Why Use PBCOR?

The details of COR (Coefficient of Restitution) are unknown to most of the pickleball community, but have been in use for centuries by scientist and engineers.  The theory was establish by Sir Issac Newton in the 1600s.  There are several reasons to use COR (or specific to pickleball PBCOR) to limit paddle power.

 

First, several sports have already "led the way" and use the theory to limit bat/club/racket power such as in baseball, tennis, golf, and badminton.  Plus, these pioneering sports have developed the equipment and procedures to measure PBCOR.

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Second, PBCOR provides the theory and equations to determine energy and velocity after the collision.  

 

The Energy Equation

The subscript 1 denotes before the collision; the subscript 2 after. 

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PBCOR = SQRT(E2/E1)

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The PBCOR specification limits the amount of energy the paddle AND ball can retain after the collision.

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The Velocity Equation

PBCOR is also a direct measure of how much velocity (V) is retained in the paddle and ball after the collision.  Sometimes a ball at rest collides with a moving paddle such as during a serve. Sometimes a moving ball collides with a stationary paddle such as during a block. Sometimes both the ball and paddle are both moving during the collision such as during a volley.
 

PBCOR is defined as the relative velocity of the ball and paddle after the collision divided by the relative velocity of the ball and paddle before the collision. The subscript 1 denotes before the collision; the subscript 2 after.

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PBCOR = (Vball2-Vpaddle2)/(Vball1-Vpaddle1)

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https://en.wikipedia.org/wiki/Coefficient_of_restitution

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​Example 1:
Here is an example of a player blocking a shot at the net. The ball is traveling toward the player at 50 mph. (Vball1 = 50 mph) The paddle is stationary. (Vpaddle1 = 0 mph). Let's suppose the PBCOR of the paddle is at the UPA-A limit of 0.385. After the collision the ball reverses direction moving at some yet-to-be determined speed toward the opponent. After the collision the paddle recoils and moves backward at some yet-to-be determined speed. Using the equation above we have:
 
 Vball2-Vpaddle2 = PBCOR * (Vball1-Vpaddle1)
 Vball2-Vpaddle2 = 0.385 * (50-0) = 19.25 mph
 
We know the relative speed after the collision (in this case 19.25 mph), but we don’t know the velocity of the ball or the velocity of the paddle.  Vball2 might be 10 mph with Vpaddle2 = -9.25 mph.  (the minus sign denotes that the paddle is traveling backward in the direction opposite the ball) Or Vball2 might be 12 mph with Vpaddle2 = -7.25 mph.  The PBCOR is tied to one specific model of ball.  Change the ball and the PBCOR changes.  For those who need to know now, the answer is Vball2 is around 11.5 mph for the typical power (PBCOR=0.385) paddle using a Vulcan Pro ball.
 
Example 2:
Likewise, an example of a serve uses the same equations.  Vball1 = 0.  Vpaddle1 = -50.  PBCOR = 0.385
 

Vball2-Vpaddle2 = PBCOR * (Vball1-Vpaddle1)
 Vball2-Vpaddle2 = 0.385 * (0-(-50)) = 19.25 mph
 
We know the relative speed after the collision, but we don’t know the velocity of the ball.  Vball2 might be 65 mph with Vpaddle2 = 45.75 mph.  Or Vball2 might be 60 mph with Vpaddle2 = 40.75 mph.  It all depends on the characteristics of the paddle and the ball which we’ll explore later.  For those who need to know now the answer is Vball2 is around 61.5 mph for the typical power (PBCOR=0.385) paddle using a Vulcan Pro ball.

 

Measuring PBCOR in the Lab

It would seem fairly straightforward to measure PBCOR by shooting a ball toward a stationary paddle at a known velocity and then measuring the resultant rebounding ball velocity and the recoiling paddle velocity.  Then plug the values into the equation below:

PBCOR = (Vball2-Vpaddle2)/(Vball1-Vpaddle1)

 

But because measuring the velocity of the recoiling paddle is problematic another method is used.  The ball mass, the paddle swing weight and the impact point are carefully measured and entered into the equations below.