How fast should a wet dog rotate its body to dry its fur?

Taken from http://www.technologyreview.com/blog/arxiv/25910/. Interesting read.

It's a question that many dog owners will have spent sleepless nights pondering. How rapidly should a wet dog oscillate its body to dry its fur?

Today we have an answer thanks to the pioneering work of Andrew Dickerson at the Georgia Institute of Technology in Atlanta and a few buddies. But more than that, their work generates an interesting new conundrum about the nature of shaken fur dynamics.

Dickerson and co filmed a number of dogs shaking their fur and used the images to measure the period of oscillation of the dogs' skin. For a labrador retriever, this turns out to be 4.3 Hz.

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.

To find out whether that applies in nature, Dickerson and pals studied films of various animals of different sizes. They found that a mouse shakes at 27 Hz, a cat at about 6 Hz while a bear shakes at 4Hz. "Shake frequencies asymptotically approach 4Hz as animals grow in size," they conclude.

But taken together the best fit for this data is not R^0.5 as predicted. Instead the universal rule for shaken fur is that the frequency increases with R^0.75.

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.

Maybe. It certainly gives paws for thought (ahem).

Further ideas in the comments section please.

Ref: arxiv.org/abs/1010.3279: The Wet-Dog Shake