The Effect of Wind Resistance on a Rotating Sphere

When a round object, such as a steel ball, is thrown through the air, the air molecules pass down both sides of the sphere at the same rate. In this case, in addition, to gravity the only force acting on the sphere is drag, which is directly linear to the direction of travel. However when a non-smooth sphere such as a golf ball or baseball travels through the air, the direction in which the ball rotates creates additional forces, which affect the sphere's trajectory.

  1. Rotational Friction

    • On an airplane wing, lift is created because the air molecules pass over the top side of the curved wing surface faster than they pass over the bottom smooth side of the wing. Faster moving air apply less force on the wing. Therefore the wing moves upward as it attempts to balance these unequal forces. The same principle affects the travel of a rotating sphere when it's thrown through the air. One side of the rotating sphere moves toward the ball's direction of travel, while the other side of this sphere rotates backwards, away from the direction of travel. The friction between the rotating sphere and the air creates imbalance forces acting on the ball.

    Lift and Resistance

    • When a golf ball is hit from the tee, it travels through the air with a significant backspin. The bottom of the ball rotates into the direction the ball is traveling. The top of the ball rotates backwards towards the golfer. This backspin is created by the angle of the golf club. Consequently, the bottom of the ball pushes against the air molecules it encounters while the top of the ball accelerates the air molecules as they pass over the top of ball. As a result, the golf ball creates lift because the faster moving air molecules exert less pressure on the golf ball than the slower moving molecules. Golfers have discovered that a dimpled golf ball travels farther than a smooth ball of because of this effect.

    The Magnus Effect

    • The difference in pressure's affecting a rotating sphere is called the Magnus Effect. The Magnus effect pulls the ball toward whichever direction is spinning away from the balls direction of motion. In other words, a ball with a topspin will sink more quickly because the ball is pulled downward by the Magnus effect. A ball with a backspin will travel farther because the ball is pulled upward by the Magnus effect. In baseball, a curve ball slides sideways into the direction of rotation because the ball's axis of rotation is neither perpendicular nor parallel to the surface of the ground.

    The Variables Involved

    • A number of variables affect the size of the Magnus Force, which affects the moving sphere. The following equation is based from Professor Robert K. Adair's book "Physics of Baseball": F=KWVCv. The variables are defined as: "F" is the Magnus Force. "K" is the Magnus Coefficient, which is based on the smoothness or texture of the sphere's surface. "W" is the sphere's rotation measured in rpm. "V" is the velocity of the ball, easured in mph. And finally "Cv" is the drag coefficient, which is based on physical qualities of the air through which the sphere travels, such as temperature, density, humidity, etc.