Pickleball paddle manufacturers often advertise that their paddles have a larger sweet spot than others based on a variety of factors, including the paddle face size, shape, thickness, weight, and materials. They do not, however, provide quantitative details about the sweet spot, such as its shape, dimensions, and location. How then, can consumers determine the size of a paddle’s sweet spot? In a previous article (“Where is the Sweet Spot?“), we determined that the sweet spot or center of percussion (cp) of a paddle is a single point located on the paddle centerline where striking a ball will result in no net force transmitted back to your hand. If the sweet spot is a single point, how can one paddle have a larger sweet spot than another one?
The answer lies in the fact that the paddle face behaves like a trampoline, as we discussed in a previous article (“Power vs Control Paddles“). The size of the trampoline region defines what we will define as the “Effective Sweet Spot” that incorporates the paddle dynamic center (cd), the center of gravity (cg), the center of percussion (cp), and face center of area (ca). The size and location of the Effective Sweet Spot can only be determined through an examination of the vibration characteristics of a paddle face.
In this article, we will perform a first-of-its-kind (as far as I know) vibration test of a pickleball paddle to provide us with the final bit of information needed to determine the location, shape, and size of the “Effective Sweet Spot”. We will then discuss how you can use this information to select a paddle appropriate to your abilities and style of play.
Vibration Testing Methodology
The vibration test was performed on the same Vulcan V530 Power paddle that was previously used to determine the location of the sweet spot and to determine ball rebound energy, together with a dynamic signal analyzer (DSA), impulse hammer, and accelerometer (Figure 1). The dynamic signal analyzer is a sophisticated electronic instrument that can measure time-based signals and extract their frequency content. The frequency-based signals comprise what are known as the impulse response functions that describe the vibration characteristics of the paddle.
The vibration test procedure involved suspending the paddle by its handle with an elastic cord, which allowed the paddle to vibrate freely without over-constraint (Figure 1). The impulse hammer was used to strike the paddle at a fixed location corresponding to its center of percussion (cp), denoted by the yellow dot on the paddle face. By striking the paddle, the impulse hammer excites several vibration modes over a wide frequency range that can be measured. As shown in the paddle geometric model (Figure 2) the paddle was subdivided into 29 regions spaced about 2” apart where the vibration response was measured. These vibration measurements were obtained by adhering the accelerometer to the paddle at one location using wax, exciting the vibration modes with the hammer, then moving the accelerometer to the next location.
Paddle Vibration
The collection of impulse response functions at various points on the paddle allow us to examine how the paddle vibrates at various frequencies. The impulse response functions for the two measurement points near the center of the paddle are shown in Figure 3. Here, we see that there are two prominent peaks, one at about 1030 Hz and the other at about 1230 Hz.
By knowing the relative vibration amplitudes and phase relationships among the different response points, we can animate the geometric model of the paddle to see how it vibrates. By clicking on the picture in Figure 4, you can see the animated deflection shape of the paddle at the first vibration peak of 1030 Hz. Positive deflections are shown in red, whereas negative deflections are shown in blue. This shows the paddle deforming like a trampoline, with the bottom edge of the paddle face (near the handle) remaining stationary, with some slight folding of the top edge. This suggests that the bottom edge of the paddle face is stiffer than the upper edge.
Figure 4. Vibration Mode at 1030 Hz
By clicking on the picture in Figure 5 you can see the animated deflection shape of the paddle at the second vibration peak of 1230 Hz. Here we see a more dramatic trampoline deflection shape where the outer edges of the paddle move completely out of phase with the paddle center.
Figure 5. Vibration Mode at 1230 Hz
The combination of the two vibration modes at 1030 Hz and 1230 Hz comprise the trampoline effect for the Vulcan V530 paddle. When the ball strikes the center of the paddle, these vibration modes are excited, giving the paddle its characteristic “pop”. The trampoline effect then adds energy back to the ball like a slingshot and propels it back towards your opponent.
Introducing the "Effective Sweet Spot"
In a previous article, “Where is the Sweet Spot?” we performed a balance test of the Vulcan V530 Power paddle and determined that its center of gravity (cg) was located at a distance of 9.25” from the bottom of the handle. We also calculated the paddle mass moment of inertia (MOI) and used it to determine that the center of percussion (cp) was located at a distance of 11.00” from the bottom of the handle. The cp location was also found to coincide directly with the paddle face geometric center (ca).
In the vibration analysis we showed that the center two points, located 10” and 12” above the bottom of the handle exhibit trampoline-like behavior at 1030 Hz and 1230 Hz. The dynamic center of the paddle must therefore lie between these two points at 11″ above the bottom of the handle. This point also happens to coincide with the center of percussion (cp) and the geometric center of area (ca)! Once again, kudos to the paddle designers at Vulcan, as the co-location of the cd and cp is highly desirable.
