Dynamic Stiffness of a Pickleball Ball
8/3/2026
The ball's impact with an object such as a wall or a paddle is over in less than 2 milliseconds. The ball compresses against the object slowing the inbound speed until it reaches zero and then decompresses propelling the ball in the opposite direction. Dynamic stiffness is a measure of the forces experienced by the ball and the distance traveled by the ball as it compresses and decompresses during the brief impact period.
Why should we care about stiffness? For the typical player, stiffness is a measure of feel and ball speed. The Lifetime ball is known for its hardness and fast play. The Franklin X40 is known for its softness and slower speeds. For the paddle designer, the dynamic stiffness of the ball interacting with the dynamic stiffness of the paddle face determines the paddle's power and feel. Future articles will explore the stiffness of the paddle face; the paddle/ball interaction and the paddle specs that determine power and feel.
Dynamic stiffness of a Penn40 ball and a Lifetime ball rebounding off a wall at an inbound ball velocity of about 50 mph. The upper half of the trace reflects the stiffness during compression. The lower half reflects stiffness during decompression. The higher stiffness for the Lifetime ball is evident (steeper slope). The lower rebound speed for the X40 (16 mph v 17.5 mph) reflects the slower play of the X40. The area inside the curve represents the energy lost to heat and residual vibration.
Apparatus and Methodology
The ball is propelled toward a piezo disk mounted against a wall. The ball/wall force was measured using the piezo disk, a charge amplifier and an A/D converter sampling at 16kHz. The inbound and rebound velocities were measured using a speed gate.
Average force was calculated using the change in momentum of the ball divided by the contact time. Ball acceleration vs time was calculated knowing the A/D readings v time, the average force and ball mass. Ball velocity was calculated by numerically integrating the acceleration and using the initial inbound velocity. Ball distance was calculated by numerically integrating the ball's velocity.
For further details see Dynamic properties of tennis balls by Rod Cross.
Force, Distance, Velocity and Time of a Lifetime ball at 6 Points of Interest Around the Stiffness Loop
Dynamic stiffness of a Lifetime ball with six points of interest.
1 The ball is just touching the wall at time zero. The ball is approaching the wall at 52 mph. The reference distance of the ball's center of mass (CM) is zero inches. There is no force exerted by the wall
2 Time = 0.18 msec. The ball's momentum begins compressing the ball against the wall. The ball face begins flattening against the wall. The CM has moved 0.15". The force exerted by the wall is 203 pounds. The force has caused the ball to slow to 43 mph.
3 Time = 0.36 msec. The ball's CM has moved 0.23" and the ball face has flattened against the wall. The force exerted by the wall is at a maximum of 350 pounds. The force has caused the ball the slow to 20 mph.
4 Time = 0.59 msec. The ball's CM has moved to a maximum distance of 0.26" and the ball face is still flattened against the wall. The force exerted by the wall has decreased to 150 pounds. The ball has reversed direction at 1 mph. The kinetic energy provided by the initial 52mph velocity is gone and the potential energy stored in the ball is accelerating the ball in the opposite direction.
5 Time = 1.19 msec. The ball's CM is returning toward its original position and has decreased to 0.12". The ball face is still flattened against the wall. The ball is decompressing and the decompression is exerting a force of 40 pounds. The decompression force has increased the rebounding speed to 18.9 mph.
6 Time = 1.54 msec. The ball's CM has returned to the starting position of zero inches. The ball has separated from the wall. The ball has returned to round. The ball has reached the maximum rebound speed of 19.6 mph. All the ball's potential energy is gone.
Old v New X40 Comparison at 6 Points of Interest
Most players have experienced the difference between a new and well used ball. The new ball is stiffer and faster. The old ball is softer and slower. The difference in behavior is reflected in the dynamic stiffness. The dynamic stiffness is plotted for both a new Franklin X40 and a well used X40. Both balls are shot at a wall at 51 mph. The new ball rebounds at 16 mph; the old ball at 10 mph. The force, distance, time and velocity for the old X40 are explored at 6 points of interest.
1 Time = 0.18 msec. Both the new and old X40 perform similarly a low forces (<100 lb). The momentum begins to compress both balls against the wall. The ball face begins flattening against the wall. The CM has moved 0.18". The force exerted by the wall is 203 pounds. The force has caused the ball to slow to 46 mph.
