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# Fit for a Princess: the Physics of Rapunzel's Gown

How the laws of physics helped style Disney's newest star

Image: Courtesy of Disney

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When the animators at Walt Disney Studios first dressed up Rapunzel, the long-haired star of the forthcoming movie Tangled, and had her spin around in front of a mirror, she froze mid-turn, and the folds in her multilayered purple dress turned stiff as shells. The filmmakers had run up against a challenge that has long plagued sartorially inclined animators.

“From very early on, we knew we wanted to get more elaborate clothing than had been done so far in [computer graphics],” says Rasmus Tamstorf, a senior research scientist at Walt Disney Animation Studios Research. “But when a character wearing free-flowing, multiple layers of clothing moves, it can create a lot of contact between the different layers, especially in the way they slide on top of one another. And that can cause problems.”

Rather than scaling back his sartorial ambitions or deploying armies of animators to illustrate complicated scenes by hand—solutions traditionally employed by ambitious animators to get around the challenge—Tamstorf and his team decided it was time to find a new way to solve the problem.

They got in touch with a computer scientist who has made a specialty of studying how materials respond to collisions. Eitan Grinspun of Columbia University’s school of engineering had become fascinated with this area of research in 2002, when he filmed a cowboy hat hitting and bouncing off the floor. He studied the film for hours in slow motion and found the simplest equation that expressed the interaction of variables affecting the hat’s bounce. These included friction, the hat’s “bendiness” (elasticity) and the momentum with which it hit the ground. Then he translated that equation into simple computer code that could be used to predict the movement of any “flexy, bendy material,” including rubber, fabric, even sheets of metal.

But depicting the movement of Rapunzel’s fancy gown posed a larger challenge. With multilayered clothing, a computer must account for potentially thousands of collisions at once. When an animation program becomes overwhelmed with data, it resorts to a “fail-safe,” a backup program that prevents the layers of fabric from creating new collisions. Previous fail-safes continued to move the fabric forward in space but did not allow the layers of material to move relative to one another, creating a rigid, shell-like appearance. After months, Grinspun and Tamstorf’s team came up with a solution. They accepted the need for a collision-stopping fail-safe, but theirs allows the layers of fabric to slide against one another, and it accounts for friction, which affects the speed with which the fabric moves. The result is far more lifelike. Now Grinspun has moved on to a new challenge—developing a program that accurately predicts the movement of hair, which collides in even more complex ways than clothing. He expects his solutions to appear in another animated feature next year.

This article was originally published with the title Fit for a Princess.

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1. 1. dbtinc 08:57 AM 10/29/10

I guess all the problems in science have been solved. THanks SA.

2. 2. candide 09:09 AM 10/29/10

This is a new low for SA, the "physics" of an imaginary fairy-tale?

3. 3. Laertes 09:10 AM 10/29/10

Technically, elasticity is not the tendency of a material to "bend" but rather its ability to return to its original shape after being bent. Hence a steel rod is more elastic than a rubber one.

4. 4. tharriss in reply to Laertes 09:20 AM 10/29/10

Just curious Laertes, does it depend on how far you bend it?

For example, if you bend the bar 90 degrees, the rubber bar would recover its original straight shape but the steel one would be permanently bent... wouldn't that make the rubber bar more elastic?

5. 5. SteveO 12:51 PM 10/29/10

Laertes has oversimplified, tharriss. The usual word "elastic" in English confounds two terms - stress and strain.

"Elastic deformation" would be defined in engineering as the realm where if you apply a force (stress) to something (say steel or rubber) which causes it to deform (strain) and when you remove that stress, the material returns to its previous shape. (REALLY technically, the modulus of elasticity (a material property) is the slope of the stress/strain plot before plastic yield.)

Once the stress is sufficient, the material enters the realm of plastic yield, where if you release the stress, the material does not go back to where it started - it springs back some but remains bent, say. (The amount it springs back is determined by that slope.) The stress at the transition between elastic and plastic is the "yield strength."

Keep stressing the material, and eventually a maximum stress is reached, and at that point maintaining the same stress will result in the material breaking. That high point is the "ultimate strength."

So (finally!) to answer your question, the steel bar has a much higher modulus of elasticity than the rubber, and a much higher yield point. But the rubber can take much higher strain before yielding and deforming plastically. So depending on what you think the English word "elastic" means, you get a different answer!

6. 6. voltaire in reply to candide 03:45 PM 11/1/10

Please lighten up. Of the top of my head, I could see applications for this program in fluid dynamics (floods, lahars, lava flows)and meteorology. Faraday gave the classic retort when someone challenged the value of his equations, "What use is a newborn baby?"

7. 7. mvhertel@yahoo.com 04:08 PM 11/1/10

It does not damage the child to use their imagination and learn something about the law of physics. Obviously, you do not have children. Take it from this point, from this link, and hopefully you will do your own research on childhood development. Cudos to the filmmakers.

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