A labrador oscillates at 4.3 hz

October 20, 2010 at 9:29 am 8 comments

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.

The video (which is excellent by the way but could not be embedded) is posted here and the original article here.

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.


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8 Comments Add your own

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  • 2. SmartDogs  |  October 20, 2010 at 4:54 pm

    Taking a minute to look at this again – I think the issue may be that the group only looked at the oscillation of the animal’s skin around the radius of the shoulder. When one is dealing with an animal that has loose skin and/or a long coat there should be a significant second oscillation down the length of the skin/coat occurring radially outward from the oscillation about the shoulder.

  • 3. Viatecio  |  October 20, 2010 at 7:33 pm

    As fascinating as this is, there’s still that little voice in the back of m head expressing concern that things like this are being funded as research.

    And then I still can’t get over how absolutely amazing it is that someone wanted to put time into studying this.

    As conflicted as I am, it’s brilliant and well-done, as opposed to studies in which animals (and not just dogs) are shocked in the name of science.

  • 4. Grahund  |  October 21, 2010 at 2:39 pm


    This was a student project. Students have to learn how to do research some how. There’s no better way than doing actual research. Think of this as student education, not research.

    On the other hand it is very difficult to predict in advance what research will have lasting value. Funding agencies should put some effort into focusing their funding on research with a high probability of long term value. But they shouldn’t put all their eggs in one basket. They should also provide good scientists with funding to look at whatever interests them a la the MacAuthur Grants. The old Hewlett-Packard used to provide its engineers one day a week (or something like that) to work on anything they wanted to. Old HP found this to be a valuable investment.

    One way to think about this is the difference between a command economy (Communism) and a free economy (Capitalism). In a command economy the powers that be dictate from above what goods should be produced. In a free economy individuals decide what they want to produce. Sometimes individuals decide wrong, but over all the economy is much stronger. Same forces are at work in scientific research. Dictating all research priorities from above would reduce the overall benefit of science by missing odd, unexpected results. Allowing scientists the freedom to pursue whatever interests them is more beneficial to society overall even if sometimes they spend time and money on ultimately fruitless projects.

  • 5. Viatecio  |  October 21, 2010 at 7:18 pm

    Grahund, thanks for the clarification. I didn’t realize that this wasn’t funded…it was quite intricately done and involved some things that we weren’t allowed to work with for our student research project. Then again, psychology is quite a different field, and even when I suggested a project that would use animals as a ice-breaker for otherwise-apathetic college students, well, I learned the disappointing way that we couldn’t use animals.

  • 6. Grahund  |  October 21, 2010 at 8:37 pm

    I didn’t say it wasn’t funded. It probably was to some extent. Most higher education is funded by sources other than tuition. I tried to make two points: First it doesn’t matter whether it was funded or not. It is better for society to fund some odd-ball research than to dictate in all top down. And second, it was part of the education process for some of the researchers; the best way to learn to do research is to do research.

  • 7. Viatecio  |  October 22, 2010 at 4:40 pm


    Sorry, I’m a little dense sometimes. This week, I’m on a rollllll.

    I had to do a capstone research project for my BA and all we needed was IRB approval. No money, just time, research and some students willing to donate an hour of their time to support our hypothesis.

    The Institute for the Bloody Obvious (as Fark submitters sometimes put it) does have use for such fruitless projects, and admittedly, they are fun and sometimes fascinating to read. Money not wasted, but in the grand scheme of things MIGHT have gone to…well…better…causes…NAH, let’s have fun with science!! 😛

  • 8. Beth - GA Tech alum  |  October 24, 2010 at 8:00 am

    Very interesting and insightful. How many of us have watched dogs shake and never thought if there was a pattern.
    Having said that, there is more to the shake then the students mentioned. First, the tail has a smaller radius. When the shake gets to the tail, does the frequency increase? Same with the head. How come my dog dries everywhere except on the lower part of his back, just before the tail? Do the back legs (being stronger and larger) change the shaking frequency? Some dogs have hair and others have fur. Do the numbers change for dogs with hair?
    So much more to learn.

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