In a previous article, we reviewed the technical basis behind the baseball / bat coefficient of restitution (BBCoR) and the pickleball paddle / ball coefficient of restitution (PBCoR). In this review, we postulated that there may be a direct correlation between the bat bending and hoop vibration modes and the paddle diving board and trampoline vibration modes.
According to Prof. Alan Nathan in his 2000 paper, the lower frequency bending modes of a bat take energy away from the ball and reduce the rebound velocity. Therefore, the greatest rebound velocity will occur when the ball contacts the nodal point of the bat. The nodal point is the location of minimal vibration amplitude along the length of the bat (also called the anti-resonance point). In his 2004 paper, Nathan, et al, found that the higher frequency bat hoop modes added rebound velocity to the ball in a manner similar to that of a trampoline. In fact, Sutton & Sherwood observed that decreasing the hoop mode frequencies increase the performance of the bat.
We evaluated Nathan’s findings by testing two paddles, the Ronbus Ripple v1 which exceeded the USAP allowable PBCoR (of 44) and their Ripple v2 paddle which passed with a PBCoR of 43. These tests found that the anti-resonance, diving board, and trampoline frequencies of the v2 paddle were higher than those of the v1 paddle. From these tests, we hypothesized that paddles with an anti-resonance less than 250 Hz and a trampoline mode less than 500 Hz will exceed USAP PBCoR limits.
We then tested several paddles to fine-tune and verify our hypothesis. These tests showed clear trends in the data for the anti-resonance and trampoline vibration modes, and enabled us to rank the paddles according to their relative reactivity or power. This article provides additional details about our testing technique (which we call the Paddle Reactivity Test) and provides the paddle reactivity rankings.
The Paddle Reactivity Test
Paddle reactivity differs from paddle power in that reactivity involves only the vibrational dynamics of the paddle, whereas paddle power also involves your ability to develop swing speed and spin. A paddle’s power must therefore consider the paddle’s reactivity, mass (e.g., swing weight), stiffness, and face friction properties.
The reactivity test involves use of an accelerometer weighted to one ounce to simulate the weight of a pickleball placed at the geometric center of the paddle. Using a modal impulse hammer, the paddle is excited at several locations to collect the paddle frequency response functions (FRFs) between the paddle excitation and response locations Figure 1.
The collection of FRF’s enable us to synthesize the paddle vibration modes, including the anti-resonance, diving board, and trampoline modes (Figure 2-4).
Figure 2. Anti-Resonance Mode
Figure 3. Diving Board Mode
Figure 4. Trampoline Mode
The driving point transfer function is of particular interest because it involves the calculation of the transfer function at the ball location due to impact at the ball location. It therefore most closely simulates the paddle response when striking the ball. As shown in Figure 5, the peaks in the FRF correspond to the anti-resonance, the diving board, and the trampoline modes.
Paddle Reactivity Rankings
In our tests, we have found that paddles that exceed the USAP PBCoR test will have an anti-resonance frequency less than 200 Hz and a trampoline mode frequency less than 500 Hz. We have also determined that while it is important for the anti-resonance frequency to be above 200 Hz, the frequency of the trampoline mode ultimately determines the reactivity of the paddle.
Table 1 provides the frequencies of the anti-resonance modes, and the frequencies and amplification factors of the diving board and trampoline vibration modes. The amplification factors indicate the relative strengths of each vibration mode in g’s of acceleration response per pound of input force. For most paddles, the amplification factor of the diving board mode is a small fraction of the amplification factor for the trampoline mode.
Table 1 ranks each paddle according to the frequency of its trampoline vibration mode, with the highest reactivity paddles near the top of the list. The common denominators are as follows:
- Paddles that are not USAP approved (highlighted in gray) have a trampoline frequency less than 500 Hz. These paddles will provide the maximum reactivity but they may exceed the USAP PBCoR limits.
- Paddles with high reactivity (highlighted in green) have trampoline frequencies of 500 – 700 Hz. These paddles might be classified as “power” paddles.
- Paddles with medium reactivity (highlighted in yellow) comprise the majority of paddles, and have trampoline frequencies of 700 – 850 Hz range. These paddles might be classified as “hybrid” paddles.
- Paddles with low reactivity (highlighted in blue) have trampoline frequencies greater than 850 Hz. These paddles might be classified as “control” paddles.
