Professor Raymond Goldstein at the University of Cambridge and his team have developed an equation which, when combined with a quantity wittily known as the ‘Rapunzel number’, can predict the shape of any ponytail.

Goldstein, Professor of Complex Physical Systems, said: "it's a remarkably simple equation.” It takes into account the stiffness of hairs, the effects of gravity, the presence of random curliness or waviness, plus the length of the ponytail.

The findings explain why a short ponytail comprising springy hair, characterised by a low Rapunzel number, fans outward, whilst a long ponytail with a high Rapunzel number hangs down, as gravity’s pull overrides the springiness.

Professor Goldstein worked on the equation with Professor Robin Ball, from the University of Warwick and Patrick Warren, from Unilever's Research and Development Centre.

The question inevitably arises of what triggered their interest in ponytails in the first place? It transpires that it was not a fatherly attempt to engage a teenage daughter in physics and minimise her time spent struggling with unruly locks each morning.

Instead, Unilever, the multinational corporation whose products include TRESemmé shampoo and Brylcreem, approached the researchers several years ago with the hope of collaborating to study the properties of hair, including its tendency to tangle and the shapes of individual strands.

In practice, the discovery should enable Unilever to create better hair products – great news for those whose ponytails are looking a little limp and lacklustre in the bitter winter cold.

Furthermore, the significance of the research goes beyond hair care. It will aid the computer graphics and animation industry, where depicting realistically the movement of characters’ hair has always been a challenge.

Ponytails may not seem like the most obvious, or consequential, phenomenon for physicists to study. However, hair has always interested scientists and artists. Leonardo Da Vinci, five centuries ago, was fascinated by the science of hair, noting the propensity for its waviness to resemble a river.

The research is published in the Physical Review Letters journal and delves deeper into why, as Professor 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.”