Biomechanics of a Tennis Serve Harry Choi BIOL438 April 17th, 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 Follow-Through Figure 1. (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 Deceleration/Finish Maximal shoulder rotation Tip of racket points toward ground

Velocity and Acceleration of Tennis Ball Knee Flexion Vavg = 32.66 m/s aball = 1487 m/s2 Δt = 0.028s

Velocity and Acceleration of Tennis Ball No Knee Flexion Vavg = 25.48 m/s aball = 1335 m/s2 Δt = 0.028s

Force, KE and Power delivered to Tennis Ball Knee Flexion Forcetennis ball = ma = (0.057 kg)(1487 m/s2) = 84.76 N KE = ½mv2 = (0.5)(.057 kg)(32.66 m/s)2 = 30.40 J Power = 𝑊 Δ𝑡 = 30.40 J/ 0.028s = 1085.71Watts Tennis Ball mball = 0.057 kg No Knee Flexion Forcetennis ball = ma = (0.057 kg)(1335 m/s2) = 76.10 N KE = ½mv2 = (0.5)(.057 kg)(25.48 m/s)2 = 18.50 J Power = W/Δt = 18.50 J/ 0.028s = 660.71 Watts

Rotational KE associated with service arm Analyze rotational motion from cocking to contact Knee flexion No Knee flexion Cocking 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 Assume upper arm and forearm to be one rod with rotation at end Moment of inertia: Iarm = 1 3 ( 𝑚 𝑢𝑝𝑝𝑒𝑟 𝑎𝑟𝑚 + 𝑚 𝑓𝑜𝑟𝑒𝑎𝑟𝑚 ) 𝐿 3 where L = length of arm Iarm = (1/3)(3.67 kg)(0.4867 m)3 = 0.141 kg m2 Angular Velocity of Service Arm 𝑆𝑖𝑛𝛼= Δ𝑌 𝐷 (Xwrist , Ywrist) 𝑆𝑖𝑛𝛼 = 𝑌 𝑤𝑟𝑖𝑠𝑡 − 𝑌 𝑠ℎ𝑜𝑢𝑙𝑑𝑒𝑟 𝑋 𝑤𝑟𝑖𝑠𝑡 − 𝑋 𝑠ℎ𝑜𝑢𝑙𝑑𝑒𝑟 2 + 𝑌 𝑤𝑟𝑖𝑠𝑡 − 𝑌 𝑠ℎ𝑜𝑢𝑙𝑑𝑒𝑟 2 D ΔY α (Xshoulder , Yshoulder) Isolate rotational component of arm swing (Dempster, 2013)

Angular Velocity of Service Arm Knee Flexion Cocking to Contact ω = 14.112 rad/s

Angular Velocity of Service Arm No Knee Flexion Cocking to Contact ω = 9.99 rad/s

Rotational Kinetic Energy Calculation Knee Flexion KEarm = ½ Iarmω2 = (0.5)(.141 kgm2)(14.112 rads/s)2 = 14.04 J No Knee Flexion KEarm = ½ Iarmω2 = (0.5)(.141 kgm2)(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/PMC3445225/