Biomechanics of a Tennis Serve Harry Choi BIOL

Biomechanics of a Tennis Serve Harry Choi BIOL 438 April 17 th, 2014

Tennis Serve • The initiating shot that starts every point of a tennis match • Stand behind the baseline and hit the ball cross-court over the net and the ball must land inside the service box diagonal to the player. • As the server, the player is in his/her most offensive and advantageous phase of the match • Can be viewed as one large kinetic chain

Muscles Involved in Tennis Serve Kinetic Chain Calves (Gastrocnemius and Soleus Muscles) Upper Legs (Hamstrings and Thighs) Butt (Gluteus Maximus and Medius) Abdominal, Obliques, Latissimus Dorsi and Erector Spinae Chest (Pectorals) Shoulder (Deltoids and Rotator Cuff Muscles) Upper back (Rhomboid and Trapezius Muscles) Upper Arms (Biceps, Triceps) Forearms (Flexor and Extensor) Basically almost every muscle in your body is engaged (Howard, 2013)

Objective • During a serve, players bend their knees before making contact with the ball. • How does knee flexion contribute to the overall velocity, power, force and energy delivered to the tennis ball? • Does knee flexion contribute to the rotational energy of the arm? Or are they just isolated movements (i. e. knee flexion only contributes to force via linear momentum)?

Tennis Serve – 8 Phase Model Preparation Acceleration Figure 1. Follow-Through (Kovacs & Ellenbecker, 2011)

Tennis Serve – 8 Phase Model Start Release Loading Lowest elbow vertical position Maximum knee flexion

Tennis Serve – 8 Phase Model Cocking Acceleration/Contact Maximal shoulder rotation Tip of racket points toward ground Deceleration/Finish

Velocity and Acceleration of Tennis Ball Knee Flexion Vavg = 32. 66 m/s aball = 1487 m/s 2 Δt = 0. 028 s

Velocity and Acceleration of Tennis Ball No Knee Flexion Vavg = 25. 48 m/s aball = 1335 m/s 2 Δt = 0. 028 s

Force, KE and Power delivered to Tennis Ball • Tennis Ball mball = 0. 057 kg No Knee Flexion • Forcetennis ball = ma = (0. 057 kg)(1335 m/s 2) = 76. 10 N • KE = ½mv 2 = (0. 5)(. 057 kg)(25. 48 m/s)2 = 18. 50 J • Power = W/Δt = 18. 50 J/ 0. 028 s = 660. 71 Watts

Rotational KE associated with service arm Analyze rotational motion from cocking to contact Knee flexion Cocking No Knee flexion Acceleration/Contact Cocking Acceleration/Contact Need to know Iarm (moment of inertia) and ω (angular velocity)

Moment of Inertia of Service Arm Angular Velocity of Service Arm (Xwrist , Ywrist) ΔY D α (Xshoulder , Yshoulder) Isolate rotational component of arm swing (Dempster, 2013)

Angular Velocity of Service Arm Knee Flexion Angular Velocity Calculation 1. 5 1 Radians 1. 6 1. 4 R 2 = 0. 9828 0. 5 0 -0. 5 0 0. 5 1 -1. 5 -2 1 Time (s) Cocking to Contact 0. 8 0. 6 ω = 14. 112 rad/s 0. 4 0. 2 0 1. 072 1. 5 -1 1. 2 Radians Angle vs. Time 2 1. 092 1. 112 1. 132 Time (s) 1. 152 1. 172 1. 192

Angular Velocity of Service Arm No Knee Flexion Angular Velocity Calculation 1. 5 1 Radians 1. 8 R 2 = 0. 9799 1. 6 1. 4 0. 5 0 -0. 5 0 0. 5 1 -1 1. 2 Radians Angle vs. Time 2 -1. 5 Time (s) 1 Cocking to Contact 0. 8 0. 6 ω = 9. 99 rad/s 0. 4 0. 2 0 0. 872 0. 892 0. 912 0. 932 0. 952 Time (s) 0. 972 0. 992 1. 012 1. 5

Rotational Kinetic Energy Calculation Knee Flexion KEarm = ½ Iarmω2 = (0. 5)(. 141 kgm 2)(14. 112 rads/s)2 = 14. 04 J No Knee Flexion KEarm = ½ Iarmω2 = (0. 5)(. 141 kgm 2)(9. 99 rads/s)2 KEarm = 7. 04 J Almost a 2 -fold increase in rotational KE of arm

Summary of Data Parameter Knee Flexion No Knee Flexion Velocity 32. 66 m/s 25. 48 m/s Force 84. 76 N 76. 10 N KEBall 30. 40 J 18. 50 J Power 1085. 71 W 660. 71 W KEArm 14. 04 J 7. 04 J

Conclusion • Knee flexion before a serve contributes to increased velocity, power, energy and force delivered to the tennis ball • Furthermore, knee flexion is linked to the rotational motion of the service arm with a almost a 2 -fold increase in the arm’s rotational kinetic energy • Engaging in upper and lower limb muscles through knee flexion induce rotation in upper legs, hip and core which contribute to the overall angular velocity of arm (Bahamonde, 2000)

Future Direction • How does variation in knee angles affect the drive of the tennis serve? • Analyze relevant parameters – determine optimal knee flexion angle • Tennis serve can be broken down into a series of segmental rotations • Analyze how each rotational segment contributes to the overall energy of the tennis serve • Analyze the rotational energy and angular momentum of racket

References • Bahamonde, R. B. (2000). Changes in angular momentum during the tennis serve. Journal of Sports Sciences, 18(8), 579 -592. Retrieved from http: //www. tandfonline. com/doi/pdf/10. 1080/02640410050082297 • Dempster, W. D. (1967). Properties of body segments based on size and weight. Informally published manuscript, Department of Anatomy, The University of Michigan, Ann Arbor, . Retrieved from http: //deepblue. lib. umich. edu/bitstream/handle/2027. 42/49638/1001200104_ftp. pdf? seq uence=1 • Howard, M. (2013, December 02). Muscles engaged while playing tennis. Retrieved from http: //www. livestrong. com/article/105577 -muscles-body-used-tennis/ • Kovacs, K. M. , & Ellenbecker, T. M. (2011). An 8 -stage model for evaluating the tennis serve. Sports Health, 3(6), 504– 513. Retrieved from http: //www. ncbi. nlm. nih. gov/pmc/articles/PMC 3445225/