The large number of pickleball paddle manufacturers and the wide variety of paddles they offer makes it virtually impossible for a player to try them all to determine the right paddle for their style of play and abilities. Among the most basic considerations in selecting a paddle are its weight characteristics; however, very few (if any) manufacturers provide more information than the paddle’s static weight. How then does a typical consumer differentiate the marketing hype from scientific fact? In this article we will explore three important factors that affect the paddle speed, maneuverability, power, and stability, including the Swing Weight, Recoil Weight, and Swing Radius. In a future article we will present the weight characteristics of several paddles so that you can select a paddle that is suitable to your style of play and capabilities.
Definitions
We discussed the differences between a paddle’s static weight and its swing weight extensively in a series of articles including “Paddle Weight vs Swing Weight” and “Paddle Selection: Swing Weight.
In summary, the paddle static weight (mpaddle) is the weight of a paddle when you place it on a scale, denoted by the variable “m” (for mass). The average paddle static weight is about 8 oz, with “light” paddles weighing less than 8 oz and “heavy” paddles weighing more than 8 oz.
The paddle swing weight (Iswing), on the other hand, pertains to the amount of effort needed to swing the paddle, usually measured about a pivot point on the handle at about the center of your palm. The swing weight is expressed in units of a mass times a distance squared. In metric units it is expressed in kg-cm2 and in imperial units it is expressed in oz-in2. In technical terms, the paddle swing weight is the paddle mass moment of inertia when swung at the paddle pivot point. We have simplified the paddle swing weight into the paddle effective weight, which allows you to more easily compare the paddle swing weights. Details are provided in our article, “Paddle Effective Weight”.
We will now introduce a couple more terms, the paddle recoil weight (Irecoil) and the paddle swing radius (rswing). The concept of recoil weight likely comes from the field of armory and firearms, where the weight and inertia of the firearm is used to counteract the “kick” from firing a bullet or projectile. The paddle recoil weight therefore defines the ability of a paddle to resist translations and rotations when striking a ball. In technical terms, the paddle recoil weight is simply the paddle mass moment of inertia measured at the paddle center of mass.
The paddle swing radius is the distance from the paddle pivot point to the paddle center of mass or center of gravity (cg). You can easily find the paddle cg location by balancing your paddle about a lateral axis on a sharp edge (Figure 1). You can calculate the paddle swing weight by knowing its static weight, recoil weight, and swing radius through the so-called parallel axis theorem:
Iswing = Irecoil + mpaddle * (rswing)2 (Equation 1)
Swing Mechanics
What does all of this mean? We need to first examine the mechanics of a swing to determine how the swing weight, recoil weight, and swing radius affect paddle performance. Figure 2 shows a top view of a pickleball player in the middle of a groundstroke. The centers of rotation of the body, shoulder, elbow, and wrist are denoted by the crosshairs.
An animated view of the groundstroke is shown in Figure 3. Frame 1 shows the backswing where the player has rotated his body sideways, dropped his forearm close to his body, coiled his elbow, and points his paddle backwards. Frames 2, 3 & 4 show the player uncoiling and extending his arm as the ball approaches. In Frame 5, the player’s arm is fully extended, he snaps his wrist forward, and makes contact with the ball. At this point the ball has no forward or backward velocity. Frame 6 shows the end of contact, where we have estimated the contact time to be on the order of four milliseconds (see “Paddle Weight and Momentum. Frame 7 shows the follow through with the ball is hit cleanly back in the same direction in which it arrived. In this instance, the player has contacted the ball at the center of mass, resulting in no rotation of the paddle (see our article, “Why is the Sweet Spot Important?”).
How does this information help you develop more speed and power with your groundstrokes? It is known that when you crack a whip, portions of the whip reach very high velocities. The cracking sound is not caused by the whip striking a surface but is due to portions of the whip breaking the sound barrier, creating a miniature sonic boom! Although the forward motion of your hand is relatively slow, the whip tip velocity can reach speeds that are 30 times the hand velocity! How does this relate to a pickleball paddle groundstroke?
The high velocity at the tip of the whip is due in part to the fact that each segment of the whip is rotating when the whip is cracked. In fact, the whip has an infinite number of centers of rotation. The arm has distinct joints where the rotation of the paddle starts from the body rotation, to the shoulder rotation, to the elbow rotation, to the wrist rotation. We can calculate the tangential velocity of the paddle (vtangential) by combining the velocity contributions of the shoulder rotating about the body (vshoulder), the elbow rotating about the shoulder (velbow), the wrist rotating about the elbow (vwrist), and the paddle rotating about the wrist (vpaddle) (Figure 4). That is,
vtangential = vpaddle + vwrist + velbow + vshoulder (Equation 2)
In a previous article (“Why is the Sweet Spot Important?”) we determined that the paddle pivots about a point that is roughly at the center of your palm (Figure 5):
The velocity due to rotation of a point around a joint center can be calculated by multiplying the angular velocity (ω) of the joint by the radius of gyration (r). That is,
vpoint = ωjoint*rpoint (Equation 3)
Figure 6 shows the radii and angular velocities of each joint.
