Tennis Industry magazine


Wrist Snap In the Serve

Physicist Rod Cross explains that the racquet snaps the wrist, not vice versa.

By Rod Cross

Amost anyone can swing a tennis racquet without knowing in detail how they do it. It’s like walking or riding a bicycle or swimming. People just do it, some better than others, but hardly anyone can describe exactly what they are doing or how they do it. The mechanics of accelerating a racquet (or a club or a bat) is essentially a three stage process, starting with the racquet behind the back (for a smash, serve, or groundstroke) and ending when the racquet contacts the ball. There are lots of variations in style between players and between different types of strokes, but all players and all racquet strokes employ the same basic three-stage process to accelerate a racquet. During each acceleration stage the rotation speed of the racquet increases smoothly right up to the time of impact with the ball, but the mechanism responsible for the rotation changes three times. So does the role of the wrist.

Stage 1: Wrist torque dominates

Figure 1
Fig. 1 Pulling on the handle with a single force F1 will cause the racquet head to rotate from A to B, in the wrong direction.

Muscles and tendons work in the same way as pulling on a piece of string. In theory, I could swing a racquet by tying several bits of string to the handle and pulling on each bit of string in the correct direction, with the correct force and at the correct time. That’s essentially what I do when I swing a racquet. I pull or push the handle with my hand rather than using bits of string, but the end result is the same. Suppose I try to swing a racquet by pulling hard on a single piece of string tied to the handle or by pushing hard on the handle with one finger as shown in Fig. 1. The handle will jerk forward but the racquet head will get left behind or even move backwards in the wrong direction. That method of swinging a racquet is obviously not a good one.

Figure 2
Fig. 2 The hand applies a force F1 near the first finger and a force F2 near the little finger. If F1 is about 40% bigger than F2 then the tip of the racquet will rotate from A to B in the correct direction as shown.

What I could do instead is to grab hold of the handle with one hand, push the handle towards the ball and simultaneously rotate my wrist so the handle and the head both swing around together. But in practice, I don’t really need to rotate my wrist to swing the head around, since I can swing a racquet with my wrist locked in a fixed position while I push on the handle. That way, I effectively apply two separate forces to the handle, one near the bottom of my hand and one near the top. The two forces are in opposite directions, as shown in Fig. 2. The forward force F1 is bigger than the backward force F2, so the whole racquet moves forward and it simultaneously rotates due to the torque on the handle. A torque is just a fancy technical word describing a twisting or turning effect. F1 needs to be about 40% bigger than F2 to make the racquet move and rotate in the right direction.

Each of the two forces would separately cause the racquet to rotate in opposite directions but F1 has a smaller rotation effect than F2 since it is closer to the balance point. Since F1 is about 30% closer to the balance point than F2 it needs to be at least 30% bigger than F1 so the racquet will rotate in the right direction. If F1 was the only force and if F1 was applied at the balance point, then the whole racquet would move forward without any rotation at all. You can prove that to yourself by pushing a pencil sideways on a desk. If you push at one end the pencil rotates, but if you push sideways in the middle the pencil moves sideways without rotating (unless one end is a bit rough and gets stuck on the desk). If you push on one end with the thumb while pushing in the other direction with one finger one inch away from the end, the pencil rotates the way you want it to.

Figure 3
Fig. 3 Swinging a racquet with the wrist locked.

All players commence the swing of a golf club or a baseball bat or a tennis serve with the wrist in a locked position so that the far end will swing around and not get left behind, as it would if the wrist remained limp. The torque applied by the wrist allows the implement in the hand to swing around at the same angular speed as the forearm. The actual speed is different but if the wrist is locked and the arm swings through say 30 degrees in 0.1 seconds, then the implement will also swing through 30 degrees in the same time as shown in Fig. 3. In this case the angular speed is 300 degrees per second and it’s the same for both the racquet and the forearm.

Stage 2: Centripetal force dominates

A wrist torque is necessary at the beginning of the swing but after the racquet picks up speed the wrist is no longer needed to swing the racquet head around. It’s the same in golf where a golfer cocks the wrist at the start of the swing, so the club and the forearms are nearly at right angles to each other. As the club picks up speed, the wrists can start to relax. During the rest of the swing the wrists apply no torque at all, or very little, and the hands rotate freely with the club about an axis through the wrist. The club and the arms are almost in line at the moment the club head strikes the ball. The same type of action occurs in a tennis serve. At the start of the swing, the racquet is behind the back, almost at right angles to the forearm. By the time the racquet has swung around to impact the ball, the racquet and the forearm are almost in line. It looks like the wrists are being used to swing the racquet around, but it’s actually the other way around. The wrist rotates because it is almost limp and the rotating racquet pulls the wrist around. The wrist might help a bit, especially in guiding the racquet onto the ball, but the wrist does almost nothing to make the racquet rotate during the middle part of the swing or towards the end of the swing.

During the first stage, the rotation speed of the racquet increases as a result of the wrist torque on the racquet, while the upper and lower arm segments increase in speed due to the torques applied by the shoulder and elbow. During the second stage, the wrist torque drops to zero but the racquet keeps rotating faster because another torque takes over from the wrist torque. This new torque is applied to the racquet by the forearm pulling on the handle in a direction from the handle towards the elbow. That torque is much bigger than the wrist torque and it develops naturally without the player being aware of it.

A racquet is usually swung in a circular arc rather than being pushed or pulled along a straight line. The racquet head follows a roughly circular path with the elbow being near the center of the circle. In order to follow a circular path there needs to be a force on the racquet that acts in a direction towards the center of the circle. Such a force is called a centripetal force, meaning that it acts towards the center of the circular path. In order for the racquet to follow a curved path, you need to pull at right angles to its path. Momentum alone would carry the racquet forward in a straight line. The force at right angles causes the racquet to follow a curved path, curving in a direction towards the pulling force. In a very fast serve, that force is almost as big as the weight of the player. In other words, it’s not a force of a few pounds, it is more like 100 pounds or more.

