There are numerous ads on the Internet by pickleball paddle manufacturers claiming that their paddles are optimized for power or control, but what is the difference? Pickleball players will tell you that paddles with more power have greater “pop”, which is a nebulous term that is understood to mean the sound of the ball hitting the paddle and/or the speed at which the ball bounces off the paddle. A paddle with good “pop” will therefore have a nice “solid” sound and the ball will seem to fly off the paddle with very little effort. On the other hand, paddles with more control have less “pop”, and the ball seems to bounce off the paddle in a slower but more predictable and controlled manner.
What are the characteristics of a paddle that determine the amount of “pop” it has? Some people claim that it has to do with the thickness or materials used in the paddle core. Others will claim that it has to do with whether the paddle face is made of fiberglass, graphite, carbon, or kevlar. Yet others claim that it has to do with the shape or weight of the paddle. Who’s right? Let’s look at the science to help us find out.
Impact Dynamics
Tennis players know that stringing their racquets with lower tension will provide more power and spin to their shots. This seems counter-intuitive, as it would appear that tighter strings (or a stiffer paddle face) would put more energy into the ball upon impact. However, an interesting thing happens that requires us to look at impact dynamics and how energy is exchanged between the ball and the paddle. Let’s first look at how the pickleball interacts with the ground.
According to USAPA equipment standards, a pickleball that is dropped from a height of 78” must bounce off the surface of a granite block to a height of 30-34”. If you drop a ball from a height and the ball returns to the same height, it is a perfectly elastic collision. That is, the kinetic energy (i.e., energy of motion) of the ball before the collision is the same as the kinetic energy of the ball after collision. We know from experience that not even a super ball will rebound to the same height. Where does the energy go? Certainly, if the granite block does not move and the force from the pickleball does not deform the block, the energy does not go into the block. The energy must therefore be absorbed and dissipated by the ball.
When the ball strikes the ground, it undergoes elastic deformation. That is, the kinetic energy from its velocity at impact deforms the ball, but the deformation is temporary. It will spring back to its original (spherical) shape after it bounces back from the ground. We can model the ball as if it were a mass on a spring as shown in Figure 1.
Just before impact, the ball has an initial velocity, and the spring is uncompressed. Knowing the mass and velocity of the ball, its kinetic energy can be calculated by:
KE = ½ mv2
When the ball strikes the ground, the mass of the ball starts to compress the spring, and the ball begins to squash (Figure 1b). When the velocity of the ball decreases to zero, all of the kinetic energy from its initial velocity is transformed into potential (stored) energy that deforms the ball causing the ball center of mass to displace by a distance Δx. Knowing the stiffness (k) of the ball, we can calculate the potential energy by:
PE = ½ kΔx2
When the ball bounces back off the ground, the spring returns to its original length, and the potential energy that was used to deform the ball is converted back into kinetic energy to propel the ball upward from the ground. However, not all of this energy is available, and the ball fails to bounce back to its original height. Where does it go?
By equating the kinetic energy before impact to the kinetic energy on rebound, we can determine how much energy was lost by deforming the ball. First, we need to calculate the coefficient of restitution (COR), which is the ratio of rebound height to the drop height. It normally ranges from 0 to 1, where a value of 1 would be a perfectly elastic collision, and a value of 0 would be a perfectly inelastic collision. The COR is usually designated by the letter ‘e’. Assuming that the drop height (H) is 78″ and the rebound height (h) is 34”:
Knowing e, we can calculate the fractional energy loss (f) which relates the loss in kinetic energy before and after the bounce:
f = 1 – e2 = 1 – 0.436 = 0.56
This shows that more than one-half of the energy in dropping the ball is lost. But where? The answer lies in the fact that all materials exhibit some form of damping, which is a tendency of materials to dissipate energy under stress and strain. When the pickleball deforms, at the microscopic level the polymeric chains within the plastic stretch and rub against each other causing friction. If the deformation is large enough, some of these polymeric chains break, resulting in micro-cracks that eventually become large cracks. The internal friction and cracking dissipate energy which is not recovered resulting in the ball bouncing lower than the initial height on rebound.
The Trampoline Effect
When tennis players string their racquets with lower tension, the strings provide a “trampoline effect”, which enables the ball to have a more energetic bounce. Here, the strings stretch against the racquet frame in the same manner that trampoline springs stretch against the outer frame. Another benefit is that the lower string tension allows the ball to stay on the strings longer, enabling tennis players to add more spin to the ball. We will deal with how the pickleball paddle adds spin to the ball in a future article. For now, let’s focus on the trampoline effect and how it enables a more energetic bounce.
It has been reported that the strings of a tennis racquet can return as much as 95% of the potential energy used to deform the strings back into kinetic energy of the ball, whereas a tennis ball is only about 45% efficient based on rebound specifications. By stringing the racquet with lower tension, the trampoline effect allows the more efficient strings of a tennis racquet to store more of the kinetic energy than the less efficient tennis ball. Consequently, less energy is lost allowing for a more energetic shot.
In order to gain the maximum benefit of the trampoline effect, it is important to contact the ball at the center of the trampoline, which we will call the “dynamic center” (cd). 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 in a direction that is perpendicular to the paddle face.