2 Time = 0.42 msec. The old X40 demonstrates that it has become softer (less stiff). Both ball have compressed by 0.3", but the new stiffer X40 requires over 275 lb while the old softer X40 requires only 206 lb. The force has caused the ball the slow to about 30 mph.
3 Time = 0.95 msec. The ball's CM has moved to a maximum distance of 0.42" and the ball face is still flattened against the wall. The force exerted by the wall has decreased to 18 pounds. The force has caused the ball's velocity to almost slow to zero. Kinetic energy is near zero while potential energy is at a maximum.
4 Time = 1.84 msec. The velocity has reversed direction
and has increased to 9.9 mph due to the force exerted by the decompressing ball during the time between step 3 and 4. What's unusual is the zero force exerted by the [supposedly] decompressing ball.
5 Time = 2.08 msec. The force exerted on the wall by the ball is zero. The velocity of the ball is still 9.9 mph. The ball's distance from the original starting position is deceasing meaning the ball is not touching the wall. The ball has dimpled; has not had time to return to round; has separated from the wall; and therefore, cannot add any additional speed to the rebounding ball.
6 Time = 3.9 msec. The ball has returned to the original starting position. There is no force sensed at the wall meaning the ball is still dimpled. The soft old X40 is traveling toward the opponent at 9.9 mph while the new X40 would be speeding along at 16 mph. The dimpled ball will eventually return to round, but the energy will be uselessly dissipated as vibrations.
Static Stiffness v Dynamic Stiffness
The static stiffness of several balls has been measured at pickleballscience.org and ranges from 112 lb/in to 171 lb/in at room temperature. Thus, if a 25 pound dumbbell is placed on top of an X40 ball (stiffness 112 lb/in) it should compress by about 0.22". A rough measurement recorded a compression of 0.24". This confirms that the static stiffness of this new X40 ball is about 112 lb/in.
In contrast, the dynamic stiffness of a new X40 in the graph is about 750 lb/in. Why the discrepancy?
First, static stiffness is a two sided compression - both the top and bottom of the ball compress. The dynamic stiffness is a one sided compression - only the side impacting the wall is compressed. The two sided static stiffness should be multiplied by two to 224 lb/in. But there is still a difference between 224 and 750.
The remaining difference is due to the nature of plastics subjected to static loads vs dynamic loads (impacts). During static loading the polymer chains have time to stretch and/or slide over each other resulting in low stiffness. During the compression phase of an impact, there is insufficient time for polymer chain movement and, hence, the stiffness is much higher. During the decompression phase the polymer chains have time to move and the stiffness approaches static stiffness. For reference, in a 2014 article entitled Impact of sports balls with striking implements by Rod Cross he comments on dynamic v static stiffness by saying, "The
stiffness during a rapid compression is typically several times larger ...".
The Circled Area
The circled area denotes a discontinuity in the stiffness plot. The discontinuity occurs when the ball has switched from compression to decompression (velocity changes direction) at velocities exceeding 45 mph. Similar behavior is observed from other balls. Most likely this is due to the flattened ball "popping out" as it begins to return to round.
Stiffness at Various Inbound Velocities
The dynamic stiffness follows the same path during the compression phase. During the decompression phase (the lower half of the curve), the force is higher for the slower balls denoting relatively more energy returning to the ball as rebound velocity and less being dissipated in the ball in the form of heat or vibration. Or stated differently the coefficient or restitution (COR) is higher at lower speeds.
Vin=13; Vre=9; COR=0.69
Vin=27; Vre=16; COR=0.59
Vin=34; Vre=18; COR=0.53
Vin=42; Vre=19; COR=0.45
Vin=50; Vre=17; COR=0.34
Stiffness of 5 Balls
The dynamic stiffness of 5 balls is graphed.
Note: The Franklin holeless ball is the fastest ball with a rebound speed of 21 mph. This ball is a duplicate of the X40, but the holes have not been drilled. The exceptional speed comes from the increasing internal pressure as the ball flattens against the wall. The increased pressure reduces the extent of "speed-killing" dimpling. The ball is used exclusively by USAP for PBCOR testing and is unavailable to the general public.
