A labrador oscillates at 4.3 hz
And a bear oscillates at 4 hz. They arrive at the point of dryness at the same time.
This sounds like the start of one of the many long and convoluted word problems I had to solve in graduate school but I found it in a press release. Today MIT’s Technology Review reports that a group of Georgia Institute of Technology students have created a simple mathematical model that helps describe how rapidly an animal needs to shake to dry its fur.
The group used high-speed videography, x-ray cinematography and particle tracking to study several different wet animals shaking themselves dry. The angular position of each animal’s shoulder skin was plotted as a function of time (producing a lovely series of sine waves) and the team calculated the conditions for water drop ejection by considering the balance of surface tension and centripetal forces on each drop.
They then developed a simple mathematical model to describe what they observed reasoning that water is bound to an animal by surface tension between the liquid and the hair. When the animal shakes, centripetal forces pull the water away. So to remove the water from its fur, the centripetal force an animal generates has to exceed the surface tension holding the water on.
The model indicated that shaking frequency was related to the shoulder radius of the animal with smaller animals needing to oscillate faster than large ones to dry themselves off. A mouse shakes at 27 Hz, a cat at 6 Hz and a bear at 4Hz. “Shake frequencies asymptotically approach 4Hz as animals grow in size,” they conclude.
Their model predicted that an animal’s shaking frequency should increase related to size with R^0.5 but the best fit for the data was when R^0.75. According to the press release:
Clearly, their model misses some important correction factor. Dickerson and co make one suggestion. In their model, the radius is the distance from the centre of the animal to its skin. Perhaps the fur makes a difference, they say in a video intended for the 2010 APS Gallery of Fluid Motion.
I think that the missing ’looseness coeffecient’ is related to a combination the length and texture of an animal’s fur and the plasticity of its skin. And I suspect that the looseness of the skin is the more important factor. To test this I would find a group of dogs that had similar shoulder radii but different coat lengths and textures and different degrees of skin looseness. A largish beagle, a Shar-pei, a small labrador, an English bulldog, an American water spaniel, a Keeshond and a golden retriever would provide a nice data set for that experiment.
In a follow-up experiment I’d test the importance of surface adhesion factors like the texture and oiliness of the coat.