The Rules of Tennis
There are no requirements in the ITF Rules of Tennis regarding Court Pace Ratings and Certification. The ITF programs that provide those measurements and assessment services are in support of court construction, rather than rules conformance. It is understood that there will be a wide range in the speed of various court surfaces. If you have watched a professional match that included a court speed graphic, the odds are very high that it was not the ITF Court Pace Rating at all.
Court Pace Index (CPI) uses the Hawk-Eye triangulation system to calculate the speed of the court based on match play. It is published on occasion by TennisTV, the official streaming channel of the ATP tour. Typically it is presented as an average calculated over a complete tournament.
According to TennisTV, CPI is calculated from the following mathematical formula:
CPI=100(1-μ)+150(0.81-e)
μ is the coefficient of friction
e is the coefficient of restitution
The coefficient of friction is essentially a ratio of the force required to move an object and the resistive force of the surface. The smaller coefficients are “slippery” and larger ones are more “grippy.” The coefficient of friction can change as the court surface is worn down and under changing weather conditions.
The coefficient of restitution is the relative speed between two objects after they collide. This can be tough of as elasticity. Essentially it is a measurement of how the kinetic energy is preserved during the collision. The coefficient of restitution has been shown to vary based on the speed of the ball at the point of collision, so it is likely that an average value is used.
Data from the Hawk-Eye system is used to calculate the coefficient of friction and the coefficient of restitution. My assumption is that friction is determined based on velocity numbers before and after the ball bounces on the plane parallel to the tennis court. The coefficient of restitution is measured off the velocity before and after the bounce along vertical plane of the trajectory of the ball.
From a practical standpoint, CPI is more informative as it captures real time data on how a particular court is playing. It also captures variable conditions such as the impacts of changing temperature and humidity. It can also illustrate how the speed can vary from court to court at a facility.
- Tennis Court Surfaces and Court Speeds, perfect-tennis.com, March 25 2020.
- Court Pace Index Explained, perfect-tennis.com, November 19, 2018.
- Coefficient of Restitution of a Tennis Ball, Andre Roux, ISB Journal of Physics, June 2007.
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