The ability to apply topspin to a pickleball is a fundamental and important tool that pickleball players should have in their arsenal. There are numerous instructional videos on the internet that describe the various techniques and exercises that a pickleball player may practice to put topspin on their serves and groundstrokes. Similarly, there are numerous articles and advertisements from paddle manufacturers that describe how their pickleball paddle designs and materials can put more spin on the ball.
Rather than reviewing these techniques and paddles, we will focus on the mechanics behind how topspin is applied to a pickleball, and examine various factors, such as paddle roughness, ball deformation, contact time, and paddle orientation, and how they affect the amount of topspin that can be placed on a pickleball.
The Benefits of Topspin
The application of topspin to a pickleball can result in several benefits:
You can hit the ball harder – As we discussed in a previous article, “Can Topspin Enable a Faster Serve?”, the ability to put topspin on a serve or groundstroke can enable you to hit the ball harder and faster without making it sail out of bounds. This is because topspin causes what is known as the “Magnus Effect”, that generates a downward force on the ball, forcing it towards the ground (Figure 1).
The ball bounces higher – The downward Magnus Force is also beneficial when the ball strikes the ground. As we discussed in our series of articles on Pickleball Kinematics, gravity is a constant vertical force that acts independently of the horizontal force that propels the pickleball towards your opponent. Furthermore, as we discussed in our article “Power vs Control Paddles”, we know that by regulation, a pickleball will rebound to a height of 30-34” if dropped from a height of 78” under the influence of the gravitational force only. When hit with topspin, the downward force from the Magnus Effect adds to the downward force of gravity and causes the ball to bounce higher.
The ball accelerates when it hits the ground – Topspin causes a forward rotation of the ball that can increase the velocity of the ball when it strikes the ground (Figure 2). This is why a topspin serve seems to “kick” when it hits the ground. The amount of kick depends on several factors, including the translational velocity of the ball, the spin rate of the ball and the friction coefficient between the ball and the ground.
The ball is more stable and difficult to return – Anyone who has played with a spinning top or gyroscope knows that a spinning object is more stable. That is, once it goes into motion it is difficult for external forces to change its path. This is because the spinning of the ball increases its angular momentum, requiring a greater amount of torque to change its path. This has several benefits. First, if your opponent wants to hit a topspin return, he will need to first overcome the topspin you put on the ball to reverse its spin direction. This is why a topspin ball feels “heavier” than a ball hit with no spin or with backspin. Advanced pickleball players will therefore recognize the topspin and add to the angular momentum of the ball by returning it with backspin. Second, if your opponent hits a “flat” return (with no spin), the ball will grip your opponent’s paddle and tend to climb, making for a higher return. Third, because of its increased angular momentum, other factors such as wind have a diminished effect on the trajectory of the ball.
How is Spin Generated?
Spin is generated by applying a tangential force that creates a tangential velocity on the ball. As shown in Figure 3, when a ball is struck with topspin, the paddle provides a force that is perpendicular (or normal) to the paddle face (Fn) and a force that is parallel (or tangential) to the paddle face (Ft). The normal force propels the ball back towards your opponent and the tangential force applies spin to the ball.
The spin rate of the ball is calculated by the formula,
where ω is the spin rate (in radians per second), vt is the tangential velocity, and r is the radius of the ball (about 1.50”).
According to videos on the internet, typical spin rates fall in the range of 1000 to 2000 revolutions per minute (RPM). We can now use Equation (1) to determine the range of the required tangential velocity:
Therefore, a pickleball player will need to generate between 9-18 mph (157–314 in/sec) of tangential velocity on a ball to obtain a spin rate of 1000-2000 RPM. Tangential velocity can be imparted to the ball by sweeping the paddle upward while striking the ball. Assuming that pickleball players can swing their paddles with a horizontal velocity of 40 mph, this means that in order to hit a ball with a 2000 RPM topspin, the paddle will need to be swung at an upward angle of 24° to the horizontal plane.
The Role of Friction
Friction, of course, plays a key role in the ability of the paddle to impart a tangential velocity (spin) to the ball. There are several different types of friction, but we are most concerned with kinetic friction, which affects two objects, the ball and the paddle, that slide against one another (Figure 4).
Topspin is imparted to the ball by sweeping the paddle upward which applies a tangential force (Ft) to the ball that acts parallel to the paddle face. The amount of tangential force that can be developed is limited by the amount of friction between the paddle and the ball. From experience we know that it is more difficult to apply topspin to a new pickleball with a smooth surface vs a used pickleball with a scuffed surface.
