A Brazilian's 'banana' goal has increased scientific interest in the simple act of kicking a ball, says Roger Highfield
SOME of the most spectacular goals in the World Cup will owe their success to the likes of Heinrich Magnus, Daniel Bernoulli and Osborne Reynolds. These are not rising stars, obscure soccer trainers or behind-the-scenes tacticians, but pioneers in the science of aerodynamic spin, which has already explained one feat of footwork that went over the heads of most spectators.
Many fans will remember last summer's free kick, taken 35 yards from France's goal, by Brazilian Roberto Carlos. It started wide of the goal before curving round a wall of four defenders and into the net.
The contributions of Magnus, Bernoulli and Reynolds to the science of football can be used to calculate that under these conditions a swerve of three or even four metres is possible, enough to give most goalies a hard time. Nevertheless, scientists admit there is still much they don't understand about what happens when a football curves through the air.
In the latest issue of Physics World, the new directions in research are explored by Professors Takeshi Asai and Takao Akatsuka and by Dr Steve Haake of Sheffield University.
Dr Haake is a spin doctor. He earned his doctorate studying golf: his research revealed that a tee-shot needs about 2.5kW of power, contact between club-head and ball lasts for half a thousandth of a second, the ball's initial velocity is 150mph, and it can spin at more than 50 times a second.
He points out that it was the German physicist Magnus who, in 1852, first explained how sideways force could be generated on a spinning shell or bullet: one side of the shell goes in the same direction as the airflow, while on the other side the directions are opposed.
The Swiss scientist and mathematician Daniel Bernoulli then postulated the theorem governing how air pressure decreases in a thin boundary layer around the ball as the speed of airflow increases. On the side of the ball where rotation and airflow are in the same direction, air speed increases and pressure decreases; on the side where the movement of the ball's surface opposes flow, air speed decreases and pressure increases.
This imbalance of forces produces the Magnus force, which explains part of Roberto Carlos's magic - the spinning ball was pushed away from the side with more pressure.
A second effect derives from kicking the ball with the right degree of force. As it rushes through the air the ball is subject to a drag force, but this depends on the turbulence in the boundary layer, which can be calculated with the help of the Reynolds number, named after the British physicist Osborne Reynolds.
This shows that the drag drops suddenly when the airflow at the surface of the ball changes from being smooth and laminar to being turbulent. At a speed of around 25 metres per second the drag is significantly lower than at 20 metres per second, so the ball does not slow down as much as may be expected.
The dependence of the Magnus force on the speed explains the "banana" trajectory of many kicks. Work by Dr Peter Bearman and colleagues at Imperial College two decades ago showed that a slow-moving ball with a lot of spin will experience a larger sideways Magnus force than a fast-moving ball with the same spin. In other words, as the drag slows the ball down towards the end of its trajectory, it will curve more. The problem with this kind of analysis is that it is very idealised. Scientists want to understand more about the real thing, so they can unravel the contribution of each force to the way the ball moves.
Dr Keith Hanna is turning his high-powered desktop computer into a virtual wind tunnel to investigate these effects, inspired in part by the Carlos goal. "We wanted to figure out the reason for the amazing trajectory and the sudden dip of the ball at the end of the flight."
Hanna's firm, Fluent, specialises in computational fluid dynamics software, which is used to design Formula One cars, golf clubs and skis. For the World Cup, the virtual air around a virtual ball is divided into tiny pockets, and software is used to work out the flows of air during its flight.
In a wind tunnel, "you are lucky to get three or four forces, whereas in the computer you end up with millions of pieces of information on forces on the ball and what the flow field around it will look like. This provides much greater understanding of the physics."
He is modelling the forces on a soccer ball at different wind speeds and ball rotations and uses these to predict the trajectory of a typical free kick, with the ball experiencing drag, lift, gravitational and Magnus forces.
He can assess the significance of thinner air, in which a ball is supposed to move further. Or humidity for that matter. The work might help design balls with different symmetries or surface properties that offer better aerodynamics.
"And it will help you identify what these Brazilians are doing," says Hanna. For example, he notices that they usually turn the ball around so the valve faces them. "Our guess is that that is the hardest part of the ball, so that if you hit it sweetly, you get more force and perhaps a different kind of spinning effect."
Another puzzle is how the ball and foot deform during a kick. Virtual kicks have been simulated at Yamagata University by Profs Asai and Akatsuka.
First, they captured real balls being kicked using a high-speed video, taking 4,500 frames per second. This information was stored in a computer to provide the basis of their simulations.
Virtual kicks confirm what players already know; for instance, that the spin picked up is closely related to the friction between foot and ball, and the distance of the foot from the ball's centre of gravity .
But the work has also provided some new insights. An impact study revealed a "sweet spot" for maximum spin: if you hit the ball too close or too far from the centre of gravity, it will not spin at all. And it showed that even on a rainy day, when there is little friction, it is possible to spin a football.
The team has now used the study to create virtual soccer players to investigate the effects of wearing different types of footwear. The ASICS corporation is now drawing on these studies to design a new generation of football boots. Any resulting edge in performance could prove to be big business.
