Since the shape, weight, and materials of the various pickleball paddles on the market may seem to be identical, one might conclude that all paddles are the same. While this may be true on the lower end of the paddle spectrum, there are significant differences in paddle performance at the higher end. What causes these differences? In this article, we will show how differences in paddle dynamics and paddle stiffness may account for differences in several performance characteristics such as power, control, spin, noise, and vibration. We will also discuss how paddle manufacturers and players can tune their paddles to achieve the optimum dynamic performance.
The Trampoline Effect
We discussed the so-called “trampoline effect” extensively in several previous articles (see for example “Power vs Control Paddles”). The trampoline effect is more pronounced with tennis racquets because they are constructed with a rigid outer frame that constrains a “fabric” of strings. When you hit a tennis ball the strings deform and stretch, thereby converting the kinetic (motion) energy of the ball into potential (stored) energy in the strings. As the ball is released, the potential energy in the strings is transferred back into kinetic energy of the ball, which propels it forward. The combined energy from the trampoline effect together with the kinetic energy of the paddle as you swing it causes the ball to be returned at a higher velocity.
For a tennis racquet, you will gain the maximum trampoline effect by striking the ball at the geometric center of the racquet face, which we will call the “dynamic center” (cD). This is because at the cD the strings will stretch evenly in all directions. Anyone who has jumped on a trampoline will attest that jumping on the center will result in the highest height and will cause your jump to be purely vertical, with no lateral motion. Therefore, contacting the ball at the dynamic center will result in the greatest rebound velocity and greatest accuracy in a direction that is perpendicular to the racquet face.
A pickleball paddle behaves somewhat differently than a tennis racquet for several reasons:
- The paddle does not have a rigid outer frame that constrains a stretchable “fabric” material in the center of the paddle.
- The in-plane stiffness (membrane elasticity) of the paddle face sheets is much greater than the tennis racquet strings.
- The honeycomb composite paddle face is much thicker than the tennis racquet strings and will therefore have a significantly greater bending stiffness.
For these reasons, we would not expect the pickleball paddle to exhibit the same amount of trampoline effect than the tennis racquet. In a previous article (see “How Large is the Sweet Spot?”) we attempted to measure the size of the sweet spot based on the paddle dynamic characteristics. This involved the performance of an impact dynamic test to extract the paddle vibration modes. From this we could determine the frequency of the trampoline vibration mode as shown in Figure 1. This vibration mode is characterized by the paddle handle and edge remaining somewhat stationary while the inside area of the paddle face oscillates like a trampoline at a frequency of about 1030 Hz.
Figure 1. Trampoline Effect for Pickleball Paddle
The Diving Board Effect
More recently, Pickleball Science has been analyzing the dynamics of several pickleball paddles based on their face bending and core compression stiffnesses (see “Paddle Technical Comparisons”). These analyses found that while there are differences in face bending stiffness among the different paddles, these differences alone do not fully explain why certain paddles have more “pop” than other paddles. It was therefore likely that we were missing a key component of the stiffness in our tests and analyses.
We have also studied the dynamics of baseball bats and hereby postulate that pickleball paddles may behave somewhat like baseball bats. These studies show that the batter’s swing and the momentum of the ball causes flexure of the bat near the handle that is stored as potential energy. On recoil, the potential energy is released in the form of kinetic energy that propels the ball off the bat at a higher velocity. This effect (which we call the “diving board effect”) occurs in several sports where a ball is struck with an implement, such as golf, tennis, baseball, lacrosse, hockey, etc. The dynamics of pickleball paddles should not differ significantly from the implements of other sports, so we should expect that the pickleball paddle will exhibit a combination of trampoline and diving board behavior.
What are the mechanics behind the diving board effect on a pickleball paddle? We know from experience that one of the weakest points on a pickleball paddle is at the base of the paddle face at the junction with the handle (known as the “throat” of the paddle). It is usually at this point where paddles are prone to breakage. On one hand, the handle has a high bending stiffness because it is thicker and often reinforced with wood or plastic. On the other hand, the paddle face in the vicinity of the throat has a low bending stiffness because its cross-sectional area is necking down from the full width of the paddle face to the width of the handle. The large differential in bending stiffness between the handle and the paddle face in the vicinity of the throat results in a lower bending stiffness and the concentration of stress in the throat area that causes premature failure.
