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A review of recent research into aerodynamics of sport projectiles

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An Erratum to this article was published on 26 May 2013

Abstract

A review of aerodynamics research connected to sport projectiles is presented here. The review’s focus is on work conducted in the current millennium, though deference is made to some classic work still invaluable to modern research. Besides serving as a resource for seasoned scientists and engineers, this article is especially geared toward young investigators who are just beginning careers in sport science. Basic and sophisticated methods are discussed, including vacuum physics, air drag, lift, numerical approaches, trajectory analysis, wind tunnels, and computational fluid dynamics. Eighteen sports are discussed with an eye to future research.

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References

  1. Daish CB (1972) The physics of ball games. The English Universities Press Ltd, London

  2. Mehta RD (1985) Aerodynamics of sports balls. Ann Rev Fluid Mech 17:151–189

    Article  Google Scholar 

  3. Frohlich C (2011) Resource Letter PS-2: Physics of Sports. Am J Phys 79:565–574

    Article  Google Scholar 

  4. White C (2011) Projectile dynamics in sport. Routledge, Abingdon

  5. Wolfson R (2012) Essential University Physics, 2nd edn. Addison-Wesley, San Francisco, p 40

  6. http://www.hittrackeronline.com

  7. Thornton ST, Marion JB (2004) Classical dynamics of particles and systems, 5th edn. Thomson Brooks/Cole, Belmont, p 59

  8. Goff JE (2004) Heuristic model of air drag on a sphere. Phys Educ 39:496–499

    Article  Google Scholar 

  9. Adair RK (2002) The physics of baseball, 3rd edn. Perennial/Harper Collins, New York

  10. White FM (2011) Fluid mechanics, 7th edn. McGraw-Hill Higher Education, New York

  11. Wesson J (2002) The science of soccer. Institute of Physics Publishing, London, p 168

  12. Goff JE, Carré MJ (2009) Trajectory analysis of a soccer ball. Am J Phys 77:1020–1027

    Article  Google Scholar 

  13. Watts RG, Bahill AT (2000) Keep your eye on the ball: curve balls, knuckleballs, and fallacies of baseball (revised and updated). WH Freeman and Co, New York

  14. Nathan AM (2008) The effect of spin on the flight of a baseball. Am J Phys 76:119–124

    Article  Google Scholar 

  15. de Mestre N (1990) The mathematics of projectiles in sport. Cambridge University Press, Cambridge

  16. Anderson Jr JD (2005) Ludwig Prandtl’s Boundary Layer. Phys Today 58:42–48

    Article  Google Scholar 

  17. Achenbach E (1972) Experiments on the flow past spheres at very high Reynolds numbers. J Fluid Mech 54:565–575

    Article  Google Scholar 

  18. Goff JE (2010) Power and spin in the beautiful game. Phys Today 63:62–63

    Article  Google Scholar 

  19. Bearman PW and Harvey JK (1976) Golf Ball Aerodynamics. Aeronautical Quarterly 27:112–122

    Google Scholar 

  20. Achenbach E (1974) The effects of surface roughness and tunnel blockage on the flow past spheres. J Fluid Mech 65:113–125

    Article  Google Scholar 

  21. Haake SJ, Goodwill SR, Carré MJ (2007) A new measure of roughness for defining the aerodynamic performance of sports balls. Proc IMechE, Part C: J Mech Eng Sci 221:789–806

    Article  Google Scholar 

  22. Koonin SE, Meredith DC (1990) Computational physics. Addison-Wesley, Boston Chapter 6

  23. Huebner KH (2001) The finite element method for engineers, 4th edn. Wiley-Interscience, New York

  24. Beer G, Smith I, Duenser C (2008) The boundary element method with programming: for engineers and scientists. Springer, New York

  25. Hanna RK (2012) CFD in Sport – a Retrospective; 1992–2012. Proc Eng 34:622–726

    Article  Google Scholar 

  26. Chung TJ (2010) Computational fluid dynamics, 2nd edn. Cambridge University Press, Cambridge

  27. http://www.huffingtonpost.com/2012/08/03/archery-olympics-hunger-games-london_n_1738182.html. Accessed Jan 2013

