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Last week I played soccer for the first time in years. The goalkeeper kicked the ball high (probably about 20 metres into the air) and a teammate called to me to head it. I realise I am lacking in skill, but the power of the ball striking my head knocked me off my feet, bruised my forehead and left me with a dreadful headache. Yet professional footballers seem able to head higher and faster-moving balls with no apparent damage or pain. What velocities and forces are they dealing with, and why did the ball leave me stunned but not a professional player?
鈥� Imagine you were able to head a stationary ball to the goalkeeper from where you were standing that day. The force your head would have to exert on the ball would be equal in magnitude to the force exerted by the keeper kicking the ball. Since the ball exerts an equal reaction force on your head, it would be as if the keeper had kicked you in the head. Consider yourself lucky to just end up with a bruise or a headache.
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In practice you would, of course, not be trying to head the ball all the way back to the keeper, but there are other things to consider with a falling ball. Ignoring air resistance, a football dropping vertically from 20 metres would hit the ground at a speed of nearly 20 metres per second. If you could reverse the velocity of the ball by heading it, assuming the ball has a mass of 400 grams and is in contact with your head for one-hundredth of a second, the force you experience is around 1500 newtons 鈥� the weight of two adults.
When professional footballers head the ball, they generally apply a small force to deflect it, usually to steer it into the net. That does not require taking the full force of the ball on the head. But if that is the only option, they use their necks, backs and knees as shock absorbers. In so doing, they increase the time the ball takes to slow down. By Newton鈥檚 second law 鈥� force equals mass times acceleration, or in this case deceleration 鈥� this reduces the ball鈥檚 deceleration and thus the force. However, as you have found, it takes skill and experience to get the timing right.
Mike Follows, Willenhall, West Midlands, UK