Ruben Meerman: Nice waves! But have you ever wondered why some people manage to catch them easily and others don't, well there's a science to surfing and I'm about to meet a mathematician whose thought about just that. G'day Neville!

Professor Neville De Mestre: G'day Ruben, how are you?

Ruben: Pretty good.

Professor De Mestre: How would you like a maths and science lesson?

Ruben: Out there?

Professor De Mestre: Out there.

Ruben: You'll need a white board won't you?

Professor De Mestre: No you won't need a white board just have this and let's go.

Narration: Professor Neville De Mestre has been body surfing since he was a nipper. He's won ten world surf masters events and thirty Australian masters surf championships. So if anyone knows about body surfing and wave dynamics its Professor Neville! Like a lot of people I've been body surfing for years. There's not that much to it really... or so I thought!

Professor De Mestre: Yes Ruben here comes one, let's go for it...

Narration: Unlike Professor Neville I certainly haven't considered this in terms of a quantitative mathematical examination.

But it's worth considering some simple mathematical models for catching and riding a wave.

Professor De Mestre: That's too early Ruben looks like it's going to break on your head...

Narration: There are definitely forces at work at work here...

Professor De Mestre: I went to university and did a science degree and became interested in research into fluid mechanic's and so I really wanted to know why a person could actually catch a wave and ride it to the beach.

Narration: As part of his research Neville used small-scale body surfer models, such as surfing barbie, to obtain an understanding of the physics involved.

Ruben: Right so what does this mathematics you've been doing look like?

Professor De Mestre: Well the mathematics of body surfing depends on how fast the person can catch the wave and so it depends on Newton's equations and if you remember newton equations where mass times acceleration of the body surfer, must be equal to in this case the propulsive force of the swimmer, plus the drag force due to the wave, that gives us a differential equation we can solve.

Narration: Professor Neville de Mestre is Emeritus Professor of Mathematics at Bond University on the Gold Coast and I've got a feeling this is about to get very complicated!

Professor De Mestre: Ruben this is a wave simulator machine and notice that the wave travels in this direction, what we're interested in is what is the particle speed in the wave just at the front, just at the front here. Now if you're swimming in a river and swimming upstream then the drags against you, you've got negative drag but if you're swimming downstream and the rivers flowing faster than you can swim you've got positive drag, that's what we're interested in here we want positive drag from the wave front so that you can get up to wave speed and catch the wave.

Ruben: Right so we need the assistance of that wave. That's great but how about those equations?

Professor De Mestre: Well let's go and have a look at them. The mass of the swimmer, times the acceleration of the swimmer equals the propulsive force of the swimmer, plus the drag. So let's expand on this drag force for the wave. It's proportional to the relative velocity squared now what's the relative velocity, well W is the speed of the wave particles and V is the speed of the swimmer and if you square it then that gives you this expression. This now is a differential equation. The solution is V is equal to W minus A times something called the hyperbolic tan, it's a very complicated mathematical expression and that involves this constant K, the time that we take off and the mass of the swimmer M.

Ruben: Hang on a minute professor! What does all that actually mean?

Professor De Mestre: From that we can work out whether the swimmer can actually catch the wave or not.

Ruben: So the trick is we've got to get our speed up to wave speed. What kind of wave speed do we have to get up to in the ocean?

Professor De Mestre: The wave speed is three metres a second and swimmers like Grant Hackett and the Olympians do about two metres a second, most of us swim about one metre a second, so we've got to increase our speed up to wave speed.

Narration: So if you're a newcomer struggling to catch waves, start where it's shallow and use your legs to push off, otherwise use flippers if you're going out into deeper water. Now of course when you're in the surf you're not supposed to be thinking about a hyperbolic tan or the value of W, I'm sure my dolphin friends don't... but I'm very glad Professor Neville has!