The World Cup draw: altitude will be the key

Every World Cup draw is accompanied by a new ball, and media speculation is never far behind.  The draw for FIFA 2010 on December 4th will focus attention on the ties in South Africa in next year, but I have some thoughts on what people are likely to be saying about the ball. Goalkeepers are invariably those asked for comment: Jens Lehman, Germany’s maverick goalkeeper said before FIFA 2006,

It may be good for the outfield players and for the crowd, but not for the goalkeepers….it gets very slippery and flutters in the air.


Last year during the semi-final 2nd leg of the Champions League (Arsenal 1 Man Utd 3), Lehman said of Ronaldo’s amazing 40 yd free kick to beat Almunia, “…from that distance the ball is moving and speeding up…”  What is it about footballers and the 1st law of thermodynamics? Doesn’t he know that for a ball to speed up in the air it would have to disobey the laws of physics? Mind you, I think I know what he means: as an experienced goalkeeper he uses player cues and the early part of the trajectory to predict where the ball will be when he tries to save it at the goal face.  If the drag force acting on the ball was to suddenly drop or ‘flutter’, as was implied by the press in FIFA 2006, then the ball would travel faster than expected, the goalkeeper’s prediction would be incorrect and the ball would end up in the back of the net.

So, assuming that Lehman gets to commentate in South Africa, just what is he likely to say?

I think that the key issue for the World Cup in South Africa is going to be altitude.

Johannesburg, the location of the final on July 11th, is at 1,743 m (5,718 ft) while half of the venues are in locations over 1,200 m (around 4,000 ft).

Soccer_City_(june_2009)[1]
Figure 1. Soccer City in Johannesburg

And the effect? Most people know that air density reduces at altitude – remember all the athletics records attributed to the thinner air at Mexico City in 1968? Air density is a function of atmospheric pressure, temperature, humidity and altitude.  A 10°C increase in temperature reduces the density by around 4% while a 50% increase in humidity reduces density by only 0.3% (most people assume wrongly that humidity increases density, but the atomic weight of water vapour is 18 g compared to 29 g for air and adding water vapour reduces density).  The biggest change by far, though, comes with a change in altitude –  the air in Johannesburg, for example, is likely to be around 20% less dense than that at Cape Town during the World Cup.

So,  Focussing on just a couple of teams for the moment, we can make a prediction on how altitude might affect their games across South Africa.  Germany starts at sea-level in Durban on 13th June, playing again at sea-level in Port Elizabeth on 18th June.  Their final group game is in Johannesburg on 23rd June at 1,743 m.


Date Time Altitude T Humidity Density
GERMANY
(local) (m) (°C) (%) (kg/m3)
Durban 13th June 16.00 0 20 51 1.18
Port Elizabeth 18th June 13.30 0 20 56 1.18
Johannesburg 23rd June 13.30 1,743 17 33 0.93

ITALY


Cape Town 14th June 20.30 0 7 91 1.24
Nelspruit 20th June 16.00 660 23 50 1.06
Johannesburg 24th June 16.00 1743 11 51 0.94

Table 1.  Games for teams selected on December 4th as D1 and F1 (Temperatures and humidities from BBC Weather). Note that the density calculations here use a 1st order approximation; for exact calculations use Massey B.S., Mechanics of Fluids, p31, 6th Ed., pub Chapman and Hall, London or another reputable fluid mechanics source.

Table 1 shows the likely temperatures and humidities during Germany’s games and the likely air densities which decrease from about 1.18 kg/m3 in the sea-level games to around 0.93 kg/m3 in Johannesburg – a drop of 22%.  The change for Italy is even greater:  they will find the air density dropping by 14% and then 28% in their 2nd and 3rd games.   The key point is how this will effect play. Consider a non-spinning 18 m free kick (about 20 yds) hit a-la Ronaldo at about 60 mph (94 km/h). A trajectory program, assuming no wind, calculates that the ball would take around 0.82 s at sea-level in Durban or Port Elizabeth.  The same shot would take about 2 hundredths of a second less time in Johannesburg. 

Put another way, the ball in Jo’burg would be around 41 cm ahead of the ball in Durban.

Does this matter?  Goalkeepers know that finger-tip saves can make all the difference and a ball that is over two diameters ahead of where they expect it to be will really test their skills.  I think 2010 will see stories in the press of unpredictable shots and criticism of the high speed of whatever ball is produced by adidas.


Date Time Shot time to goal Distance ball ahead by
GERMANY
(local) (s) (cm)
Durban 13th June 16.00 0.815 0
Port Elizabeth 18th June 13.30 0.815 0
Johannesburg 23rd June 13.30 0.797 41
ITALY
Cape Town 14th June 20.30 0.820 0
Nelspruit 20th June 16.00 0.807 30
Johannesburg 24th June 16.00 0.797 49

Table 2.  The likely effect of altitude on a 60 mph shot for Germany and Italy’s group games.

So what advice would I give to the England manager?  Well, Capello already seems to have made the first correct choice of the World Cup since England’s training camp is at 1,500m in Rustenberg, also the location of the first game against the USA.  He might like to put on big hitters like Lampard, Gerrard and Beckham to maximise the speed of our shots and free kicks, particularly if the USA have been training at lower altitude.  With any luck, the German  Football Associations won’t read this blog and will go out to a wickedly curling free kick by Michael Essien.

Figure 2. Beckham could certainly do well at altitude in the final in Johannesburg on 11th July 2010

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About stevehaake

Steve did a first degree in Physics at the University of Leeds before landing two job offers: the first with BT turned out to be in a porta-cabin in the middle of a marsh, while the second was supposed to be image processing but was really smart-bomb design. This left a third option – a PhD in the mechanics of golf ball impacts on golf greens for a person who’d never hit a golf ball. It was a simple choice (the PhD if you didn’t guess) which led 25 years later to being head of a research team of 30-40 looking into similarly unlikely topics. Highlights of the career so far? The early years setting up the ISEA with the likes of Steve Mather, Ron Thompson, Clive Grant and Ron Morgan; the fact that the 1st International Conference on Sports Engineering in Sheffield in 1996 didn’t also turn out to be the last; and getting out the first issue of the first journal on Sports Engineering in 1998. The absolute high point, though, was being in the British Club in Singapore as a guest of the High Commission when the bid for the 2012 Olympics was announced. This has led to the team delivering projects with Olympic athletes that every scientist with a love of sport can only dream of. Steve is now a Senior Media Fellow funded by the EPSRC to encourage the public to engage in science, particularly in the lead up to the London 2012 Olympic Games.

3 Responses

  1. theclownshoes

    Will players or teams who regularly play at altitude have an advantage over their opponents? In addition is it possible to measure and control any advantage? Maybe football should have a special high altitude ball as per tennis.

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