Physics of curly hair

Print edition : March 07, 2014

The flexible segments of tubing, with varying degrees of curliness, used as part of the research. Photo: James Miller and Pedroreis, MIT

A TEAM of researchers from the Massachusetts Institute of Technology (MIT) and the Université Pierre et Marie Curie in Paris have been able to arrive at the first detailed model for a 3-D strand of curly hair. The work was published in a recent issue of Physical Review Letters. It is rare to see an animated character with bouncy, curly hair since computer animators do not have a simple mathematical means to describe it. With this development, animators will be able to achieve that in the near future, and engineers could predict the curve that long steel pipes, tubing and cables develop after being coiled around a spool for transport. In the field, these materials often act like a stubborn garden hose whose intrinsic curves make it behave in unpredictable ways. In engineering terminology, these items, and hair, are all examples of a slender, flexible rod.

When Pedro Reis of MIT set out to investigate the natural curvature in flexible rods, he was not thinking of hair. But as he studied several small flexible, curved segments of tubing suspended from a structure in his laboratory, he realised they were not so different from strands of curly hair hanging on a head and contacted Basil Audoly from Paris, who had previously developed a theory to explain the 2-D shape of human hair.

Using experimentation, computer simulation and theory, the team identified the main parameters for curly hair and simplified them into two dimensionless parameters for curvature and weight. Given curvature, length, weight and stiffness, their model will predict the shape of a hair, steel pipe or Internet cable suspended under its own weight.

A curl can change phase if its parameters change. Because a strand of hair is weighted from the bottom by gravity, the top of the strand has more weight under it than the tip, which has none. Thus, if the weight on a hair is too great for its innate curliness, the curl will fail and become either straight or helical, depending on the strand’s length and stiffness. The importance of the work, Audoly pointed out, is being able to take the intrinsic natural curvature of rods into account for this class of problems, which can dramatically affect their mechanical behaviour.

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