Your ability to impart spin to the pickleball is an important skill that can add new dimensions to your game. Spin affects the ball’s aerodynamics, causing it to drop, rise, float, or curve as it sails through the air. This might allow you to drive the ball harder, drop it softly into the kitchen, lob it over your opponent’s head, or move your opponent out of position. When the ball hits the ground, spin may also cause it to bounce higher, lower, or sideways, making the ball more difficult to return. Along with power and control, spin capability has become an important consideration in selecting your next paddle.
Fundamental Concepts
In this article, we will use certain terms, such as texture, surface roughness, and friction, which have been used interchangeably in the past, but for our purposes these terms have distinct meanings.
- Texture is a qualitative measure of the surface flatness determined by the tactile feel of the surface when you drag your fingers across it. When a surface feels smooth, it means that our fingers cannot detect any bumps, dips, or imperfections (known as asperities). The relative height and spacing of these asperities are therefore important when judging whether a surface is smooth or rough.
- Surface roughness, on the other hand, is a numerical or quantitative measure of the relative heights of asperities across a surface over a certain distance. It is usually measured with an instrument such as a profilometer. A rough surface can feel smooth if the peaks and valleys on the surface are tightly spaced.
- Friction pertains to the amount of force developed between two surfaces to resist relative motion without sliding (i.e., static friction) or while sliding (kinetic friction). Friction therefore requires an examination of the two surfaces and how they interact. It is therefore impossible to know if the coefficient of friction of one object will be high without knowing the characteristics of the surface against which it will slide.
Conventional wisdom suggests that paddles with rougher faces will produce more spin on a pickleball. In fact, this belief is so widely held that paddle companies have gone through extraordinary lengths to develop paddles with textured face sheets, gritty coatings, and custom weaves to increase friction. Based on the belief that paddles with high surface roughness and high kinetic COF create more spin, the USAP tests for and limits the allowable paddle surface roughness and (kinetic) coefficient of friction (COF) as described in their Equipment Standards Manual. Furthermore, numerous pickleball paddle reviewers, videographers, and bloggers discuss at length how certain paddles have greater spin capability than others, and how certain paddles lose spin capability over time.
Fundamental Questions
With all of this attention on paddle texture, roughness, friction and spin, we need to step back and answer some fundamental questions:
- Do paddles with rougher textures have higher surface roughness?
- Do paddles with rougher textures have higher COF’s?
- Do paddles with higher COF’s generate more spin?
In this article, we will answer these questions by measuring the coefficient of friction of several different types of paddles and performing a rigorous analysis based on sound scientific principles.
Do Paddles with Rougher Textures Have Higher Surface Roughness?
Digital Metrology Solutions, a developer and provider of innovative measurement systems, performed an analysis of pickleball paddle friction, where they compared two paddles, one with a smoother-textured fiberglass face against another with a rougher-textured carbon face. In the first part of their analysis, they looked at the paddle surfaces with a 3D optical profiler, which is commonly used to measure wafer flatness in the semiconductor industry. They later measured the static coefficient of friction of the two paddles using a “sled” apparatus. Their results are shown in Figure 1 below.
These results show that the smoother-textured fiberglass paddle had a higher average surface roughness (Sa = 3.9 microns) than the rougher-textured carbon fiber paddle (Sa = 2.9 microns). However, the rougher-textured carbon fiber paddle was found to have a higher static COF than the smoother-textured fiberglass paddle. These results might also suggest that the current surface roughness test performed by USAP to qualify paddles may not be a good indicator of paddle friction and spin capability.
Do Paddles with Rougher Textures Have Higher COF’s?
Pickleball Science duplicated the Digital Metrology COF test by creating an improved version of the pickleball “sled”, and rather than tilting the paddles by their handles, the paddles were placed on a tilt table designed to improve repeatability (Figure 2). We also tested paddles that represented a wide range of face textures, including raw carbon fiber, textured carbon, textured fiberglass, and titanium-integrated carbon fiber. Five sliding tests were performed on each side of each paddle using new and worn Franklin X-40 balls.
Table 1 shows our test results. The paddles are arranged in order of the average COF obtained from new and worn balls. We also ranked the paddles in terms of their perceived texture, where the smoothest paddle (the Brick House Heritage 74T) was ranked #1 and the roughest paddle (the TMPR LX) was ranked #8.
Table 1. Paddle Static COFs
There are a few surprises in the table, as follows.
- Conventional wisdom would suggest that worn balls will have a higher COF than new balls because their surfaces would be rougher. However, this was not true for the TMPR LX, Joola Hyperion, and Mozi Gold Rush paddles, as the worn balls produced lower COF’s.
- The smoothest paddle, the Brick House Heritage 74T, did not have the lowest COF. In fact, considering worn balls, the COF of the Brick House paddle is on the same order as the Joola Hyperion and TMPR Terra LX.
- The Ronbus R3, although having the second smoothest face (behind the Brick House paddle), has the second highest COF.
- The paddle with the roughest texture (the TMPR Terra LX) had the third lowest COF.
These results indicate that it is not possible to generalize with certainty whether paddles with rougher textures will have higher COF’s. We do not have access to a profilometer, but it would be interesting to measure the surface roughness of these paddles and correlate these measurements with texture and COF. It would also be interesting to compare the surface roughness measurements of new and worn balls to determine how they match up with the paddle COF’s.
Do Paddles with Higher COF’s Generate More Spin?
Crawford Lindsey, a well-respected engineer and author, studied the relationship between pickleball spin and paddle face roughness in his article, “Pickleball Spin — The Role of Surface Roughness in Spin Generation”. In his study, he first measured the coefficient of static friction of several different paddles and surfaces. The paddles were then placed on a tilt table, and balls were fired at the paddles at different speeds, contact angles, and incident spin rates. The motions of the balls were recorded on a video camera and further processed to determine the incoming and outgoing spin rates.
