Abstract
The shots of a professional tennis player may look like magic, seemingly defying the laws of science before your eyes. But it all becomes much simpler when you understand the physics behind tennis. This article focuses on the generation of spin on a tennis ball, how to maximize the power of a shot, and finding the “sweet spot” on the racquet.
Physics Is All Around Us
Do you ever watch a professional athlete and wonder how they are able to perform such an astonishing feat? How does bowling legend Pete Weber throw the ball dangerously close to the gutter, only for it to curve back toward the pins for a strike? How does Olympic champion figure skater Kristi Yamaguchi increase the speed of her spin just by adjusting her posture? The answers to these questions, and many more, lie in the vast world of physics.
In
tennis, players often appear to hit shots that defy physics, whether it’s
a groundstroke that resists gravity—floating through the air with
backspin—or a serve that leaves the racquet at an incredible speed. But just
like every other sport, tennis is governed by the laws of physics. With advancements
in racquet technology allowing the tennis ball to be literally stretched to its
limits, it is becoming increasingly important for players to take advantage of
aspects of the sport like spin and velocity. For a player interested in
bettering their tennis game by implementing such concepts, an understanding of
the physics behind tennis is key.
Tennis Is Evolving
Recently, tennis has evolved tremendously, becoming a faster sport with tennis shots increasing in velocity and spin, mainly due to the advancements made in racquet technology. In the 1980s, many players still used wooden racquets. Now, all players are equipped with racquets made of newer materials, including graphite, carbon fiber, and fiberglass. These materials are capable of producing much more spin and power than their wooden counterparts. Because racquets are now capable of such feats, tennis players are making adjustments to their game and coaches are teaching different, newer techniques. Rather than focusing on finesse and precision—two aspects of tennis that are losing importance due to the evolution of the sport—players are now trying to maximize the generation of spin and power.
A New Spin on Things
Arguably the most important aspect of tennis, spin allows players to control the flight path of the ball with the flick of a wrist. The spin they generate can cause the ball to float in the air, seemingly defying gravity; it can curve the ball sideways, away from the opponent scrambling across the opposite baseline; it can send the ball on an outward trajectory, only to aggressively dive during the final third of its flight path. Spin wins matches and frustrates opponents. But how is spin generated? To answer that question, we need to discuss the concept of friction.
Creating Spin
Friction is the resistive force between two objects, and opposes the direction of travel [1]. In the case of tennis, friction occurs between the ball and the highly tensioned strings of the racquet. The player swings the racquet in such a way that the face of the racquet is not square with the intended direction of travel. However, the strings “grab” the ball with the help of the rough fuzz on the ball’s exterior. This action helps aim the ball in the intended direction, and also generates torque, or rotation, on the ball. This concept is further explained in Figure 1.
The left image shows a ball being hit with backspin. The racquet face (blue) moves downward and is angled upward. Upon impact, the racquet transfers two forces to the ball: a rebound force (green) that is angled upward, and a friction force (red) that is angled downward, parallel with the face of the racquet. The friction force is not aligned with the ball’s center of mass, thus it creates rotation in the counter-clockwise direction, relative to this view. Similarly, the right image shows a ball being hit with topspin. The racquet face moves upward and is closed, meaning it faces downward. In this case, the rebound force points down, and the friction force points up. This ball, after impact, will have clockwise rotation. Friction is the driving force behind the creation of spin on a tennis ball, but how does spin affect the flight of a tennis ball? That’s where fluid mechanics—how a fluid (in this case, air) interacts with outside forces—comes into play.
The Effects of Spin
A phenomenon known as the Magnus effect describes the fascinating interaction between the spin of a moving object and the passing fluid. The Magnus effect is a principle that causes a spinning object traveling through a fluid to curve in one direction. This occurs because the spin and the friction between the object and the fluid allows the object to divert the flow of the fluid in a certain direction. Since the object “pushes” the fluid in one direction, the object feels the reaction force and is “pushed” in the opposite direction as a result [2]. Figures 2 and 3 further explain this concept.
How Spin Can be Advantageous
The most common spin in tennis, topspin, has many advantages. A ball struck with topspin will have a steeper trajectory due to the downward Magnus force caused by the topspin [3]. The downward Magnus force also allows the player to hit the ball harder and more aggressively, because the downward force keeps the ball from traveling beyond the lines of the court, despite its high velocity. Furthermore, the high bounce that results from a topspin ball striking the ground at a steep trajectory may force the opponent to adjust their stroke, potentially leading to suboptimal contact between the racquet and ball. While topspin is most commonly used during rallies, players also often hit shots with backspin, which induces a much different physical response.
