Engineers find the answer to a curly question


In 2012, Disney's Brave crowned Scottish princess Merida with wild, flame-tinged spirals, the ideal physical manifestation of her gutsy, fiery temperament. Her hair - an uncommon texture for animated heroes and heroines - saw Merida stand out from the pack. Why? Not because of an inherent prejudice in the film industry towards curly hair (we hope), but because the process of animating curls is a fraught one that computers can't readily adapt to.

New developments in the field, however, look to make that process several steps easier. Scientists from France and MIT have created a detailed model, for the first time, of a strand of 3D animated hair. Their research isn't limited to giving Disney princesses stylish locks, however; but could be instrumental in analyzing the paths and structural integrity of the curve of steel pipes, cables, and tubing.

Published in Physical Review Letters, the report, Shapes of a Suspended Curly Hair, examines the physical bearing of curly hair, as well as its gravitational response to being suspended under its own weight. Though the research doesn't factor in the manifold ways in which hair moves and interacts on the head, it does crunch the numbers to quantify the behavior of individual curly strands. "Our work doesn't deal with the collisions of all the hairs on a head, which is a very important effect for animators to control a hairstyle," said study co-author Pedro Reis, an assistant professor at MIT's Department of Civil and Environmental Engineering and Department of Mechanical Engineering. "But it characterizes all the different degrees of curliness of a hair and describes mathematically how the properties of the curl change along the arc length of a hair."

In doing so, the same findings can be applied to tubular steel. Despite appearing rigid and straight, steel in large quantities is remarkably flexible, and can prove unwieldy and unpredictable for engineers. The findings from this study will allow scientists and engineers to project the shape and curve of steel pipes and Ethernet cables. It'll also be able to negotiate the springiness of curly, animated hair.  

Reis didn't initially intend to study the physics of curly hair, but upon analyzing flexible rods, found the patterns and behavior to mimic that of wavy strands. He then made contact with Basile Audoboly of the Universite Pierre et Marie Curie, who had previously studied two dimensional hair strands.

Raymond Goldstein of the University of Cambridge spoke highly of the findings. "One of the key issues was how to handle the distribution of intrinsic curliness found in real hair. Reis et al. focus in exquisite detail on the properties of a single curly hair under gravity, which is itself a very nontrivial problem due to the nonlinearities in the physics," said Goldstein, who was not involved with the study.

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