Why does a spinning ball follow a curved pattern?
August 1, 2005 4:19 AM 
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Beckham-physics filter. The curling ball.
I like to kick a ball in the yard sometimes and particularly enjoy trying to swerve or curl the ball around stationary objects. So I'll kick it with the instep on my right foot and from above it goes in a counterclockwise and will (on those occasions I get it right !) move from right to left in the air in a sort of curving arc* . And of course the opposite occurs if I use the outstep, spinning it in a clockwise direction (ie. it curls from right to left)
If we accept for the exercise that there's no prevailing wind, why is it that a spinning ball will curl - what forces are at play? And sometimes the ball seems to spin at a similar speed but doesn't actually follow a curling path (less often). Why? Bonus points for explaining why a ball will sometimes dip +/- weave --- not in the backyard, but you can see it for instance when David Beckham does a freekick around a wall of players over 25-40 yards distance towards the goal.
(Is the direction of spin the single variable here +\- weight or...?)
*[It's not a true flat (horizontal) arc of course because of gravity ie. the ball curls but also falls]
posted by peacay to science & nature (13 comments total)
Consider a ball that is spinning about an axis perpendicular to the flow of air across it. The air travels faster relative to the centre of the ball where the periphery of the ball is moving in the same direction as the airflow. This reduces the pressure, according to Bernouilli's principle. The opposite effect happens on the other side of the ball, where the air travels slower relative to the centre of the ball. There is therefore an imbalance in the forces and the ball deflects. This lateral deflection of a ball in flight is generally known as the "Magnus effect".
The forces on a spinning ball that is flying through the air are generally divided into two types: a lift force and a drag force. The lift force is the upwards or sidewards force that is responsible for the Magnus effect. The drag force acts in the opposite direction to the path of the ball.
The drag force, FD, on a ball increases with the square of the velocity, v, assuming that the density, r, of the ball and its cross-sectional area, A, remain unchanged: FD = CDrAv2/2. It appears, however, that the "drag coefficient", CD, also depends on the velocity of the ball. For example, if we plot the drag coefficient against Reynold's number - a non-dimensional parameter equal to rv D /µ, where D is the diameter of the ball and µ is the kinematic viscosity of the air - we find that the drag coefficient drops suddenly when the airflow at the surface of the ball changes from being smooth and laminar to being turbulent.
When the airflow is laminar and the drag coefficient is high, the boundary layer of air on the surface of the ball "separates" relatively early as it flows over the ball, producing vortices in its wake. However, when the airflow is turbulent, the boundary layer sticks to the ball for longer. This produces late separation and a small drag.
The Reynold's number at which the drag coefficient drops therefore depends on the surface roughness of the ball. For example, golf balls, which are heavily dimpled, have quite a high surface roughness and the drag coefficient drops at a relatively low Reynold's number (~ 2 x 104). A football, however, is smoother than a golf ball and the critical transition is reached at a much higher Reynold's number (~ 4 x 105) .
The upshot of all of this is that a slow-moving football experiences a relatively high retarding force. But if you can hit the ball fast enough so that the airflow over it is turbulent, the ball experiences a small retarding force (see right). A fast-moving football is therefore double trouble for a goalkeeper hoping to make a save - not only is the ball moving at high speed, it also does not slow down as much as might be expected. Perhaps the best goalkeepers intuitively understand more physics than they realize.
In 1976 Peter Bearman and colleagues from Imperial College, London, carried out a classic series of experiments on golf balls. They found that increasing the spin on a ball produced a higher lift coefficient and hence a bigger Magnus force. However, increasing the velocity at a given spin reduced the lift coefficient. What this means for a football is that a slow-moving ball with a lot of spin will have a larger sideways force than a fast-moving ball with the same spin. So as a ball slows down at the end of its trajectory, the curve becomes more pronounced."
~via
posted by cyphill at 5:16 AM on August 1, 2005