The Forehand: Slice vs. Topspin Pranav Reddy

Background The 3 basic strokes: -topspin- offense or defense -slice: defensive -flat- offensive I will concentrate on the first two

Grips

Professional Topspin shot http://www.youtube.com/watch?v=pM0jYWfVFMw&feature=related

Professional Slice http://www.youtube.com/watch?v=wFcamvUEulQ

Kinetic Chain -Power in tennis is generated via muscles working together as a chain -transfer of energy from one part of body to another -the arm alone won’t generate enough power

Kinetic Chain: Transfer of energy Kinetic chain starts in lower body Begins in feet: power is created as feet push off ground Lower legs (calves) Upper legs (quadriceps and hamstrings) Gluteus maximus

Kinetic Chain: Transfer of Energy Energy then transferred to hips( abductors and adductors) and core; used for rotation Pectorals Shoulder(deltoids) Upper arm (biceps) Forearm (brachialis) hand

Tennis Injuries But I will focus on more common injuries…

Overuse Injuries Tennis elbow Bursitis of elbow Rotator cuff tendonitis Shoulder tendinitis Frozen shoulder Wrist tendonitis

Acute Injuries Wrist sprain Shoulder separation Torn rotator cuff Therefore proper form and training needed

Experiment Compare the topspin and the slice shots Differences in racquet contact Differences in spin Differences in translational kinetic energy Differences in rotational KE

Contact and spin slice stroke: racquet head cuts under the ball topspin: racquet face comes over the ball This difference in contact leads to differences in KE See my videos

Differences in KE KE=1/2(mv^2) KE is transferred from racquet to ball Rotational KE(1/2 Iw^2) See results next slide

Topspin: Translational KE Mass of tennis ball: 0.58 kg Initial X- velocity of ball: 1.81 m/s Initial Y- velocity of ball: 1.32 m/s total initial velocity: 2.24 m/s Initial KE= 0.5(0.058)(2.24^2)=0.1455 Joules X-velocity after: 20.2 m/s Y-velocity after: 10.4 m/s Total velocity after : 22.72m/s KE after: 0.5(0.058)(22.72^2)=14.97 Joules

Topspin: KE Rotational assume ball is coming at racquet with no spin; rotational KE is not a factor before impact Rotational KE after 1 revolution of ball took 4 frames Camera shot in 240 frames per sec Time for one full rev (T)= 4/240= 0.0167 sec Angular velocity(w)= 2pi/T= 376.3 rad/sec KE=0.5(I)(w^2)=0.5(3.96e-5)(376.3)=0.0074 J Note: the moment of inertia of tennis ball(hollow sphere) is equal to 2/3(m)(r^2) Now lets compare with slice….

Slice: Translational KE Initial X- velocity of ball: 1.85 m/s Initial Y- velocity of ball: 1.37 m/s total initial velocity: 2.30 m/s Initial KE= 0.5(0.058)(2.30^2)=0.1534 Joules X-velocity after: 14.7 m/s Y-velocity after: 5.1 m/s Total velocity after : 15.56m/s KE after: 0.5(0.058)(15.56^2)=7.02 Joules

Slice: KE rotational Again, assume ball is coming at racquet with no spin; rotational KE is not a factor before impact Rotational KE after 1 revolution of ball took 7 frames Camera shot in 240 frames per sec Time for one full rev (T)= 7/240= 0.029sec Angular velocity(w)= 2pi/T= 216.7 rad/sec KE=0.5(I)(w^2)=0.5(3.96e-5)(216.7)=0.0043 J Note: the moment of inertia of tennis ball(hollow sphere) is equal to 2/3(m)(r^2)

KE transfer A total of 14.83 Joules were transferred from racquet to ball in the topspin shot Whereas only 6.87 Joules were transferred in the slice shot Topspin case: 99.95% of ball’s KE after impact was translational Slice case: 99.94% of the ball’s KE after impact was translational

Conclusions Regardless of the type of shot, the rotational KE of ball after impact is very little compared to the translational KE of the ball after impact. The ratios of rotational KE to translational KE after impact were essentially the same for both shots. The type of shot certainly affects the amount of energy transferred from the racquet to the tennis ball. The topspin shot had a greater rotational KE transfer compared to the slice. This is expected: the racquet comes over the ball faster in a topspin shot than it does in cutting underneath the ball in a slice shot. If the racquet cuts too fast under the ball in a slice, this will result in a drop shot rather than a normal slice. The topspin shot also had a greater transfer of translational KE. This is expected since the topspin is more of an offensive shot therefore it is hit with a greater velocity, while the slice is more of a defensive shot and therefore is expected to involve a smaller transfer of translational kinetic energy.

Further Investigation -Many possibilities for future experiments Elasticity of strings: certain types and tensions The flat shot: quite powerful two handed vs. one handed: different players have different styles

Further Investigation Why does forehand tend to be more powerful compared to backhand? -uses deltoids and biceps rather than weaker muscles(triceps and anterior shoulder muscles) -uses more hip due to open stance, therefore more rotation

References http://sportsmedicine.about.com/od/tennisinjuries/a/tennisinjuries.htm http://www.livestrong.com/article/105577-muscles-body-used-tennis/ https://www.msu.edu/~jochmans/physicsoftennis.html

Thank You