In a previous article, “Paddle Dynamics”, we described the trampoline and diving board effects and how these paddle dynamic characteristics affect paddle power. We further postulated that if the paddle dynamics are properly tuned, both the trampoline and diving board modes will reach maximum amplitude simultaneously with the release of the ball, thereby increasing the amount of power or “pop” of the paddle. This will require that the stiffness that governs the trampoline and diving board modes be about the same. In this article we will take a more in-depth look at the paddle diving board effect and describe a testing methodology to determine the paddle throat stiffness, which defines the diving board mode.
Paddle Stiffness Components
A pickleball paddle has different stiffness components which contribute to spin, power, and control. These include the core stiffness, the face stiffness, and the throat stiffness, described below.
Core Stiffness – The core stiffness is simply the stiffness of the honeycomb core, which is measured by applying a force on one side of the paddle face and reacting the force through a support directly on the opposite face of the paddle (Figure 1). It is the test that USAPA uses to qualify paddles for stiffness. We believe that the core stiffness contributes to the ability of the paddle to apply spin to the ball, as we discussed in our article, “Paddle Spin Capability, Friction, & Stiffness”.
Face Stiffness – The face stiffness is the bending stiffness measured in the middle of the paddle face. Pickleball Science developed a three point bending test (see “Jansen vs Devidze Revisited”) where a force is applied to one side of the paddle face and reacted on the opposite face of the paddle through three equally-spaced spherical supports (Figure 2). The face stiffness (and three-point bending test) is a better indicator of the paddle power (and the trampoline effect) than the core stiffness test.
Throat Stiffness – The paddle throat is located at
the top of the handle where it transitions to the paddle face. The throat stiffness is simply the bending
stiffness with a force applied at the paddle throat. As described in our article, “Paddle Dynamics”, we
suspect that the throat stiffness governs the so-called diving board
effect. We discuss this in detail below.
Rationale Behind Throat Stiffness
The paddle throat has long been known to be the weakest part of the paddle, since most paddles fail by breakage across the throat. Logically, the paddle throat is suspected of having the highest bending stress, greatest deflection, and lowest stiffness. Why is this so?
The bending stiffness of any object such as a beam, is directly proportional to the beam width, and the cube of the beam height. As an example, if a pickleball paddle has a width 7.5” across the face and a width of 1.5” across the handle, it will have a stiffness at the throat that is a factor of 7.5/1.5 or 5 times less than the stiffness of the paddle face. Furthermore, the pickleball handle typically consists of the carbon fiber honeycomb sandwich structure that is about 16 mm thick (0.625”) with a glued-on handle made of wood or plastic that more than doubles the thickness. The stiffness of the handle will therefore be a factor of two to the third power (23) or eight times stiffer than the paddle face! It is therefore easy to see why the throat region is the weakest link of a paddle, having a bending stiffness that is 8 times lower than the handle and 5 times lower than the paddle face.
The paddle therefore acts like a compound catapult (or “trebuchet”) where the paddle face “catches” the ball and begins to stretch like a trampoline. During the stroke the paddle bends backward like a diving board about the paddle throat and the ball compresses and flattens. At release, the stored (potential) energy in the ball, paddle core, face, and throat convert back into kinetic energy, and the ball is catapulted forward with increased acceleration and velocity. We discussed the mechanics behind this energy transfer in our article, “Paddle Dynamics” and may re-visit this topic in a future article as it has some big implications regarding the stiffness of the paddle core, face, and throat, as well as the handle design and location of the sweet spot. For now, let’s see how the core, face, and throat stiffnesses measure up on a real paddle.
Throat Stiffness Test
Pickleball Science has developed a new methodology using the three-point bending test apparatus to measure the bending stiffness at the paddle throat. This test involves placing the geometric center of the three-point bending apparatus at the paddle throat, applying a force to the throat, and reacting the force through one point on the handle and two points on the paddle face (Figure 3).
We applied this methodology to calculate the throat stiffness of a ProKennex Black Ace paddle (Figure 4). The handle over-wrap was removed it to enable firm and direct contact of the spherical support with the handle. Since the surface of the handle is on a different plane than the surface of the face, the paddle has a slight tilt angle with respect to the force gauge. It is believed, however, that any error due to this slight tilt will be negligible (we will verify this in future tests). When we aligned the force gauge with the paddle throat and the centroid of the three spherical contact points, we found that the handle contact point is conveniently located near the paddle pivot point which we assume is about 2” above the butt of the handle. This will not happen with all paddles because handle lengths are different.
Results and Conclusions
Test results found that the throat stiffness of the ProKennex Black Ace is about 1005 lb/in. This stiffness is close to the measured face stiffness of 980 lb/in (see “Paddle Technical Comparisons”). This would indicate that the paddle diving board and trampoline vibration modes are almost coincident, which would maximize the velocity of the ball as it is released from the paddle as described in our article, “Paddle Dynamics”. Based on this analysis, the ProKennex Black Ace would be classified as a “power” paddle.
Further analyses suggest that the “ideal” tuning of a paddle will be to set the face and throat stiffnesses both in the range of about 900 lb/in to 1100 lb/in to maximize the power potential of the paddle. This will be discussed in detail in a future article. In the meantime, we will continue to measure the throat stiffness of several paddles and publish the results in the “Paddle Technical Comparisons” article.
