Science Unravels Ponytail Mystery: The Rapunzel Number

A trio of UK-based scientists has developed a mathematical equation explaining the shape of human ponytails. Their discovery, which encompasses everything from hair stiffness to curls, could help textile manufacturers, animators, and personal care companies improve their products.

Reuters News report by Jim Drury.

Video Transcript:

Fashion guru Karl Lagerfeld is known for his clothes, his outspoken views….and his ponytail. This simple hairstyle is one that’s puzzled scientists and artists ever since Leonardo da Vinci mused on hair waviness 500 years ago. Now Cambridge University Professor Ray Goldstein believes he can explain how ponytail shapes are formed. His team has developed the Ponytail Shape Equation, which takes into account four major factors.

Soundbite (English) Prof. Ray Goldstein, Professor of Complex Physical Systems at the University of Cambridge, saying:

“The first is the elasticity, the fact that the individual bundles – or effectively this outer edge – has a resistance to bending like any elastic object. The second is the tension. And then the third contribution is just the weight itself… and that is opposed by the pressure which comes from the random curvatures of the filaments in here, which are pushing out and trying to swell the bundle.”

An average head contains 100,000 individual hairs. But Goldstein believes a ponytail’s shape can be deduced from the properties of a single strand. Working with Warwick University Professor Robin Ball and Unilever scientist Patrick Warren, he took numerous photographs with a high-resolution camera in the lab.

Soundbite (English) Prof. Ray Goldstein, Professor of Complex Physical Systems at the University of Cambridge, saying: “The quantity of great interest is the typical excursion that the hair makes from side to side if you were to hold it vertically, so in that case we held individual hairs from this and then we would take an image and then rotate at 90 degrees and take another image, thus giving us a kind of stereoscopic view.”

To predict the shape of a ponytail the equation must take into account its length – the so-called Rapunzel Number, named after the fairytail in which a young long-haired girl is exiled to a tower.

Soundbite (English) Prof. Ray Goldstein, Professor of Complex Physical Systems at the University of Cambridge, saying:

“The crucial test was to actually cut the ponytail down in stages and see if the theory continued to predict the proper shape, and once you get down to this length you observe that the hair is basically unaffected by gravity, and that means there’s a characteristic length, which turns out to be about two inches, below which you can ignore gravity and above which you must consider it.”

A short ponytail, like this one sported by David Beckham a decade ago, is characterised by a low Rapunzel number, and fans outward. A long ponytail has a high Rapunzel number and hangs down, the pull of gravity overwhelming its springiness. The research could aid computer animators, who find it difficult to accurately represent hair. Consumer goods giant Unilever believes the research could lead to better quality shampoos and hair gels. Many companies have followed the trio’s research with great interest… as they seek to untangle one of history’s hairiest puzzles.

Original story by Jim Drury, Reuters.

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