Related Experiment Video
Updated: May 24, 2026

Physiological Preparation of Hair Cells from the Sacculus of the American Bullfrog (Rana catesbeiana)
Published on: March 17, 2017
Shape of a ponytail and the statistical physics of hair fiber bundles
Raymond E Goldstein1, Patrick B Warren, Robin C Ball
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom.
Abstract:
A general continuum theory for the distribution of hairs in a bundle is developed, treating individual fibers as elastic filaments with random intrinsic curvatures. Applying this formalism to the iconic problem of the ponytail, the combined effects of bending elasticity, gravity, and orientational disorder are recast as a differential equation for the envelope of the bundle, in which the compressibility enters through an "equation of state." From this, we identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs.
Related Concept Videos
Accessory Structures of the Skin: Hair and Hair Follicles
Hair is a keratinous filament growing out of the epidermis. It is primarily made of dead, keratinized cells. Hair strands originate at the epidermal penetration called the hair follicle. The hair shaft is the part...
Hyperbolic Functions
Hooke's Law
Divergence and Curl of Electric Field
Accessory Structures of the Skin: Hair Growth and Types
Generalized Hooke's Law

