![CoR is a Material Control]()
CoR is a Material Control
Coefficient of restitution can be measured a number of ways. We do not think this metric is needed in pickleball but we do recognize that it has the value as a control for materials. It should be openly used for that purpose though and use thoughtfully.
When a ball from a cannon is shot at a paddle the angle will directly influence the measured coefficient of restitution as well as outbound law velocity and angle. To be clear we assume this method will not be used to measure exit velocity.
Consider low angles (θ ≈ 0 degrees)
When θ is small, cos(θ) is close to 1. Thus:
v_in,n ≈ v_in
The COR can be expressed as:
e_low = v_out / v_in
Since v_in,n is close to v_in, energy transfer is efficient, leading to a stable and representative COR.
At High Angles (θ ≈ 90 degrees)
Normal Component:
For large θ, cos(θ) becomes very small. For example, at θ = 89 degrees:
cos(89 degrees) ≈ 0.0175
If v_in = 10 m/s:
v_in,n ≈ 0.175 m/s
The rebound velocity v_out is then:
v_out ≈ e_high * v_in,n
Given the small v_in,n, v_out is reduced, leading to a lower COR:
e_high ≈ v_out / (v_in * cos(θ))
Simply put coefficient of restitution has a greater effect on outbound ball velocity as angle increases. Performed at low angles paddles which would be ideal and representative of both material and play testing would be literally mathematically meaningless. If you want to measure it you can download phyphox and do it at home with an anchored paddle. Pro tip if you don't have a cannon use gravity.
There are no clear goals or needs for this. Coefficient of restitution restricts materials directly. Has an indirect effect on ball speed conditionally at high angles but this metric has next to no effect on it at low angles which are representative of play.
Impact velocity is another can of worms but acts as an integer. At higher angles higher ball speeds will create a greater distribution of coefficient of restitution among tested paddles than at lower impact angles.
In this young sport introducing such a severe restraint on materials is not reasonable. Putting a cap on ball speed would essentially solve the reported issues whose existence is even questionable based on their data collection.
Going after the actual problem is the correct way to solve it. That is not how the usap works though as with coefficient of friction they go after secondary factors first. To be clear we consider this essentially an attempt to control materials and preserve large manufacturers ability to sell paddles without having to actually innovate. Introducing a ball speed cap would be far more reasonable. It would allow for innovation and solve the problem.
We strongly predict that the usap will introduce a coefficient of restitution at around 0.65 but certainly less. This will in effect work to control ball speed indirectly but have the added effect of strongly controlling materials. We hope manufacturers will take note of this and take action especially smaller manufacturers.
