Three professors of physics have taken on the ultimate challenge: “Why does a “ponytail” look so interesting?
Professors Raymond E. Goldstein, Patrick B. Warren and Robin C. Ball have solved the problem.
“It’s elementary, Dear Watson” they could have said. “Just an equation that takes into consideration molecular balance, gravity, the effect of rotating hair and the tightness of the rubber band.”
Here is their posting in Physical Review Letters of the American Physical Society…
Shape of a ponytail and the statistical physics of hair fiber bundles
Raymond E. Goldstein, Patrick B. Warren, and Robin C. Ball
Accepted Wednesday Jan 18, 2012
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.”
This is very clear to anyone with the least exposure to differential equations.
We must remember that it is not the head underneath the ponytail that is important, it is the hair!
Its elasticity and whether a shampoo has been applied in the recent past.
Many experts on ponytails were consulted prior to the elaboration of the equation.
Some critics have noted that there seemed to be a “sexist” element in the research, because the experts were all males.
However, now the problem has been solved, and better products will be produced in laboratories across world in the ultimate search for the “Perfect Ponytail.”
For those who feel that their ponytail is the best, they should contact the authors listed above for their comments.