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A review of tennis racket performance parameters

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Abstract

The application of advanced engineering to tennis racket design has influenced the nature of the sport. As a result, the International Tennis Federation has established rules to limit performance, with the aim of protecting the nature of the game. This paper illustrates how changes to the racket affect the player-racket system. The review integrates engineering and biomechanical issues related to tennis racket performance, covering the biomechanical characteristics of tennis strokes, tennis racket performance, the effect of racket parameters on ball rebound and biomechanical interactions. Racket properties influence the rebound of the ball. Ball rebound speed increases with frame stiffness and as string tension decreases. Reducing inter-string contacting forces increases rebound topspin. Historical trends and predictive modelling indicate swingweights of around 0.030–0.035 kg/m2 are best for high ball speed and accuracy. To fully understand the effect of their design changes, engineers should use impact conditions in their experiments, or models, which reflect those of actual tennis strokes. Sports engineers, therefore, benefit from working closely with biomechanists to ensure realistic impact conditions.

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  • 12 November 2020

    In the original version of the article, Equation was published incorrectly and the correct Equation.

References

  1. Haake SJ, Allen TB, Choppin SB, Goodwill SR (2007) The evolution of the tennis racket and its effect on serve speed. In: Miller S, Capel-Davies J (eds) Tennis science and technology, vol 3. International Tennis Federation, London, pp 257–271

  2. Knudson D, Allen TB, Choppin SB (2013) Interaction of tennis racket design and biomechanical factors. In: Hong Y (ed) Routledge handbook of ergonomics in sport and exercise. Routledge, New York, pp 423–439

    Google Scholar 

  3. Lammer H, Kotze J (2003) Materials and tennis rackets. In: Jenkins M (ed) Materials in sports equipment, vol 1. Woodhead Publishing, Cambridge, pp 222–248

    Chapter  Google Scholar 

  4. Head H (1976) US Patent 3,999,756. US Patent and Trademark Office, Washington, DC

  5. ITF (2013) ITF Technical Department Web Resource. http://www.itftennis.com/technical/. Accessed 29 Nov 2013

  6. Miller S (2006) Modern tennis rackets, balls, and surfaces. Br J Sports Med 40:401–405. doi:10.1136/bjsm.2005.023283

    Article  Google Scholar 

  7. Choppin SB, Goodwill SR, Haake SJ (2011) Impact characteristics of the ball and racket during play at the Wimbledon qualifying tournament. Sport Eng. doi:10.1007/s12283-011-0062-7

    Google Scholar 

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

    Article  Google Scholar 

  9. Brody H (1987) Models of tennis racket impacts. J Appl Biomech 3:293–296

    Google Scholar 

  10. Kotze J, Mitchell SR, Rothberg SJ (2000) The role of the racket in high speed tennis serves. Sport Eng 3:67–84

    Article  Google Scholar 

  11. Cross R (2013) Impact of sports balls with striking implements. Sport Eng 17(1):3–22. doi:10.1007/s12283-013-0132-0

    Article  MathSciNet  Google Scholar 

  12. Elliott BC (1989) Tennis strokes and equipment. In: Vaughan CL (ed) Biomechanics of sport. CRC Press, Florida, pp 263–288

    Google Scholar 

  13. Knudson DV (2006) Biomechanical principles of tennis technique: using science to improve your strokes. Racquet Tech Publishing, Vista, p 136

    Google Scholar 

  14. Knudson D, Elliott B (2004) Biomechanics of tennis strokes. In: Biomedical engineering principles in sports. Springer, New York, pp 153–181

    Chapter  Google Scholar 

  15. Ariel GB, Braden V (1979) Biomechanical analysis of ballistic vs. tracking movements in tennis skills. In: Proceeding of a national symposium on racquet sport, Champaign, pp 105–124

  16. Elliott B, Marsh T, Overheu P (1989) A biomechanical comparison of the multisegment and single unit topspin forehand drives in tennis. J Sport Biomech 5:350–364

    Google Scholar 

  17. Elliott BC, Takahashi K, Noffal G (1997) The influence of grip position on upper limb contributions to racket head velocity in a tennis forehand. J Appl Biomech 13:182–196

    Google Scholar 

  18. Seeley MK, Funk MD, Denning WM et al (2011) Tennis forehand kinematics change as post-impact ball speed is altered. Sport Biomech 10:415–426

