where r is the radius of the ball, ω the angular velocity (or spin rate) of the ball, ρ the density of air, and v the velocity of the ball relative to air. This force is directed perpendicular to the motion and perpendicular to the axis of rotation (in the direction of ω ω ^ ^ × × v ^ ^ ). The force is directed upwards for backspin and downwards for topspin. In reality, flow is never inviscid, and the Magnus lift is better described by