The Physics of Pixar's Hair

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How is a curling hair like a long-range oil pipeline? And what two groups are working on the physics that apply to both? Learn about the science of engineering mop-tops.

Over at Physics Central's podcast, there's a fascinating discussion with an MIT grad student, Jay Miller, who looks at the curve of the flagella on an amoeba, the spiral of a double helix, and the buckling of an oil pipeline. Through a group of acquaintances, he found out that the movie-makers at Pixar were doing the same. They were trying to figure out the exact motion of the curly hair that the heroine in Brave flips around the screen. Each separate group was studying the same curling motion.

As Miller says on the podcast, "Hair actually is the easiest example of a whole class of problems."


So what do a human hair, a steel pipeline and an amoeba's flagella have in common? Once they all assume the right proportions, they all work the same. A miles-long pipeline, though it can be massively thick when looked at up close, looks like a long, spindly hair when it's spread across the landscape. When a hair is short enough (like a military buzz cut) it's sticking out from the head directly as it grows. It's short enough that its internal strength can stand up to the force of gravity. As it grows, however, it has to 'carry' a longer length, and gravity pulls it down.

Even those of us who aren't at MIT — or working for Pixar — can see the interplay of gravity, exerting a force in in one direction, and the structure of the actual 'hair' curling in on itself. Grow a hair long enough, and its own weight will pull it straight. However, as you get to the very tips of the hair, which don't have as much weight on them, the curl will come back. The more towards the end you get, the less weight is on it, and the more extreme the curl.


You can see this successfully rendered in the table scene above. Although it's clear that the young boys have larger, softer curls than the girl, the hair on the top of their heads is piled up, while hers is pulled straighter than the rest of her hair. The weight is pulling the top of her hair straight while the bottom is in tighter ringlets. In real life, people will notice that their 'straight' hair will curl at the end, showing that what they have is curly hair that only has enough strength to curl at places that don't support a lot of weight. Meanwhile, in the macro scale, an oil pipeline will 'curl' in reverse. Its length it set out horizontally, so gravity 'pulls' its straight structure into a curl. Shifting earth or driving wind can cause it to curl in on itself, at exactly the point that are feeling the most force. The ends, or the parts that are supported by struts, will remain. A straight pipeline is, essentially, a curly hair in reverse, but the interplay of forces is the same.

That relationship, the length of the 'hair,' the internal strength of the 'hair' and the force causing the internal structure of the hair to bend out of its shape are the same model, even if the specifics change. Both groups, the movie makers and the engineers, are figuring out how to 'plug in' certain characteristics to the model in order to get the kind of structure that they want. The structure, both in scale and in purpose, is very different. Animators want a springy, chaotic, visually interesting head of hair. Engineers want an orderly structure capable of pushing an amoeba around a petri dish or water through a pipeline. But both are working on the same idea, and using the same physical relationships.


Top Image: Pixar Planet

Via Physics Central.