A review of several advertisements, articles, and videos on the internet finds numerous misconceptions, contradictions, and erroneous claims regarding paddle weight, power, and speed. Proponents of both lighter and heavier paddles each claim that their lighter or heavier paddles will allow you to hit the ball harder, faster, and with increased accuracy. Who is right? Does your ideal paddle weight depend on whether you are a novice, intermediate, or advanced player? Should your next paddle be heavier or lighter? Let’s see if the science can provide us with some insight.
Energy and Momentum
When you strike the pickleball with your paddle, there is an exchange of kinetic energy between the paddle and the ball, where the desired outcome is to change the velocity and direction of the ball. The kinetic energy of an object comes about because the object has a mass and a velocity. It is calculated according to the following formula:
KE = ½ mv2
Where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object. An elastic collision is one in which there is no net loss in kinetic energy for either the ball or the paddle. In reality, some energy is lost in friction and dynamic deformation of the ball and the paddle, which creates heat and noise that is radiated to the environment. Kinetic energy is therefore not conserved in the collision between the paddle and pickleball.
The term “momentum” is often used interchangeably with kinetic energy, however, unlike kinetic energy, momentum must be conserved in a collision. In other words, the total momentum regardless of how it is exchanged between the ball and paddle, must be constant. The momentum of an object is calculated according to the following formula:
p = mv (1)
Where p is the momentum, m is the mass of the object and v is the velocity of the object. Clearly, when striking a ball, all of the momentum in the paddle does not go into accelerating the ball. Otherwise, the ball would fly over the back fence and the paddle would come to a full stop when the ball is struck, just like when releasing one ball in Newton’s Cradle (Figure 1).
Instead, after the ball is struck there is a decrease in paddle velocity, and the excess momentum is absorbed by your arm during follow-through as the paddle decelerates.
It is possible to estimate the amount of momentum transferred to the ball during a serve, because we know that the ball is initially at rest (v=0) and the speed of the ball is equal to the speed of the paddle at the moment of impact. In a previous article (“How Fast is a Pickleball Serve?”) we assumed that the paddle / ball impact speed was about 18 meters/sec (40 mph). Since a typical pickleball weighs about 0.024 kg (0.86 oz), we can calculate that the change in momentum of the ball will be 0.432 kg-m/sec.
Knowing that the paddle speed must equal the ball speed at impact (18 m/s or 40 mph), we can calculate the percentage of the paddle momentum that is transferred to the ball using a light (7.5 oz or 0.21 kg) paddle verses a heavy (8.5 oz or 0.24 kg) paddle. Substituting these weights into Equation (1), we find that a light paddle transfers about 11.4% of its momentum to the ball, whereas the heavy paddle transfers 10.0% of its momentum to the ball, a difference of only 1.4%!
Let’s look at a different scenario where a ball is hit towards a player that has a velocity of about 25 mph (11 m/s). If the player’s maximum swing speed is 40 mph (18 m/sec), we can calculate that the change in momentum of a groundstroke will be 0.936 kg-m/sec. To effect this change in momentum, the light paddle would need to transfer 24.8% of its momentum to the ball, whereas the heavy paddle would need to transfer 21.7% of its momentum to the ball, a difference of only 3.1%!
This analysis shows that regardless of whether a light or heavy paddle is used, the difference in the amount of momentum transferred from the paddle to the ball is small. This suggests that the paddle weight may not contribute significantly to the power or speed transferred between the paddle and the ball.
What About Swing Speed?
The analysis above assumes that pickleball players have adequate arm strength where they can achieve the same paddle velocity of 18 m/sec (40 mph) whether they are using a heavy or light paddle. In certain sports, such as baseball, tennis, golf, etc. the players are swinging as hard as they can to maximize swing speed, ball speed, distance, and power. Numerous studies of swing weight verses swing speed in several different sports, however, have determined that when players have reached their limit on swing effort, their swing speed decreases according to a power law with increasing swing weight.
This is more easily explained when examining Equation (1). If paddle mass (m) is increased beyond the swing capability of the player, it can have a significant detrimental effect at reducing swing velocity (v). Since momentum (p) is the product of mass (m) multiplied by velocity (v), the decrease in velocity (v) can be greater than the increase in mass (m) causing a net reduction in momentum (p). In this case, the use of a heavier paddle can cause slower and less powerful shots!
Fortunately, this is not true for all cases because pickleball players might reach their maximum swing capability on only a few shots, such as overhead smashes, some serves, and drives from the baseline. Other shots, such as dinks, volleys, and drop shots require more “finesse” requiring a much slower swing speed.
