Ponytail physics

Hair has been of enduring interest for centuries. Leonardo da Vinci pondered the fluid-like streamlines of hair in his notes written more than 500 years ago.

Now a team of scientists have come up with a mathematical formula to determine the distribution, or shape, of bundled hair from the properties of a single strand.

Raymond Goldstein from the University of Cambridge, Robin Ball from the University of Warwick and Patrick Warren, a researcher in the corporate lab of Unilever, published their findings on Monday in the journal, Physical Review Letters.

"We wanted to figure out what mathematical variables we could use to describe hair," Goldstein told DW. "We came up with a formulation that looks a lot like the theoretical approach to fluids."

Let down your hair

The scientists have called their formula the Rapunzel Number, which takes into account crucial characteristics such as the stiffness of hair, the effects of gravity and the random curliness that provides body.

"We looked at what in physics we call a many-body problem - in this case the approximate 10,000 hairs of a ponytail - and rewrote it in such a way to be an equivalent single-hair problem," Goldstein added. "But the single hair is actually the edge of the ponytail."

Goldstein, who has researched elasticity, was approached by Unilever a couple of years ago to collaborate on research on the basic properties of hair, including tangling and the shapes of individual strands.

"Part of the issue was how to characterize individual hairs," he said. "What makes hair, say in Brazil, different from hair in Japan?"

The new research, which delves deeply into mathematics and physics, sheds light on the complex physical system of bundled hair. Unilever hopes to use the research to create new products someday.

"We're particularly interested in adding volume to hair, which is a very high priority among female consumers," said Dominic Tildesley, Unilever's vice president for research and development. "We can coat hair, but a more interesting - and perhaps more difficult - target is to modify the mechanical properties of hair by reversibly absorbing small molecules into it."

Creating hair volume

Tildesley said that the research could be especially helpful in this area - and another.

"We're also very interested in the ability to change the volume in hair without wetting it too much," he told DW, pointing to the need to conserve resources, particularly in markets where the supply of water is an issue.

Goldstein and his colleagues believe their work has implications for understanding not only hair but also the structure of materials made up of random fibers, such as wool and fur, and could be of interest to the textile industries, as well as the computer animation industry, which has struggled with the representation of hair in its products.

A next step, Goldstein added, could be to merge the team's approach to hair shape with the findings of Joseph Keller, a mathematician from Stanford University who studied hair motion.

Author: John Blau
Editor: Cyrus Farivar