    Article  Google Scholar 

  19. Sheets AL, Abrams GD, Corazza S et al (2011) Kinematics differences between the flat, kick, and slice serves measured using a markerless motion capture method. Ann Biomed Eng 39:3011–3020. doi:10.1007/s10439-011-0418-y

    Article  Google Scholar 

  20. Knudson D, Bahamonde RE (2001) Effect of endpoint conditions on position and velocity near impact in tennis. J Sports Sci 19:839–844

    Article  Google Scholar 

  21. Reid MM, Campbell AC, Elliott BC (2012) Comparison of endpoint data treatment methods for estimation of kinematics and kinetics near impact during the tennis serve. J Appl Biomech 28:93–98

    Google Scholar 

  22. Tanabe S, Ito A (2007) Application of the extrapolation method to motion analysis of the flat power serve in tennis. Int J Sport Health Sci 5:157–167. doi:10.5432/ijshs.5.157

    Article  Google Scholar 

  23. Goodwill SR, Capel-Davies J, Haake SJ, Miller S (2007) Ball spin generation by elite players during match play. In: Miller S, Capel-Davies J (eds) Tennis science and technology 3, International Tennis Federation, London, pp 349–356

  24. Kelley J, Goodwill SR, Capel-Davies J, Haake SJ (2008) Ball spin generation at the 2007 Wimbledon qualifying tournament (P110). In: The engineering of sport 7, vol 1. Springer, Paris, pp 571–578

  25. Cross R (2011) The kick serve in tennis. Sport Technol 4:19–28

    Google Scholar 

  26. Elliott BC (1983) Spin and the power serve in tennis. J Hum Mov Stud 9:97–103

    Google Scholar 

  27. Sakurai S, Reid MM, Elliott BC (2013) Ball spin in the tennis serve: spin rate and axis of rotation. Sport Biomech 12:23–29

    Article  Google Scholar 

  28. American Society for Testing and Materials, ASTM F1881-11: Standard Test Method for Measuring Baseball Bat Performance Factor

  29. Knudson D (1993) Effect of string tension and impact location on ball rebound accuracy in static tennis impacts. J Appl Biomech 9:143–148

    Google Scholar 

  30. Bower R, Sinclair P (1999) Tennis racquet stiffness and string tension effects on rebound velocity and angle for an oblique impact. J Hum Mov Stud 37:271–286

    Google Scholar 

  31. Cross R (2003) Oblique impact of a tennis ball on the strings of a tennis racket. Sport Eng 6:235–254. doi:10.1007/BF02844026

    Article  Google Scholar 

  32. Goodwill SR, Haake SJ (2004) Ball spin generation for oblique impacts with a tennis racket. Exp Mech 44:195–206. doi:10.1177/0014485104039763

    Article  Google Scholar 

  33. Allen TB, Haake SJ, Goodwill SR (2009) Comparison of a finite element model of a tennis racket to experimental data. Sport Eng 12:87–98. doi:10.1007/s12283-009-0032-5

    Article  Google Scholar 

  34. Allen TB, Haake SJ, Goodwill SR (2010) Effect of friction on tennis ball impacts. Proc Inst Mech Eng Part P J Sport Eng Technol 224:229–236. doi:10.1243/17543371JSET66

    Google Scholar 

  35. Allen TB, Haake SJ, Goodwill SR (2011) Effect of tennis racket parameters on a simulated groundstroke. J Sports Sci 29:311–325. doi:10.1080/02640414.2010.526131

    Article  Google Scholar 

  36. Haake SJ, Allen TB, Spurr J, Goodwill SR (2012) Effect of inter-string friction on tennis ball rebound. Proc Inst Mech Eng Part J Eng Tribol 226:626–635

    Article  Google Scholar 

  37. Nicolaides A, Elliott N, Kelley J et al (2013) Effect of string bed pattern on ball spin generation from a tennis racket. Sport Eng 16:181–188

    Article  Google Scholar 

  38. Cross R, Lindsey C (2005) Technical tennis: racquets, strings, balls, courts, spin, and bounce. Racquet Tech Publishing, Vista, CA, p 152

