaking their fur and measuring the periods of oscillation. Clever, but then they took it to the next step by developing a mathematical model for fur-shaking across hairy animals.
They then created a simple mathematical model of what’s going on. They reasoned that the water is bound to the dog by surface tension between the liquid and the hair. When the dog shakes, centripetal forces pull the water away. So for the water to be ejected from the fur, the centripetal force has to exceed the surface tension.
This model leads to an interesting prediction. If the animal has a radius R, the shaking frequency must scale with R^0.5. That makes sense, smaller animals will need to oscillate faster to generate forces large enough to dry themselves.
But as it, er, shakes out in nature, “the universal rule for shaken fur is that the frequency increases with R^0.75,” and theory still lags practice as to why.
In any event, while this might seem an Ig Nobel shoo-in, there are potential applications for this in computer animation and gaming. One Slashdot commenter compares the potential applications of the findings to those developed from fluid dynamics: “The formula is significant for us in the ad/entertainment industry who relies on algorithms to animate such motions. It sure beats trying to manually animating each fur (impossible), or coming up with a workaround that only approximates reality through trial and error. This will significantly reduce render times.”
More explanation in the video below:
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