View Full Version : Article on the "Ponytail Shape Equation"

February 13th, 2012, 02:57 PM
Some scientists have developed an equation that predicts the shape of a ponytail. Link to BBC website (http://www.bbc.co.uk/news/science-environment-17012795)

There's also mention of the "Rapunzel Number. Sadly, there's no explanation of either of either thing...

February 13th, 2012, 03:05 PM
Hee, I just read that and was wondering if anyone would post it here...

The thing about strands of hair kind of behaving like fluid (I think? I'm not so good at the science) was really interesting, i thought.

February 13th, 2012, 03:13 PM
Well, I can get the full scholarly article here (http://prl.aps.org/pdf/PRL/v108/i7/e078101) (Link opens a PDF, at least when clicked from my university). A brief skim tells me that it's fairly complicated math dealing with the how hairs, each having different wave patterns, will behave spreading out from where they're compacted at the base of the ponytail. "Rapunzel number" is term they've assigned to a dimensionless variable describing the length of the hair, and is the ratio of the length of the hair over how much it is bent by gravity.

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.

February 13th, 2012, 03:18 PM
Oh, the things we spend money to find out :rolleyes:

It is kinda cool though. I thought it was going to be more the shape of a ponytail due to the length of hairs. I, for instance, love layers, but hate the way they look in a high pony. It gets all one legth and blunt at the end. Hair with a blunt hemline, to me, looks much nicer in a pony because it makes its own layers.