Skip to main content
SpringerLink
Log in

Comparison of a finite element model of a tennis racket to experimental data

  • Original Article
  • Published:
Sports Engineering Aims and scope Submit manuscript

Abstract

Modern tennis rackets are manufactured from composite materials with high stiffness-to-weight ratios. In this paper, a finite element (FE) model was constructed to simulate an impact of a tennis ball on a freely suspended racket. The FE model was in good agreement with experimental data collected in a laboratory. The model showed racket stiffness to have no influence on the rebound characteristics of the ball, when simulating oblique spinning impacts at the geometric stringbed centre. The rebound velocity and topspin of the ball increased with the resultant impact velocity. It is likely that the maximum speed at which a player can swing a racket will increase as the moment of inertia (swingweight) decreases. Therefore, a player has the capacity to hit the ball faster, and with more topspin, when using a racket with a low swingweight.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Haines R (1993) The sporting use of polymers, vol 22. Shell petrochemicals

  2. ITF TECHNICAL DEPARTMENT (2009) International Tennis Federation (online). Accessed 1 May 2009. http://www.itftennis.com/technical

  3. Lammer H, Kotze J (2003) Materials and tennis rackets. In: Jenkins M (ed) Materials in sports equipment. Woodhead Publishing Limited, Cambridge, pp 222–248

    Google Scholar 

  4. Brody H (1997) The physics of tennis 3: the ball–racket interaction. Am J Phys 65(10):981–987

    Article  MathSciNet  Google Scholar 

  5. Brody H (1997) The influence of racquet technology on tennis strokes. Tennis Pro (1):10–11

  6. Haake S, Allen T, Choppin S, Goodwill S (2007) The evolution of the tennis racket and its effect on serve speed. In: Tennis science and technology 3, vol 1. International Tennis Federation, London, pp 257–271

    Google Scholar 

  7. Allen T, Goodwill S, Haake S (2008) Experimental validation of a FE model of a head-clamped tennis racket. ANSYS UK Users Conference, Oxford

  8. Allen T, Goodwill S, Haake S (2008) Experimental validation of a finite-element model of a tennis ball for different temperatures. The engineering of sport 7, vol 1. Springer, Biarritz, pp 125–133

    Google Scholar 

  9. Allen T, Goodwill S, Haake S (2008) Experimental validation of a finite-element model of a tennis racket stringbed. The engineering of sport 7, vol 1. Springer, Biarritz, pp 115–123

    Google Scholar 

  10. Allen T, Goodwill S, Haake S (2007) Experimental validation of a tennis ball finite-element model. In: Tennis science and technology 3, vol 1. International Tennis Federation, London, pp 21–30

    Google Scholar 

  11. Goodwill SR, Kirk R, Haake SJ (2005) Experimental and finite element analysis of a tennis ball impact on a rigid surface. Sports Eng 8(3):145–158

    Google Scholar 

  12. Goodwill SR, Haake SJ (2004) Ball spin generation for oblique impacts with a tennis racket. Exp Mech 44(2):195–206

    Article  Google Scholar 

  13. Brody H (1987) Models of tennis racket impacts/(modeles d’ impacts sur raquette de tennis.). Intern J Sport Biomech 3(3):293–296

    Google Scholar 

  14. Goodwill SR, Haake SJ (2001) Spring damper model of an impact between a tennis ball and racket. Proceedings of the Institution of Mechanical Engineers. Part C. J Mech Eng Sci 215(11):1331–1341

    Google Scholar 

  15. Goodwill S, Haake S (2003) Modelling of an impact between a tennis ball and racket. In: Tennis science and technology 2, vol 1. International Tennis Federation, London, pp 79–86

    Google Scholar 

  16. Choppin S, Goodwill S, Haake S, Miller S (2008) Ball and racket movements recorded at the 2006 Wimbledon qualifying tournament. The engineering of sport 7, vol 1. Springer, Biarritz, pp 563–569

    Google Scholar 

  17. Goodwill SR, Haake SJ (2004) Effect of string tension on the impact between a tennis ball and racket. In: The engineering of sport 5. Davis, California, pp 3–9

    Google Scholar 

  18. Goodwill S, Capel-Davies J, Haake S, Miller S (2007) Ball spin generation of elite players during match play. In: Tennis science and technology 3, vol 1. International Tennis Federation, London, pp 349–356

    Google Scholar 

  19. Kelley J, Goodwill S, Capel-Davies J, Haake S (2008) Ball spin generation at the 2007 Wimbledon qualifying tournament. The engineering of sport 7, vol 1. Springer, Biarritz, pp 571–578

    Google Scholar 

  20. Mase T, Kersten AM (2004) Experimental evaluation of a 3-D hyperelastic, rate-dependent golf ball constitutive model. In: The engineering of sport 5. International Sports Engineering Association, California, pp 238–244

    Google Scholar 

  21. Beisen E, Smith L (2007) Describing the plastic deformation of aluminium softball bats. Sports Eng 10(4):185–194

    Article  Google Scholar 

  22. Peterson W, McPhee J (2008) Shape optimization of golf clubheads using finite element impact models. In: The engineering of sport 7, vol 1. Springer, France, pp 465–473

    Google Scholar 

  23. Goodwill SR (2002) The dynamics of tennis ball impacts on tennis rackets. Ph.D. thesis, The University of Sheffield

  24. Walker P (1991) Chambers science and technology dictionary. W & R Chamber Limited, Edinburgh

    Google Scholar 

  25. Cross R (2000) Effects of friction between the ball and strings in tennis. Sports Eng 3(1):85–97

    Article  Google Scholar 

  26. Allen TB (2009) Finite element model of a tennis ball impact with a racket. Ph.D. thesis, Sheffield Hallam University

  27. Choppin SB (2008) Modelling of tennis racket impacts in 3D using elite players. Ph.D. thesis, The University of Sheffield

  28. Bouguet J (2008) Camera calibration toolbox for matlab. http://www.vision.caltech.edu/bouguetj/calib_doc

  29. Zhang Z (1999) Flexible camera calibration by viewing a plane from unknown orientations. In: International conference on computer vision. Corfu, Greece, pp 666–673

  30. Kanda Y, Nagao H, Naruo T (2002) Estimation of tennis racket power using three-dimensional finite element analysis. In: The engineering of sport 4, Kyoto, Japan, pp 207–214

  31. Cross R (2003) Oblique impact of a tennis ball on the strings of a tennis racket. Sports Eng 6(1):235–254

    Google Scholar 

  32. Mitchell SR, Jones R, King M (2000) Head speed vs. racket inertia in the tennis serve. Sports Eng 3(2):99–110

    Article  Google Scholar 

  33. Miller S (2006) Modern tennis rackets, balls and surfaces. Br J Sports Med 40:401–405

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Prince for sponsoring the project. They would also like to thank Terry Senior, Simon Choppin and John Kelley.

Author information

Authors and Affiliations

  1. Faculty of Health and Wellbeing, Sports Engineering Research Group, Centre for Sport and Exercise Science, Sheffield Hallam University, Sheffield, UK

    Tom Allen, Steve Haake & Simon Goodwill

Authors
  1. Tom Allen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steve Haake
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Simon Goodwill
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tom Allen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Allen, T., Haake, S. & Goodwill, S. Comparison of a finite element model of a tennis racket to experimental data. Sports Eng 12, 87–98 (2009). https://doi.org/10.1007/s12283-009-0032-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12283-009-0032-5

Keywords

Search

Navigation