Table 1. Paddle Reactivity Rankings
| Paddle / Model | Price & Link* | Anti-Resonance Freq (Hz) | Diving Board Mode | Trampoline Mode | ||
| Freq (Hz) | Ampl (g's/lbf) | Freq (Hz) | Ampl (g's/lbf) | |||
| Master Athletics Q1 | $ 179 | 115 | 264 | 46 | 321 | 72 |
| Diadem Vice | $ 110 | 142 | 280 | 36 | 308 | 26 |
| Ronbus EV2 | $ 120 | 138 | 320 | 29 | 380 | 35 |
| Diadem Hush | $ 190 | 237 | 295 | 6 | 484 | 16 |
| Ronbus Ripple v1 | N/A | 221 | 393 | 29 | 487 | 47 |
| Onix Evoke Premier Pro 10 | $ 200 | 224 | 363 | 17 | 537 | 96 |
| CRBN 1X | $ 229 | 248 | 382 | 16 | 566 | 64 |
| Paddletek Bantam TS-5 | $ 100 | 202 | 238 | 5 | 570 | 31 |
| Players Rogue 2 Hybrid Fiberglass | $ 130 | 203 | 230 | 4 | 572 | 12 |
| ProKennex Pro Flight | $ 195 | 270 | 354 | 12 | 605 | 74 |
| Quiet Play Whoop Ass | $ 275 | 206 | 253 | 4 | 613 | 12 |
| Engage Pursuit MX 6.0 Pro | $ 208 | 270 | 303 | 2 | 660 | 18 |
| Ronbus Ripple v2 | $ TBD | 272 | 439 | 43 | 683 | 51 |
| Players Rogue 2 Hybrid Carbon | $ 124 | 254 | 292 | 4 | 690 | 23 |
| Selkirk Vanguard Power Air Invikta | $ 180 | 220 | 243 | 10 | 698 | 66 |
| Selkirk Labs Project 008 13mm | $ 288 | 268 | 394 | 18 | 710 | 68 |
| ProKennex Black Ace Pro | $ 142 | 284 | 336 | 10 | 720 | 91 |
| Neonic Flare Prime X | $ 140 | 278 | 374 | 7 | 726 | 38 |
| CRBN 2X | $ 229 | 268 | 410 | 7 | 729 | 43 |
| Wowlly Surge | $ 180 | 262 | 336 | 27 | 734 | 43 |
| Ronbus R3 Pulsar | $ 115 | 290 | 382 | 6 | 737 | 23 |
| Diadem Icon Infinity Pro | $ 200 | 264 | 356 | 16 | 740 | 70 |
| Selkirk LUXX Control Air Epic | $ 200 | 239 | 259 | 7 | 751 | 58 |
| Master Athletics P3 | $ 259 | 290 | 353 | 19 | 760 | 38 |
| TMPR Terra TC-16 | $ 169 | 316 | 348 | 2 | 764 | 21 |
| Onix Mayhem | $ 187 | 283 | 338 | 14 | 778 | 82 |
| Selkirk Vanguard Invikta Pro | $ 230 | 300 | 406 | 15 | 785 | 68 |
| TMPR Terra TC-14 Pro | $ 169 | 288 | 376 | 33 | 786 | 60 |
| TMPR Terra TC-13 | $ 169 | 285 | 328 | 3 | 808 | 37 |
| Paddletek Tempest Wave Pro-C | $ 200 | 274 | 317 | 3 | 815 | 56 |
| Volair Mach 1 | $ 180 | 318 | 373 | 3 | 824 | 27 |
| Mozi Gold Rush | $ 219 | 306 | 379 | 15 | 849 | 60 |
| Bread & Butter Filth | $ 165 | 318 | 348 | 6 | 862 | 36 |
| Joola Hyperion | $ 160 | 356 | 450 | 8 | 863 | 66 |
| Selkirk Labs Project 007 10mm | $ 333 | 272 | 578 | 117 | 866 | 74 |
| Electrum Elite | $ 210 | 338 | 478 | 18 | 867 | 53 |
| Selkirk Amped Control Invikta | $ 100 | 338 | 603 | 29 | 882 | 47 |
| Onix Malice DB14 | $ 250 | 380 | 784 | 49 | 894 | 57 |
| Selkirk LUXX Control Air Invikta | $ 200 | 314 | 361 | 5 | 908 | 68 |
| Diadem Edge 18K SP | $ 240 | 332 | 403 | 14 | 911 | 61 |
| Vatic Pro Prism-Flash | $ 100 | 347 | 393 | 7 | 937 | 65 |
| Selkirk Labs Project 007 14 mm | $ 333 | 326 | 687 | 81 | 970 | 40 |
*Prices shown are list prices obtained from the linked website on the publish date. These prices do not include discounts offered by the website or manufacturer. Prices are subject to change by the retailer and/or manufacturer, and readers should obtain the latest pricing by clicking on the embedded links.
**Some of the embedded links in our website are affiliate links, meaning that at no cost to you, Pickleball Science will earn an affiliate commission if you click through the link and finalize a purchase**. Purchase of merchandise through these affiliate links will help support the website so that we can continue to provide meaningful content to our readers.
**For CRBN paddles, you can receive a 10% discount by entering coupon code PSCIENCE10
**For all TMPR paddles, you can receive $10 off your purchase by entering coupon code “PSCIENCE10”
**For all Ronbus paddles, you can receive $20 off of your purchase by entering coupon code “PSCIENCE20”
**Onix customers can get a 15% discount on their purchases by accessing the Onix website through the link provided in the table or by entering discount code “PSCIENCE15”.
Future Work
Pickleball Science is in the process of performing reactivity tests of several more paddles with the goal of correlating the paddle trampoline mode with the paddle PBCoR, in the manner that Sutton and Sherwood did for baseball bats. In their study, they tested several hollow aluminum and composite baseball bats and found a definite correlation between the bat BBCoR and its hoop mode frequency (Figure 6).
Because the Paddle Reactivity Test is easier to implement and more repeatable than the PBCoR test, the development of such a correlation for pickleball paddles will offer several advantages.
- During the paddle development process, paddle manufacturers can more easily test for reactivity, adjust and optimize paddle mass and stiffness properties, and have a high degree of confidence that their paddle will pass the PBCoR test when development is completed.
- Since paddles are known to increase in reactivity after use, pickleball governing bodies can easily test for reactivity to ensure that paddles used in tournaments meet the minimum trampoline frequency guidelines with a simple test that can be conducted prior to or during tournaments.
- Pickleball players can more easily select their ideal paddle through an objective test for reactivity (or ideally a Paddle Reactivity Index) instead of having to rely on expert opinions or manufacturer claims regarding paddle power.
