# How fast should a large dog shake, if a large dog could shake dry?

Have you ever wondered what the optimal shaking frequency is for a dog that is trying to dry its fur by shaking itself?

… yeah, me either.

But a couple of physicists have thought long and hard about this and have created a mathematical model that allows one to solve to find the optimal oscillation frequency for doggy drying:

“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.”

Turns out there’s a bit of a problem with the model. The oscillation doesn’t scale as the square root of the radius of the dog, it scales as the radius to the 3/4th’s power. At least that’s what the observational data is showing. So clearly the model will need some refining.

So… now you know.

The Author

Episcopal bishop, dad, astronomer, erstwhile dancer...