1. Biomechanics of a Tennis Serve
Harry Choi
BIOL438
April 17th, 2014

2. 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

3. 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)

4. 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)?

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

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

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

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

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

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

11. 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)

12. 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)( m)3 = kg m2
Angular Velocity of Service Arm
𝑆𝑖𝑛𝛼= Δ𝑌 𝐷
(Xwrist , Ywrist)
𝑆𝑖𝑛𝛼 = 𝑌 𝑤𝑟𝑖𝑠𝑡 − 𝑌 𝑠ℎ𝑜𝑢𝑙𝑑𝑒𝑟 𝑋 𝑤𝑟𝑖𝑠𝑡 − 𝑋 𝑠ℎ𝑜𝑢𝑙𝑑𝑒𝑟 𝑌 𝑤𝑟𝑖𝑠𝑡 − 𝑌 𝑠ℎ𝑜𝑢𝑙𝑑𝑒𝑟 2 D ΔY α
(Xshoulder , Yshoulder)
Isolate rotational component of arm swing
(Dempster, 2013)

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

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

15. Rotational Kinetic Energy Calculation
Knee Flexion
KEarm = ½ Iarmω2 = (0.5)(.141 kgm2)( rads/s)2 = J
No Knee Flexion
KEarm = ½ Iarmω2 = (0.5)(.141 kgm2)(9.99 rads/s)2 KEarm = J
Almost a 2-fold increase in rotational KE of arm

16. 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 W W
KEArm
14.04 J
7.04 J

17. 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)

18. 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

19. References
Bahamonde, R. B. (2000). Changes in angular momentum during the tennis serve. Journal of Sports Sciences,18(8), Retrieved from
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 uence=1
Howard, M. (2013, December 02). Muscles engaged while playing tennis. Retrieved from
Kovacs, K. M., & Ellenbecker, T. M. (2011). An 8-stage model for evaluating the tennis serve. Sports Health, 3(6), 504–513. Retrieved from