The tangential force (Ft) is related to the normal force Fn, through the coefficient of kinetic friction (µk) as follows:
Ft = µk Fn Equation (2)
According to the USA Pickleball Association (USAPA) Equipment Standards Manual, the maximum allowable coefficient of kinetic friction between a ball and paddle face is 0.1875. If the force required to overcome the momentum of the ball in the vertical direction exceeds the tangential force (Ft), slippage between the ball and the paddle will occur, thereby limiting the amount of spin that can be applied to the ball. We can estimate the average tangential force (Ft) using Newton’s Second Law of Motion:
Where:
Ft is the average tangential force
mb is the mass of the ball (0.9 oz)
vf is the final velocity of the ball
vi is the initial velocity of the ball
Δt is the contact time
By combining Equations (2) and (3), we can develop an equation that relates the average normal force (Fn) to the contact time (Δt):
For a serve, the initial velocity of the ball (vi) is zero, and the final velocity (vf) is equal to the tangential velocity (vt) of the ball. For a 1000-2000 RPM rotation, we used Equation (1) above to show that vt must be 157–314 in/sec. Figure 5 shows the result of solving Equation (4) for 1000 RPM and 2000 RPM serves for a paddle with the maximum allowable coefficient of kinetic friction of 0.1875.
This plot reveals certain aspects of topspin that will benefit an average pickleball player. First and foremost is the fact that the amount of topspin that a player can impart to the ball is dependent on both the contact force and the contact time. That is, a greater amount of topspin can be generated by hitting the ball harder. While it is easy to see that we can increase the contact force by hitting the ball harder, how can we increase the contact time?
Contact Time
For purposes of illustration, let’s assume that we have a paddle with the maximum allowable coefficient of friction (µk) of 0.1875. Let’s also assume that the maximum average force that we can put on the ball is 60 lbs. According to Figure 5, we can obtain a 2000 RPM topspin if we can maintain contact with the ball over about 4 milliseconds. This might seem like a very short duration, but scientific studies in baseball have found that a ball is in contact with a bat for less than 1 millisecond. The very short duration is because baseballs and bats move much faster and are much harder than pickleballs and paddles.
What happens in the 4 milliseconds when the paddle contacts the ball? Clearly, no human can react that quickly to a ball striking the paddle, since the fastest recorded human reaction time is on the order of 100 milliseconds, or 25 times slower than the paddle-ball contact time! This would also rule out the idea that topspin is generated by rolling the paddle while the ball is in contact with it, because 4 milliseconds is simply not enough time for our muscles to react.
Figure 6a shows a side view as the paddle prior to contact with the ball. The ball has an initial velocity vb, and although the paddle face is vertical, it is traveling with a horizontal velocity of 60 ft/sec and a vertical velocity of 26 ft/sec. This corresponds to a sweep angle of about 24 degrees to the horizontal plane.
According to studies of impact interactions between baseballs and bats, the force exerted on the ball is not constant and follows the form of a sine-squared function as shown in Figure 7.
During initial contact from 0-2 milliseconds, the ball squashes and the paddle bends until the force is at its maximum (peak) value at 2 milliseconds (Figure 6b). In the 2-4 millisecond time frame, the force decreases, and the ball and paddle start to rebound to their original shapes. After 4 milliseconds the ball and paddle have completely rebounded and the ball separates from the paddle (Figure 6c). This illustrates why we cannot normally control the contact time between the paddle and ball, as the contact duration is dependent on how quickly the ball and paddle can spring back to their original shapes.
Key Observations
In this article, we took an in-depth look at how topspin is generated and developed a mathematical relationship for the paddle / ball contact force and contact time. We also determined that topspin is generated by sweeping the paddle upwards during a serve or groundstroke. Because the contact time is so short, the amount of topspin is not affected by rotating the paddle about the roll axis during the stroke. Rather, it is generated based on the tangential velocity of the paddle when the ball is struck. In our example, we found that in order to hit a stroke at 40 mph with a 2000 RPM topspin, the paddle will need to be swept upward at an angle of about 24 degrees to the horizontal plane.
The amount of topspin that can be generated on a pickleball is limited by the coefficient of kinetic friction between the paddle and the ball. Using the same stroke, a paddle with a lower friction coefficient will apply less topspin to a ball verses a paddle with a higher friction coefficient. Similarly, it will be easier to apply topspin to an older scuffed pickleball vs a newer smooth pickleball. Pickleball players need to adjust their strokes according to the friction characteristics between their paddles and the pickleball.
Pickleball players will apply the same average force (Fn) to a ball regardless of whether they use a soft or stiff paddle. On one hand, a stiffer paddle will increase the peak force, but it will reduce the contact time. On the other hand, a softer paddle face will increase the contact time, but it will reduce the peak force. In either case, the area under the Force Profile curve in Figure 7 will be the same! A delicate balance must be struck between obtaining a longer contact time vs obtaining a higher peak force, based on a player’s strength and swing speed. This would suggest that there is no “one-size-fits-all” regarding the selection of so-called “power” and “control” paddles (see our article, “Power vs. Control Paddles”). Pickleball players should therefore select their paddles based on their abilities and a variety of other factors, such as weight, balance, and comfort.
