Rapunzel, Leonardo and the physics of the ponytail

New research provides the first mathematical understanding of the shape of a ponytail and could have implications for the textile industry, computer animation and personal care products. Our findings 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." - —Professor Ray Goldstein From Leonardo Da Vinci to the Brothers Grimm, the properties of hair have been of enduring interest in science and art. Now, a University of Cambridge physicist and collaborators have quantified the curliness of human hair and developed a mathematical theory that explains the shape of a ponytail. Research published today (13 February) in Physical Review Letters provides the first quantitative understanding of the distribution of hairs in a ponytail. To derive the Ponytail Shape Equation, the scientists took account of the stiffness of the hairs, the effects of gravity and the presence of the random curliness or waviness that is ubiquitous in human hair. Together with a new quantity described in the article - the Rapunzel Number -  the equation can, they say, be used to predict the shape of any ponytail. The research by Professor Raymond Goldstein from the University of Cambridge, 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.