1. T ENNIS S TRING T ENSION Landon Chin Physics Form A

2. O BJECTIVE The goal of this project is to determine how variations in string tension of a tennis racquet will affect playability A playability score was generated for three different string tensions on the same racquet High 65 lbs Med 60 lbs Low 55 lbs Each string tension was scored by the following: Power Comfort Control Spin Accuracy

3. P ROCEDURE 1. String tennis racquet (Babolat AeroPro Drive) at high tension – 65 lbs 2. Use a tennis ball machine to project balls to the deuce court baseline (forehand side) 3. Stroke the ball cross-court into the opposing singles deuce court. 4. Record the placement of ball landing 5. Repeat for 70 forehand strokes 6. Record score (out of 10) for 1. Power 2. Comfort 3. Control 4. Spin 5. Accuracy 7. Calculate overall performance score 8. Repeat steps 1-7 with 1. Medium tension – 60 lbs 2. Low tension – 55 lbs

4. V ARIABLES Forehand stroke repeatability Bounce of tennis balls projected from machine Dead balls were ignored Height of ball bounce on racquet impact Effort to keep stroke consistent for each ball String tension loss after stringing Racquet was tested the same day as strung to minimize tension loss. Contact location and on stringbed Effort to stroke ball in sweetspot of stringbed Racquet head angle on contact Consistent natural topspin stroke (Western Grip)

5. H YPOTHESIS 55 will have the most power and topspin 55 will have most comfort 65 will have the best ball placement and accuracy 55 will have the highest score, then 60 and 65 60 will highest score combination of power and control Comfort will have the least change between string tensions Power and Accuracy will have the most change

6. W HAT IS T ENNIS S TRING T ENSION ? Tightness at which the strings are set in the frame of the tennis racquet Affects the power the racquet will generate and transfer to the ball Tension affects power, control, and comfort Most racquets have a recommended tension range Typically 50 – 60 lbs or 55 – 65 lbs Higher tension: more control, less comfort Lower tension: more power, more comfort Racket strings return 90% of force Tennis balls return 55% of force

7. T ENSION : S HOT P OWER & B ALL C ONTROL In general, lower tension produces more power Lower tension allows the strings to bend more when striking a ball Stores more energy before it whips back transferring it into the ball Control is defined as the ability to place the ball with the desired speed and spin to a particular area of the opponent’s court Affects the ball opposite of power More tension – More control A tighter strung racquet will cause the ball to deform more when it contacts (since it is more like striking a solid wall) which allows the angle at which it bounces to be more exact than the trampolining caused by looser strings

8. O BSERVATIONS

9. TensionPowerComfortControlSpinAccuracyOverall 65 5697936 60 8887839 55 9958536

10. V ELOCITY AND F ORCE C OMPONENTS a) Velocity components on impact b) Force components of ball on racquet c) Reaction force components of racquet on ball F N – normal (perpendicuar) forces pushes the ball off the strings and responsible for the racquets power F r – friction (parallel) forces influences the rebound angle by slowing the ball's tangential speed as it slides across the stringbed (v x ), and it changes the speed and direction of the spin (ω) Reaction force increases with decreasing string tension

11. B OUNCE M ODEL F OR B ALL I NCIDENT O N S TRINGS The symbols represent the following parameters: ω 1 — The angular velocity (spin) of the incident ball (radians/sec). ω 2 — The angular velocity of the rebounding ball (radians/sec). v 1 — Incident velocity of ball (m/s). v 2 — Rebound velocity of ball (m/s). v y1 — Component of incident velocity perpendicular to stringbed (m/s). v y2 — Component of rebound velocity perpendicular to stringbed (m/s). v x1 — Component of incident velocity parallel to stringbed (m/s). v x2 — Component of rebound velocity parallel to stringbed (m/s). θ 1 — Incident angle measured from perpendicular to stringbed (degrees). θ 2 — Rebound angle measured from perpendicular to stringbed (degrees). F — Friction force acting opposite to the direction of the bottom of the incident ball (Newtons). N — Normal reaction force of strings on ball (equal and opposite of force of ball on strings) (Newtons). R — Radius of ball = 0.033 m. D — The offset distance between a radius to the center of mass and the net action of the normal force (mm) V x — Component of racquet impact point rebound velocity parallel to stringbed (m/s). V y — Component of racquet impact point rebound velocity perpendicular to stringbed (m/s).

12. S TRING DEFLECTION &B ALL D EFORMATION

13. B ALL D EPTH VS. S TRING T ENSION <> HIGH LOW MED

14. H IGH T ENSION B ALL P LACEMENT

16. L OW T ENSION B ALL P LACEMENT

17. M ED T ENSION B ALL P LACEMENT

18. T ENSION VS F LIGHT P ATH Ball clearance over the net increased with decreasing tension which indicates that lower tensions produce greater rebound angles off the racquet stringbed LOW HIGH MED

19. C ONCLUSION 60 had the highest score 55 had most topspin and power 65 had highest control Spin changed the least Control, Accuracy, and Power changed the most Recommended tension for power: 56-58 Recommended tension for control: 62-64 Recommended tension for consistency: 59-61 Extreme power: 55 and lower More control: 65 and higher I would use a tension slightly lower the 60 to I can keep the ball deep without overhitting

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