The Problematic Clamp
USAP's Questionable PBCOR Measurement
3/12/26
As part of the USAP certification program each paddle has to go through the Paddle Ball Coefficient of Restitution (PBCOR) test. The test is done to weed out paddles that are deemed to be too powerful for competitive play. The current standard is 0.43. Any paddle with a PBCOR value above 0.43 is too powerful and is not certified. There are tens of thousands of dollars invested by paddle manufacturers during new paddle design and the process of bringing it to market. If a paddle fails PBCOR testing that money is lost. Therefore, it's important that the test be a true representation of how a paddle performs on the court.
USAP's Test Process
The paddle's handle is stripped of the grip, any soft pallets and butt cap. The handle is inserted in a relatively massive rotating steel clamp as shown in the picture. A ball is shot toward the paddle at 60 mph. The inbound velocity of the ball and the rebound velocity of the ball along with the rotational velocity of the paddle is recorded. These three variable along with the physical characteristics of the paddle are entered into a complex equation to determine the PBCOR value. An excellent video of USAP's testing facility is here.
Questionable Test Results
Recent testing brings into question whether USAP's test is a reliable representation of the on-court performance of a paddle. The PBCOR test results measured by USAP for a Flik F3 Elongated paddle were obtained. USAP measured the PBCOR at 0.40. The same model paddle was tested under similar conditions with the exception that a lightweight paddle clamp was used. In the latter case the measured PBCOR was 0.44. The difference is large. In one test the paddle easily passed; with the lightweight clamp it failed.
The Problem
USAP uses a massive clamp with a swing weight (33 kg*cm^2) that is relatively large compared to a typical paddle's swing weight (~115 kg*cm^2). USAP mistakenly characterizes the paddle as a rigid body and always includes the clamp's swing weight into the PBCOR calculation. But the paddle is not a rigid body and with most paddles there are several vibration modes that can propel the ball off the paddle face before the clamp can have any significant influence on the ball's speed. In other words, the ball doesn't always "see" the clamp, yet the clamp's moment of inertia (swing weight) is mistakenly included in USAP's PBCOR calculation.
Having trouble conceptualizing why the clamp does not significantly affect ball speed and should be ignored in certain circumstances? It seems intuitive that a paddle that is gripped (clamped) tightly would propel a ball off the paddle faster compared to a paddle that was barely gripped at all. But that is not always the case. There is an excellent parallel example of how a baseball's speed is unaffected by how the bat is gripped (clamped). See the video of Todd Frazer hitting a home run while his hands are off the bat.
Unintended Consequences
The use of a massive clamp and the inclusion of the clamp's swing weight (33 kg*cm^2) into the PBCOR calculation has several unintended consequences.
-
USAP significantly understates the PBCOR value of the Flik F3 paddle and probably many other paddles. The inclusion of the clamp's swing weight into the PBCOR calculation artificially lowers the PBCOR value in the preferred hitting area (sweet spot).
-
USAP's PBCOR value does not correctly predict a paddle's power and resultant ball speed on the court.
-
Independent testing labs cannot reliably duplicate USAP's PBCOR value. Many manufacturers test their paddles at an independent lab before submission to USAP. Unless the independent lab has an exact duplicate of the USAP massive clamp, the PBCOR values will be different.
The Solution
The favored solution would be to replace the current clamp (SW=33) with lightweight clamp (SW<1). The low swing weight would have a negligible effect on ball speed regardless of whether the ball "sees" the clamp or not. USAP's current clamp is borrowed from baseball bat testing where impact forces are much higher. There is no need for such a massive clamp. The downside of this solution is the need to reset the PBCOR limit and mathematically adjust the PBCOR values of previously certified paddles or retest them to determine their true values.
The less desirable solution is for USAP to continue with the same testing methodology and the same clamp. While the PBCOR value is artificially low, USAP's method still correctly ranks most paddles according to power.
USAP's clamp
Todd Frazer hitting a "no hands" homerun
Details
Anomalous Test Results
A Flik F3 Elongated paddle was obtained along with USAP's test results. For clarity, my testing was done with the same model paddle, but not the identical paddle tested by USAP. The PBCOR results are graphed.
The wide difference in results initiated an investigation. USAP's testing had the PBCOR below the 0.43 limit which made the paddle eligible for certification. My testing said the paddle was above the limit and ineligible for certification. Did I get a "hot" paddle? Was there some error in my measurements? Was there something different in my test equipment?
Further investigation was warranted.
The Clamps
The one glaring difference between USAP's testing apparatus and mine was the clamp.
USAP's clamp, pictured to the right, is most likely borrowed from baseball bat testing. There are two steel clamping arms attached to a base.
The Moment of Inertia (MOI) or swing weight is 33 kg*cm^2 which is significant in comparison to the swing weight of a typical paddle at 115 kg*cm^2.
The clamp used in my testing is a lightweight aluminum split ring clamp and is pictured to the right. OD 56mm, ID 31mm, Ht 15 mm, static weight 94 grams
The swing weight is less than 1 kg*cm^2 which is negligible in comparison to a typical paddle at 115 kg*cm^2.
