Wednesday, 28 November 2012

The physics of a curveball

The Physics of a Curveball

It was originally believed that a curveball was an optical illusion, Physicists were not able to explain why the ball would have a curved flight path. Although in 1671 Isaac Newton wrote a paper on the topic of the curved path of a ball with spin. The topic was later renewed in 1852, when Gustav Magnus performed an experiment with spinning objects moving through a liquid. He came to the conclusion that there is a force acting perpendicular to the initial velocity

Figure 1.
**Please ignore speech bubbles**  This diagram shows what Magnus’ finding was, that the reason a spinning ball had a curved path was because of the magnus force acting perpendicular to its motion.

Magnus Effect in Baseball

          When an object is moving through the air it comes into contact with a thin layer of air called the “boundary layer”. Since a baseball is not very aerodynamic the air peels away from the surface. This creates an area behind the ball where there is no air, which is called a “wake” which is a low pressure area behind it. The difference of pressures on the front of the ball and  the back creates air resistance and slows the ball’s forward motion. Although if the ball is spinning, the air and ball’s friction will cause the air around the ball to drag with the curve of the ball on one side and away from the ball on the other side. This results in an angled .Figure 2. 
Shows the effect of spin on the wake.

The ball has exerted a force of friction on the air, this force pulls the air down (using the bottom half of Figure 2.)  and because of Newton’s third law which is “for every action there is an equal and opposite reaction” this means that the air is exerting a force on the ball in the opposite direction which is the magnus force.

The stronger the magnus force is the more the ball will curve. The strength of the force is directly related to the rate of spin and the forward speed of the ball. Knowing this, Magnus was able to create the equation
Figure 3. 

Fm- Magnus force  

 S- Air resistance coefficient across the surface of the object                                                                                                                                                                                          
            W-Angular velocity vector of the object
            V-Velocity of the object

The discovery of the Magnus force has helped physicists understand the science of a curveball and overcome the myth that a curveball is not an optical illusion, but there is a force creating the curved flight path. (demonstration) (Video which demonstrates magnus effect well)

These videos both demonstrate the Magnus effect, the first video gives a demonstration of how wind on a non-spinning object alone does not create a Magnus force, but it takes the combination of wind and a spinning object to produce the Magnus force. As well, the second video provides a summary of some points covered in this post, as well it shows a demonstration which shows the Magnus force very well (rolling the paper off of the board).

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