  28. Klopsteg PE (1943) Physics of Bows and Arrows. Am J Phys 11:175–192

    Article  Google Scholar 

  29. Denny M (2011) Their arrows will darken the sun: the evolution and science of ballistics. The Johns Hopkins University Press, Baltimore

  30. French K and Kirk T (2005) Measuring the flight of an arrow using the Acoustic Doppler Shift. Mech Sys and Sig Proc 21:1188–1191

    Article  Google Scholar 

  31. Park JL (2010) The behaviour of an arrow shot from a compound archery bow. Proc Inst Mech Eng Part P J Sports Eng and Tech 225:8–21

    Google Scholar 

  32. Park JL, Hodge MR, Al-Mulla S, Sherry M, Sheridan J (2011) Air flow around the point of an arrow. Proc Inst Mech Eng Part P J Sports Eng Tech (published online 15 Dec 2011)

  33. Park JL (2011) The aerodynamic drag and axial rotation of an arrow. Proc Inst Mech Eng Part P J Sports Eng and Tech 225:199–211

    Article  Google Scholar 

  34. Miyazaki T, Mukaiyama K, Komori Y, Okawa K, Taguchi S, Sugiura H (2012) Aerodynamic properties of an archery arrow. Sports Eng (published online 10 Oct 2012)

  35. Barton J, Včelák J, Torres-Sanchez J, O’Flynn B, O’Mathuna C, and Donahoe RV (2012) Arrow-mounted Ballistic System for Measuring Performance of Arrows Equipped with Hunting Broadheads. Proc Eng 34:455–460

    Article  Google Scholar 

  36. Rieckmann M, Park JL, Codrington J, Cazzolato B (2012) Modeling the 3D vibration of composite archery arrows under free-free boundary conditions. Proc Inst Mech Eng P J Sports Eng Techn 226:114–122

    Google Scholar 

  37. Chen LM, P YH, Chen YJ (2009) A study of shuttlecock’s trajectory in badminton. J Sports Sci and Med 8:657–662

    Google Scholar 

  38. Alam F, Chowdhury H, Theppadungporn C, and Subic A (2010) Measurements of Aerodynamic Properties of Badminton Shuttlecocks. Proc Eng 2:2487–2492

    Article  Google Scholar 

  39. Chan CM, Rossmann JS (2012) Badminton shuttlecock aerodynamics: synthesizing experiment and theory. Sports Eng 15:61–71

    Article  Google Scholar 

  40. Nakagawa K, Hasegawa H, Murakami M, Obayashi S (2012) Aerodynamic Properties and Flow Behavior for a Badminton Shuttlecock with Spin at High Reynolds Numbers. Proc Eng 34:104–109

    Article  Google Scholar 

  41. Texier BD, Cohen C, Quéré D, and Claneta C (2012) Shuttlecock dynamics. Proc Eng 34:176–181

    Article  Google Scholar 

  42. Briggs LJ (1959) Effect of Spin and Speed on the Lateral Deflection (Curve) of a Baseball; and the Magnus Effect for Smooth Spheres. Am J Phys 27:589–596

    Article  MATH  Google Scholar 

  43. Alawys LW, Hubbard M (2001) Experimental determination of baseball spin and lift. J Sports Sci 19:349–358

    Article  Google Scholar 

  44. Sawicki GS, Hubbard M, Stronge WJ (2003) How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories. Am J Phys 71:1152–1162

    Article  Google Scholar 

  45. McBeath MK, Nathan AM, Bahill AT, Baldwin DG (2008) Paradoxical pop-ups: Why are they difficult to catch? Am J Phys 76:723–729

