What Makes it Curve?

There are three forces acting on a baseball in flight:

1. The Force of Gravity:

The earth's gravitational field causes masses near the surface of the earth to be accelerated towards the center of the earth at approximately 9.8 m/s2

2. The Drag Force:

When an object (such as a baseball) moves through a fluid (such as air), there is a force that opposes this motion (the drag force). The baseball experiences drag because when it to moves in air it collides with air molecules and pushes them out of the way. The drag force is proportional to the square of the velocity. This seems reasonable when you consider that if you double the velocity the drag force will increase by four because you need to push twice as much air out of the way and you need to push the air twice as hard. The key idea you need to keep in mind in order to understand how the Magnus Force works is: if you increase the speed of the ball the drag increases.

3. The Magnus Force

First, consider a baseball traveling 75 mph on a path to home plate. There is 100 pounds of pressure pushing the ball towards first base, but the ball travels in a straight path because there is 100 pounds of pressure pushing the ball back towards third base. However, if there happens to be only an ounce and a half difference in the pressure across the ball, the ball will be deflected about 14" towards the side with lower pressure.

The Magnus force can explain what causes this pressure difference.  Consider a ball traveling with no spin traveling through the air. The top and the bottom of the ball both have the same velocity, V.






Now consider a ball that's center is stationary but the ball is spinning about that point with an angular frequency, ω. Now the top and bottom of the ball are moving in opposite directions with velocity V=ωr.





When you throw a baseball the ball has velocity and is spinning. Thus, the velocity on one side of the ball will be larger than the velocity on the other. We know that if an increase the velocity results in an increase in the drag. Therefore, the drag on one side of the ball will be larger than the drag on the other and the ball will be deflected towards the side with lower pressure.

                                                                                                                                                        V              ωr



                                                                                             ωr                                                         V