Figure 4
Fig. 4 During stage 2, the force on the racquet is directed along the arm and the wrist is relaxed. The rotation speed of the racquet increases due to the torque acting about the balance point.

Figure 4 shows the force on a racquet handle during stage 2 of the swing. The force is not exactly at right angles to the path of the racquet head. The force acts along a line from the hand to the elbow, so it acts slightly backwards. Being such a large force, around 100 pounds, it exerts a large torque on the racquet. The result is that the racquet head swings around rapidly, without any assistance from the wrist. The same effect would result if you tied a piece of string to the handle and swung the racquet on the end of the string. If you tie a piece of string to a racquet handle and pull in a line along the handle, the racquet will move in that direction but it won’t rotate. To get the racquet to rotate, you need to pull the string at an angle to the handle, as shown in Fig. 4.

You can in fact swing a racquet this way, but holding onto the handle is better because you can control the angle of the racquet head more easily with a slight twist of the wrist.

The fact that a racquet can indeed be swung on the end of a length of string proves that a wrist torque is not needed to swing a racquet. A wrist torque helps to get things started, but it’s really the centripetal force that matters most. A wrist torque also helps to stop the rotation after the ball is struck. It is much harder to stop a racquet rotating if the handle is dangling on the end of a piece of string.

The torque on the racquet during stage 2 depends on the angle between the forearm and the racquet. The angle decreases just before impact, with the result that the torque due to the centripetal force drops almost to zero just before impact. Since the torque due to the centripetal force drops rapidly just before impact, most players instinctively switch to stage 3 by pulling backwards on the handle. They do that by slowing down the rotation speed of their forearm before striking the ball, and they slow it down even further after they strike the ball in order to bring the racquet to a stop.

Stage 3: Forearm speed drops

In order for the racquet head speed to keep increasing throughout the swing, the arm must slow down just before the racquet (or club or bat) hits the ball. That might be hard to believe, but it is a very common phenomenon. It even happens when you are walking. As the lower leg swings out just before you put your foot on the ground, the upper leg slows down. Or when you throw a ball, the forearm picks up speed while the upper arm slows down. Or when you kick a ball, the lower leg speeds up while the upper leg slows down. When you hit a tennis ball, the upper arm slows down first, then the forearm slows down, but the racquet itself keeps increasing in speed. In that way, rotational energy developed in the upper arm is transferred to the forearm, and rotational energy developed in the forearm is transferred to the racquet. The whole process actually starts even earlier with the hips then the trunk slowing down before the upper arm starts to slow down. If you watch a javelin thrower in action, these effects are even more noticeable.

Figure 5
Fig. 5 Angular velocity of racquet and forearm for a 115 mph serve. The racquet was rotating at 72 rad/s = 11.4 rev/s = 687 rpm just before impact. The forearm reached maximum rotation speed 0.035 s before impact.

Figure 5 shows the first serve of a good college player recorded by John Yandell on video at 250 frames/sec. The speed of the racquet tip increased rapidly during the last 0.04 seconds of the swing up to a maximum of 103 mph just at impact. The ball came off the racquet slightly faster, at 115 mph. The rotation speed of the racquet increased up to a maximum of 72 radians/sec (11.4 revolutions per second) just at impact. The rotation speed of the forearm increased to a maximum of 38 radians/sec (6.0 revolutions/sec) 0.035 seconds before impact then dropped to 12 radians/s (1.9 revolutions/s) at impact.

The centripetal force on the racquet is given by the formula F = M·V·V/R where M = mass of racquet, V = speed of its center of mass (i.e. its balance point) and R = radius of circular arc followed by the center of mass. Assuming M = 0.35 kg, R = 15 inches = 0.38 m and V = 60 mph = 27 m/s, we get F = 671 N = 151 lb. A 350 gm racquet weighs only 0.77 lb, but it takes a force of 151 lb to make it rotate at 60 mph in a tight circular arc of radius 15 inches.

It is obvious in Fig. 5 that the forearm rotation speed decreased quite a lot just before impact. An interesting question is whether the player deliberately chose to do that or whether he had no choice in the matter. Just before impact the racquet is rotating rapidly. The tip rotates forward towards the ball so the handle rotates backward towards the player’s hand. If the player pushes forward on the handle and the handle pushes backward on the player, then the handle can still move forward but it will either slow down or speed up depending on who or what is pushing the hardest. In Fig. 5 it was the racquet pushing back on the hand that pushed the hardest and it caused the hand to slow down and the rotation speed of the forearm to decrease. Early on during the swing, the rotation speed of the forearm increases because the racquet offers very little resistance and because the player exerts a torque on his forearm using his muscles. Later on, the direction of the torque reverses, and the forearm slows down, since the racquet is rotating much faster and pushes against the player’s hand.

The action of the wrist in a groundstroke is quite different to that in a serve and it depends on the speed at which the player swings the racquet. At low speed, a player can keep the wrist locked during the whole swing. In a high speed swing the racquet will rotate so fast that it will forcefully unlock the wrist if the player tries to keep it locked. Usually, the player relaxes the wrist beforehand and allows the racquet to pull the wrist around smoothly. However, the player can still flick the racquet head vertically upwards using wrist action to generate topspin, even though the racquet pulls the wrist around in the horizontal direction.

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About the Author

Rod Cross retired in 2003 as an honorary member of the Sydney University staff and continues to work on the physics of sport and forensic physics. He is a physicist and co-author of The Physics and Technology of Tennis available from the USRSA.



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