Hit a football with a clean, straight kick and it flies straight. Clip it with the side of your boot and it bends around a wall of defenders and into the corner. Nothing touched it in the air. The bend comes from a force that exists only because the ball is spinning.
You are looking down on the pitch from above. The ball starts on the left, 30 metres from goal. The dashed line is where it would go with no spin. Drag the lime target along the goal line, or use the sliders, then press Kick.
Positive spin turns the ball anticlockwise as seen from above, and it curves left. Negative spin does the opposite. Set the spin to zero and aim at the goal: the ball flies dead straight. Aim wide of the post, add spin, and watch it come back.
A moving ball pushes air out of its way. Seen from the ball, the air streams past it, front to back. A smooth, non-spinning ball splits that stream evenly on both sides.
A spinning ball drags a thin layer of air around with its surface. On one side the surface moves with the passing air and speeds it up. On the other side the surface moves against it and slows it down. The ball ends up shoving the air in a lopsided way, and the wake leaves it slanted to one side.
There are two ways to say what happens next. In the pressure view, faster air on one side means lower pressure there, so the ball is pushed toward the fast side. In the momentum view, the ball throws air one way, so the air pushes the ball the other way. Both describe the same force, and it is called the Magnus force.
The rule: the ball is pushed toward the side where its surface is moving in the same direction as the air flowing past it. Equivalently, its nose turns toward the curve.
Apply the rule to a tennis ball with topspin. The top surface moves forward, against the air, and the bottom surface moves with it. The push is downward, so the ball dips faster than gravity alone would pull it. Backspin does the reverse and holds a ball up. Sidespin bends it sideways, and that is what you are controlling in the demo above.
Isaac Newton noticed it first. In a letter to the Royal Society in 1672 he described watching tennis players at a Cambridge college and seeing how a struck ball curved. In 1742 the mathematician Benjamin Robins used the same idea to explain why musket balls wandered off line. The effect carries the name of the German physicist Heinrich Gustav Magnus, who in 1852 showed it with a rapidly spinning brass cylinder in a stream of air from a blower.
Physics World ran the numbers for a well-hit free kick. A football weighs 410 to 450 grams. Struck at 25 to 30 metres per second, so about 90 to 110 kilometres per hour, and spinning at 8 to 10 turns a second, it feels a sideways force of about 3.5 newtons. That is a sideways acceleration of about 8 metres per second squared, close to the pull of gravity on a falling object.
It sounds small. But the flight of a long free kick takes about a second, and a steady push over a second moves the ball sideways by metres. The same article puts the possible sideways drift at as much as 4 metres over a 30-metre kick. It also estimates that Roberto Carlos's famous free kick against France in 1997 was struck from about 30 metres at over 30 metres per second, with perhaps more than ten turns each second. The ball cleared the wall by at least a metre and then curved into the top corner. Those figures are estimates, not measurements.
The model in the demo is deliberately simple. It treats the lift as proportional to how fast the surface moves compared with the ball's speed, and it is tuned to give a sideways force of the same order as the figure above. Real balls also change behaviour at certain speeds, so the real curve is not a perfect arc. The principle is the same.
A steady sideways push makes the sideways distance grow with the square of the time. Half the flight time gives only a quarter of the sideways drift. So the ball spends the first half of its flight heading almost straight and does three quarters of its swerving in the second half. To the goalkeeper it looks like a sudden hook, though the path is a smooth arc.
Speed matters too, and in this model slower is curvier. Try a fast kick and then a slower kick with the same spin and the same aim. The slower ball bends more over the same 30 metres, because it spends longer in the air and the spin is large compared with its speed.
Next time you see a kick bend, look at the spin. Seen from above, a ball that curves left is spinning anticlockwise, and a ball that curves right is spinning clockwise. That is the whole secret.