Shape of a ponytail
What determines the characteristic drooping, fanned-out shape of a bundle of hair such as a ponytail?
History and references
Settled in 2012 by Raymond E. Goldstein, Patrick B. Warren, Robin C. Ball.
Leonardo da Vinci sketched studies of flowing hair centuries ago, but a quantitative theory of why a bundle of hair splays into its familiar ponytail shape was lacking. In 2012 Goldstein, Warren and Ball modeled each hair as an elastic filament with a random intrinsic curvature and derived a continuum 'equation of state' balancing gravity, tension, elastic restoring forces, and a curl-driven swelling pressure analogous to pressure in a gas of rods. The resulting theory correctly predicted measured ponytail profiles as a function of hair length, and the same swelling-pressure idea also explained related problems like the springiness of curly hair. The work won a 2012 Ig Nobel Prize for its playful subject alongside its genuine statistical-physics content.
An everyday hairstyle turns out to obey the same statistical mechanics used to describe pressurized gases, with hair curliness playing the role of gas pressure.
Explanations that circulated
- A ponytail's shape is determined by gravity alone bending stiff hairs downward — in fact the curl/waviness of individual hairs produces an effective 'swelling pressure' that pushes hairs apart, and this pressure competing with gravity, fiber stiffness and confinement (the hair tie) is what sets the characteristic fanned, drooping profile.
References
- Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles, R. E. Goldstein, P. B. Warren, R. C. Ball, Physical Review Letters, 2012
Solutions 0
Sign in or create an account to publish a solution