The Grand Unified Theory of Tennis

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We've seen how we can use engineering to communicate with athletes and coaches. And we've seen how we can take measurements of sports without disturbing it. But what we could model a whole sport from the equipment, to the elite athlete, to the environment, and even to the rules? Well, we've been working on a grand unified theory, not of gravity and quantum mechanics, but of something much closer to home.

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Constructing a grand unified theory of a sport is about painting the whole scientific picture. In tennis, we look at the friction between the surface and the player's footwear. And there are many properties of the racket that we measure and model-- the strength and balance of the frame, the string tension and elasticity, the impact point and swing speed, and how the racket imparts spin to the ball.

For the ball itself, we look at aerodynamic drag and lift, spin and movement vectors, how it bounces, and how all of that is affected by atmospheric factors like humidity, pressure, and wind speed. We could even look at reaction times in the biomechanics of the players using motion tracking and 3-D modelling to analyse how they move and slide on the surface, and how their perceptions affect their play. We combine these sorts of factors to make one overarching computer simulation-- the grand unified theory of tennis, Tennis GUT.

Now we can change any of these variables. We connected them all together and they're all here in this laptop. If I run one of my simulations, here I'm solving my models individually. And here we have 120 mile-an-hour serve at Wimbledon. You can see the ball reaching the baseline there. Now what I can do now is, I can make a change, and we can look at verifying some of the anecdotes that players come up with. So if I look at playing the same tennis shots at 3,000 metres-- at, say, Mexico City. Well, one of the things that players say is that the ball arrives much, much quicker at the baseline. So we can use the model to test that theory.

And here we have the two shots. The red one is Mexico City, and the blue one is at Wimbledon. And you can see that the shot at Mexico City arrives much quicker at the baseline. And the reason for that is because the density of the air has decreased, allowing the ball to fly faster. The consequence of that is, there is actually a ball for playing at altitude to readdress that balance.

Any mathematical model needs to be validated experimentally. And we're here in the laboratories of the international tennis federation. And here I am with Dr. Stewart Miller. And we've helped you over the years develop a few machines. And here's a racket power machine which is there to mimic the serve of a player. It's been a bit of a beast to get working. And it hasn't always worked how we wanted. Now, why would we even want a machine like this?

Because of the way in which tennis racket technology is changing. For many, many years all rackets were the same size. They with 27 inches long and 9 inches wide. But when Howard Head found that you could make rackets out of different materials that were bigger, longer, wider than the old wooden rackets, then the ITF decided that it'd better write some rules for tennis rackets.

So we've got a rule for the rackets, and then sometimes other things come up, like spin, for instance. So what expense have we got for that?

Once you've found out how the ball comes off the rackets in terms of speed, you need to know the amount of spin that's generated as well. And this device here allows us to quantify the amount of spin that different rackets and string combinations can generate.

So we've got spin, what next?

Well, then we need to know how that spin affects the flight of the ball through the air?

So that means we go to the wind tunnel?

Indeed.

Lead on.

Wow, I've forgotten how beautiful this thing is. It's like a space shuttle, or a rocket, or something. So if we open up the working section here, right, so we've got our ball on a little axle here. So, it's a while since I've looked at this, can you remind me of the specifications of this wind tunnel?

It simulates the aerodynamic affects and measures those aerodynamic characteristics for balls travelling up to 160 miles per hour, which is just a little bit faster than the fastest serve that's ever been recorded. It also allows us to spin the ball at speeds of up to 6 and 1/2 thousand revolutions per minute, which is just a bit faster than the fastest spin rate that's ever been recorded. So that means, with this device we can simulate just about any tennis shot that can be generated.

Now, the spin rate has gone up since we first developed this. So that's changed. What other things might change in tennis?

Well really, we're not sure because that's in some ways up to the manufacturers. But what we can do through these experiments is assess the effects of those changes. And when we put them together in Tennis GUT, that allows us to predict what might happen in the future and to protect the nature of the game.

The grand unified theory is just a model of reality. And we can use the physics to understand what is going on. Equipment manufacturers would love to get their hands on the model, but the ITF is using it to preserve the balance between the tradition and technology within the game. Now Tennis GUT has shown us the way forward, and we can use the same modelling techniques and the way its used for any sport.