The topic of pickleball topspin seems to be a little contentious. On one hand, there are bloggers and players who claim that putting topspin on the ball has little effect on speed or direction. On the other hand, there are several videos, blogs, and professionals teaching topspin, and numerous racquet companies touting the spin capabilities of their paddles. Who should you believe? Let’s let the science help us decide. In this article, we will develop the mathematics behind the aerodynamics of pickleball spin and use these equations to determine if topspin will enable you to increase the speed of your serves.
Spin and Sports Balls
A quick search on the Internet will find several videos showing how the application of spin will cause the curving of baseballs, soccer balls, ping pong balls, and tennis balls. The phenomenon of curving the trajectory of a ball using spin is therefore well known. Researchers, scientists, and engineers have studied the effects of spin on balls used in sports for several years. In fact, if you look for technical or scholarly articles on the subject, you will find several good analytical papers and laboratory tests on the effects of spin on baseballs, golf balls, tennis balls, soccer balls, whiffle balls, ping pong balls, etc. These papers show that spin influences the trajectories of small lightweight smooth objects, such as ping pong balls, to objects similar to pickleballs, such as whiffle balls, to large heavier objects with rough surfaces, such as soccer balls and baseballs.
From this, one may surmise that spin does influence the trajectory of a pickleball, however, there are very few (if any) technical articles on this subject. So in a sense, we are breaking some new ground here. How much does spin really affect a pickleball? Let’s see if the science can provide us with some insight.
The History Behind the Science
The initial observation that spinning objects tend to have curved paths is attributed to the German physicist Heinrich Gustav Magnus when he studied the deflection of projectiles from firearms in the mid-1800’s. His discovery, now known as the “Magnus Effect”, found that differences in air pressure on opposite sides of spinning objects caused these objects to deflect in a direction perpendicular to their paths or trajectories.
In the early 1900’s, Martin Kutta and Nikolai Joukowski studied the effects of airflow on lift of two-dimensional bodies, and found that a cylinder, spinning about its longitudinal or cylindrical axis, can affect the airflow across the cylinder in the same manner as an airfoil (Figure 1). Spinning the cylinder with forward spin (or topspin), causes the airflow to be directed upward, causing a net downward force (negative lift) on the cylinder (Figure 1a). Conversely, spinning the cylinder with backward spin, (or backspin), causes the airflow to be deflected downward, causing a net upward force (positive lift) on the cylinder (Figure 1b). The scientific reason for this behavior has to do with where along the boundary layer (circumference) of the cylinder that the airflow transitions from being laminar to turbulent.
This illustrates how the use of spin can transform an object, such as a cylinder with no aerodynamic features, into an airfoil that can be directed upwards or downwards according to the direction of spin. Moreover, the tilt or angle of attack of the pseudo-airfoil can be controlled by controlling the amount or speed of topspin or backspin on the cylinder.
More recently, researchers at the NASA Glenn Research Center (GRC) adapted the Kutta-Joukowski theorem to spherical objects in order to study the Aerodynamics of Baseball. Their analysis showed that it is possible to predict the trajectory of a curveball using the modified Kutta-Joukowski theorem. In the analysis below, I adapt the NASA GRC equations to determine if topspin can enable you to increase the speed of your serves.
The Mathematical Model of Spin
The fundamental equation to calculate the aerodynamic lift force on a spinning ball is:
Where: FLift is the lift force
CL is the lift coefficient
r is the radius of the ball
s is the rotational speed of the ball (rev/sec)
ρ is the density of air
V is the translational velocity of the ball
From this we can observe that the magnitude of the lift force (FLift) is dependent on the rotational speed (s) of the ball (which we knew) and it is dependent on how fast the ball is traveling (V), which is less obvious. This means that balls that are not spinning fast enough or are traveling at low speed do not benefit from aerodynamic lift as their faster spinning or higher speed counterparts. This will be an important factor when we analyze the effects of spin on “finesse shots”, such as dropshots and dinks in future articles. For now, let’s concentrate on serves and drives from the baseline that can be propelled at higher velocities.
The lift coefficient of lift (CL) is a “catch all” term (in scientific vernacular we call this a “fudge factor”) that accounts for several complex dependencies associated with lift, such as the object’s shape, surface condition, air viscosity and compressibility, velocity, air flow patterns, etc. While there are some closed-form equations to calculate CL, it is usually determined experimentally using a wind tunnel.
According to NASA GRC, the lift coefficient for a big-league curve ball is about 0.15; however, professional baseball pitchers will throw curveballs at speeds of 65 to 80 mph, which is much faster than a pickleball. Furthermore, the strings on a baseball are likely more effective at interacting with the airflow than the holes in a pickleball. For these reasons, I assumed that the lift coefficient for a pickleball would be one-half that of the baseball (CL = 0.075). This should be verified by future researchers who have access to a wind tunnel and the instrumentation to measure the lift coefficient. However, as we will see in the analysis below, a lift coefficient of 0.075 is probably not a bad assumption.