    Article  Google Scholar 

  46. www.sportvision.com/baseball/pitchfx. Accessed Jan 2013

  47. Nathan AM (2012) Analysis of knuckleball trajectories. Proc Eng 34:116–121

    Article  Google Scholar 

  48. Meyer ER, Bohn JL (2008) Influence of a humidor on the aerodynamics of baseballs. Am J Phys 76:1015–1021

    Article  Google Scholar 

  49. Nathan AM, Cantakos J, Kesmna R, Mathew B, Lukash W (2012) Spin of a batted baseball. Proc Eng 34:182–187

    Article  Google Scholar 

  50. McGinnis RS, Perkins NC, King K (2012) Pitcher training aided by instrumented baseball. Proc Eng 34:580–585

    Article  Google Scholar 

  51. Fontanella JJ (2006) The physics of basketball, The Johns Hopkins University Press, Baltimore

  52. Huston RL, Grau CA (2003) Basketball shooting strategies – the free throw, direct shot and layup. Sports Eng 6:49–64

    Article  Google Scholar 

  53. Okubo H, Hubbard M (2012) Defense for basketball field shots. Proc Eng 34:730–735

    Article  Google Scholar 

  54. Mehta RD (2005) An overview of cricket ball swing. Sports Eng 8:181–192

    Article  Google Scholar 

  55. James DM, Carré MJ, and Haake SJ (2004) The playing performance of country cricket pitches. Sports Eng 7:1–14

    Article  Google Scholar 

  56. James D, MacDonald DC, and Hart J (2012) The effect of atmospheric conditions on the swing of a cricket ball. Proc Eng 34:188–193

    Article  Google Scholar 

  57. Fuss FK, Smith RM, Subic A (2012) Determination of spin rate and axes with an instrumented cricket ball. Proc Eng 34:128–133

    Article  Google Scholar 

  58. Penrose JMT, Hose DR, Trowbridge EA (1996) Cricket ball swing: a preliminary analysis using computational fluid dynamics. In: Haake (ed) The engineering of sport. AA Balkema, Rotterdam, pp 11–19

  59. Hubbard M, Cheng KB (2007) Optimal discus trajectories. J Biomech 40:3650–3659

    Article  Google Scholar 

  60. Frohlich C (1981) Aerodynamic and mechanical forces in discus flight. Am J Phys 49:1125–1132

    Article  Google Scholar 

  61. Goff JE (2010) Gold medal physics: the science of sports. The Johns Hopkins University Press, Baltimore, Chapter 8

  62. Seo K, Shimoyama K, Ohta K, Ohgi Y, Kimura Y (2012) Aerodynamic behavior of a discus. Proc Eng 34:92–97

    Article  Google Scholar 

  63. Crowther WJ, Potts JR (2007) Simulation of a spin-stabilised sports disc. Sports Eng 10:3–21

    Article  Google Scholar 

  64. Lissaman P, Hubbard M (2010) Maximum range of flying discs. Proc Eng 2:2529–2535

    Article  Google Scholar 

  65. Gay T (2005) The physics of football. HarperCollins, New York

  66. Goff JE (2010) Gold medal physics: the science of sports. The Johns Hopkins University Press, Baltimore, Chapter 3

  67. Rae WJ (2003) Flight dynamics of an American football in a forward pass. Sports Eng 6:149–163

    Article  Google Scholar 

  68. Rae WJ, Steit RJ (2002) Wind-tunnel measurements of the aerodynamic loads on an American football. Sport Eng 5:165–172

    Article  Google Scholar 

  69. Alam F, Smith S, Chowdhury H, and Moria H (2012) Aerodynamic drag measurements of American footballs. Proc Eng 34:98–103

