One of the keys to hitting an accurate shot as explained in our article, How to Avoid Pickleball Mis-Hits, is to strike the ball on the paddle face at a location that does not induce misorientation of the paddle. This location is known as the Sweet Spot on the paddle. In this article, we delve further into the Sweet Spot and discuss why it is important to know where the sweet spot is on your paddle.
This is the second article on our series on the sweet spot. In the previous article, “What is the Sweet Spot“, we discussed the special characteristics of the pickleball paddle sweet spot. In a subsequent article, Where is the Sweet Spot? we will explain the mathematics of the sweet spot and calculate its location on an actual paddle.
Forces Acting on a Paddle
According to Newton’s Third Law of Motion when two bodies interact, they exert forces on each other that are equal in magnitude but in opposite in direction. That is, when you strike a pickleball, the force that propels the pickleball back towards your opponent is equal to the force that is applied by the pickleball back to you through your paddle.
The key to hitting an accurate shot is to understand the forces acting on your paddle at the moment of impact and to control any unwanted rotations of your paddle to return the ball in the desired direction. This is easier said than done, however. For example, you might properly anticipate the location, direction, and speed of the pickleball coming towards you. When you are ready to hit the ball, you pull your racquet back and stiffen the muscles in your arm in preparation of your swing. However, you might mis-judge the spin on the ball or wind may affect its trajectory, so that when you swing, the ball contacts the wrong spot on your paddle. The force of the ball then causes misorientation of your paddle, causing you to return the ball in the wrong direction.
A better approach might be to learn to always contact the ball at a point on your paddle face where it is not sensitive to misorientation. This location is known as the “sweet spot”.
Paddle Pivot Point Determination
In order to gain an understanding of where the sweet spot is located, let’s assume that the pickleball paddle is rigid, freely suspended in space, and is subjected to an impact load caused by striking a pickleball. The paddle has a center of gravity (cg) somewhere along the longitudinal centerline (Figure 1) and a “pivot point”, which is established by the biomechanics of the player’s wrist and where along the handle the player grips the paddle.
We can find the pivot point by examining a player’s wrist in different orientations. Figure 2a shows the player’s wrist with the paddle in the “neutral” position with no rotation, Figure 2b shows a positive rotation with the paddle face pitched forward, and Figure 2c shows a negative rotation with the paddle face pitched backward.
By superimposing the three figures on top of each other and plotting the longitudinal centerline of the paddle (Figure 3a) we can determine the pivot point by finding the intersection of the three centerlines. From this analysis, we can show that the center of rotation or the pivot point is located about 3” up from the end of the handle.
Further analysis finds that the location of the pivot point is simply at the center of the palm of your hand. As shown in Figure 3b, this player grips the racquet high on the handle with his index finger along the bottom edge of the paddle face. If you grip the paddle in your usual manner and open up your hand, you can see that the pivot point lies at the center of your palm.
Interestingly, you can change the location of the pivot point by changing your grip along the length of the handle. We will discuss this later in a future article. The pivot point location will become important later when we develop a mathematical equation for predicting the location of the sweet spot in our article, “Where is the Sweet Spot?“.
Paddle Rotations
The pickleball paddle has a preferred axis about which it wants to rotate when subjected to external forces. In engineering terms, this axis is known as the “principal axis of rotation”, which passes through the cg of the paddle. Figures 4a, 4b, and 4c show different side views of the paddle where the principal axis extends from the cg perpendicular to the page. There are three cases that are of interest to us:
- In Case #1 (Figure 4a) the ball contacts the paddle at the cg location causing pure translation of the paddle cg and pivot point with no rotations. This is normally a good thing because when the ball strikes, the paddle face remains perpendicular to the intended direction of travel and the ball will bounce off the paddle face in the desired direction. The pickleball player just needs enough arm strength to counterbalance the translational motion caused by the ball.
