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:

Coefficient of impact e

8,054,2

473,1

7,054,2

346,1

MAX

MIN

e

e

It is effective for the :

Different coefficients of impact

rubber ball: 0,9

golf ball: 0,84

baseball: 0,5

Experiments of Balldeformity

double load = double deformity

Hooke‘s lawdouble force double way of the feather!!!!!

Hooke´s law: F = k *x

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)

Sweet Spot

Rotation of theBack-Spin Top-Spin

Drive

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!

Reading with the help of the sensors

2 kinds of playing tennis

ForehandServe

Forehand

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

What a tennis teacher has to know

s=g/2 * t2

t2 = 2s/gt 0,43s

v = s/t 28m/s 100km/h

Serve

Serve

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

The worldrecord of serving:

13.4.2004

Andy Roddick

150 mph

Rotationtable

Rotationtable

We hope you have enjoyed our presentation

A presentation from: Raphaela Böhm, Petra Fegerl, Evelin Nagelmaier, Verena Weinberger

And we are grateful for the help of our teacher

MR. BINDER