The relationship between swing weight and swing speed warrants further examination, which we will address in a future article. The differences between paddle weight and swing weight were examined in a previous article (see “Paddle Weight vs Swing Weight”).
How is Momentum Transferred?
At the instant when the ball is hit, momentum is exchanged between the ball and paddle. How is this done? How can the exchange of momentum cause the ball to change direction and velocity?
Returning to Equation 1, we know that velocity (v) is equal to the product of acceleration (a) multiplied by time (t):
p = mv = m(at)
We also know that force (F) is equal to the product of mass (m) multiplied by acceleration (a). Re-arranging, we arrive at the impulse-momentum equation:
p = mv = (ma)t = Ft
The product Ft is termed the “impulse”. When the paddle contacts the ball it provides a force (F) to the ball over a contact time (t) creating momentum (p). For the same level of momentum, you can contact the ball with a higher force over a shorter contact time, or with a lower force over a longer contact time.
As a validation of the impulse-momentum principle, using Equation (1) above, we calculated the change in momentum to the ball during a serve is 0.432 kg-m/sec. In previous articles (see “How is Topspin Generated?“) we assumed that the contact time for a serve is on the order of 4 milliseconds. Solving the impulse-momentum equation for the peak impact force (F), we find that it is about 108 Newtons, or 24 lbs, which is reasonable.
Automobile manufacturers and packaging companies routinely use the impulse-momentum principle to protect vehicle occupants and package contents. By spreading the impact force over a longer time duration, it is possible to significantly reduce the magnitude of the force required to overcome the momentum during a collision. This is accomplished by the use of crumple zones that are effective at absorbing kinetic energy before it can be transferred to vehicle passengers or packaging contents.
How is Contact Time Affected?
When a pickleball paddle strikes a ball, the ball flattens and the paddle face bends until they both eventually rebound and the ball is released from the paddle face (Figure 2). The elapsed time between initial contact with the ball and separation defines the contact time.
Figure 2 illustrates how impact force, swing speed and contact time are inter-related. Swinging the paddle faster has several benefits:
- It generates more momentum that can overcome higher levels of forward ball momentum and create returns with greater velocity.
- It causes greater deformation of the pickleball and paddle face, resulting in more time of contact before the ball and paddle face can rebound and separate.
- The increased contact time can enable a pickleball player to impart more spin to the ball. We discuss how this is accomplished in our article, “How is Topspin Generated?”
- The increased contact time can result in more accurate shots by enabling the ball to follow the paddle over a greater distance.
Contact time is also affected by the stiffness of the paddle face. A softer paddle face will have a longer contact time (and lower contact force) because it will more gradually compress, absorb, and release the deformation energy in the ball. A harder paddle face will have a shorter contact time (and higher contact force) because it will more rapidly compress and release the ball.
Although the USAPA has strict requirements on paddle face stiffness, this data is usually not provided by paddle manufacturers. Pickleball Science is in the process of developing a more realistic face stiffness test utilizing the contact stiffness and area of a pickleball under a more representative load level. In the meantime, pickleball players may assess the relative face stiffness of different paddles by pressing their thumbs into the paddle surface. We discuss the pros and cons of softer and stiffer paddle faces in our article, “Power vs Control Paddles”.
Is a Heavier or Lighter Paddle Right for You?
The choice of using a heavier or a lighter paddle is of course, a matter of preference, however, the mathematics suggest that an average player (with average reflexes, strength, and swing speed) may benefit from a using lighter paddle with a softer face swung at a faster speed than using a heavier paddle with a stiffer face swung at a slower speed for the following reasons:
- A lighter paddle will be easier to maneuver when defending volleys at the net, or if the player needs to rapidly shift from hitting forehand and backhand shots.
- A lighter paddle will put less stress on the body, reducing muscle fatigue and potential injury to muscles and joints.
- A lighter paddle with a softer face will increase the contact time, enabling faster ball speeds and a greater capability of applying spin to the ball.
More advanced players with good reflexes, stronger arms, faster swings, and better paddle control may benefit from heavier paddles with stiffer faces for the following reasons:
- The higher mass can create more momentum that can be transferred to the ball.
- The stiffer face will reduce contact time, but enable a higher peak force to be developed between the paddle and the ball, resulting in faster and more powerful shots.
- The increased mass increases the paddle moment of inertia, enabling greater rotational stability when balls are hit off center, or with high velocity, or with lots of spin.
We discuss the paddle moment of inertia in our article, “Paddle Weight vs Swing Weight” and how unwanted paddle rotations can be controlled by contacting the ball at the paddle sweet spot in our article, “Why is the Sweet Spot Important?”