Spin-Enhanced Equations of Motion
In a previous article, I updated the pickleball equations of motion to include aerodynamic drag (see “How Does Aerodynamic Drag Affect a Pickleball?”) In this analysis, I updated the aerodynamic drag model to include the lift force, for which the pickleball free body diagram is shown in Figure 2.
Conveniently, the lift force acting on the ball for pure topspin (and backspin) is always in the vertical direction, either adding to or subtracting from the force of gravity. The spin-enhanced equations of motion therefore only affect the trajectory in the vertical (y) direction. Updating the equations of motion, we have:
Where the sign for the lift term in the square brackets of Equation 2 depends on whether topspin (negative lift) or backspin (positive lift) is used. Since we are solving these equations recursively, at each time step we need to determine the velocity components (vy and V) for aerodynamic drag and lift at each time step and use these values to calculate the equations of motion at the next time step. The difference between the small v’s in the drag term and the large V in the lift term is that the small v is the y-component of the velocity, and the large V is the total (vector sum) of the ball velocity.
The input data used for this analysis is shown in Table 1. The rotational speed of the ball was obtained from the excellent You Tube video by the Pickleball Studio Podcast, The Ultimate Pickleball Paddle Spin Comparison. Here they used photography to determine the spin speed of a pickleball using several different paddles to determine the best paddles for spin. Low spin paddles were found to rotate the ball at less than 1200 RPM, medium spin paddles obtained rotational speeds of 1200 – 1500 RPM, and high spin paddles obtained speeds greater than 1500 RPM. For this analysis, I picked 1200 RPM, which is the low end of the medium speed range. This level of spin was determined to be achievable by average pickleball players using average paddles
Table 1. Input Data for Topspin Serve Analysis
How Does Topspin Affect the Serve?
In a previous article, “How Does Aerodynamic Drag Affect a Pickleball?” we analyzed the maximum speed of a serve with and without aerodynamic drag. This analysis found that in order to match the trajectory of the fastest serve the initial velocity of the serve needed to be about 54 mph in the presence of aerodynamic drag. The question now is, “Does topspin allow you to increase the speed of a serve?”
The analysis started with the trajectory of the fastest serve with aerodynamic drag, then topspin at 1200 RPM was added. The initial velocity and contact angle of the serve were then adjusted to match the trajectory of the fastest serve. As mentioned in previous articles, the trajectory of the fastest serve can be matched only with a unique combination of initial velocity and contact angle.
Figure 3 verifies that it is possible to match the trajectory of the fastest serve by adding topspin at 1200 RPM, allowing an increase in serve initial velocity from 54 mph to almost 65 mph! Additionally, the time of flight (T) of the topspin serve is 0.64 seconds, which is 0.13 seconds faster than the serve without topspin. The faster time of flight can mean a difference of 1-3 feet (depending on the foot speed of the receiver) and could prevent them from effectively returning the ball.
Dealing with average velocities, the serve without topspin covers 44 feet in 0.77 seconds, translating into about 39 mph, whereas the serve with topspin covers the same distance in 0.64 seconds, translating into an average of about 47 mph. The addition of a modest amount of topspin to a serve therefore increases the average speed of a serve by about 20%!
The Advantages of Spin
The big “take-away” here is that even a modest amount of topspin (1200 RPM) is beneficial in increasing the velocity and reducing the time of flight of a serve. However, the effective use of spin involves a delicate balance between ball velocity, spin rate, and contact angle.
Pickleball players who do not use topspin should learn the technique from friends, pickleball professionals, or by viewing the numerous “how-to” videos on the Internet. Pickleball players who understand how to use topspin should further improve their technique and/or select paddles that can increase the amount of topspin in their shots. Furthermore, all players should learn how to use spin to add more variety to their shots to keep their opponents guessing. We will apply the drag- and spin-enhanced equations of motion to analyze the effects of topspin and backspin on overhead smashes, drives, dropshots and dinks.
Future Topics
The various types of spin, including topspin, backspin and sidespin are effective in different situations for different shots, including serves, drives, dropshots, and dinks on different court surfaces and in the presence of wind. In future articles, we will look at how spin can be used to your advantage in these different situations.
The airfoil effect is only one advantage of adding spin to your game. Spin will also improve the stability of the ball in the presence of wind, cause the ball to bounce differently when it hits the ground, and cause different interactions when it strikes your opponent’s paddle. We will cover these topics when we discuss the aerodynamics of wind and impact dynamics. Here, we will also learn about the characteristics of pickleball paddles (e.g., paddle face and core materials, stiffness, and design) that may affect spin speed to help players pick an appropriate paddle.
Eventually, we will also study the biomechanics of the arm and wrist to better understand techniques by which a player can improve their ability to apply spin to the ball. Stay tuned, as this promises to be very interesting.