    Google Scholar 

  39. Brody H, Lindsey C, Cross R (2002) The physics and technology of tennis. Racquet Tech Publishing, Vista, p 437

    Google Scholar 

  40. Brody H (1981) Physics of the tennis racket II: the “sweet spot”. Am J Phys 49:816–819

    Article  Google Scholar 

  41. Cross R (1998) The sweet spots of a tennis racquet. Sport Eng 1:63–78. doi:10.1046/j.1460-2687.1999.00011.x

    Article  Google Scholar 

  42. Brody H, Roetert P (2004) Optimizing ball and racket interaction. In: Biomedical Engineering Principles in Sports. Springer, New York, pp 183–206

    Chapter  Google Scholar 

  43. Choppin SB (2013) An investigation into the power point in tennis. Sport Eng 16:173–180. doi:10.1007/s12283-013-0122-2

    Article  Google Scholar 

  44. Hatze H (1994) Impact probability distribution, sweet spot, and the concept of an effective power region in tennis rackets. J Appl Biomech 10:43–50

    Google Scholar 

  45. Hatze H (1998) The centre of percussion of tennis rackets: a concept of limited applicability. Sport Eng 1:17–25

    Article  Google Scholar 

  46. Cross R (2004) Center of percussion of hand-held implements. Am J Phys 72:622. doi:10.1119/1.1634965

    Article  Google Scholar 

  47. Brody H (1985) The moment of inertia of a tennis racket. Phys Teach 23(4):213–216

    Article  Google Scholar 

  48. Spurr J, Goodwill S, Kelley J, Haake S (2014) Measuring the inertial properties of a tennis racket. Procedia Eng 72:569–574. doi:10.1016/j.proeng.2014.06.098

    Article  Google Scholar 

  49. British Standards, ISO 11416:1995 Tennis rackets––racket components and physical parameters

  50. Kawazoe Y (1997) Experimental identification of a hand-held tennis racket and prediction of rebound ball velocity in an impact. Theor Appl Mech 46:177–188

    Google Scholar 

  51. Cross R (1999) Impact of a ball with a bat or racket. Am J Phys 67:692–702

    Article  Google Scholar 

  52. Knudson D, White SC (1989) Forces on the hand in the tennis forehand drive: application of force sensing resistors. Int J Sport Biomech 5:324–331

    Google Scholar 

  53. Brody H (1997) The physics of tennis III: the ball-racket interaction. Am J Phys 65:981–987

    Article  Google Scholar 

  54. Goodwill SR, Haake SJ (2001) Spring damper model of an impact between a tennis ball and racket. Proc Inst Mech Eng Part C J Mech Eng Sci 215:1331–1341. doi:10.1243/0954406011524711

    Article  Google Scholar 

  55. Goodwill SR, Haake SJ, Miller S (2007) Validation of the ITF racket power machine. In: Miller S, Capel-Davies J (eds) Tennis science and technology, vol 3. International Tennis Federation, London, pp 113–120

    Google Scholar 

  56. Lui KY (1983) Mechanical analysis of racket and ball during impact. Med Sci Sports Exerc 15:388–392

    Google Scholar 

  57. Casolo F, Ruggieri G (1991) Dynamic analysis of the ball–racket impact in the game of tennis. Meccanica 26:67–73

    Article  MATH  Google Scholar 

  58. Cross R (2000) Flexible beam analysis of the effects of string tension and frame stiffness on racket performance. Sport Eng 3:111–122. doi:10.1046/j.1460-2687.2000.00046.x

    Article  Google Scholar 

  59. Goodwill SR, Haake SJ (2002) Modelling of an impact between a tennis ball and racket. In: Tennis science and technology, vol 2. The International Tennis Federation, London, pp 79–86

  60. Cross R (2010) Impact forces and torques transmitted to the hand by tennis racquets. Sport Technol 3:102–111. doi:10.1080/19346182.2010.538398

    Google Scholar 

  61. Glynn JA, King MA, Mitchell SR (2010) A computer simulation model of tennis racket/ball impacts. Sport Eng 13:65–72. doi:10.1007/s12283-010-0056-x

