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Physics Behind Pitching

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The physics of pitching entails that one uses a barrage of techniques to hurl a baseball towards home plate and cause the batter to not hit it.  A throw is different than typical standard projectile due to rotational force that is applied to the baseball.  The forces which act on the ball are the drag force, the normal force, the force of gravity on the ball, the initial force applied to the ball causing it’s initial acceleration.  However, it also was angular velocity which in turn exerts a force on the ball altering its flight path (a sample diagram of the forces in action are pictured to the left).  Furthermore, in order to calculate the drag, gravity and normal forces which in turn all have an effect on the ball’s trajectory can be calculated by the formula to the left.  The flight plan of the ball is made even more interesting by the “Magnus Force” to which is created by high angular rotation of a ball.

The Curve Ball and How it Works

           This “Magnus Force” to which I referred to in the previous slide is as a direct result of the pitcher throwing the ball so that the axis of rotation in relation to the ball is not perpendicular to the ground.  As a result of this altered axis the Magnus force of the ball will ultimately curve left or right.  An example of this is pictured at right.  This is based on the Newtons second law of physics F=ma.  The Magnus Force is a direct result of the mass of the ball multiplied by the rotational and translational acceleration generated by the ball, however this formula is altered to produce the formula on the bottom right. This same theory can be applied to other pitches in baseball as well, including but not limited to the screwball, slider, drop-ball, and knuckleball.  By altering the ball’s axis and rotational velocity an individual can throw any of these pitches to deceive a batter.  A simplified formula in which one can use to calculate the amount that a ball will curve or drop is at right.  This explanation seems complex, however, it is the mere use of simple theories applied over and over in order to explain physics in action in the world around us. 

                                                                                                                                                                                                

where A is the cross sectional area of the ball, v is its speed,

_ is the air density _1.23 kg/m3_, and CD and CL are the drag

and lift coefficients, respectively.15We will focus only on CL.

Data on other spherical sports balls suggest that CL is mainly

a function of the spin factor S=R_/v,

 120 Am. J. Phys., Vol. 76, No. 2, February 2008 Alan M. Nathan 120                                                                                                                       


 When a pitcher throws a curve ball, he will throw it such that the axis of rotation is not perpendicular to the ground, as it is in a fastball.
 Because it is spinning in a skewed axis, the Magnus force will force the ball to curve in a horizontal direction instead of vertical "curve" of a fastball.

How much will a baseball curve?.
The equation is as follows (from Prof. Adair's book Physics of Baseball):
Magnuson Force = KwVCv
where:

  • FMagnus Force is the Magnus Force
  • K is the Magnus Coefficient
  • w is the spin frequency measured in rpm
  • V is the velocity of the ball in mph
  • Cv is the drag coefficient

http://library.thinkquest.org/11902/physics/curve2.html

 

 

http://www.thecompletepitcher.com/pitching_grips.htm#q7