It is important to note that the dynamic center (cd) of the paddle is not necessarily the sweet spot or center of percussion (cp). In a previous series of articles, we determined the location of the paddle sweet spot considering that the paddle was rigid, whereas the calculation of the dynamic center involves a flexible paddle. It would be desirable for the dynamic center to coincide with the sweet spot, as a shot from this location will result in no reaction force in your hand and the maximum rebound velocity in the intended direction of travel. However, there are no guarantees. To establish the dynamic center, a vibration analysis of the paddle would need to be performed, which may be the topic of a future article. For the time being, it is safe to assume that the dynamic center coincides with the geometric center of the paddle face.
Do Stiffer or Softer Paddles Provide More Pop?
Unfortunately for pickleball players, we cannot control the tension or stiffness of our paddle faces like tennis players can control the tension of their strings. We must get our paddles “as-is” from the manufacturer; however, how do we know how much “pop” is in a paddle? It is difficult to know because paddle manufacturers tend to confuse consumers with different and sometimes contradictory claims that the “pop” of their paddles has to do with paddle face materials (e.g., fiberglass, graphite, carbon, wood, etc.), the core materials or thickness, the shape of their paddles, etc. How would you quantify “pop”? Do you get more “pop” with a softer or a harder paddle face?
To measure “pop”, I created a simple experiment, where a pickleball was dropped from a height of 78” onto a hard, heavy surface (a quartz countertop). The countertop was sufficiently massive (50 lbs) and rigid that the pickleball would not cause motion or deformation of the countertop. At first, the rebound height of the pickleball was measured when dropped on the bare countertop (Figure 2a). Next, a pickleball paddle was clamped firmly to the countertop and the experiment was repeated (Figure 2b). The difference in rebound height would provide a measure of how much energy the paddle returned to the ball.
For either case, it was difficult to see the maximum rebound height of the ball for all drops, so a GoPro camera was used to record each drop. This camera has a limited frame rate and is not technically a high-speed camera. Therefore, numerous (Franklin X-40 outdoor) balls were dropped, but only the maximum height was used in the energy calculations. In future tests, a high-speed camera should be used more accurately measure the height and to ensure that the ball lands at the paddle face center.
The paddle that was tested was a Vulcan V530 Power, which was used in previous articles to determine its sweet spot. When the paddle is clamped, the face sheets do not contact the quartz surface or the clamping bars because the paddle has a small lip around the edge (Figure 3). Paddles without this feature may need to be tested in a different manner.
Example photos of the maximum drop height detected by the GoPro camera can be seen in Figure 4a for the ball landing on the bare quartz countertop and in Figure 4b for the ball landing on the paddle. These photos show that when the ball is bounced on the bare quartz, it rebounds to a height of about 33 inches, but when it is bounced on the paddle, it rebounds to a height of 36 inches.
What does this mean in terms of energy exchange? The coefficient of restitution (e) of the ball alone is 0.65, corresponding to a fractional energy loss (f) of 0.57, meaning that 57% of the kinetic energy of the ball is lost in the bounce on the bare quartz countertop. When the paddle is added, the coefficient of restitution (e) is 0.68 with a corresponding fractional energy loss (f) of 0.54 or 54%. Therefore, the paddle increases the amount of kinetic energy of the ball at rebound by only 3%!
In contrast, when a pickleball is bounced off the strings of a tennis racquet, the rebound height is about 58”, corresponding to a coefficient of restitution (e) of 0.86 and a fractional energy loss (f) of only 26%! The tennis racquet therefore increases the amount of kinetic energy of the ball at rebound by a whopping 31% — more than ten times more efficient than the pickleball racquet! The reason why the tennis racquet is better than the pickleball racquet in returning energy to the ball will be discussed in a future article.
Further investigation of paddle material specifications found that according to USA Pickleball, the static stiffness of the paddle face be between 1100 – 1320 lb/in, and that “paddles that exceed these specifications may provide a trampoline effect and will fail to be approved by the USA Pickleball Association (USAPA)”. If the trampoline effect is dependent on static stiffness alone, this narrow stiffness range may not be sufficient to differentiate a “power” paddle from a “control” paddle.
Based on the static stiffness specification on the USA Pickleball website, it is possible to use the paddle face stiffness to calculate the maximum displacement of the paddle face when subjected to the ball drop then determine the upward acceleration that the paddle provides to the ball. However, this result would be misleading because as we have seen above, a key component of the rebound problem pertains the amount of damping in the pickleball and the paddle. Therefore, two different paddles that each satisfy the USA Pickleball static stiffness requirement may have different rebound (“pop”) characteristics depending on the amount of damping in the paddle face sheets and core.
Introducing the Paddle Reactivity Index (PRI)
As we have seen above, the “pop” or what I am calling the “reactivity” of a pickleball paddle is (sort of) governed out by USA Pickleball based on their stiffness requirement. However, static stiffness alone does not determine the amount of reactivity of a pickleball paddle — its damping and dynamic response may play a more prominent role. How then, should a pickleball player select a paddle based on “power” (high reactivity) or “control” (low reactivity)?
To assist their customers, perhaps pickleball paddle manufacturers and governing bodies should consider a dynamic test, such as a form of the drop test performed herein, to gain a quantitative measure of how much energy a pickleball paddle contributes to the rebound of a ball on their paddles. The results of these tests can be used to create a Paddle Reactivity Index (PRI) rating, where low PRI paddles could be classified as “control” paddles and high PRI paddles can be classified as “power” paddles.