    Article  Google Scholar 

  62. Haake SJ, Chadwick SG, Dignall RJ et al (2000) Engineering tennis––slowing the game down. Sport Eng 3:131–143

    Article  Google Scholar 

  63. Choppin SB, Goodwill SR, Haake SJ (2010) Investigations into the effect of grip tightness on off-centre forehand strikes in tennis. Proc Inst Mech Eng Part P J Sport Eng Technol 224:249–257. doi:10.1243/17543371JSET75

    Article  Google Scholar 

  64. Goff JE (2013) A review of recent research into aerodynamics of sport projectiles. Sport Eng 16(3):137–154. doi:10.1007/s12283-013-0117-z

    Google Scholar 

  65. Cross R, Lindsey C (2013) Measurements of drag and lift on tennis balls in flight. Sport Eng 17:89–96. doi:10.1007/s12283-013-0144-9

    Article  Google Scholar 

  66. Mehta R, Alam F, Subic A (2008) Review of tennis ball aerodynamics. Sport Technol 1:7–16. doi:10.1002/jst.11

    Article  Google Scholar 

  67. Arthur C (1992) Anyone for slower tennis. New Sci 134:24–28

    Google Scholar 

  68. Coe A (2000) The balance between technology and tradition in tennis. In: Haake SJ, Coe A (eds) Tennis Science and Technology. Blackwell Science, Oxford, pp 3–40

  69. Sheridan H (2006) Tennis technologies: de-skilling and re-skilling players and the implications for the game. Sport Soc 9:32–50. doi:10.1080/17430430500355782

    Article  Google Scholar 

  70. Cross R, Bower R (2006) Effects of swing-weight on swing speed and racket power. J Sports Sci 24:23–30. doi:10.1080/02640410500127876

    Article  Google Scholar 

  71. Hatze H (1993) The relationship between the coeeicient sf restitution and energy losses in tennis rackets. J Appl Biomech 9:142

    Google Scholar 

  72. Cross R, Nathan AM (2009) Performance versus moment of inertia of sporting implements. Sport Technol 2:7–15. doi:10.1080/19346182.2009.9648493

    Article  Google Scholar 

  73. Kanda Y (2004) Estimation of tennis racket power using three-dimensional finite element analysis. Eng Sport 4:207–214

    Google Scholar 

  74. Nass D, Hennig EM, Schnabel G (1998) Ball impact location on a tennis racket head and its influence on ball speed, arm shock, and vibration. In: Proceedings of 16th international symposium on biomechanics in sport, Konstanz, pp 229–232

  75. Kern JC, Zimmerman WJ (1993) The effect of tennis racquet flexibility on rebound velocity. In: Hamill J, Derrick TR, Elliott HE (eds) Biomechanics in sports XI. Amherst, MA, pp 193–195

    Google Scholar 

  76. Baker JAW, Wilson BD (1978) The effect of tennis racket stiffness and string tension on ball velocity after impact. Res Q 49:255–259

    Google Scholar 

  77. Elliott B (1982) The influence of tennis racket flexibility and string tension on rebound velocity following a dynamic impact. Res Q Exerc Sport 53:277–281. doi:10.1080/02701367.1982.10605249

    Article  Google Scholar 

  78. Haake SJ, Carré M, Goodwill SR (2003) The dynamic impact characteristics of tennis balls with tennis rackets. J Sport Sci 21:839–850

    Article  Google Scholar 

  79. Bower R, Cross R (2005) String tension effects on tennis ball rebound speed and accuracy during playing conditions. J Sports Sci 23:765–771. doi:10.1080/02640410400021914

    Article  Google Scholar 

  80. Goodwill SR, Haake SJ (2004) Effect of string tension on the impact between a tennis ball and racket. In: Hubbard M, Mehtra RD, Pallis JM (eds) The engineering of sports 5, International sports engineering association, pp 3–9

  81. Fischer W (1981) US Patent 4,273,331. US Patent and Trademark Office, Washington, DC

  82. Goodwill SR, Haake SJ (2002) Why were “Spaghetti String” rackets banned in the game of tennis? In: Ujihashi S, Haake SJ (eds) The engineering of sports 4, Blackwell, pp 231–237

  83. Washida Y, Elliott N, Allen T (2014) Measurement of main strings movement and its effect on tennis ball spin. Procedia Eng 72:557–562. doi:10.1016/j.proeng.2014.06.097