Returning to our dynamic test (see “How Large is the Sweet Spot?”) we find a second vibration mode at 1230 Hz (Figure 2) that is close in frequency to the trampoline mode (Figure 2). Here we see that the paddle bends about the center of the face, but more importantly, there appears to be a “hinge point” at the interface of the handle with the face. In this manner, the paddle behaves like a diving board, with the base at the intersection of the handle with the paddle face. We believe that the diving board vibration mode together with the trampoline mode is the missing link that explains the differences in power among the different paddles.
Figure 2. Diving Board Effect for Pickleball Paddle
Putting it All Together
Which is more important – the trampoline effect or the diving board effect? As an illustration, we can model a pickleball paddle as a diving board with a trampoline on the end (Figure 3). When the diving board stiffness is too high or too low when compared to the trampoline stiffness (Figures 3a and 3b), we see that the ball does not achieve the same velocity as when the trampoline and diving board stiffnesses are balanced (Figure 3c). Therefore, by “tuning” the trampoline and diving board vibration modes to coincide, it is possible for the paddle to generate more power and velocity. Another benefit is that the trampoline and diving board reach full extension at the end of contact, increasing the contact time, thereby enabling greater shot accuracy and spin capability.
Figure 3. Superposition of Diving Board and Trampoline Effects
How much extra power can be generated? From our vibration test (Figure 4) we can see the dynamic amplification factors for the trampoline mode (at 1030 Hz) and the diving board mode (at 1230 Hz). Since the trampoline and diving board vibration modes do not coincide at the same frequency, the amount of power (or energy) generated by the paddle is compromised by the fact that the two vibration modes “fight” against each other.
We can illustrate this by looking at the interactions of simple waves. Let’s assume that by themselves, the trampoline and diving board vibrations each have a peak dynamic amplitude of 1.0 (Figure 5a). On one hand, if these vibration modes do not match in frequency or phase, destructive interference occurs, causing a lower amplitude when the waves are combined. In our example, the superposition of the two waves results in a single wave with an amplitude of roughly one-half that of the constituent waves. On the other hand, if the two vibration modes coincide with each other in frequency and phase (Figure 5b), we can realize constructive interference where the superimposed wave achieves an amplitude that is twice that of the constituent waves! This illustrates how the matching of the trampoline and diving board modes can result in greater paddle power.
Paddle Tuning
Paddle manufacturers should take heed and perform dynamic analyses of their paddles to ensure that the trampoline vibration mode coincides with the diving board mode to maximize the power potential of their paddles. Pickleball Science is in the process of developing a simplified methodology to extract the trampoline and diving board modes of paddles using a dynamic signal analyzer. Knowing the frequency of these vibration modes can allow the paddle manufacturers to properly tune their paddles for maximum power potential.
Without this sophisticated test equipment, what can a typical pickleball player do to maximize the power potential of their paddle? In our example, we vibration tested a Vulcan V530 Power paddle. It is fortunate that the diving board mode occurs at a higher frequency than the trampoline mode because we can add mass to the edge of the paddle to effectively reduce the frequency of this mode.
Where should you put the weights? We can answer this question by first examining the animated vibration shape of the diving board mode (Figure 5). The most effective locations to place the weight(s) are at the points of greatest amplitude. Here, we would consider placing weights along the lower and upper sides of the paddle face, however, we would not want to place the weights at locations that will adversely affect the trampoline mode. Examination of the trampoline mode (Figure 2) shows that both the upper and lower inside corners of the paddle face are so-called nodal points with zero deflection. Therefore, placing weights at these locations will not affect the trampoline mode. Figure 6 illustrates the ideal locations for placing weighted tapes on the Vulcan paddle to effectively lower the frequency of the paddle diving board mode. It is important to note that these weights would be added to these locations to re-tune the frequency of the diving board mode. Readers should also consider the effects of these weights on the paddle swing weight and twist weight.
How much weight should be added? This is actually a difficult question to answer without further vibration testing, which we will address in a future article. For the time being, players should judiciously apply small amounts of weighted tapes to their paddles and evaluate the paddle’s performance through a trial-and-error process. This illustrates one of the problems of arbitrarily adding weighted tapes to your paddle. While they may affect the balance, swing, and twist weights of your paddle, they may also shift the frequency of the paddle trampoline and diving board vibration modes and compromise the paddle power potential. In a future article we will take a closer look at how weighted tapes affect paddle static and dynamic performance.
