The dynamic impact characteristics of tennis balls with tennis rackets

Abstract

The dynamic properties of six types of tennis balls were measured using a force platform and high-speed digital video images of ball impacts on rigidly clamped tennis rackets. It was found that the coefficient of restitution reduced with velocity for impacts on a rigid surface or with a rigidly clamped tennis racket. Pressurized balls had the highest coefficient of restitution, which decreased by 20% when punctured. Pressureless balls had a coefficient of restitution approaching that of a punctured ball at high speeds. The dynamic stiffness of the ball or the ball-racket system increased with velocity and pressurized balls had the highest stiffness, which decreased by 35% when punctured. The characteristics of pressureless balls were shown to be similar to those of punctured balls at high velocity and it was found that lowering the string tension produced a smaller range of stiffness or coefficient of restitution. It was hypothesized that players might consider high ball stiffness to imply a high coefficient of restitution. Plots of coefficient of restitution versus stiffness confirmed the relationship and it was found that, generally, pressurized balls had a higher coefficient of restitution and stiffness than pressureless balls. The players might perceive these parameters through a combination of sound, vibration and perception of ball speed off the racket.

Carbon outclasses wood in racket paddles: Ratings of expert and intermediate tennis players

“…Since the athletes' preferences (Question 4) were exactly in this order, it can then be presumed that as the coefficient of restitution increases, the racket becomes more favourable to the greatest number of tennis players. This is in line with Haake et al (2003), who suggested that tennis players prefer tennis balls of high stiffness, since they generally imply a high coefficient of restitution and are therefore perceived to fly faster off the racket.…”

“…Some studies have examined these issues in golf (Roberts, Jones, Harwood, Mitchell, & Rothberg, 2001;Roberts, Jones, Mansfield, & Rothberg, 2005a, 2005b and showed correlations between the feel of a shot and the vibration and sound of a club. Most of the other studies have either focused on the sweet spot of an implement (Carello, Thuot, Anderson, & Turvey, 1999;Cross, 1998;Haake, Carré, & Goodwill, 2003) or on the biomechanics (Cross, 1998;Stroede, Noble, & Walker, 1999) and have therefore dealt more specifically with the equipment rather than the athletes. To our knowledge, no study to date has focused on tennis players' perception of different mechanical and dynamic properties of rackets.…”

“…Our interest was mainly in the entire racket and how it is perceived as a whole rather than investigating the effect of the sweet spot. In this regard, racket paddles were ideal implements, since they do not have any preferred region to hit, although they do have a sweet spot, as any percussion device has (Haake et al, 2003;Timme & Morrisson, 2009).…”

Ritualized fighting and biological armor: the impact mechanics of the mantis shrimp's telson

“…The coefficient of restitution is most notably used to characterize and regulate a variety of objects that experience collisions, including automobiles, body armor, sports equipment, and even fruits and vegetables (e.g. Dikshit and Sundararajan, 1992;Haake et al, 2003;Jindal and Mohsenin, 1978;McHenry and McHenry, 1997;Nathan, 2003;Pang et al, 1992;Shenoy et al, 2001). The coefficient of restitution has the advantage of providing a quantifiable characteristic of impact to compare among structures of diverse shapes and sizes.…”

Simulation of the impact response of a sliotar core with linear and non-linear contact models

“…More specifically, the Kelvine-Voigt model predicts that contact forces at the beginning of the impact are discontinuous (due to the damping term being proportional to velocity alone), that coefficients of restitution do not vary impact velocity (which is inaccurate, as COR has been shown experimentally to decrease with impact speed) and that small attractive force terms appear directly prior to the separation of the bodies (when from physical reasoning, if the body has expanded back to its original dimensions, no net force should act upon it). Such deficiencies were also observed by Haake et al (2003) and Haake (2001,2004) [10,17,18]. None-theless,comparing the Hunte-Crossley model predictions to an analogous Kelvine-Voigt model can facilitate understanding of the impact process.…”