Ponytail Physics

The Ig Nobel Prizes were held on September 20^th. This ceremony is essentially a more comedic version of the Nobel science prizes, and is designed to honor achievements that first make people laugh, and then think. This year, the physics prize went to Joseph Keller, Raymond Goldstein, Patrick Warren, and Robin Ball for their work on determining the balance of forces that shape and move the hair in the human ponytail hairstyle. Past scientists have apparently been interested in hair as well (who knew hair was so exciting), including Leonardo da Vinci who felt that hair flowed like water. “Somehow,” Dr. Goldstein recalled, “a bunch of balding, middle-aged men sitting around a table came up with the idea that the ponytail was the embodiment of all this interesting physics.” Consequently, these men set to work examining the forces involved in the shape and movement of a ponytail.

The scientists examined individual hairs (in terms of curliness/springyness) and then assembled different ponytails and took note of the average shape of these ponytails. They developed a simple model to predict the shape of a ponytail based on the force of gravity, the force of tension, an elastic restoring force, and a swelling pressure due to the curliness of the hair. This model is able to describe the shape of a ponytail when the individual hairs are bundled together and is represented by a value the authors termed the Rapunzel number. In terms of shape, a short ponytail of springy hair (low Rapunzel number) will fan outward, while a long ponytail (high Rapunzel number) will hang down because the force of gravity on the bundle is greater than the springiness of the hair.

In terms of motion, the men wanted to know why a ponytail swings side to side when people run even though the head is only going up and down. The ponytail cannot in fact be treated as a single object, but rather the individual hairs that make it up must be examined. These hairs all exert elastic forces on each other. Essentially, they found that it was unstable for the ponytail to swing up and down (due to an unfavorable relationship between the jogging frequency and the pendulum frequency of the ponytail) and that a runner’s head prevents the ponytail from swinging forward and backward. Therefore, side to side swinging occurs. On a basic level, it seems like the upward force of tension (y-axis) and the downward force of gravity (y-axis) must cancel each other out, and the elastic forces between the hairs (x-axis) must be responsible for this pendulum like horizontal motion. In terms of the hair not swinging forwards and backwards (z-axis), it seems as if the force of the head on the hair may push back on the z-axis elastic force of the hair and prevent the hair from swinging forward.

I thought that this article was just a neat application of physics. It was interesting to gain some insight into the physics behind something we see nearly every day; the ponytail.

Related Articles:

September 2012 Article:
http://news.sciencemag.org/sciencenow/2012/09/ig-nobels-go-to-studies-of-swayi.html?rss=1

February 2012 Article with Additional Information:

http://www.nytimes.com/2012/02/11/science/ponytail-shape-is-determined-by-complex-physics.html?_r=1

Actual Ponytail Study:

http://prl.aps.org/pdf/PRL/v108/i7/e078101