Contrary to popular belief, a paddle’s swing weight is not an intrinsic property of the paddle, nor will the same paddle provide the same swing weight for every player. This is because the paddle swing weight depends on how and where a player grips the paddle. Therefore, a paddle that might seem to have a high swing weight to one player might seem to have a low swing weight to another. As a further complication, the published swing weight and twist weight data provided by several reviewers and paddle manufacturers is often confusing. Typically, they will claim something like, “… the paddle has a swing weight of 109 and a twist weight of 6…” What do these numbers mean? What are the units of measurement? Furthermore, how do these number compare to our calculations of swing weight and twist weight in our “Paddle Technical Data” table?
To answer these questions, we will first need to review the basics.
The Basics
The swing weight of a pickleball paddle is simply the mass moment of inertia (MOI) of the paddle about the pitch axis referenced from a pivot point (Figure 1).
You can measure the swing weight of a pickleball paddle using a “swing weight machine” which is essentially a pendulum that measures the period of oscillation of an object about a pivot axis or point. Knowing the location of the object’s center of mass (cg) with respect to the pivot point allows the machine to calculate the object’s mass moment of inertia, or in our case, the swing weight of the paddle about its pitch axis. The swing weight machines typically provide the paddle’s MOI in units of kg-cm2. While this may seem like an odd unit of measure to most readers, the MOI has a real physical meaning.
As we described in our article, “Paddle Swing Weight, Recoil Weight, and Swing Radius”, you must translate and rotate your paddle while hitting the ball. From Newton’s Laws of Motion, we know that an object at rest tends to stay at rest, and an object in motion tends to stay in motion unless acted upon by an outside force (or torque). For translational motion, we must apply a force to move the object that is equal to the object’s mass multiplied by its acceleration, i.e., F=ma. For rotational motion about an axis, we must apply a torque to the object equal to its MOI multiplied by its angular acceleration, i.e., T=Iα.
The angular acceleration (α) relates to how fast you can change the rotational velocity of your paddle. The MOI or swing weight is therefore the “rotational mass” of the pickleball paddle that must be overcome with torque from your arm and wrist to change the orientation angle of your paddle. Of course, a paddle with a lighter swing weight will be much easier to maneuver than one with a heavier swing weight.
To calculate the swing weight, you would simply divide the torque (T) by its angular acceleration (α), where the units for torque are N-cm, or [(kg-cm/sec2) * cm] or kg-cm2/sec2. The angular acceleration (α) is expressed in radians/sec2, where radians are unitless. Dividing the torque by 1/sec2 yields the units for the swing weight in kg-cm2.
Now that we know what the swing weight is, let’s move on to how we can determine the swing weight of a paddle without using a swing weight machine.
Swing Weight Calculation
We can calculate the swing weight (Iswing) by first calculating the MOI of the paddle about its center of mass (Icg) then mathematically shifting it to a pivot point using the well-known parallel axis theorem:
Iswing = Icg + m*r2
The MOI about the cg (Icg) defines another important parameter, the paddle “recoil weight”, which we discuss in our article, “Paddle Swing Weight, Recoil Weight, and Swing Radius”. The recoil weight (Icg) is not easy to calculate without use of a CAD program like SketchUp. We describe our methodology for calculating this in our article, “Where is the Sweet Spot?” While you would normally want a paddle with a low swing weight, a high recoil weight is desirable as it will reduce the tendency of the paddle to rotate if you contact the ball off-axis or away from the paddle sweet spot.
Besides the paddle mass, the one critical component in determining the paddle swing weight is the location of the paddle pivot point with respect to the paddle center of mass. This defines what we call the “swing radius” (r) in our swing weight calculation. Paddle manufacturers and paddle reviewers often do not tell us where they assume the pivot point to be.
In our calculations, we assume that the pivot point is at the center of your palm when you grip the paddle. The rationale for this is described in our article, “Why is the Sweet Spot Important?”. Therefore, if you grip your paddle at the bottom of the handle, it will appear to have a higher swing weight than if you grip your paddle near the throat. For our swing weight calculations, we assume that the pivot point is roughly 2” (or 5 cm) above the butt of the handle for all paddles.
Knowing the paddle recoil weight (Icg), the paddle mass (m) and the paddle swing radius (r), it is possible to calculate the paddle swing weight (Iswing) using the parallel axis calculation defined above. The swing weights of several paddles are provided in our article, “Paddle Technical Data”.
How Do You Use the Swing Weight Data?