Based on the results of his tests, Lindsey drew some general conclusions about the relationship between paddle friction and spin capability. He found that at contact angles steeper than 45 degrees (which are the majority of pickleball hits), the ball will not slide relative to the paddle face, regardless of the paddle face COF. Lindsey therefore concludes that “all paddles will produce about the same spin”. He further states that “when a player feels one racket produces more spin than another, it is most likely due to the speed, spin, and angle of the ball sent by the opponent, or the player can swing faster or steeper with a particular racket or against a particular style of player. It is not because of the racket surface roughness.” These findings are somewhat controversial and warrant further investigation.
Analytical Approach to Friction Problem
Pickleball Science took a simpler analytical approach to this problem that involves principles of momentum exchange. In our article, “Can Topspin Enable a Faster Serve?” we determined that by adding a modest amount of topspin to the ball (1200 RPM), it is possible to increase the speed of the fastest possible serve at impact from about 54 MPH to 65 MPH. Aerodynamic drag then reduces the average velocity of the ball to about 47 MPH. We can use this information together with our COF tests to determine the minimum friction coefficient needed to generate spin at 1200 RPM for the fastest possible serve.
The relationships among the forces acting on the ball at impact are shown in Figure 3.
The force perpendicular or normal to the paddle face (Fn) propels the ball in a forward direction. If the paddle is swept upward, it will grip the ball and impart a tangential force (Ft) that puts a torque on the ball causing it to spin with an angular velocity (ω). The key to determining the minimum coefficient of friction (µs) between the ball and the paddle is to determine the magnitudes of the normal (Fn) and tangential (Ft) forces.
We can first calculate the normal force (Fn) by using the impulse-momentum equation:
Fn ∆t = m ∆v
Where the contact time (∆t) is on the order of 4 milliseconds (0.004 sec), the mass of the ball is 0.9 oz (0.0255 kg), and the change in velocity of the ball (∆v) at impact is 65 MPH (29.06 m/sec). This yields a normal force (Fn) of 41.7 lbs (185.3 N).
We can use the impulse-momentum equation in rotational coordinates to determine the angular velocity of the ball:
T = I α
Where T is the torque needed to generate spin, I is the moment of inertia of the ball, and α is the angular acceleration of the ball. The torque (T) is equal to the product of the tangential force (Ft) acting on the ball at the radial distance (r). Therefore,
Ft r = I α
We also know that the angular acceleration (α) is equal to the change in angular velocity of the ball (∆ω) divided by the contact time (∆t), and the moment of inertia of the ball can be modeled by a hollow sphere where I = (2/3) mr2. Substituting and rearranging, we have:
Ft ∆t = (2/3) m r ∆ω
We can calculate the tangential force (Ft) Knowing that the change in angular velocity of the ball (∆ω) is 1200 RPM (125.7 rad/sec), the mass of the ball (m) is 0.9 oz (0.0255 kg), the radius of the ball (r) is about 1.5 in( (0.038 m), and the contact time (∆t) is 4 milliseconds (0.004 sec). Substituting these known quantities, the tangential force (Ft) acting on the ball is about 4.6 lbs (20.3 N).
Knowing both the tangential and normal forces acting on the ball at impact, it is possible to calculate the coefficient of static friction (µs):
µs = Ft / Fn = 4.6 / 41.7 = 0.110
This means that paddles with a coefficient of static friction (µs) greater than 0.110 will grip the ball and will be capable of generating spin at 1200 RPM during a serve. An examination of our COF tests of several paddles (Table 1) finds that all of the paddles have a static COF greater than 0.110 and will therefore generate about the same amount of spin during a serve.
We would expect the results to be different when you return a ball, since the normal force applied by your paddle must be greater to overcome the forward momentum of the ball and apply backward momentum to propel the ball back over the net. Additionally, your paddle must apply greater torque to the ball because it hits your paddle with an initial angular velocity developed by your opponent’s paddle and interactions with the court surface. This will be a topic of a future article.
Findings and Conclusions
Our study of friction and spin has resulted in several eye-opening findings and conclusions:
- First, the texture or tactile “feel” of a paddle surface does not correlate with its measured surface roughness or coefficient of static friction (COF). You therefore cannot judge a paddle by the feel of its face.
- Second, the measured paddle surface roughness does not correlate with the paddle COF. The USAP test of paddle surface roughness using a profilometer is therefore not a good indicator of paddle spin capability and should be discontinued.
- Third, and most important, paddles with a static COF greater than 0.110 (which we believe are virtually all paddles) will generate the same amount of spin during a serve. This result confirms the Crawford Lindsey conclusion.
- Fourth, the USAP use of the kinetic COF to qualify paddles is not a good indicator because the static COF between the paddle and ball is sufficiently high that the ball will not slip relative to the paddle.
Are the paddle reviewers, manufacturers, and the USAP wrong in their assessments of paddle spin capability and face friction? Perhaps. As we alluded to in a previous article, “Paddle Spin Capability, Friction, and Stiffness”, we believe that the paddle/ball contact time is the key element in determining the spin capability of a paddle. Paddles with softer faces and softer cores might have a greater contact time and may therefore generate more spin (and power) than harder paddles. This might explain why delaminated paddles or paddles with foam cores hit with more spin and power than their stiffer counterparts. If face friction does not determine paddle spin capability, how might we explain why paddle reviewers and pickleball players feel that paddles lose spin capability over time? Rather than speculating, we will examine this topic in depth in a future article.
