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:Definition of the coefficient of impact e:It follows:

Coefficient of impact eIt is effective for the :

Different coefficients of impactrubber ball: 0,9

golf ball: 0,84

baseball: 0,5

Experiments of Balldeformitydouble load = double deformity

Hookes lawdouble force double way of the feather!!!!!Hookes law: F = k *x

Period of oscillation and contact time of the Period of oscillation T = 10 - 12mscontact 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 stringDifferent 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 Mcnroe)

Sweet Spot

Rotation of theBack-SpinTop-SpinDrive

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 balls felt are carried away.This effectuates that the airstream speads up the ball.Bernoulli-equationLift or downward pressure!!

The Magnus effect in tennisThe 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 tennisForehandServe

Forehand

Rotationtable

Tabelle1

Shot: Men's Forehand

PlayerRPM RangeAvg RPM

Sergi Bruguera2941-3751 rpm3331 rpm

Thomas Muster1500-3750 rpm2882 rpm

Marcelo Rios1875-3750 rpm2647 rpm

Mark Philippoussis2143-2727 rpm2546 rpm

Jim Courier938-3264 rpm2527 rpm

Michael Chang1271-3192 rpm2334 rpm

Pete Sampras1000-3409 rpm1842 rpm

Andre Agassi1154-3333 rpm1718 rpm

Todd Martin1154-2308 rpm1659 rpm

Tim Henman833-2000 rpm1288 rpm

Petr Korda968-2500 rpm1333 rpm

Tabelle2

Tabelle3

Rotationtable

Tabelle1

Shot: Women's Forehand

PlayerRPM RangeAvg RPM

Venus Williams1071-3488 rpm2154 rpm

Mary Pierce1667-2500 rpm1941 rpm

Arantxa Sanches1875-2000 rpm1916 rpm

Anna Kournikova1154-2143 rpm1713 rpm

Jana Novotna1500-1875 rpm1673 rpm

Lindsay Davenport1271-3192 rpm1346 rpm

Monica Seles790-1829 rpm1215 rpm

Martina Hingis600-2143 rpm1147 rpm

Mary Jo Fernandez417-1500 rpm1068 rpm

Tabelle2

Tabelle3

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 knows=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-sensorWhat you have to know:

arm+masse of the racket weigh

destine a with the wrist-sensor

contact time = 5ms

masse of the ball = 0,058kg

The worldrecord of serving:13.4.2004

Andy Roddick 150 mph

Rotationtable

Rotationtable

We hope you have enjoyed our presentationA presentation from: Raphaela Bhm, Petra Fegerl, Evelin Nagelmaier, Verena WeinbergerAnd we are grateful for the help of our teacher MR. BINDER