One aspect of our swing weight data that causes confusion among our readers are the units that we use. As indicated by the parallel axis theorem equation, the swing weight should have units of mass times distance squared. Why do we use oz-in2? Strictly speaking, if we were to use imperial units, the swing weight would be expressed in slug-feet-squared, and in metric units, the swing weight would be expressed in kg-centimeter-squared. Both terms are somewhat nebulous.
We decided to use (oz-in2) because paddle manufacturers express the paddle weight in ounces and it is relatively easy to measure the paddle cg location and pivot point with a 12″ ruler. Our readers could therefore easily calculate the m-r-squared contribution of their paddle’s swing weight themselves by doing the following:
- Measure the weight of your paddle using a kitchen or postal scale set to measure in ounces.
- Balance your paddle about its lateral axis on a straight edge. Mark the location where your paddle balances with a pencil. This point is the paddle cg or “balance point”.
- Determine the location of the pivot point by gripping your paddle and noting where the center of your palm is on the handle.
- Measure the distance from the pivot point to the balance point to obtain the paddle swing radius (r).
- Multiply the paddle weight (in ounces) by the square of the swing radius (r). This provides you with the m-r-squared contribution to the paddle’s swing weight.
How do you calculate the recoil weight (Icg)? Without using a CAD program like SketchUp, we must estimate it. In our “Paddle Technical Data” table, the average paddle weight is 8.0 oz, and the average swing radius is 7.33”. The m-r-squared component of the swing weight (Iswing) for the average paddle is therefore 8*(7.33)2 or 430 oz-in2. We calculated the average recoil weight (Icg) to be 145 oz-in2 or roughly one-third of the m-r-squared term. Therefore,
So, for the average paddle, the swing weight can be estimated at 430*1.33 = 572 oz-in2, which is about equal to our calculated swing weight of 577 oz-in2. You would therefore estimate the swing weight of your paddle by multiplying your calculated m-r-squared result by 1.33.
What Now?
Now that you know how to estimate the swing weight of your paddle, what do you do with it? In reality, the paddle swing weight is used only for purposes of comparing different paddles. Since swing weight machines provide the swing weight in units of kg-cm2, how do we convert oz-in2 to kg-cm2, and vice versa? If you have the swing weight in oz-in2 you simply multiply it by 0.183. The swing weight of an average paddle is 577 oz-in2, which is equal to 105 kg-cm2. If the swing weight is given to you in kg-cm2 you simply divide it by 0.183 to convert it to oz-in2. Swing weights for most pickleball paddles should fall withing the range of 400 – 700 oz-in2 or 70 – 130 kg-cm2 if they are gripped 2” from the bottom of the handle.
What if you don’t grip your paddle near the bottom of the handle? Is it possible to figure out the swing weight of the paddle when gripped at the top of the handle? Of course! Let’s say your handle is 5.0” long, and you grip it near the top, reducing the swing radius by one inch. The recoil weight is invariant since it is the mass moment of inertia about the cg, and for the average paddle it is 145 oz-in2. We can calculate the new m-r-squared term to be 8.0*(7.33-1.00)2 = 321 oz-in2. The swing weight is therefore (145 + 321) oz-in2 = 466 oz-in2, a whopping 110 oz-in2 (20 kg-cm2), or 20% less by just gripping the paddle one inch higher up the handle!
This example demonstrates that one of the critical elements in determining the swing weight is the assumed location of the paddle pivot point. Since there do not appear to be industry standards on the location of the pivot point, it may be difficult to make apples-to-apples comparisons of swing weights among different paddle manufacturers or reviewers. For example, the pivot point might be assumed to be anywhere from the bottom of the handle up to 4” from the bottom the handle (which is commonly used for tennis racquets). In all of our analyses, we set the pivot point 2” from the bottom of the handle. Therefore, by shifting it by ± 2”, the swing weight of the average paddle can appear to range from 372-841 oz-in2 (68-145 kg-cm2)!
Conclusions and Recommendations
In this article, we showed that the paddle swing weight published by paddle manufacturers and reviewers is not really an intrinsic property of the paddle, since it depends on how and where you grip your paddle. You can increase or decrease the apparent swing weight of your paddle by gripping it higher or lower on the handle. We also showed a simple way to estimate your paddle’s swing weight by knowing its weight, the cg location (or balance point), and the location of the center of your palm when gripping the paddle. When you are selecting your next paddle based on published technical specifications for the swing weight, make sure that you understand where the manufacturer or reviewer has defined the pivot location for the swing weight number.