    Article  Google Scholar 

  70. Watts RG, Moore G (2003) The drag on an American football. Am J Phys 71:791–793

    Article  Google Scholar 

  71. Jorgensen TP (1999) The physics of golf, 2nd edn. Springer, New York

  72. Davies JM (1949) The Aerodynamics of Golf Balls. J Appl Phys 20:821–828

    Article  Google Scholar 

  73. Choi J, Jeon WP, Choi H (2006) Mechanism of drag reduction by dimples on a sphere. Phys Fluids 18:041702

    Google Scholar 

  74. Penner AR (2001) The physics of golf: The optimum loft of a driver. Am J Phys 69:563–568

    Article  Google Scholar 

  75. Penner AR (2001) The physics of golf: The convex face of a driver. Am J Phys 69:1073–1081

    Article  Google Scholar 

  76. Parviz M, Kim J (1997) Tackling Turbulence with Supercomputers. Sci Am 276:62–68

    Google Scholar 

  77. Tanaka K, Teranishi Y, Ujihashi S (2010) Experimental and finite element analyses of a golf ball colliding with a simplified club during a two-dimensional swing. Proc Eng 2:3249–3254

    Article  Google Scholar 

  78. Dapena J, Gutiérrez-Dávila G, Soto VM, Rojas FJ (2003) Prediction of distance in hammer throwing. J Sports Sci 21:21–28

    Article  Google Scholar 

  79. Haché A (2002) The physics of hockey. The Johns Hopkins University Press, Baltimore

  80. Böhm H, Schwiewagner C, and Senner V (2007) Simulation of puck flight to determine spectator safety for various ice hockey board heights. Sports Eng 10:75–86

    Article  Google Scholar 

  81. Hubbard M, Rust HJ (1984) Simulation of Javelin Flight Using Experimental Aerodynamic Data. J Biomech 17:769–776

    Article  Google Scholar 

  82. Hubbard M (1984) Optimal Javelin Trajectories. J Biomech 17:777–787

    Article  Google Scholar 

  83. Hubbard M, Alaways LW (1987) Optimum Release Conditions for the New Rules Javelin. Int J Sport Biomech 3:207–221

    Google Scholar 

  84. Hubbard M, Bergman CD (1989) Effect of Vibrations on Javelin Lift and Drag. Int J Sport Biomech 5:40–59

    Google Scholar 

  85. Hubbard M, Laport S (1997) Damping of Javelin Vibrations in Flight. J Appl Biomech 13:269–286

    Google Scholar 

  86. Maryniak J, Ladyźyńska-Kozdraś E, Golińska E (2009) Mathematical Modeling and Numerical Simulations of Javelin Throw. Hum Dev 10:16–20

    Google Scholar 

  87. Maszczyk A, Zając A, Ryguła I (2011) A neural network model approach to athlete selection. Sports Eng 13:83–93

    Article  Google Scholar 

  88. Lipscombe TD (2009) The physics of rugby. Nottingham University Press, Nottingham

  89. Seo K, Kobayashi O, Murakami M (2006) Flight dynamics of the screw kick in rugby. Sports Eng 9:49–58

    Article  Google Scholar 

  90. Alam F, Subic A, Watkins S, Smits AJ (2010) Aerodynamics of an Australian rules foot ball and rugby ball. In: Peters M (ed) Computational fluid dynamics for sport simulation. Springer, Berlin

  91. Djamovski V, Rosette P, Chowdhury H, Alam F, Steiner T (2012) A comparative study of rugby ball aerodynamics. Proc Eng 34:74–79

    Article  Google Scholar 

  92. Taha Z, Sugiyono (2009) Effect of diameter on the aerodynamics of sepaktakraw balls, a computational study. Int J Sports Sci Eng 3:17–21

  93. Seo K, Watanabe I, Murakami M (2004) Aerodynamic force data for a V-style ski jumping flight. Sports Eng 7:31–39

    Article  Google Scholar 

  94. Seo K, Murakami M, Yoshida K (2004) Optimal flight technique for V-style ski jumping. Sports Eng 7:97–104

    Article  Google Scholar 

  95. Nørstrud H, Øye IJ (2010) On CFD simulation of ski jumping. In: Peters M (ed) Computational fluid dynamics for sport simulation. Springer, Berlin

