Pitching Physics

Pitchers and batters are quite familiar with the effect of spin on the trajectory of a ball.  A fastball with slow spin is straight as an arrow and fodder for a hitter, but with strong spin it slips more easily through the air and has ‘movement’ that frustrates batters.  In fastpitch softball, strong backspin on the notorious riseball creates the powerfully deceptive appearance of ‘hop’ as it resists the downward pull of gravity.  Scientists have studied the phenomenon and many have mathematically described the effect.  It's simple, more spin creates more curve.

Coaches have had the benefit of radar guns for years, but no way to measure spin rate.  And, until recently, few coaches could tell you how much spin their pitchers impart on the ball or what criteria they set for breaking ball performance. When world-renowned management coach Peter Drucker said “If you can’t measure it, you can’t manage it”, he probably didn’t have in mind the spin rate of a ball, but the value of measurement and feedback is universal.  Just as an athlete’s performance benefits from objective and immediate feedback, coaches’ training techniques evolve with the benefit of that same hard data. Pitchers rely on feedback from catchers and coaches, some of whom are hard pressed to accurately quantify breaking ball performance. Technology from RevFire Corporation has given coaches and pitchers and new tool - precise, reliable, and immediate spin rate measurement.

Magnus Force
A sideways force, lift force, or downward force on a pitched ball will result from the interaction with surrounding air when the ball’s spin orientation has one side of the ball moving into the oncoming air and one side retreating from the oncoming air.  This force that causes curve or ‘movement’ is known as the Magnus force.  

The greater the Magnus force, the more the curve of the pitch.  Pitchers can control four aspects of a pitch which will affect the Magnus force.  These four are listed below.  There exist other minor factors, such as the roughness of the ball’s surface that will not be considered here.

Primary Breaking Ball Factors:
  • Spin Rate
  • Velocity
  • Seam Orientation
  • Orientation of the ball’s axis of rotation

Spin Rate and Velocity
The Magnus force on a pitch is proportional to the spin rate and the velocity of the pitch (1). That means that doubling the spin rate while holding the velocity constant will double the Magnus force and double the amount of curve on a pitch.  The more a pitcher can increase the spin rate on pitches, the more a batter will be challenged.

Correspondingly, increasing the velocity on a curveball while keeping the spin rate constant will proportionately increase the Magnus force as well, but since it is traveling faster the sideways deflection will not be greater.  This is because the ball makes it to the catcher’s glove in less time then the slower ball; hence, the Magnus force has less time to act on pushing the ball sideways.  However, greater velocity provides two challenges to the batter: 1) the batter has less time to react, and 2) the sideways motion of the ball is faster due to the greater Magnus force.

You can see the effect of changing the spin rate and speed on the curve of a pitch online at the 
NASA Curveball Simulator  (2).  For example, an 82 MPH pitch with 25 Revolutions Per Second (RPS) will deviate from the center of home plate by 14 inches.  An 82 MPH pitch with 33 RPS will deviate from the center of home plate by 19 inches. 

Seam Orientation
Seam orientation is an important factor as well.  Studies have shown that for the spin rates and speeds typical for collegiate and professional baseball players, a 4-seam fastball will have 10% to 20% more lift than a 2-seam fastball (3).  This is a significant difference.  The advantage of a 4-seam pitch over a 2-seam pitch is slightly more pronounced for high school age pitchers that are unable to achieve the higher spin rates of collegiate level pitchers.

Axis of Rotation
The orientation of the axis of rotation of a pitched ball is important in determining the effectiveness of a pitch.  It is possible, but uncommon to throw a spin orientation such that the ball is ‘rifling’ toward the plate; that is, the axis of rotation of the ball lies along the line from pitching rubber to home plate.  This would be similar to the spin direction of a bullet shot out of a gun toward home plate.  A ‘rifled’ pitch has little or no Magnus force on it and, therefore, no deflection to its flight path due to Magnus forces.

One technique used by pitching coaches to more easily discern the quality of the axis of rotation is to mark a ball with a circle around a major diameter of the ball.  If the rotation is as desired, the coach can see the line, otherwise it will be a blur.  Another technique is to draw a large dot on the ball.  The dot would be put where the coach wants the axis of rotation to intersect with the surface of the ball.  If the pitcher achieves this, the dot appears as a dot in flight.  If the pitcher does not achieve the desired axis of rotation, the dot appears as a big blurred area on the ball in flight.

More Information
To gain a greater understanding of the physics involved in the game of baseball, a good resource that is an enjoyable read is “The Physics of Baseball” by Robert K. Adair, Sterling Professor of Physics, Yale University. 

(1) Bearman, P.W. and Harvey, J.K., 1976, “Golf ball aerodynamics”, Aeronautical Quarterly, Issue 27.
(2) http://www.grc.nasa.gov/WWW/K-12/airplane/foil2ba.html
(3)  Alaways, L.W. and Hubbard, M. 2001, “Experimental determination of baseball spin and lift”, Journal of 
Sport Sciences, 2001, Issue 19.

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