October 1, 2012 | 3
This year’s Ignobel prize in physics goes to two separate research groups, one of whom also received a backdated Ignobel prize for a previous study*! Two Ignobels in one lifetime! Famous? Or Infamous?
Girls, and long-haired guys, haven’t we been there? You’re jogging along, and the next thing you know your ponytail is tick-tocking along behind you. Or in my case, whipping back and forth and then sticking to my sweaty back (We all know the romantic image of a pretty jogging girl with a swinging ponytail, but of course they leave out the part where she sweats). Sure, no one expects their ponytail to stay still, precisely, but when you’re moving up and down and forward…why is it moving side to side?
For this, we need some physicists.
“Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles.” Raymond E. Goldstein, Patrick B. Warren, and Robin C. Ball, Physical Review Letters, vol. 198, no. 7, 2012.
“Ponytail Motion,” Joseph B. Keller, SIAM [Society for Industrial and Applied Mathematics] Journal of Applied Mathematics, vol. 70, no. 7, 2010, pp. 2667–72
It all started with Joseph Keller. He used to go jogging around the Stanford campus, and was struck by all the women jogging around as well. In particular he was struck by their lovely, bouncing…ponytails. Why DID the ponytails swing from side to side like that? Being a physicist, he set out to understand why.
To look at this in theory, he compared the ponytail to a pendulum. He looked at both a stiff pendulum and a more flexible string (of more than 10 inches), bounced it up and down, and did some math. It turns out that the motions of both the pendulum and the string satisfy the Hill equation, which refers to oscillations in a solution. Air still counts as a solution. And when you work out the math, the Hill equation predicts that the natural frequency of the pendulum (the ponytail) will grow over time, causing the ponytail to swing from side to side even though the head is only going up and down. This is particularly true when the ponytail frequency is HALF of the jogging frequency, which it generally is.
You’d think then that if you just ran faster, you’d make the jogging frequency too quick, but in fact that’s not true. When people run faster their feet generally don’t MOVE faster, instead their steps lengthen. So the ponytail frequency remains close to half the jogging frequency, and the ponytail is doomed to swing.
Of course, this is looking at the ponytail as a single pendulum unit, as a string. In reality, a ponytail is a whole pile of strings. Up to 100,000 strings, to be exact.
This is where the second group honored with the Ignobel, Goldstein et al, took up the research. The question is now, how do the individual fibers make up the shape of the ponytail? They were looking for the balance of forces in each area of the ponytail, and came up with three major forces: the unit weight per length, which will be affected by gravity and pull their hair down, the stiffness of each hair, and the random curvatures in the hair.
You see, even hair that seems pin straight isn’t really, each hair will have tiny curvatures. These give the ponytail its “fluff” and springyness, and cause it to take the triangular shape at the bottom. All this doesn’t too much impact the swingyness of the ponytail while running, because the ponytail will still act, as a whole, like a pendulum.
All that from watching students jogging around campus!
*Joseph Keller took home his second Ignobel for the theory of why teapots drip and how to make them stop. It was originally awarded in 1999 and he was accidentally left off the prize. Keller now basks in the award of the theory of the teapot, and tea drinkers everywhere rejoice over the invention of those little spigots that stop the teapot from dripping. Brilliant.