Pony Up

Some women and some men with long hair tie it back in a ponytail. When I see a young woman walking down the street with her ponytail, my attention is drawn to her face as with the hair drawn back, the bone structure is more clearly visible.

However, some physicists are drawn to the shape of the ponytail and want to describe it in the purest poetic terms, that is, in terms of mathematics so that its essence can be captured by a single number.

Goldstein, Warren and Ball have been discussing ponytails at length and have come up with the correct poetry, which they have released on an unsuspecting world via Physical Review Letters (1).

They waxed mathematically lyrical about the gravitational force on each hair producing a tension which is balanced by the restoring force from the elasticity of the hair along with the local density of hair in the bundle which forces the hairs to spread apart, an effect which is exacerbated by the average curliness of the hair.

The beauty of getting all these forces into perfect balance allows the shape to be defined by their ratio. That ratio is now called the Rapunzel Number. That number will go up or down as the hair grows, is cut or is treated with caring hands anointing it with expensive products.

I’ve no doubt that many physicist enjoy fairy tails and the tale Rapunzel’s golden locks hanging down from her tower, but I feel obligated to point out that she didn’t wear them in a ponytail, but in strong braids.

And where is Dame Gothell (the enchantress) and the prince in all this?

  1. http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.108.078101

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