The Ball's Surprising Behavior
8/28/25
As kids, we've all thrown a rubber ball against a wall and caught the rebound. We've come to expect that if we throw the ball faster toward the wall it will rebound back to us faster. But a pickleball ball's behavior is unusual and surprising. There is a point where throwing the ball faster results in a rebound speed that is slower! It all depends on how much the ball deforms as it impacts the wall.
The article explores -
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the "fold over" of the rebound velocity
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the behavior of four different balls
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the time the ball is in contact with the wall (or ground) during impact
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the force profile developed by the impact
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implications for paddle design
So, why are we concerned with how a ball bounces off a wall or the ground? Shouldn't we be more concerned with how the ball bounces off the paddle face? The explanation is that it's easier to understand the complex behavior of a two element collision (ball & paddle) once both of the elements are understood separately. Future articles will isolate the paddle's performance by exploring the response to a steel ball impact. Eventually the ball/paddle impact will be explored. Issues such as power, pop, dwell time and plushness will be addressed.
This graph depicts the rebound velocity of a Franklin X40 ball as a function of the inbound velocity. If the X40 behaved as a typical rubber ball the plot would follow a straight line as depicted by the blue arrow. Below inbound velocities of 20 mph (dinking speeds) the X40 follows the straight line mimicking the behavior of a rubber ball in that limited region with the rebound velocity being 66% of the incoming velocity.
However, above 20 mph the rebound velocity deviates away from the ideal line. Above 45 mph the rebound velocities "fold over". Surprisingly, the rebound velocity of a 60 mph ball (~12 mph) is less than that of a 25 mph ball (~14 mph).
The ball is shot at a marble slab using an air cannon. Both inbound and rebound velocities are recorded using a speed gate.
The Ball's Surprising Behavior
Ball Comparison
This graph compares the "bounciness" of four popular balls. Note that at inbound velocities below 20 mph all four balls behave identically. But at inbound velocities larger than 20 mph the Penn and Lifetime balls exhibit higher rebound velocities - They are more lively balls and play that way on the court.
All balls do not rebound repeatably. For instance, the Franklin ball in the 60 mph region has rebound velocities between 11 and 14 mph. This variability is probably due to whether the impact location of the ball face is on the hole, near the hole or away from the hole. The Penn ball has the least variability.
USAP requires a ball to bounce to a height of between 30 and 34 inches when dropped from a height of 78 inches (about 10 mph). This converts to a coefficient of restitution (COR or e) of between 0.62 and 0.66 (rebound velocity divided by inbound velocity). As shown by the straight line, all 4 balls have approximately the same COR of 0.66 at incoming velocities below 20 mph. USAP has no specification on behavior above 10 mph. Some balls (e.g. Penn Pro40, Lifetime) are more lively than others. Some balls (e.g. Franklin X40, Lifetime, Vulcan) exhibit more variability in rebound velocity.
For reference a superball would have a COR near 1. Putty would have a COR near zero. Tennis ball 0.71. Golf ball 0.85.
Temperature Sensitivity
Balls get softer at higher temperatures and play slower. A Franklin X40 was tested at three temperatures. What does this mean on the court?
During 70'F weather, a player blocking an approaching ball at 50 mph would expect the ball to rebound across the net at about 15 mph. During 100'F weather the same block would rebound across the net at about 12 mph or 3 mph slower.
At 70'F a player swinging the paddle at 50 mph would create a serve speed of 65 mph (50 +15). At 100'F a player swinging the paddle at the same speed 50 mph would create a serve speed of 62 mph (50+12). Or 3 mph slower.
During 40'F winter weather the ball "speeds up" about a half mph which is much less than the three mph "slow down" at 100'F.
Franklin X40 performance at three temperatures. Ball immersed in either an ice bath or heated bath before testing with an air cannon
Impact Duration
Pictured below is a six frame sequence of a typical ball (Vulcan) hitting the ground at about 60 mph and rebounding. In frame 1 the ball is round and is approaching the ground. The circles are added as an aide to identify when the ball is deformed. In frame 2 the ball has hit the ground at time zero. In frame 3 the ball has reached its maximum deformation at 0.85 msec and begins rebounding. A bulge at ground level is visible in frame 3. In frame 4 the back edge of the ball has left the ground at 1.7 msec. In fame 5 the ball has rebounded completely off the ground and is still deformed at 2.5 msec. The impact duration is approximately 2.5 msec. The ball snaps back to round in frame 6 at 6.0 msec. Sequence captured from a Pickleball Studio Instagram video.
Force Profile
If we're going to unlock the interaction of the ball and paddle it's important to understand the force exerted on the wall by the ball as a function of time. There is some well developed science explaining the ball/bat impact in baseball that can be applied to the ball/paddle impact if the force profile is known.
