Sports Engineering

, Volume 13, Issue 2, pp 65–72

A computer simulation model of tennis racket/ball impacts

  • Jonathan A. Glynn
  • Mark A. King
  • Sean R. Mitchell
Original Article


A forward dynamics computer simulation for replicating tennis racket/ball impacts is described consisting of two rigid segments coupled with two degrees of rotational freedom for the racket frame, nine equally spaced point masses connected by 24 visco-elastic springs for the string-bed and a point mass visco-elastic ball model. The first and second modal responses both in and perpendicular to the racket string-bed plane have been reproduced for two contrasting racket frames, each strung at a high and a low tension. Ball/string-bed normal impact simulations of real impacts at nine locations on each string-bed and six different initial ball velocities resulted in <3% RMS error in rebound velocity (over the 16–27 m/s range observed). The RMS difference between simulated and measured oblique impact rebound angles across nine impact locations was 1°. Thus, careful measurement of ball and racket characteristics to configure the model parameters enables researchers to accurately introduce ball impact at different locations and subsequent modal response of the tennis racket to rigid body simulations of tennis strokes without punitive computational cost.


Ball Impact Model Racket Simulation Tennis 


  1. 1.
    Brannigan M, Adali S (1981) Mathematical modeling and simulation of a tennis racket. Med Sci Sports Exerc 13:44–53Google Scholar
  2. 2.
    Brody H (1985) The moment of inertia of a tennis racket. Phys Teach 23:213–216CrossRefGoogle Scholar
  3. 3.
    Brody H (1997) The physics of tennis III: the ball–racket interaction. Am J Phys 65:981–987CrossRefGoogle Scholar
  4. 4.
    Corana A, Marchesi M, Martini C, Ridella S (1987) Minimizing multimodal functions of continuous variables with the “Simulated Annealing” algorithm. ACM Trans Math Softw 13:262–280MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cottey R, Kotze J, Lammer H, Zirngibl W (2006) An extended study investigating the effects of tennis rackets with active damping technology on the symptoms of tennis elbow. Eng Sport 6(9):391–396CrossRefGoogle Scholar
  6. 6.
    Davies G (2005) Feel and tennis ball impacts. PhD thesis, Loughborough UniversityGoogle Scholar
  7. 7.
    De Smedt T, de Jong A, Van Leemput W, Lieven D, Van Glabbeekk F (2007) Lateral epicondylitis in tennis: update on aetiology, biomechanics and treatment. Br J Sports Med 41:816–819CrossRefGoogle Scholar
  8. 8.
    Dignall RJ, Haake SJ, Chadwick SG (2000) Modelling of an oblique tennis ball impact on a court surface. In: Subic AJ, Haake SJ (eds) The Engineering of Sport. Blackwell Sciences, Oxford, pp 185–192Google Scholar
  9. 9.
    Glynn JA, Kentel BB, King MA, Mitchell SR (2007) A comparison of wrist angular kinematics and forearm EMG data for an elite, intermediate and novice standard tennis player performing a one-handed backhand groundstroke. Int J Sports Sci Eng 01:157–164Google Scholar
  10. 10.
    Goodwill SR Haake SJ (2003) Modelling of an impact between a tennis ball and racket. In: Miller S (ed) 2nd international tennis, science and technology, Blackwell, OxfordGoogle Scholar
  11. 11.
    Hatch GF, Pink MM, Mohr KJ, Sethi PM, Jobe FW (2006) The effect of tennis racket grip size on forearm muscle firing patterns. Am J Sports Med 34:1977–1983CrossRefGoogle Scholar
  12. 12.
    Hennig EM, Rosenbaum D, Milani TL (1992) Transfer of tennis racket vibrations onto the human forearm. Med Sci Sports Exerc 24:1134–1140Google Scholar
  13. 13.
    Hocknell A, Mitchell SR, Jones R, Rothberg SJ (1998) Hollow golf club head modal characteristics: determination and impact applications. Exp mech 38:140–146CrossRefGoogle Scholar
  14. 14.
    International Tennis Federation (2004). ITF approved tennis balls & classified court surfaces—a guide to products and test methods. ITF Licensing (UK) Ltd, London, pp 4–20Google Scholar
  15. 15.
    Li FX, Fewtrell D, Jenkins M (2004) String vibration dampers do not reduce racket frame vibration transfer to the forearm. J Sports Sci 22:1041–1052CrossRefGoogle Scholar
  16. 16.
    Mitchell SR, Jones R, King M (2000) Head speed vs. racket inertia in the tennis serve. Sports Eng 3:99–110CrossRefGoogle Scholar
  17. 17.
    Nesbit SN, Elzinga M, Herchenroder C, Serrano M (2006) The effects of racket inertia tensor on elbow loadings and racket behaviour for central and eccentric impacts. J Sports Sci Med 5:304–317Google Scholar
  18. 18.
    Riek S, Chapman AE, Milner T (1999) A simulation of muscle force and internal kinematics of extensor carpi radialis brevis during backhand tennis stroke: implications for injury. Clin Biomech 14:477–483CrossRefGoogle Scholar
  19. 19.
    Schlarb H, Kneib B, Glitsch U (1998) Modelling of the elastic racket properties in the dynamic computer simulation of tennis. In: Riehle H, Vieten M (eds) Proceedings of the XVI international symposium on biomechanics in sports, Konstanz, Germany pp 379–382Google Scholar
  20. 20.
    Stroede CL, Nobel L, Walker HS (1999) The effect of tennis racket string vibration dampers on racket handle vibration and discomfort following impacts. J Sports Sci 17:379–385CrossRefGoogle Scholar
  21. 21.
    Yeadon MR, Challis JH (1994) The future of performance-related sports biomechanics research. J Sports Sci 12:3–32CrossRefGoogle Scholar

Copyright information

© International Sports Engineering Association 2010

Authors and Affiliations

  • Jonathan A. Glynn
    • 1
  • Mark A. King
    • 2
  • Sean R. Mitchell
    • 3
  1. 1.ASPIRE Academy for Sports ExcellenceDohaQatar
  2. 2.School of Sport, Exercise and Health SciencesLoughborough UniversityLoughboroughUK
  3. 3.Sports Technology Institute, Wolfson School of Mechanical and Manufacturing EngineeringLoughborough UniversityLoughboroughUK

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