"The physics of the ponytail"
New research by Cambridge University provides the first mathematical understanding of the shape of a ponytail and could have implications for the textile industry, computer animation
Research published today (February 13) in Physical Review Letters provides the first quantitative understanding of the distribution of hairs in a ponytail.
To come up with the Ponytail Shape Equation, the scientists took account of the stiffness of the hairs, the effects of gravity and the presence of random curliness or waviness in human hair. Together with a new quantity – the Rapunzel Number – the equation can be used to predict the shape of any ponytail.
The research by Professor Raymond Goldstein, Professor Robin Ball from the University of Warwick, and colleagues, provides new understanding of how a bundle is swelled by the outward pressure which arises from collisions between the component hairs. This has important implications for understanding the structure of many materials made up of random fibres, such as wool and fur. The research will also help with the computer graphics and animation industry, where the representation of hair has been a challenging problem.
Professor Raymond Goldstein said: “It’s a remarkably simple equation. Our findings extend some central paradigms in statistical physics and show how they can be used to solve a problem that has puzzled scientists and artists ever since Leonardo da Vinci remarked on the fluid-like streamlines of hair in his notebooks 500 years ago.
“To be able to reduce this problem to a very simple mathematical form which speaks immediately to the way in which the random curliness of hair swells a ponytail is deeply satisfying. Physicists aim to find simplicity out of complexity, and this is a case in point.
“We imagine that at least half of the population has direct experience with the properties of ponytails, and we all have likely wondered about the fluffiness of hair. We now have the first quantitative description of this phenomenon and how it competes with gravity.”
Professor Goldstein will be presenting the research at the March meeting of the American Physical Society in Boston on February 28.