- In Case #2 (Figure 4) the ball contacts the paddle low near the handle. This causes positive rotation of the paddle about the cg, making the paddle face pitch or rotate forward. The combination of negative displacement of the cg plus the positive rotation of the paddle about the cg results in a net positive translation of the paddle pivot point. If you are a right-handed player, positive pitch will cause the ball to track to your left on a sidearm shot or it will cause the ball to land into the net on an overhead smash. Once again, since the force of the ball causes this rotation of the paddle, it may not be possible for the pickleball player to recognize the forward pitch and correct the paddle orientation before the ball bounces off the paddle.
- In Case #3 (Figure 4) the ball strikes the paddle high near the top. This causes negative rotation of the paddle about its cg, and positive translation of the cg, making the paddle face pitch or rotate backward. The combination of positive displacement of the cg plus the negative rotation of the paddle about the cg results in a net negative translation of the paddle pivot point. If you are a right-handed player, negative pitch will cause the ball to track to your right on a sidearm shot or it will cause the ball to sail beyond the baseline on an overhead smash. Similar to Case #2 above, since the force of the ball causes this rotation of the paddle, it may not be possible for the pickleball player to recognize the rearward pitch and correct the paddle orientation before the ball bounces off the paddle.
Because we are forcing the paddle to rotate about the pivot point instead of the cg, the forces, torques, and motions of the racquet can become exaggerated at the pivot point. In fact, the amount of translation at the pivot point is proportional to the amount of force needed to be exerted by your arm to counter-balance the force of the ball. Similarly, the amount of rotation at the pivot point is proportional to the amount of torque needed to be generated by your wrist to counter-balance the rotation of the racquet.
The Importance of the Sweet Spot
From this one can surmise that there must exist a point along the length of the paddle where the force of the ball would cause a positive translation of the paddle cg, but the negative rotation about the cg creates a translation of the pivot point that is equal and opposite to the positive translation of the cg. In essence, the pivot point remains stationary. This is illustrated in Figure 5 where the ball contacts the paddle at a point that is slightly higher than the paddle cg. This point, known in scientific circles as the “center of percussion” (or cp) defines the “sweet spot” as we all know it.
Your arm and wrist must supply a force or torque to not only counter the translations and rotations caused by the ball striking your paddle, but it must also propel the ball back across the net at a speed and direction of your choosing. By hitting the ball in the vicinity of your paddle’s sweet spot, you accomplish several things: (1) you can reduce unwanted or unforeseen rotations of your paddle and thereby improve your shot accuracy, (2) you will expend less effort and energy to correct the angular rotation of your paddle, allowing you to focus your efforts on directing your shots towards specific targets on the court, and (3) you will put less shock and vibration into your arm and wrist joints and muscles, thereby reducing fatigue and stress, which may be distracting and uncomfortable and may cause injury.
The importance of the sweet spot cannot be over-stated: when you hit the ball at the paddle sweet spot, the displacement of the pivot point is zero, and therefore the reaction force going back into your wrist and arm will also be zero no matter how hard the ball hits the paddle. We have all experienced situations where the force of the ball hitting the paddle pushes your arm back, causes rotation of your wrist or almost knocks the paddle out of your hand. By contacting the ball at the sweet spot, the ball will seem to jump off of your paddle almost effortlessly. In fact, when you contact the ball at the paddle sweet spot, it feels as if you don’t even need to grip your racquet! So there is truth in the paddle manufacturer’s claims that contacting the ball at their paddle’s sweet spot will result in “less vibration”, “greater stability and accuracy”, “solid feel”, “greater pop”, “lower arm fatigue”, etc.
In this article we discussed why it is important to hit the ball at the sweet spot, but we did not address how you find it on your paddle, whether it is dependent on the weight or shape of your paddle, the thickness of its core, the materials used in the paddle, etc, etc, etc. In the next article, “Where is the Sweet Spot?”, we will provide you with the mathematical equations that define the sweet spot and use these equations to determine the location of the sweet spot on an actual pickleball paddle. The factors that determine the location of the sweet spot may surprise you.
