 All that is necessary to create lift is to turn a flow of air. An airfoil of a wing will turn a flow, and so will a rotating cylinder. A spinning ball will also turn a flow and create a force.

The details of how a spinning ball creates lift are fairly complex. Next to any surface, the molecules of the air will stick to the surface, as discussed in the properties of air slide. This thin layer of molecules will entrain or pull the surrounding flow for a spinning ball in the direction of the spin. If the ball were not moving, we would have a spinning, vortex-like flow set up around the spinning ball (if we neglect three-dimensional and viscous effects in the outer flow). If the ball is moving through the air at some velocity, on one side of the ball the entrained flow will oppose the free stream flow, while on the other side of the ball, the entrained and free stream flows will be in the same direction. If we add the components of velocity for the entrained flow to the free stream flow, on one side of the ball the net velocity will be less than free stream; while on the other, the net velocity will be greater than free stream. The flow will then be turned by the spinning ball, and a force will be generated. Because of the change to the velocity field, the pressure field will also be altered around the ball. The magnitude of the force can be computed by integrating the surface pressure times the area around the ball. The direction of the force is perpendicular (at a right angle) to the flow direction. The right part of the slide shows a view of the flow as if we were moving with the ball looking down from above. The ball appears stationary and the flow moves from left to right. On this figure the ball spins clockwise, so the free stream flow over the top of the ball is assisted by the circular flow; the free stream flow below the ball is opposed by the circular flow. In the figure we can see that the net streamlines around the ball are distorted because of the spinning. The net turning of the flow has produced an upward force.

To determine the equations which describe the force on the ball, we shall consider the spinning ball to be similar to the two-dimensional rotating cylinder. We can then use the Kutta-Joukowski lift theorem for cylinders to approximate the magnitude of the force (F) generated by a spinning ball. The Kutta-Joukowski lift theorem states the lift per unit length of a spinning cylinder is equal to the density (r) of the air times the strength of the rotation (G) times the velocity (V) of the air. (See the page on the lift of a rotating cylinder to determine the strength of rotation.) The lift on any cylinder is equal to the lift per unit length times the length of the cylinder. For our ball, the length of "cylinder" is equal to twice the radius of the ball (2b), as shown in the left portion of the figure. We have to make one additional correction to this force, because the area over which the force acts is different for a cylinder and for a ball. For a cylinder, this force would act over a cross-sectional area which would appear as a square of side 2b. (Area = (2b)^2). The ball would have a projected area of pi times the radius (b) squared. (Area = pi b ^2) So we can correct the force generated by the cylinder by the ratio of these areas to get the final approximate force equation.

F = (r * G * V) * (2 * b) * (pi / 4)

Let's investigate the lift on a spinning ball by using a Java simulator.

The left window shows a view of a ball placed in a flow of air. The ball is a foot in diameter and it is moving 100 miles an hour. You can spin the ball by using the slider below the view window or by backspacing over the input box, typing in your new value and hitting the Enter key on the keyboard. On the right is a graph of the lift versus spin. The red dot shows your conditions. Below the graph is the numerical value of the lift. You can display either the lift value (in English or Metric units) or the lift coefficient by using the choice buttons surrounding the output box. Click on the choice button and select from the drop-menu.

As an experiment, set the spin to 200 rpm (revolutions per minute) and note the amount of lift. Now increase the spin to 400 rpm. Did the lift increase or decrease? Set the spin to -400 rpm. What is the value of lift? Which way would this ball move?

You can further investigate the lift of a spinning ball, and a variety of other shapes by using the FoilSim II Java Applet. You can also download your own copy of FoilSim to play with for free. There is also a Java Applet called CurveBall to help you explore the aerodynamics of big league pitching. It will compute the path of a thrown curveball.

(Be particularly aware of the simplifying assumptions that have gone into this analysis. The type of flow field shown in the right part of this figure is called an ideal flow field. We have produced the ideal flow field by superimposing the flow field from an ideal vortex centered on the ball with a uniform free stream flow. There is no viscosity in this model, no boundary layer on the ball, even though this is the real origin of the circulating flow! In reality, the flow around a spinning baseball is very complex. The ball isn't even smooth; the stitches used to hold the covering together stick up out of the boundary layer. In addition, the flow off the rear of the ball is separated and can even be unsteady. BUT, the simplified model does give the first order effects--it gives an initial good prediction of the motion of the ball.) Guided Tours