    Article  Google Scholar 

  84. Kawazoe Y, Okimoto K (2008) Tennis top spin comparison between new, used and lubricated used strings by high speed video analysis with impact simulation. Theor Appl Mech Jpn 57:511–522

    Google Scholar 

  85. Cross R (2010) The polar moment of inertia of striking implements. Sport Technol 3(3):215–219. doi:10.1080/19346182.2011.564287

    Google Scholar 

  86. Whiteside D, Elliott B, Lay B, Reid M (2013) The effect of racquet swing weight on serve kinematics in elite adolescent female tennis players. J Sci Med Sport 17(1):124–128. doi:10.1016/j.jsams.2013.03.001

    Google Scholar 

  87. Sol H (1995) Computer aided design of rackets. In: Reilly T, Hughes M, Lees A (eds) Science and racket sports. E & FN Spon., London, pp 125–133

  88. Brody H (2000) Player sensitivity to the moments of inertia of a tennis racket. Sport Eng 3:145–148

    Article  Google Scholar 

  89. Cross R (2001) Customising a tennis racket by adding weights. Sport Eng 4:1–14

    Article  Google Scholar 

  90. Smith L, Kensrud J (2013) Field and laboratory measurements of softball player swing speed and bat performance. Sport Eng 17(2):75–82. doi:10.1007/s12283-013-0126-y

    Google Scholar 

  91. Gagen LM, Haywood KM, Spaner SD (2005) Predicting the scale of tennis rackets for optimal striking from body dimensions. Pediatr Exerc Sci 17:190–200

    Google Scholar 

  92. Knudson D (2008) Biomechanical aspects of the tennis racket. In: Hong Y, Bartlett R (eds) Routledge handbook of biomechanics and human movement science. Routledge, London, pp 248–260

    Google Scholar 

  93. Kawazoe Y (2002) Mechanism of high-tech tennis rackets performance. Theor Appl Mech 51:177–190

    Google Scholar 

  94. Groppel JL, Shin I, Thomas J, Welk G (1987) The effects of string type and tension on impact in midsized and oversized tennis racquets. Int J Sports Biomech 3(1):40–46

    Google Scholar 

  95. Knudson D (1991) Factors affecting force loading on the hand in the tennis forehand. J Sports Med Phys Fit 31:527–531

    Google Scholar 

  96. Savage N, Subic A (2006) Relating grip characteristics to the dynamic response of tennis racquets. In: Moritz EF, Haake SJ (eds) The engineering of sport, vol 6. Springer, Munich, pp 155–160

    Google Scholar 

  97. Baker JAW, Putnam CA (1979) Tennis racket and ball responses during impact under clamped and freestanding conditions. Res Q 50:164–170

    Google Scholar 

  98. Hennig EM (2007) Influence of racket properties on injuries and performance in tennis. Exerc Sport Sci Rev 35:62–66. doi:10.1249/JES.0b013e31803ec43e

    Article  Google Scholar 

  99. Knudson D (1989) Hand forces and impact effectiveness in the tennis forehand. J Hum Mov Stud 17:1–7

    Google Scholar 

  100. Watanabe T, Ikegami Y, Miyashita M (1979) Tennis: the effects of grip firmness on ball velocity after impact. Med Sci Sport 11:359–361

    Google Scholar 

  101. Knudson D (1997) Effect of grip models on rebound accuracy of off-center tennis impacts. In: XV international symposium on biomechanics in sports. Denton, Texas, USA, pp 483–487

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Acknowledgments

The authors are grateful to several colleagues who we have collaborated with over the years. Several at the ITF Technical Department and the Centre for Sports Engineering Research at Sheffield Hallam University were particularly helpful in the writing of this paper.

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Authors and Affiliations

  1. Centre for Sports Engineering Research, Sheffield Hallam University, Sheffield, UK

    Tom Allen & Simon Choppin

  2. Department of Engineering and Maths, Sheffield Hallam University, Sheffield, UK

    Tom Allen

  3. Department of Health and Human Performance, Texas State University, San Marcos, USA

    Duane Knudson

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  1. Tom Allen
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  2. Simon Choppin
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  3. Duane Knudson
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Correspondence to Tom Allen.

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Allen, T., Choppin, S. & Knudson, D. A review of tennis racket performance parameters. Sports Eng 19, 1–11 (2016). https://doi.org/10.1007/s12283-014-0167-x

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