# The IgNobel Prize for "Hairodynamics"

## Interview with

This year's IgNobel Prizes saw the physics award going to Ray Goldstein and colleagues, for understanding the physics of a human ponytail. Ray now calls this the science of "hairodynamics"...

Chris - So, what was the award for? What did you do to win your Ig Nobel?

Ray - Well, the award was given to two separate groups. The first, myself in collaboration with Patrick Warren a Research Scientist at Unilever Research and Robin Ball, Physicist at the University of Warwick for explaining the shape of a ponytail. And the second half of the prize went to Professor Joe Keller at Stanford University who explained the swing of a ponytail.

Chris - Why? I mean, is this a big problem? It must be of someone like you who's working on it.

Ray - Well, the genesis of half of the prize work is really at the Unilever research labs in the UK. As you know, Unilever is a global manufacturer of personal care products including shampoos and conditioners. And for obvious reasons therefore, they have great interest in the properties of hair and for a number of years, scientists including Patrick at Unilever had been trying to understand difficult problems involving say, the tangling of hair and in general, understanding the properties of bundles of hair as in a ponytail. And they reached out to me several years ago to join their team to help them solve these kinds of problems. Now I have to say, when I was first contacted by them, just like with the Ig Nobel Prize, I first laughed hilariously. I actually thought this was a Nigerian email scam or something like that, but I simply begun to realise that there was very interesting physics there and on my first visit to Unilever, a bunch of us were sitting around the table and they were explaining to me these scientific questions they were after. And we were given what are called hair swatches which are commercial bundles of hair that are used to test shampoo and conditioner. They're about 25 centimetres long, they have about 10,000 hairs and they're clamped at the top, and so in fact, if you hold them vertically, it looks like a ponytail. And in trying to figure out how to get into this project, there was understanding the properties of large numbers of hairs, we realised that actually, the shape of the ponytail was the right testing ground. That is, if we couldn't solve that problem and understand something that seems as simple as that then we couldn't go any further. So, we set ourselves the task of trying to explain the shape of a ponytail.

Chris - Is it tricky? Because when you're dealing with a ponytail and you have lots of individual hairs and they all have their own behaviour as a material, and they're all interacting with each other which means that there's not just one type of behaviour, the individual hair. It's the behaviour and how that behaviour influences the behaviour of all the other components in the ponytail.

Ray - Exactly, so we now understand and historically, much of this was understood as well, but there are at least 3 main features that matter for this problem. The first two are easy. Hair has elasticity. It resist bending and so, it tends to remain as straight as it is isolated. The hair also has weight, so gravity pulls it down and that would tend to make a collection of hairs just hang vertically. But most importantly, hair has random curvatures or meandering and it's accounting for that. And as you said, this is a problem involving large numbers of individual and distinct interacting objects, and that's where the difficulty lies in the theory. And so, we borrowed some tricks from other areas in physics, in particular, the study of fluids and the study of electronic systems where there's the notion that all of these complicated randomness could somehow be accounted for, if one knew just a few average quantities of the hair bundle. That is, instead of keeping track of 10,000 hairs, we'll just keep track of say, the local orientation of the filaments in the bundle and just the local concentration of them, the number of per unit volume. And so, we formulated a theory using that idea, that the effects of the randomness with some of yet unknown function of these quantities. And after a lot of crank-turning, theoretically, we came up with an expression, which we called the ponytail shape equation

Chris - The hair comes in lots of different flavours, doesn't it? Or at least you've got people who have Chinese hair which tends to be quite different in characteristics than people who are say, blonde and have that very fine wispy hair like my son for example. So, does the equation have a component or parameter that accounts for that ethnicity?

Ray - Exactly. It turns out that this pressure, the magnitude of this pressure and the scale of radius of the ponytail at which the pressure disappears is very crucially dependent on the average squared curvature of the filaments and their stiffness. So, it's basically like a spring. Ifyou have a curly piece of hair and you would flatten it between two sheets, you'll have to do work to compress it. And so, the more curly the hair, the more work you have to do, the greater the pressure pushing out. So in principle, there's a way of sort of cataloguing different types of hair by the pressure with which they push out of a bundle.

Chris - Does that mean then that now, if you take that equation, you can model hair much more accurately? And so, computer games designers, people making Hollywood movies where they don't want to pay extras, they can pay a computer instead who can make much more lifelike and realistic renditions of hair, which I understand has always been a major headache right now.

Ray - It has been a major headache, absolutely, and there are lots of groups that have made wonderful progress on this including a particular interesting work in Paris. But the incorporation of this bundle effect is something which we think could be an exciting new twist on this that could actually make things much more realistic. And we hope in the future, to be able to think about that, as well as about what might be called the hairodynamics problem. That is how hair interacts with hair flow as in when you wave your head or you're in the wind.

Chris - So how did this go down in front of the Ig Nobel ceremony? You have about 1 ½ minutes to tell the story, didn't you?

Ray - Yes. Well in fact, since there were two parts of the prize, we just had 30 seconds. So, we distilled it down to the essence. In fact, we joked about this on 2012, the search for understanding deep properties of the universe was partially successful in the sense that the Higgs Boson appears to be found and of course, that's supposed to be the explanation for the origin of mass, and we have to come up with an explanation for the origin of volume.

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