The problem of the Wimbledon roof
The comments made about the new roof over Wimbledon’s Centre Court have puzzled me. The Wall Street Journal and the Times had the headline “Wimbledon Roof Slows Balls Down” while the Daily Mail had “How Centre Court’s new roof puts a dampener on Andy Murray’s serve” (I admit that I’m quoted in this one). One comment suggested that “due to the increase in humidity when the roof is closed, balls are heavier and travel slightly slower through the air“.
Well, I’ve done a lot of work for the International Tennis Federation (ITF) on ball impacts, aerodynamics and surfaces and the comments above are physically contradictory (although not necessarily obvious). I want to explain the contradictions and in the process figure out what happens when the roof closes to make the players complain that the ball is slowing down. Hawkeye data has shown the ball to be travelling up to 5 mph slower when it reaches the reciever if the roof is shut.
Our research with the ITF has provided us with a fantastic award winning tool called Tennis GUT (GUT stands for Grand Unified Theory – a little physics joke) that allows you to look at the effects of the racket, the ball, the surface, the air temperature and even the altitude. I will use Tennis GUT to look at a serve and see how the change in environment affects it.
The British weather
The roof’s architect Rod Sheard is quoted as saying that the resultant conditions depend upon the weather before the roof closed and the temperamental nature of the British weather means that this could be almost anything. So, let’s take two scenarios: (1) a warm front of rain appears over Wimbledon taking the temperature to 29 °C with a humidity of 100%; (2) a cold front of rain attacks Centre Court taking with a temperature of 19 °C and a humidity of 100%.
The roof takes around 10 minutes to close and another 20 minutes to acclimatise the temperature and humidity at 24 degrees Celsius and 50% humidity (roughly the average for late June in Wimbledon). In both scenarios above, the humidity is reduced by the air conditioning units in the stadium which makes air density go up by around 0.3% (since the atomic weight of water vapour is 18 g compared to 29 g for air and there is now less water vapour around, click here for a detailed explanation). If closing the roof makes the temperature go down – as with the warm front – then the air density increases. The opposite happens with the cold front. The air densities in the three scenarios are shown in Figure 3; with a warm front the the density goes up when the roof closes, while with the cold front the density goes down.
A 130 mph serve
Now, let’s take a 130 mph first serve with 3,000 rpm of spin (we have found this to be typical using in-house software – SpinDoctor), aim it into the service box and see what happens at the baseline where the receiver stands (Figures 4 and 5). When the roof is shut, the serve takes 0.611 s to go from the server to the baseline after bouncing once in the serve box, arriving at 53.2 mph. This is about 0.9 mph slower than during warm rain (29 °C, 100% humidity), and 0.6 mph faster than during the cold rain (19 °C, 100% humidity). So, while the effect of the closed roof on air density depends upon the weather conditions beforehand, the size of the effect is really not the magnitude of 5 mph quoted in the press. So, if it’s not an air density effect, what else could it be?
Size really does matter
So what about the ball absorbing water and slowing down? Well, interestingly enough, this has the opposite effect to the one you might expect. The ball comes off the racket slightly slower but, because it has more inertia (as a result of higher mass), doesn’t slow up quite so much through the air. The consequence is that a slightly heavier ball arrives at the receiver marginally faster (a 5 g increase in mass increases the speed at the baseline by about 1 mph). Mass, then, isn’t the cause of the apparent slowing up of the ball when the roof closes.
What about the surface changing because of the rain? It could get softer due to the rain if there is enough of it, although usually there has to be several mm of rain to make a difference, and the Wimbledon referee is just too quick to allow this to happen. It is more likely to be a friction effect, a little water can make the surface slippy, but a lot can make the surface sticky. Using Tennis GUT shows that softening the surface and reducing the friction of the surface at the same time slows the speed of the ball at the receiver. However, a change of over 30% is needed to produce the 5 mph reduction needed which is just not likely.
The only thing left that I can think of is the size of the ball. How would rain affect this? Well, it just so happens that when tennis balls are made, one of the last manufacturing processes is to steam the balls to raise the nap of the felt. It is probable that the balls getting wet and then drying out raises the felt and has an effect of increasing temporarily the effective diameter of the ball. An increase in diameter of less than 2 mm is needed to reduce the speed at the receiver by the 5 mph we’re looking for.
The best guess?
What is my best guess then? Without inspecting Hawkeye data in more detail, I think that the biggest effect is likely to be the fluffing up of the felt with a lesser effect coming from the change in surface characteristics. The change in air temperature could slow the ball down by a small amount if we change from warm to cold conditions when the roof closes. Finally, the effect of humidity on air density is negligible – the most likely effect is to increase the wetting of the felt and enhance the fluffing up of the ball. A simple solution could be to change the balls when the roof closes.
Watch the players next time the roof closes at Wimbledon – if the players start inspecting the felt and throwing balls away, then they are likely to be choosing the least fuzzy ones.
Steve Haake also writes a blog for The Engineer; see Tennis Engineering.