In a previous article, “How is Topspin Generated?”, we showed that topspin is created by sweeping your arm in an upward arc while striking the ball. During contact, the ball flattens and the paddle face bends, increasing the contact time and contact area between the paddle and ball (Figure 1). The upward motion of your arm imparts a forward rotation to the ball, causing it to roll off your paddle as you finish your stroke. The ball continues to roll forward as it travels through the air, where the topspin provides a downward force that keeps the ball inbounds (see “Can Topspin Enable a Faster Serve?”)
Paddle manufacturers tend to place a premium on creating paddles with high-friction or rough surfaces, identifiable under several different names, such as “textured carbon”, “raw carbon”, “carbon friction”, “high grit”, etc. While conventional wisdom suggests that paddle faces with higher friction will create more spin than smoother paddles, experience suggests otherwise. As we alluded to in our article, “Predicting a Paddle’s Spin Capability”, paddles with seemingly identical face sheets and surface roughness can have different spin capabilities. How can that be? What are the other factors that affect a paddle’s spin capability? To answer this question, we must first examine what happens to the paddle and the ball at the moment of contact.
Forces at Contact
We can determine how much force is imparted to the ball by examining the face of a raw carbon fiber pickleball paddle after striking a ball. Raw carbon fiber pickleball paddles will tend to pick up the residue from the ball during particularly hard hits. This residue is caused by contact between the ball and the court surface, which abrades the ball, causing it to be covered with a fine plastic dust during play. This dust collects within the “pores” of a textured carbon fiber paddle leaving an imprint of the ball on the paddle face as shown in Figure 2. These imprints are typically circular, indicating that the ball does not slide against the paddle face during contact (which we postulated in our article, “Predicting a Paddle’s Spin Capability”). The diameters of the circular imprints in Figure 2 are roughly 1.50”.
In a previous post, “Pickleball Reviews”, we tested several balls under compression using a force gauge. Using these tests, we determined the ball “stiffness”, however, the measured stiffness is actually the two-sided stiffness of the ball. As shown in Figure 3 the force gauge applies an equal and opposite force to the ball on its top and bottom surfaces, causing an equal displacement on either side of the ball. The measured stiffness is therefore the “effective stiffness”.
In reality, we strike the ball from one side (see Figure 1), causing compression on one side of the ball. We can calculate the stiffness on one side of the ball by assuming that the top and bottom sides of the ball act like two (equal) springs in series (Figure 3c). Therefore,
This shows that the one-sided ball stiffness (K) is equal to two times the measured ball stiffness (Keff). From our post, “Pickleball Reviews”, the typical effective ball stiffness (Keff) was about 100 lb/in, making the one-sided ball stiffness (K) about 200 lb/in.
From Figure 2, knowing that the ball marks have a diameter of about 1.50”, it is possible to calculate the force imparted to the ball based on purely geometric considerations. Analysis of these marks (Figure 4) indicates that the change in radius of the ball (Δr) is about 0.20”. Knowing that the average ball one-sided stiffness is about 200 lbs/in, the force imparted to the ball must be about 40 lbs.
Contact Time
In several previous articles (see for example, “How is Topspin Generated?”) we made an “educated guess” that the paddle is in contact with the ball for 4 milliseconds. We can validate this assumption now that we know the force acting on the ball by using the impulse-momentum equation:
m * Δv = F * Δt
where:
m is the mass of the ball (0.86 oz or 0.000139 sl)
Δv is the change in velocity of the ball
F is the force applied to the ball (40 lbs)
Δt is the contact time
In a previous post (see “Can Topspin Enable a Faster Serve?”) we determined that the maximum velocity of a serve with topspin at the moment of impact is 65 mph (1144 in/sec) to achieve the trajectory of the fastest possible serve. Solving for Δt, we arrive at a contact time of 4 milliseconds, which validates our assumptions in several previous articles!
Spin Capability
If this is an article on spin capability, why have we not discussed the “f-word” (friction, that is)? How exactly does any of this affect the spin capability of a paddle?
The USAPA provides guidelines on the paddle maximum coefficient of kinetic friction and the maximum allowable surface roughness in an attempt to limit the amount of spin the paddle can impart to the ball. Excessive spin can provide an unfair advantage to a player, allowing the the player to hit the ball harder and faster while keeping the ball inbounds. According to the USAPA Equipment Standards Manual, the maximum coefficient of kinetic friction of a paddle must be less than or equal to 0.1875 and have a surface roughness less than 40 microns (0.0016”). Paddles that exceed these guidelines may not be approved.
If both the paddle face and ball were rigid, contact would occur at a single point (Figure 5a). In this case, we would have to rely only on friction between the ball and paddle to provide topspin to the ball. However, since they are both flexible, we know that the ball flattens, and the paddle face bends, increasing the contact surface area between the paddle and ball (Figure 5b).
Knowing that the average conventional (i.e., non-EVA) paddle face has a bending stiffness of about 900 lbs/in (see “Paddle Technical Comparisons”), we find that the ball will make an indentation that is roughly 0.04” deep on the paddle face during contact. While this may seem like a small number, the USAPA allowable surface roughness of a paddle face is only 0.0016”. This means that the indentation that a ball makes on the paddle face is almost 27 times the allowable surface roughness! This indentation allows the paddle to “grip” or “cradle” the ball during contact, allowing a player to impart a greater amount of topspin to the ball.
Conclusions
While static (not kinetic) friction has a role in determining the spin capability of a paddle, it may not be as important as paddle manufacturers (and the USAPA) have led you to believe. This has been validated in another study, “The Physics of Pickleball Spin“, where they state that “… all paddles will produce about the same spin…” However, one defect of this study is that it considers only the paddle face coefficient of friction — it does not consider how the deformation of the ball or paddle face contribute to spin capability.
The application of spin on soft shots that do not cause a considerable amount of ball or paddle deformation is certainly dependent on face friction. However, hard shots have the added benefit that the deformation of the ball and paddle face increase the paddle’s “grip” on the ball and thus the paddle’s spin capability. This explains why two paddles with identical face sheets can have different spin capability. We must therefore consider paddle core stiffness and face stiffness to gain a full picture of a paddles spin capability.
If spin and power are what you are looking for, refer to our article, “Paddle Technical Comparisons”, and try using a paddle with a bending stiffness less than 900 lbs/in. Such a paddle will provide a greater trampoline effect (i.e., “pop”) and greater spin capability.
