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.
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Abbreviations
- A K :
-
ball compression factor
- F :
-
friction force
- R :
-
reaction force
- r B :
-
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
- T C :
-
contact time
- U x(f) :
-
stringbed velocity parallel to string plane (at the end of the impact)
- V B(i) :
-
inbound ball velocity
- V B(f) :
-
rebound ball velocity
- V x(i) :
-
inbound ball velocity parallel to string plane
- V y(i) :
-
inbound ball velocity normal to string plane
- V y(f) :
-
rebound ball velocity normal to string plane
- V x(f) :
-
rebound ball velocity parallel to string plane
- V x(t) :
-
ball velocity parallel to string plane (at time=t)
- V y(t) :
-
ball velocity normal to string plane (at time=t)
- V x(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)
- μ S :
-
coefficient of sliding friction
- θ B(i) :
-
inbound angle of trajectory
- θ B(f) :
-
rebound angle of trajectory
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