The trampoline vibration mode likely accounts for the high frequency “ping” of the paddle when it is struck near the center of percussion. We can approximate the trampoline region by defining an oval centered on the cd with a length along the major (longitudinal) axis of about 4-5” and a width along the minor (lateral) axis of 2-3” as shown in Figure 6. The collection of points defining the dynamic center (cd), center of percussion (cp), center of gravity (cg), and area center (ca) within the trampoline region define an “Effective Sweet Spot”. It is desirable to contact a ball at the Effective Sweet Spot because it will:
- Provide the greatest amount of energy returned to the ball (i.e., greatest reactivity) through the trampoline effect, causing the ball to fly off the paddle at a higher velocity.
- Result in the least amount of force and vibration that is reacted back to your hand
- Reduce the tendency of your paddle to rotate, thereby increasing the accuracy of your shots
How Do You Use This Information?
Most pickleball players do not have access to dynamic signal analyzers to measure paddle dynamics or the software (or test equipment) needed to calculate the center of percussion of their paddles. Furthermore, paddle manufacturers do not readily provide this information to consumers. So how do you use this information to pick the right paddle for your abilities and style of play or modify your current paddle? Following are some general lessons learned from this analysis.
It is generally desirable for your paddle to exhibit a trampoline effect, as the dynamics of the paddle face will allow a greater amount of energy to be returned to the ball, resulting in greater velocity. Softer paddle faces will exhibit greater reactivity (or bounce) and have a larger trampoline region than paddles with stiffer faces (see the article, “Power vs Control Paddles”). In fact, as you increase the paddle face stiffness, the frequency of the trampoline vibration mode increases and the size of the trampoline region decreases until it eventually disappears for very stiff paddle faces. The shape of the sweet spot will generally follow the shape of the paddle face, with elongated paddle faces having longer and thinner effective sweet spots than the more standard square paddle faces.
Why wouldn’t you just select a paddle with the softest face? Those of you who have bounced on a trampoline know that by jumping on the center you can achieve the greatest height in a purely vertical direction. However, bouncing off center causes a force imbalance that will impart a lateral (horizontal) component to your bounce. The same thing happens for pickleball paddles. The so-called “power” paddles with softer faces must be hit on center to gain the maximum benefit of the trampoline effect. Hitting the ball hard off-center may cause the ball to bounce off the paddle in a direction that is not perpendicular to the paddle face. Paddles with softer faces are therefore more difficult to control. Because paddles with stiffer faces will undergo less deflection, hitting the ball hard off-center may result in fewer mis-hits. For this reason, paddles with stiffer faces tend to be more “forgiving”. Both the soft and stiff paddles should behave similarly for soft shots, such as dinks.
How can you tell the difference between a paddle with a soft face vs a paddle with a stiff face? It is possible to determine the static stiffness of a paddle face by using a simple push-pull gauge. According to USA Pickleball, the paddle face must deflect no more than 0.005” under a weight of 6.6 lbs and no more than 0.010” under a weight of 11.0 lbs. This means that the paddle face stiffness must lie between 1100-1320 lbs/in, which is information that paddle manufacturers should supply to their customers. Until that happens, though, the most effective way to determine the stiffness of a paddle face is by listening to the tone the paddle produces when striking the ball hard. Low stiffness paddle faces will provide a low frequency “thud”, whereas high stiffness paddle faces will provide a higher frequency “ping”.
Is it possible for a paddle to have a dynamic center (cd) different from the center of percussion (cp) or center of gravity (cg)? Yes. The cp and cg are dependent only on the weight distribution of the paddle and are somewhat independent of the ca and cd, which are dependent on paddle geometry and paddle vibration characteristics, respectively. While pickleball paddle manufacturers may try to put the cp and cg at the dynamic center of their paddles, there are no guarantees. Furthermore, pickleball players may inadvertently shift the cp and cg locations away from the cd by adding heavy over-grips to their handles or weighted tapes to their paddle faces. In a future article we will discuss how to “tune” your paddle by use of weighted tapes.
Is this the only information needed to pick out the right paddle for your style of play and abilities? Unfortunately, the answer is ‘no’. Another piece of information concerns the ability of the paddle face to “grip” the ball to provide spin. This is determined by the roughness of the surface of the paddle and the stiffness of the paddle face. Softer paddle faces can provide a longer “dwell time”, which will allow the ball to remain in contact with the paddle over a longer stroke distance, enabling the pickleball player to impart a greater amount of spin to the ball. Harder paddle faces will allow the ball to quickly glance off the paddle face over a shorter stroke distance, reducing the amount of spin a player can impart to the ball. We will look at how paddle interactions affect spin in a future article.
The choice of whether you choose a softer or stiffer paddle face depends on user preference, and the amount of power, spin, and control that is desired. In general, novice players who have not yet mastered the technique of hitting the ball at the paddle center or have not yet learned how to put spin on the ball might want a stiffer standard size/shape paddle to start out with. When their skills improve, they might graduate to a softer paddle to gain velocity on their shots, to put spin on the ball, or to better place “finesse” shots. In our article, “Pickleball Paddle Materials“, we will examine the construction of a pickleball paddle and review the different types of composite materials used in pickleball paddles to better understand the differences between paddles and how these differences affect performance.
