Experimental Mechanics

, Volume 44, Issue 2, pp 195–206

Ball spin generation for oblique impacts with a tennis racket

  • S. R. Goodwill
  • S. J. Haake
Article

DOI: 10.1007/BF02428179

Cite this article as:
Goodwill, S.R. & Haake, S.J. Experimental Mechanics (2004) 44: 195. doi:10.1007/BF02428179

Abstract

In this paper, we describe an experimental investigation of the oblique impact between a tennis ball and head clamped tennis racket. It was found that the magnitude of the ball rebound spin was not a function of the material, gage or tension of the string used in the tennis racket. Furthermore, it was concluded that all strings exhibit a sufficiently large friction coefficient that the ball begins to roll during impact. There is anecdotal evidence from tennis players that suggests that a high string tension or a rough string surface enable them to impart more spin to the ball. For example, players have been quoted as saying that a high string tension makes the strings “bite” into the ball, giving more spin. The data reported in this study do not support these observations. Analysis of the experimental data has shown that the balls are rebounding from the surface with more spin than would typically be associated with rolling. A second experiment showed that the balls commenced rolling at the mid-point of the impact. This information was used in a theoretical model to show that the spin that acts on the ball during the impact can be higher than the value of the rolling spin at the end of the impact.

Key Words

Tennisballracketspin

Nomenclature

AK

ball compression factor

F

friction force

R

reaction force

rB

radius of undeformed ball (=32 mm)

r(t)

radius of ball (at time=t)

r(MID)

radius of ball (at the mid-point of impact)

t

time

TC

contact time

Ux(f)

stringbed velocity parallel to string plane (at the end of the impact)

VB(i)

inbound ball velocity

VB(f)

rebound ball velocity

Vx(i)

inbound ball velocity parallel to string plane

Vy(i)

inbound ball velocity normal to string plane

Vy(f)

rebound ball velocity normal to string plane

Vx(f)

rebound ball velocity parallel to string plane

Vx(t)

ball velocity parallel to string plane (at time=t)

Vy(t)

ball velocity normal to string plane (at time=t)

Vx(MID)

ball velocity parallel to string plane (at the midpoint of the impact)

ω(i)

inbound ball spin

ω(f)

rebound ball spin

ω(MID)

ball spin (at the mid-point of impact)

ω(ROLL)

rolling spin (ball leaving surface)

μS

coefficient of sliding friction

θB(i)

inbound angle of trajectory

θB(f)

rebound angle of trajectory

Copyright information

© Society for Experimental Mechanics 2004

Authors and Affiliations

  • S. R. Goodwill
    • 1
  • S. J. Haake
    • 1
  1. 1.Sports Engineering Research Group, Department of Mechanical EngineeringUniversity of SheffieldUK