The Clamp's Inertia in the PBCOR Formula
USAP's formula for calculating PBCOR is displayed to the right. We want the same PBCOR value no matter if a large massive clamp is used or a lightweight clamp is used during testing. There is a term in the formula (MOIp) that supposedly compensates for the clamp's added inertia so the PBCOR of the paddle alone can be determined.
Let's assess the reliability of the formula by testing the exact same paddle with a massive clamp (similar to the one USAP uses) and a lightweight clamp (my clamp). We expect to get the same PBCOR results.
PBCOR - Massive Clamp v Lightweight Clamp
A massive clamp with a large inertia was created to mimic USAP's clamp. A four inch section of 2"x2" square steel tubing was used. The static weight was 31 ounces or over three 3 times the weight of a typical paddle. The inertia of the clamp alone was calculated to be 56 kg*cm^2. The combined inertia of the clamp and paddle is 166.
The lightweight clamp was the split ring clamp described above with an inertia less than 1. The combined inertia of the clamp and paddle is 110.
The PBCOR results for the massive clamp and the lightweight clamp are quite different as shown in the graph It is apparent that the PBCOR formula used by USAP does not properly account for differences in clamp design.
This graph looks similar to the graph in the Anomalous Test Results section above. The paddle tested with a massive clamp has much lower PBCOR values.
The formula to account for differences in clamp inertia is not working.
Ball Speed with Added Inertia
To understand why the PBCOR formula doesn't properly account for difference in clamp inertia it's important to understand, in general, how added inertia affects ball speed. The graph to the right displays three traces of rebounding ball speeds off an F3 paddle with different peripheral weights in response to a 60 mph inbound ball speed.
1. The rebounding ball speed of the unmodified F3 with a swing weight of 110.5
2. The F3 with nine 3 gram lead strips added (3 each side; 3 on the top) with a swing weight of 129
3. The F3 with twelve 3 gram lead strips added (3 each side; 6 on the top) with a swing weight of 142
Intuitively, we know that adding weight to the paddle's edge guard will increase ball speed. As expected, the ball speed increases with added peripheral inertia.
Ball Speed with a Massive Clamp
Ball speed was measured using the massive clamp described above. The static weight was 31 ounces or over three 3 times the weight of a typical paddle. The inertia of the clamp alone was calculated to be 56 kg*cm^2. The combined inertia of the clamp and paddle is 166 which is larger than the two examples of added peripheral inertia above. Intuitively, the rebound speed is expected to increase and increase more than the two examples above because the inertia of the clamp is larger.
Unexpectedly, the rebound speed of the ball with the heavy clamp is almost identical to the ball speed with the lightweight clamp. The ball speed did not increase. What's going on?
Answer: The ball has rebounded off the paddle face before any energy stored in the bending mode can be returned to the ball. Essentially, the ball doesn't "see" the extra inertia added by the clamp because the clamp is far away from the impact location. The ball has left the paddle face before the shock wave from the impact has had time to travel to the clamp and back.
Backing Out the Clamp's MOI
If the ball doesn't see the clamp's moment of inertia (MOI, swing weight) then the inertia of the clamp should be removed from the calculation to determine the true PBCOR. The effect of removing the clamp's MOI on PBCOR values is depicted in the graph. There is much better agreement between my PBCOR values and USAP's. While the match is not perfect, the difference can be attributed to different labs and different paddles (same model, different paddle). The true value of the F3's PBCOR is near 0.44.
Is it as simple as using a spreadsheet to remove the clamp's inertia from the PBCOR equation to determine the true PBCOR? Probably not. Removing the clamp's inertia is valid as long as the ball doesn't "see" the clamp. It worked for this paddle at the 3" to 5" impact range. However, preliminary experimentation at the 6" and 7" impact location indicates that the ball begins to "see" the clamp. This will be a subject of a future article.
Is the F3 Above the 0.43 Limit?
It would seem the the Flik F3 should be decertified by USAP for being over the 0.43 limit. That would be the wrong take-away. The 0.43 limit was set by looking at PBCOR values from a population of paddles that were artificially low. The limit would have to adjusted higher, possibly to around 0.46, to account for the new higher PBCOR values.
Conclusions
Caveats:
1. The conclusions are based on experimentation using one paddle. Extrapolation to a wider range of paddles is probably valid, but needs to be proven
2. The conclusion are based on impacts at three locations. These locations encompass the sweet spot of most paddles and the hitting area favored by players. Impacts at other locations, especially closer to the clamp, may exhibit different behavior.
-
The ball does not "see" the inertia of USAP's clamp at locations between approximately 3 and 5 inches - the sweet spot.
-
The inclusion of the clamp's inertia in the PBCOR calculation significantly lowers the paddle's reported PBCOR value below the actual value.
-
Independent testing labs cannot reliably duplicate USAP's [inaccurate] PBCOR values unless an exact copy of USAP's clamp is used along with the [erroneous] inclusion of the clamp's inertia into the PBCOR equation.