Three piezoelectric discs were used to measure the force during the ball/wall impact at several inbound velocities.
Force profile of a Franklin X40 at 60 mph. The ball initiates impact with the wall at time zero and begins slowing down from an inbound velocity of 60 mph. The ball begins compressing and deforming. At 0.5 msec all the kinetic energy has been converted to potential energy. The ball has zero velocity and begins to rebound. At 1.0 msec there is a secondary peak probably due to one of the deformations "unwinding". At 1.5 msec the force is near zero and almost all the potential energy has been converted to kinetic energy. The ball has increased it's rebound velocity to near 14 mph. At 1.8 msec there is a tertiary peak possibly due to the ball vibrating or another deformation "unwinding". The ball exits contact with the wall with a rebound velocity of 14 mph.
Force profile of a Franklin X40 at 25 mph. A The ball initiates impact with the wall at 25 mph. B The ball velocity has slowed to zero; all kinetic energy has been converted to potential energy; the ball begins rebounding. C The ball exits contact with the wall at a velocity of 14 mph.
Force profile of a Franklin X40 at several inbound velocities. The force profile takes longer to develop and longer to unwind as the velocity decreases.
All 4 balls have similar force profiles.
Force Units
The piezoelectric disc was not calibrated, but the peak force in Newtons can be estimated . The average force can be calculated using the change in momentum and the impact time. The incoming momentum at 60 mph is 0.70 kg*m/sec. The rebound momentum at 14 mph is -0.16 kg*m/sec. The change in momentum is 0.86 kg*m/sec. The impact time is around 2 msec. The average force is 430 Newtons. The peak force is about 1.4 * 430 or 602 Newtons.
Apparatus
The ball is propelled toward the force sensor using an air cannon. The ball's force profile was measured using the integrated current signal from three 50 mm piezoelectric discs arranged in a triangle formation and wired in parallel. The current was sensed at 10 kHz as a voltage across a 1 kohm resistor using the A/D converter in a Nano ESP32 processor. The disc was sandwiched between two printed circuit boards for protection and then clamped to an 8" concrete block.
Force profiles of 4 balls at an inbound velocity of 60 mph
Left: 50mm piezo disc with ball for perspective. Right: 3 piezo discs clamped to a concrete block.
Double Peaks - Tennis Ball
Double peaks in pickleballs are not unique. Double peaks in the force profile of a tennis ball were measured by Rod Cross in Dynamic properties of tennis balls. The second peak was "due to the internal bubble `popping' back out of the ball at the end of the impact".
Force profile of a tennis ball showing a double peak
Preliminary Results - Ball/Paddle Collision
Substituting a paddle for a wall mimics actual play, but adds complexity. The paddle is swinging (as it would if held by a hand) and begins moving away from the ball ( a block at the net) or slows down (a serve) as a result of the collision. The paddle face has "spingyness". Sometimes the face is a stiff spring (a control paddle); sometimes the face is a soft spring and acts like a trampoline (a power paddle).
A Penn40 ball was shot at 27 mph (dinking speed) toward two paddles - a Gen1 Joola Vision and a core crushed Pickleball Apes Pulse V. The ball rebound velocity from both paddles is the same. at 11 mph. Both paddles play similarly at this speed
The force profile (solid blue line) for the Vision is higher and narrower as might be expected from a stiff faced Gen1 paddle. The Vision might feel "poppy" as the impact force is higher and the ball leaves the face quickly at about 1.3 msec.
The force profile (dotted blue line) for the PulseV is lower and wider as might be expected from a "trampoline" power paddle. The PulseV might feel "plush" as the impact force is lower and the ball is in contact with the face longer at 2 msec. The face vibrates at a frequency of about 480 Hz
The apex of both profiles occurs at about half a millisecond and is coincident with a ball/wall force profile (orange line) at a similar speed (20 mph). There is no double peak visible at this low speed.
At a higher incoming velocity the picture becomes more complicated. The ball impacts both paddles at about 50 mph. The rebound velocities are quite different with the Vision at 9 mph and the PulseV at 15 mph. The Vision vibrates at about 1200 Hz; the PulseV at 480 Hz.
The Vision has a secondary peak at 2 msec (circled in green); the PulseV at 1.5 msec. Neither coincides with the 50 mph Penn40 ball/wall collision.
More experimentation needed!
Apparatus
The paddle's force profile was measured using the integrated current signal from a 16 mm piezoelectric disc. The current was sensed at 10 kHz as a voltage across a 1 kohm resistor using the A/D converter in a Nano ESP32 processor. The disc is attached to the paddle face using double sided tape at a location 12" from the butt.
The paddle was pivoted at the 2" from the butt location. The ball was shot toward the paddle with an air cannon.
