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The science of soccer

2010-06-10 11:31
First we set the stage: Ronaldo is lining up a corner, he has the goal towards his right hand side and the sideline of the field towards his left and the whole world watching. There is one minute of injury time left and the scores are level. After a short run up he strikes the ball with the outside of his right foot, but he has a secret...he strikes the ball slightly to the left of the its centre and also aims the ball to the left of where he wants it to go.

By striking the ball this way it begins to spin like a top. The left hand side of the ball is spinning away from him, and the right hands side towards him. If the ball were perfectly smooth, that would be the end of the story, the ball would travel straight, the defenders would read it easily, defend the goal, and the game would be a draw or go into injury time. Since the ball not smooth, its surface interacts with the air rushing over it as the ball flies out into the field.

As the ball spins, it drags the air near to it in the direction of the spin. The air rushes over the ball towards Ronaldo as it moves towards the penalty box. The air on the left side of the ball gets slowed down by the spin moving in an opposing direction to the rushing air, and the air on the right side of the ball gets a helping hand and speeds up in the direction of the rushing air. The net result is: on the left side you have air moving slower, and the right side you have air moving faster. Just like with an airplane wing, fast air has lower pressure than slow air. As a consequence the high pressure on the left hand side of the ball pushes the ball harder right than the low pressure pushing the ball left. The force to the right wins the battle and the ball starts to curve right.

At every moment, the ball has a new direction and the battle between the left and right pressure begins again allowing the ball be forced closer and closer to its own right hand side. The curve fools the defenders and Portugal win 1-0 and proceed to face Bafana Bafana in the final.

In a theoretical world, where we imagine the ball never slowing down due to drag and no gravity, the ball would eventually complete a full circle and hit Ranaldo in the back of the head, but in reality it would be difficult for a player to curve a ball more than about four metres away from the line joining it's start point and end point, or more simple put, around a wall of defenders 4 m wide. Objects besides soccer balls can complete a full loop-de-loop in flight.

Several factors affect the how much curve there will be: how fast the ball is struck, its shape, roughness, weight, speed of rotation and the air density. The matter also gets very complicated when you want to examine the non-ideal effects created by the turbulence over the ball at different speeds. To make matters simple, if Ranaldo wanted to score a goal from a corner, he'd have to kick the ball with a medium speed and as much spin as possible. Having boots which can grip the ball well would also help. Incidentally, a simple analysis of fundamentals show that a ball curves 20% less over a 30m kick (3.2 m) on the high-veld than it would in Cape Town due to the difference in air pressure.

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