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.
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.
PBCOR = SQRT(E2/E1)
The PBCOR specification limits the amount of energy the paddle AND ball can retain after the collision.
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.
PBCOR = (Vball2-Vpaddle2)/(Vball1-Vpaddle1)
https://en.wikipedia.org/wiki/Coefficient_of_restitution
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.
A future section will reveal the paddle characteristics (e.g. static weight; swing weight, balance point) that determine the ball’s actual speed.
PBCOR Limitations
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See the discussion below on Is PBCOR the Best Metric
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Both USAP and UPA-A test for a paddle’s PBCOR, but don’t release the results. The results are the property of the manufacturer and can only be released by them. But, to date, no manufacturer has published PBCORs for their paddles. The only information to be gleaned from a paddle that has passed certification is that the PBCOR is at or less than the limit.
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Location Specific - the PBCOR value is applicable to one specific impact location. Move the impact location 1" and the PBCOR value changes.
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Velocity Specific - The PBCOR value is applicable to one specific ball velocity. (50 mph for UPA-A; 60 mph for USAP) Change the incoming ball velocity and the PBCOR value changes.
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Ball Specific - The PBCOR value is applicable to one brand of ball. (holeless Franklin X40 for USAP; Vulcan Pro Flight for UPA-A). Change the ball to any other brand and the PBCOR value changes.
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There is no equation to compare USAP’s PBCOR values to the UPA-A’s values.
Is PBCOR the Best Metric?
For safety reasons and to prevent pickleball from becoming a power only sport the two governing agencies have adopted PBCOR as a way to limit ball speed. But PBCOR is not a direct measure of ball speed on the court. PBCOR is a measure of the power retained in the ball and paddle after the collision. What we'd really like to know is the power retained only in the ball and hence ball speed using the equation E=mv^2. We really don't care how much power is retained in the paddle. We're only concerned with the ball's power (not the paddle's power) and about how fast the ball is approaching our face.
One would hope that 5 paddles with the same PBCOR would also produce the same ball speed. Or stated another way, one would hope that 10 paddles ranked by PBCOR would have the same ranking for ball speed. Unfortunately, neither agency has run an experiment where 10 players each use 10 paddles where balls speeds are measured with a radar gun.
It's still an open question - Does the on-court ball speed mirror the PBCOR ranking?