Expert: Paul Soderman - 6/8/2010

Question
Whilst playing soccer with my two young children, I noticed that the ball (a very cheap plastic toy ball) curved in the opposite direction to what I would expect. A standard leather ball curves to the the left if it has anticlockwise spin (looking from above), but this plastic ball swerved to the right with the same direction of spin. I repeated the kick several times with the same result. So the question is, why is this happening? Is the airflow affected by the material of the ball as well as the spin?  As an aeronautical engineer with expertise in fluid dynamics, I thought that you might be able to help. Thank you.

Answer
Andy
This is a very good question.  You are correct, a baseball thrown with anticlockwise spin (looking down) will curve to the left due to aerodynamic forces.  Those forces result from a pressure distribution (Magnus effect) that is well understood.  The plastic ball would do the same thing if the aerodynamic forces dominated. But they do not, gyroscopic forces take over.  A baseball has a reasonably uniform mass distribution.  It has gyroscopic forces that are small compared to aerodynamic and gravitational forces, and inertia.  The plastic ball has all its mass at the surface and is light.  So gyroscopic forces are strong relative to the other forces.

In order to get a force in the direction you describe, there has to be a torque on the ball that has a component perpendicular to the rotational inertia.  Gravity acts through the center of mass.  But the aerodynamic forces act through the center of pressure which is not necessarily the center of mass.  Thus we have a couple, which is the moment we need.  I haven't worked out the exact moments and angles, but I assume your kick has generated a gyroscopic recession moment that causes the ball to curve as you describe.  This is complicated by the fact that the rotational axis is not necessarily vertical, but may lean off vertical. So the aerodynamic forces, gravity force, rotational inertia, and recession moment can have various angles relative to each other depending on how you kick the ball.  In any case, the induced gyroscopic moment must have a component that causes the ball to curve opposite to that expected from a baseball.  Very interesting.  I hope this helps.
Paul