The Physics of Tennis by Blake Sharin Introduction

The Physics of Tennis by Blake Sharin

Introduction • • • The Sweet Spots Vibration Node Centre of Percussion The Dead Spot Coefficient of Restitution

The Sweet Spot • Two Sweet Spots – Vibration Node – COP • Force Transmitted to hand – Motions of the handle • Rotation • Translation • Vibration • Maximum Speed of Ball

Vibration Node • Behaves like a Uniform Beam • Fundamental Mode • Frequency – 100 Hz for flexible frame – 140 Hz for stiff frame • Two nodes – Near the center of strings – Near the handle

Vibration Node (Contd. ) • Frequency is 2. 75 times the fundamental frequency • Not excited with any significant amplitude – Duration, T=5 ms – Peaks at Zero at f=1. 5/T=300 Hz • Close to second mode frequency

Centre of Percussion • Known as the impact point • Conjugate points – Impact near tip • Axis of rotation is about ½ way between the end of the handle and the CM – Impact near throat • Axis of rotation is beyond the end of the handle

Power Swinging • More power when you swing at the ball near throat of racquet. • When ball hits near the throat of racquet, the ball will have more ball speed. • Heavier the racquet, more speed applied to the ball • Many types of racquets

Coefficient of Restitution • Main factor in the formation of a tennis racquet • Ratio of rebound height to incident height of the ball • COR varies when the ball bounces off a certain spot on the racket • Maximum power is when COR is greatest • COR=square root of Rebound height/initial height

COR Data • • • Center of Mass 1 st set: hd = 20 cm, hr = 11 cm 2 nd set: hd = 40 cm, hr = 22 cm 3 rd set: hd = 60 cm, hr = 33 cm 4 th set: hd = 80 cm, hr = 44 cm 5 th set: hd = 100 cm, hr = 55 cm • • • Tip of Head 1 st set: hd = 20 cm, hr = 12 cm 2 nd set: hd = 40 cm, hr = 24 cm 3 rd set: hd = 60 cm, hr = 36 cm 4 th set: hd = 80 cm, hr = 48 cm 5 th set: hd = 100 cm, hr = 60 cm • • • Near Throat 1 st set: hd = 20 cm, hr = 8 cm 2 nd set: hd = 40 cm, hr = 16 cm 3 rd set: hd = 60 cm, hr = 24 cm 4 th set: hd = 80 cm, hr = 32 cm 5 th set: hd = 100 cm, hr = 40 cm • • COR (center of mass): . 74162 COR (near the throat): . 63246 COR (tip of the head): . 7746 hr = rebound height, hd = Initial height

COR Data Analysis • Rebound height remains constant • Best spot to hit the ball – Near tip – Center of mass – Disregard throat

The Dead Spot • Spot near the tip where ball doesn’t bounce at all – All of the energy is given to the racquet – Racquet doesn’t give any energy back to the ball • Effective mass of the racquet at that point is equal to the ball • Effective mass is F=ma, therefore m=F/a • When serving, the best place to hit the ball is at the dead spot • When returning, dead spot is the worst

Strings on the Racquet • Act as a medium – Absorb much of the ball’s kinetic energy – Returns some of that energy back to the ball • Tighter strings produce slower ball speeds • Loose strings – Leads to slightly higher rebound velocities • More power

Conclusion • Performance of the racquet – Strings – Size of the head • Larger the head = more speed applied to ball – Game depends on two main things • How well you hit with the racquet • The “spot”

Bibliography • Brody, H. (1979) Physics of the tennis racket. American Journal of Physics 47, 482 -487 • Brody, H. (1981) Physics of the tennis racket II: The sweet spot. American Journal of Physics, 49, 816 -819. • Brody, H. (1995) How would a physicist design a tennis racket? . Physics Today, 48, 26 -31 • Pallis, Jani. "The Flight of the Tennis Ball" www. Tennisserver. com