The Mathematics Of Tear Free Hair Brushing.

I ran across an article on this topic and was totally intrigued.  I have hair down to the bottom of my rear and sometimes it gets nicely tangled and over the years I've learned enough tricks to make it almost manageable to brush my hair without pulling tons out. It requires a good detangled which doesn't always do much, tons of conditioner, and some swearing on occasion. As we all know, you start combing from the ends up. So I had to read this article and share it with everyone based on the title.  It's nice to learn how math explains the way to make brushing hair easier.

A professor of applied math who used to try to detangle and comb his daughters hair noted that the topology, geometry, and mechanics involved in detangling posed some very interesting mathematical questions. The answers to these questions can also be applied to textile manufacturing, and certain chemical processes such as polymer processing.

This gentleman and two others recently published a paper explaining why the standard brushing method is the most effective way to detangle fibers. In order to look at the problem, they simplified it by simulating two helically entwined filaments rather than looking a whole head of hair. Using this model, they examined how the double helix is detangled via a single stiff tine that leaves two separate filaments and they measured the forces involved and the deformations connected with combing hair before simulating the results numerically.

They assigned a mathematical value to the short strokes that begin at the free end and move up towards the clamped end and end up removing the tangles as link density.  Link density refers to the amount of hair strands that are braided with each other. They also identified the optimal minimal length of the stroke, or the minimal length needed to detangle the hair.  Any shorter and the hair would never get detangled. Other people took this information and used it to create an algorithm that allows a robot to comb hair. 

The next step for these researchers is to look at the mechanics involved in brushing curlier hair and how it reacts to humidity and temperature. So they know have the mathematics to explain this method and it's interesting that the information could be utilized to teach a robot to comb hair effectively.  Let me know what you think, I'd love to hear.  Have a great day.