The Physics of Curly Hair

 A major problem in animation is accurately depicting the movement of curly hair. Seeing as only in recent times there has been a representation of diverse hair textures, animators and physicists are tasked with creating models that account for the mechanics of curly hair. From a physics standpoint, different degrees of curliness of a hair need to be described mathematically and how the properties of the curl change along the arc length of a hair.

Using lab experimentation, computer simulation, and theory, a team of researchers identified the main parameters for curly hair and simplified them into two dimensionless parameters for curvature (relating to the ratio of curvature and length) and weight (relating to the ratio of weight and stiffness). 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.

As a strand of hair curls up from the bottom, its 2-D hook grows larger until it reaches a point where it becomes unstable under its own weight and falls out of plane to become a 3-D helix. 

A curl can change phase — from 2-D to 3-D local helix to 3-D global helix, and back again — 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.