Wicked dips versus perfect proportions: the physics of football revisited

On May 23, 2014

800px-Maracana_Stadium_June_2013

Despite a science that suggests the design, manufacture, testing and modelling of soccer balls is a fairly precise activity, when it comes to kicking the thing around a pitch it may as well behave like a rapidly deflating balloon.

In truth, there could be many issues that account for the discrepancy between theory and practice, but, for the sake of brevity, I’ll single out what I believe to be the three main issues.

Firstly: wind. As stated in my previous post, the soccer ball possesses the highest drag-to-weight ratio of any sports ball, and so its trajectory is going to be significantly deviated by gusts compared with other types of ball. Projectile trajectory analysis is usually capable of making allowances for deviation caused by wind – at least up to a point. Stochastic methods are used to create a range of variations in trajectory path in terms of mean and standard deviations. Good models even include the typical windspeed variation with height above the ground (usually taken as a log10 function, since you asked) and, in the most advanced models, chaos theory may be used to recreate more realistic wind variations over time.

This would all be fine if the ball was kicked in an open area subject to a fairy invariant wind velocity. However, put the ball in a stadium with tiered seating and cantilevered canopies, and a gentle steady breeze can turn into a series of gusts, eddies and vortices that can vary sharply over even short distances, and certainly over the distance of a typical football pass. (An eddy is a circular rotation of the wind vector which can whip the ball around quite sharply; a vortex is much the same, only the spin is so great that the ball can also experience an upward or downward draught force synonymous with a tornado or whirlwind.) The unpredictability of wind within large stadia is easy to observe: just look at the corner flags. Even in very steady and gentle breezes, the four flags will be pointing in different directions and changing rapidly.

In summary, good soccer projectile models can produce a predicted trajectory from a ball kicked under windy conditions, but it will be a best-guess probabilistic choice taken from the calculated mean and standard deviation values. Try explaining that to your supporter on the terrace when they’re 3-0 down at half time!

Secondly, let’s look at the essence of the subject we call sports science. I am speaking as a physicist who spent a decade in a sports science university department. I went into the department under the misapprehension that sport science is a simple degree: it’s not. I still don’t think I could achieve a grade I could be proud of. But, what I will affirm is that I believe the subject of sport science is an oxymoron.

Nine years ago I stood on the terrace at Old Trafford awaiting the kick-off at a game between a top premiership league team, Manchester United, and a non-league team, Exeter City, in the FA Cup Third Round. There were 67,000 spectators there, and 66,500 assumed United would win with, I guess, about a five-goal difference. But about 500 of us had travelled 250 miles, and we hadn’t come to watch our team lose. Against all the statistical odds, against all sense of logic, against all sense of common sense, we would not lose. I am a scientist. I am dispassionate, professional. I weigh the odds on all sides and arrive at a conclusion following a careful balance of the arguments from all angles. That’s what being a scientist is.

But sport is all about passion. No player goes into a game thinking there’s even the slightest possibility of losing, even if the odds are stacked against them like a National Lotto ticket. No spectator travels 250 miles and pays upward of £70 to watch their team lose.

It’s this unshakeable conviction that skews our perceptions. Fouls that didn’t occur, did. Fouls that did occur were just an opponent diving. Balls that went over the line, didn’t. Balls that did go over the line… well, you get the idea. It’s not all in the mind, either. The three-dimensional, approximately parabolic movement of the ball can create parallax and other relative-motion illusions. How much a ball is thought to deviate very much depends on the observation point. Just to highlight one major misconception: if a ball swing is fundamentally parabolic in nature then we are going to witness a so-called ‘late swing’ every time.

Speed and timing can also deceive us. Maradona’s ‘Hand of God’ goal from the 1986 World Cup is only considered a handball by one nation: the one that was disadvantaged. Frame-by frame analysis of the four cameras provide no evidence of foul play; neutral commentators saw nothing untoward; the referee and linesmen stand by their decision. Most of the ‘Hand of God’ business was stoked by the British tabloid press at the time. We are considering an event which may have happened within a time slot of about a tenth of a second, but even that ‘blink of an eye’ represents about ten frames of images captured from the four cameras.

Oh, and on that January night in 2005, Exeter City held Manchester United to a goalless draw, so it was worth the trip. You see, I told you we wouldn’t lose.

Finally, and I’ll keep this short, not only because I’m running out of space, but also because the fewer words I use, the lower the odds of litigation: money. You might be forgiven for thinking that, for such a major event as the World Cup, the best possible ball would be chosen, regardless of cost. You would expect a ball designed by the foremost materials engineers, fluid dynamicists, computer modellers and quality assurance scientists. A ball tested rigorously by independent objective scientists under strict environmental conditions, and then independently field tested by elite soccer players. All possibility of partiality tuned out of the development procedure.

Maybe that is the scenario, but consider this. One company has provided all the World Cup footballs since the 1970 World Cup. Better still, they have even been awarded the contract to continue providing the World Cup balls up until at least 2030. That’s a continuous 60-year sponsorship deal for Adidas. Not bad, considering the dissatisfaction expressed in many quarters over their last design attempt, the Jabulani.

So, do Adidas produce the best balls known to man or beast? Who knows. What we do know is that they paid FIFA $350 m just for the privilege of using their balls in both the 2010 and 2014 World Cups. We may never know how much they paid to allow their ball to be used in the next four World Cups. So, might Nike or Mitre (other ball manufacturers are available!) be able to produce a better ball? We may never know. I will refrain from speculating on the internal financial arrangements that may or may not exist between Adidas and their design and test centres, as well as the teams and players charged with testing the product. Suffice it to say, FIFA’s choice of ball, its design and testing, has been driven by both commercial and scientific interests. Which takes precedence is the question.

The games will start; the balls will behave either predictably or erratically. They will either “dip wickedly” (David James’ complaint about the Jabulani), or be “perfectly proportionate” (Adidas’ own statement on the Jabulani). The pundits will have their say; we will read about the controversy and wade in with our own opinions, whether informed or not, and… the battle will commence. Have a great World Cup.

Image: The Estádio do Maracanã in Rio de Janeiro, Brazil, which will stage the World Cup final on 13 July. The structure of large football stadia can create atmospheric eddies and vortices that affect the flight of the ball. Credit: Government of Brazil.

About Colin White

Colin White began his career as a software engineer working on guidance systems before joining the academic fraternity as a physics lecturer, teaching microwaves and computer science while researching ferrite applications. He branched for a short time into geology to work on climate models, and latterly into sports science working on the dynamics of breast motion and sport projectile dynamics. He is the author of Projectile Dynamics in Sport – Principles and Applications, published by Routledge. He is supposed to have retired three years ago, and yet strangely still finds himself with project students, tutorials and lectures. He happily draws the line at marking though!