Physics of the Ponytail

Have you ever thought about the shape of a pony tail? Unless you are an artist or an animator, this question probably never crossed your mind. But when paying closer attention, it’s easy to notice that pony tails have different shapes due to different hair textures and lengths, whether with or without hair extensions.

On February 13^th, 2012 a new research has been published in Physical Review Letters by Professor Goldstein, Professor Ball and their colleagues. They have established a mathematical theory that provides numerical understanding of the dispersal of hairs in any ponytail thus explaining its shape.

They came up with this equation after taking in an account the hair stiffness, hair curliness and effects of gravity. This equation also consists of a new quantity called the Rapunzel Number which can predict the shape of any ponytail. This equation is simple but it utilizes and extends the central hypotheses in statistical physics.

The new findings explain how a bundle of hair can swell from outward pressure that is caused by the collisions of hair strands. This research can also be used for many other fiber materials such as fur and wool. Furthermore these findings will benefit other industries such as animation and computer graphics as the representation of hair has been found a challenging problem in the past.

How will these findings change our everyday lives? We will have to wait and see. They are however, likely to impact not only the computer animation and textile industry, but also personal care products.