Conventional wisdom suggests that paddles with higher weight, lower stiffness, and higher PBCoR (Paddle/Ball Coefficient of Restitution) ratings will have greater power than paddles with lower weight, higher stiffness, and lower PBCoR ratings. As we know, this is not always the case. There are numerous instances where a paddle might appear (on paper) to have more power based on weight, stiffness, and PBCoR, however, when playing with it, we find that the opposite is true. Why? If players cannot select an appropriate paddle based on weight, stiffness, and PBCoR, how can we possibly select an ideal paddle? Do we need to trust the so-called “experts”? Or do we need to test paddles ourselves before committing to purchasing them?
We believe that the paddle/ball contact dynamics (which is an extension of our paddle reactivity tests) may provide an objective means for rating paddles according to power potential. To illustrate this, let’s look at the Paddletek Bantam TKO-C 12.7mm and Bantam TKO-C 14.3mm paddles (Figure 1). These paddles each use a conventional polypropylene (Gen 2) honeycomb core with PT-700 unidirectional RAW carbon fiber face sheets. Other than the obvious differences in core thickness, the two paddles appear to be identical.
Static Mass & Stiffness
We analyzed and measured static mass and stiffness properties of each paddle, which are summarized in Table 1. We highlighted (in yellow) the data that would suggest a greater power potential of the two paddles. From this, one would surmise that the 14.3mm paddle has more power than the 12.7mm paddle.
Table 1. TKO-C Static Mass & Stiffness Properties
Dynamic Properties
We performed dynamic impulse tests of both paddles, where the dynamic response at the ball strike location at the center of the paddle face is shown in Figure 2. Here we see that the 14.3mm paddle has two peaks in the dynamic response at frequencies of 673 Hz and 744 Hz, but the 12.7mm paddle has only one peak at 757 Hz. Furthermore, we see that the peaks for the 14.3mm paddle have greater amplitude than the single peak of the 12.3mm paddle. From these results, one would surmise that the 14.3mm paddle has greater reactivity (and more power) than the 12.7mm paddle.
An examination of the vibration modes (Figure 3) shows that the 14.3mm paddle has a “potato chip” bending mode at 673 Hz (Figure 3a), and a “taco bending” mode at 744 Hz (Figure 3b). An explanation of these modes is provided in our article, Paddle Trampoline Modes. The 12.7mm paddle shows a single “taco bending” mode at 757 Hz (Figure 3c).
PBCoR
The paddle/ball coefficient of restitution (PBCoR) test has recently been adopted by the USAP to screen paddles for power. PBCoR test results are a well-kept secret since the USAP does not provide the test data and manufacturers refrain from publishing PBCoR test results for their paddles. We analyzed the PBCoR test and believe that it may be flawed since only a small amount of the impact energy (2.3%) goes into the deformation of the paddle (see “Analysis of the PBCoR Test”). In one instance where we obtained the PBCoR test data from the manufacturer, we found that their “power” paddle had a much lower (USAP-tested) PBCoR than their “control” paddles (see “11Six24 Hurache-X Review”). Because of these technical inconsistencies, we do not believe that the PBCoR as tested by the USAP is a reliable indicator of paddle power. We have therefore developed alternative means of characterizing paddle power based on our paddle reactivity tests and the contact dynamic tests described herein.
Paddle Performance
We assembled a group of intermediate-to-advanced pickleball players who evaluated the paddles under practice and game conditions. In general, they agreed that the Paddletek TKO-C paddles have a surprisingly large amount of “pop” for Gen 2 paddles that could compete with many Gen 3 paddles currently on the market. They also agreed that the 12.7mm paddle had greater “pop” than the 14.3mm paddle.
According to the Paddletek website, numerous on-line paddle reviews, and our own subjective evaluation of the paddles, the 12.7mm paddle has more “pop” and can generate more power than the 14.3mm paddle. This runs counter to conventional knowledge regarding the paddle mass, stiffness, and dynamic tests described above. If we cannot rely on these tests, how can we possibly select a paddle based on published paddle specifications? We believe that the answer to the question lies in an examination of the paddle/ball contact dynamics.
Contact Dynamics
In numerous previous articles (see for example, Paddle Weight and Momentum) we used the impulse-momentum relationship to determine that the contact time between the ball and paddle is on the order of 4 milliseconds (4 msec or 0.004 sec). We also described how a paddle’s vibration modes during the contact period determine how much power is transmitted between the paddle and ball (see for example, Paddle Trampoline Modes). Since the paddle can affect the ball only when they are in contact, it behooves us to understand how the paddle dynamically interacts with the ball during the 4 msec contact period.
The contact dynamics test involved a similar test set-up that we used to measure paddle reactivity (see Paddle Reactivity Rankings). This test involved attaching an accelerometer to the center of the paddle face that was weighted to simulate the mass of a pickleball. We then applied an impulse with a peak force of 30 lbs to the center of the paddle face and measured the vibration response with respect to time at a rate of 10,000 samples per second.
The impulse time history (Figure 4) shows that the contact duration was on the order of 2.8 msec. It is shorter than the 4 msec contact duration of a pickleball because the impulse hammer tip is harder than a pickleball. A pickleball will squash on impact, which will increase the contact duration. This should not matter because the vibration modes of the paddle are intrinsic properties of the paddle alone and would not be expected to change with the shorter contact duration of the impulse hammer.
The response time history (Figure 5) shows a greater peak-to-peak variation for the 12.7mm paddle verses the 14.3mm paddle over the 2.8 msec contact time. This would indicate that the 12.7mm paddle has greater reactivity or power than the 14.3mm paddle. We believe that the peaks in the 14.3mm paddle are lower because the double trampoline vibration modes destructively interfere with one another. That is, since the two trampoline vibration modes occur at different frequencies, they will have an inherent phase difference which causes the waves to reduce each other’s amplitude over the 2.8 msec contact duration.
When averaged over the 2.8 msec contact time, we can calculate the offset acceleration of the 12.7mm paddle to be 25.8 g’s, and the 14.3mm paddle to be 28.3 g’s (Figure 6). The offset can be looked upon as a “steady-state” deformation of the paddle during contact with the ball. We then integrated the acceleration time histories over the 2.8 msec contact duration relative to their steady-state offset accelerations. This yields a new parameter which we invented that we call the “apparent velocity” (or V-app), for which results are summarized in Table 2. As indicated, the V-app for the 12.7mm paddle is a factor of 1.5 times greater than that of the 14.3mm paddle! This might explain why the 12.7mm paddle appears to have more “pop” and power than the 14.3mm paddle.
Table 2. Apparent Velocities
Summary & Conclusions
The Paddletek TKO-C Bantam paddles* are high quality power paddles that are suitable for intermediate-to-advanced players. Based on conventional knowledge of their static mass, stiffness, and dynamic properties, one would conclude that the TKO-C 14.3mm paddle has more power than the TKO-C 12.7mm paddle. However, this was not the case.
In our dynamic analyses, we found that the presence of two trampoline vibration modes for the 14.3mm paddle cause destructive interference that reduce the power potential of the paddle. Integrating the acceleration response of the paddles with respect to time, we developed a new parameter that we call the “apparent velocity” (or “V-app”) and found that the V-app of the 12.7mm paddle is 1.5 times greater than that of the 14.3mm paddle. The destructive interaction of the two trampoline vibration modes for the 14.3mm paddle might therefore explain why it has less power than the 12.7mm paddle.
The dynamic interaction of the trampoline modes could only be seen in an examination of the paddle/ball contact dynamics. However, as a general rule, paddles with multiple trampoline vibration modes will have less power than those with a single trampoline mode.
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