Tennis and Physics
The and his features
Diameter: 6,35 - 6,67cm Wheight: 56,70 - 58,47g Jumphight: 1,346 -
1,473m on hard floor from 2,54m height of fall (20° C temperature)
Coefficient of impact eThe conservation of energy is effective:
ghv
mvmgh
EE KINPOT
2
2
2
1
1'
v
ve Definition of the coefficient of impact e:
1
1
1
1'* *2
' * *2
hh
h g
h ge It follows:
Period of oscillation and contact time of the
Period of oscillation T = 10 - 12ms
contact time T/2 = 5 - 6ms
Contact time of the racket
The contact time is approximately 15ms!
The time is too big to make a contribution for the ball. That means that the racket ,,wastes“ energie!
The oscillation is available and doesn`t pass over the ball, but loads the wrist and mainly the ellbow.
Tennisellbow!
Contact time of the string The contact time is 5 ms and that is the same as that from the ball!
Attention: „Vibrastop“ losses the oscillation of the string!
Contact time of the string
Different strings are a result of clamping different weights of the strings in the racket. It is effective that there are soft and hard strings.
The hard strings are very good for the controlled Top-Spin-Game, but not for very fast and varied game. (Thomas Muster)
The soft string is very difficult to play but you can bang very hard and strong balls, because of the elasticity of the soft strings like a trampoline does. (John McÉnroe)
Magnus effectThe Magnus effect has his name of his inventor Gustaf Magnus!
No spin of the ball causes that the airstream regularly streams over and under the ball.
If you play the spin, the air molecules in the ball‘s felt are carried away.This effectuates that the airstream speads up the ball.
Bernoulli-equationLift or
downward pressure!!
The Magnus effect in tennis
The Magnus effect is specially set in by playing the back and the topspin.
First because the magnus effect changes the trajectory of the ball!
To effectuate different effects at the time of the impact of the ball in the field!
To change the interplay between the ball and the racket because of the spin!
Rotationtable
Player RPM Range Avg RPMSergi Bruguera 2941-3751 rpm 3331 rpmThomas Muster 1500-3750 rpm 2882 rpmMarcelo Rios 1875-3750 rpm 2647 rpmMark Philippoussis 2143-2727 rpm 2546 rpmJim Courier 938-3264 rpm 2527 rpmMichael Chang 1271-3192 rpm 2334 rpmPete Sampras 1000-3409 rpm 1842 rpmAndre Agassi 1154-3333 rpm 1718 rpmTodd Martin 1154-2308 rpm 1659 rpmTim Henman 833-2000 rpm 1288 rpmPetr Korda 968-2500 rpm 1333 rpm
Shot: Men's Forehand
Rotationtable
Player RPM Range Avg RPMVenus Williams 1071-3488 rpm 2154 rpmMary Pierce 1667-2500 rpm 1941 rpmArantxa Sanches 1875-2000 rpm 1916 rpmAnna Kournikova 1154-2143 rpm 1713 rpmJana Novotna 1500-1875 rpm 1673 rpmLindsay Davenport 1271-3192 rpm 1346 rpmMonica Seles 790-1829 rpm 1215 rpmMartina Hingis 600-2143 rpm 1147 rpmMary Jo Fernandez 417-1500 rpm 1068 rpm
Shot: Women's Forehand
What a tennis teacher has to know
Principle of independence of the motion!
Height of the net: s = 91cmdistance of the net-baseline: 12macceleration of gravity: 10m/s2
The Speed of the Serve with the Help of the wrist-
sensor
What you have to know:
arm+masse of the racket weigh
destine a with the wrist-sensor
contact time = 5ms
masse of the ball = 0,058kgB
ASB m
tamv