Substituting Equations (3) into Equation (2) we have:
vtangential = ωwrist*rswing
+ ωelbow*(rswing+rwrist)
+ ωshoulder*(rswing+rwrist+relbow)
+ ωbody*(rswing+rwrist+relbow+rshoulder)
(Equation 4)
Rearranging we get:
vtangential = rswing*(ωwrist + ωelbow + ωshoulder + ωbody)
+ rwrist*(ωelbow + ωshoulder + ωbody)
+ relbow*(ωshoulder + ωbody)
+ rshoulder*(ωbody)
(Equation 5)
We see that the swing radius is acted upon by the angular rotations of the wrist, elbow, shoulder, and body very much like the tip of a whip is affected by rotations along the entire length of the whip. The radii of the shoulder, elbow, and wrist must be constant, and if the swing speed (ω) is constant, the only variable in Equation (5) is the swing radius (rswing). Therefore, very small changes in paddle swing radius can have a significant multiplier effect on tangential velocity of the paddle cg. Players seeking greater paddle power and paddle speed should therefore look for a paddle with a long swing radius.
In our example shown in Figure 3, the player is contacting the ball at the paddle center of mass. If he contacts the ball above the center of mass (towards the top of the paddle) the paddle will rotate backwards, causing the ball to pull to the right (for a right-handed player). If he contacts the ball below the center of mass (near the handle) the paddle will rotate forward, causing the ball to pull to the left (for a right-handed player). These are illustrated in Figures 7 and 8.
Because the contact time is only 4 milliseconds and the average human reaction time is between 150-300 milliseconds, it is impossible to correct your swing after you contact the ball. Instead, you must rely on the paddle having a sufficient recoil weight to resist unwanted rotations during contact.
Putting it All Together
There are several key take-aways from the above discussion:
- In a study of different implements including baseball bats, tennis racquets and golf clubs, it was found that the implement mass and swing weight had an effect on the so-called “power” of the implement. Further, it was found that the swing speed depends on the implement’s swing weight and not on its mass. That is, you can have two paddles – one that is “light” with a static weight of 7.5 oz and one that is “heavy” with a static weight of 8.5 oz. Just as long as the swing weights are equal, you will be able to swing the paddles at the same speed! It is therefore desirable to select a paddle with a low swing weight to increase paddle swing speed.
- Since paddle static weight does not affect the paddle swing speed, it is desirable to select a paddle with a high static weight (but low swing weight). The higher static weight will impart more momentum to the ball and increase the ball velocity. Even though two paddles with different static weights will result in the same swing speed, the paddle with the higher static weight will appear to have more power.
- It is now possible to make a distinction between the paddle’s swing weight (Iswing) and its recoil weight (Irecoil). The swing weight pertains to how fast you can swing your paddle up until you make contact with the ball (Frames 1-4 in Figure 3, 7 & 8). During contact (Frames 5 & 6), the paddle’s recoil weight takes over and determines how the paddle will react when striking the ball. The paddle’s reaction (and therefore its recoil weight) determines how “true” you hit the ball.
- Examination of the tangential velocity (Equation 5) above shows that the rotational speeds of the body, shoulder, elbow, and wrist will be constant for paddles with the same swing weight. We also know that the distances between rotational points on the body must be constant. The only variable pertains to the distance from the pivot point to the paddle cg (i.e., the swing radius). Since the paddle swing radius is acted upon by the rotations of the wrist, elbow, shoulder and body, it is the key factor that determines the velocity and power that can be imparted to the ball. Paddles with a long swing radius will therefore have more power than paddles with a short swing radius.
- Short of adding weighted tapes to your paddle (which we will discuss in a future article), the paddle static weight and recoil weight cannot be changed. However, a player can change the paddle swing radius and swing weight by holding the paddle higher or lower on the grip. Many novice players use a “ping pong” grip (Figure 5) by “choking up” on the paddle and holding it near the throat. Some players will even place one or more fingers on the paddle face. Such a grip will reduce the swing radius (rswing) and swing weight (Iswing) and restrict wrist rotation (ωwrist), making the paddle feel more controllable. However, more advanced players will hold the paddle closer to the butt increasing the swing radius and allowing greater wrist rotation (i.e., snap) to increase the power and velocity of their shots.
- As shown in Figures 7 and 8, it is desirable to contact the ball at or near the center of mass (cg) to avoid unwanted paddle rotations during contact. Paddles with a high mass moment of inertia about the cg will therefore be less prone to rotation. In order to maximize paddle stability, it is desirable to select a paddle with a high recoil weight.
The paddle weight characteristics are all inter-related through the paddle shape, materials, and weight distribution. You should select a paddle with the ideal combination of static weight, swing weight, recoil weight, and swing radius depending on your style of play and physical abilities.
Future Articles
In a future article we will compare the weight characteristics of several paddles so that you can make an informed decision on which paddle is right for you. In another future article we will discuss how to tailor the weight characteristics of your paddle with different grips and weighted tapes.