A shot hit with backspin, called a slice, will have a flat trajectory, due to the upward Magnus force resisting the downward pull of gravity [3]. It is difficult for a player to hit a slice with much velocity because the backspin induces an upward force that keeps the ball in the air. This can result in the ball “floating” beyond the lines of the court. Still players will hit slices for a certain reason. Due to their flat trajectories, slices bounce lower on the opponent’s side than a shot with topspin or no spin would. This forces the opponent to hit the ball upward in order to clear the net, making it difficult for them to generate power.
Power Play: How Players Use Physics Concepts to Hit Harder Shots
With the increasing importance of hitting powerful shots in tennis, players and racquet manufacturers adapt to optimize power generation. They use techniques such as adding weight to the racquet and increasing the size of the “sweet spot” to maximize the momentum of the racquet and generate more power.
Using Lead Tape to Increase Momentum
Whether they know it or not, tennis players take advantage of the physical principles of momentum, defined as an object’s mass multiplied by its velocity. The Law of Conservation of Momentum states that the momentum of a system will not change unless it is acted upon by an outside source [4]. In the case of tennis, the system in question is the ball in flight, along with the body of the player and their racquet. This means that the momentum of the ball, body, and racquet will be the same before and after the ball is struck. Thus, momentum generated by the mass and velocity of the player and racquet will be transferred to the ball. Players use this concept to optimize their equipment based on their strengths, finding the right balance between velocity and mass. To do this, they select and customize their racquets to be light enough for them to swing with a high velocity, yet heavy enough to maximize the mass of the system. But what if a player likes their racquet and wants it to be a little bit heavier? There’s a solution for that, and it’s called lead tape. Lead is a heavy, dense metal, so adding lead tape to various points on the racquet will increase the mass of the racquet and help the player transfer more momentum to the ball. Players can optimize momentum transfer not only by weighting the racquet, but also by selecting one with a larger “sweet spot.”
The Sweet Spot
As racquet technology has advanced, the face of the tennis racquet has become larger. Figure 4 (shows modern racquet technology and how the racquet has changed since the early stages of tennis.
A larger racquet is beneficial since the size of the sweet spot is larger and easier to make contact with. But what exactly is a sweet spot? It’s a point located on the racquet’s center of mass (see Figure 5).
When an object is met with a force aligned with its center of mass, it will experience no rotation; however, when an object is acted upon by a force not aligned with the center of mass, it will experience rotation. For this reason, when a ball strikes the racquet at a point outside of the racquet’s sweet spot, the racquet experiences rotation. This rotational momentum reduces the linear momentum of the racquet, since the total momentum of a system is always conserved; with less linear momentum, the racquet generates less power and thus a lower shot velocity [5].
Conclusion
Understanding physics can tremendously increase your ability to improve your tennis game. It is highly beneficial to comprehend the physical effects that your actions have, as this will allow you to modify your tennis game to maximize your potential. The mysteries of spin can be easily understood through studying air flow and friction. Similarly, you can begin to hit more powerful shots by learning how power is generated in the first place. Even if you are just an observer of the sport, learning the science behind tennis can demystify thesuperhuman feats of the professional players, and leave you with a better understanding of the game.
References
[1] E.W. Weisstein. (2007). Friction [Online]. Available:
http://scienceworld.wolfram.com/physics/Friction.html
[2] Scientia. (2015). What Is the Magnus Effect and How Does it Work? [Online]. Available:
https://www.freedawn.co.uk/scientia/2015/07/23/what-is-the-magnus-effect-and-how-does-it-work/
[3] R. Cross. (2006). Ball Trajectories: Factors Influencing the Flight of the Ball [Online].
Available:
http://www.physics.usyd.edu.au/~cross/TRAJECTORIES/42.%20Ball%20Trajectories.pdf
[4] The Physics Classroom. (2018). Momentum Conservation Principle [Online]. Available:
http://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-
Principle
[5] Fabio Bocchi. (2015). The Physics of Tennis Racket Sweet Spots [Online]. Available:
www.comsol.com/blogs/the-physics-of-tennis-racket-sweet-spots/
[6] J. M. Pallis. (2002). Trajectories 101A: The Flight of the Tennis Ball [Online]. Available:
http://www.tennisserver.com/set/set_02_01.html
[7] R. Cross. (2006). Customizing a Tennis Racquet by Adding Weights [Online]. Available:
http://www.physics.usyd.edu.au/~cross/PUBLICATIONS/16.%20Customising.PDF
[8] R. Lott-Lavigna. (2016). Game, Set and Match: How Tennis Balls Are Made Inside Wilson’s Factories. Available: http://www.wired.co.uk/article/tennis-ball-factory