  96. McNeil JA, McNeil JB (2009) Dynamical analysis of winter terrain park jumps. Sports Eng 11:159–164

    Article  Google Scholar 

  97. McNeil JA, Hubbard M, Swedberg AD (2012) Designing tomorrow’s snow park jump. Sports Eng 15:1–20

    Article  Google Scholar 

  98. Chardonnens J, Favre J, Callennec BL, Cuendet F, Gremion G, Aminian K (2012) Automatic measurement of key ski jumping phases and temporal events with a wearable system. J Sports Sci 30:53–61

    Article  Google Scholar 

  99. Goff JE (2010) Gold medal physics: the science of sports. The Johns Hopkins University Press, Baltimore, Chapter 7

  100. Carré MJ, Asai T, Akatsuka T, Haake SJ (2002) The curve kick of a football II: flight through the air. Sports Eng 5:193–200

    Article  Google Scholar 

  101. Goff JE, Carré MJ (2010) Soccer ball lift coefficients via trajectory analysis. Euro J Phys 31:775–784

    Article  Google Scholar 

  102. Barber S, Carré MJ (2010) The effect of surface geometry on soccer ball trajectories. Sports Eng 13:47–55

    Article  Google Scholar 

  103. Myers TG, Mitchell SL (2012) A mathematical analysis of the motion of an in-flight soccer ball. Sports Eng (published online 16 October 2012)

  104. Bray K, Kerwin DG (2003) Modelling the flight of a soccer ball in a direct free kick. J Sports Sci 21:75–85

    Article  Google Scholar 

  105. Cook BG, Goff JE (2006) Parameter space for successful soccer kicks. Euro J Phys 27:865–874

    Article  Google Scholar 

  106. Asai T, Seo K, Kobayashi O, Sakashita R (2007) Fundamental aerodynamics of the soccer ball. Sports Eng 10:101–110

    Article  Google Scholar 

  107. Goff JE, Smith WH, Carré MJ (2011) Football boundary-layer separation via dust experiments. Sports Eng 14:139–146

    Article  Google Scholar 

  108. Goff JE, Carré MJ (2012) Investigations into soccer aerodynamics via trajectory analysis and dust experiments. Proc Eng 34:158–163

    Article  Google Scholar 

  109. Carré MJ, Goodwill SR, Haake SJ (2005) Understanding the effect of seams on the aerodynamics of an association football. Proc IMechE, Part C: J Mech Eng Sci 219:657–666

    Article  Google Scholar 

  110. Passmore MA, Tuplin S, Spencer A, Jones R (2008) Experimental studies of the aerodynamics of spinning and stationary footballs. Proc IMechE, Part C: J Mech Eng Sci 222:195–205

    Article  Google Scholar 

  111. Alam F, Chowdhury H, Moria H, Fuss FK (2010) A comparative study of football aerodynamics. Proc Eng 2:2443–2448

    Google Scholar 

  112. Alam F, Chowdhury H, Moria H, Fuss FK, Khan I, Aldawi F, Subic A (2011) Aerodynamics of contemporary FIFA soccer balls. Proc Eng 13:188–193

    Article  Google Scholar 

  113. Asai T, Ito S, Seo K, Koike S (2012) Characteristics of modern soccer balls. Proc Eng 34:122–127

    Article  Google Scholar 

  114. Alam F, Chowdhury H, Stemmer M, Wang Z, Yang J (2012) Effects of surface structure on soccer ball aerodynamics. Proc Eng 34:146–151

    Google Scholar 

  115. Hong S, Chung C, Nakayama M, Asai T (2010) Unsteady Aerodynamic Force on a Knuckleball in Soccer. Proc Eng 2:2455–2460

    Article  Google Scholar 

  116. Asai T, Kamemoto K (2011) Flow structure of knuckling effects in footballs. J Fluids Struc 27:727–733

    Article  Google Scholar 

  117. Murakami M, Seo K, Kondoh M, Iwai Y (2012) Wind tunnel measurement and flow visualisation of soccer ball knuckle effect. Sports Eng 15:29–40

    Article  Google Scholar 

  118. Ito S, Kamata M, Asai T, Seo K (2012) Factors of unpredictable shots concerning new soccer balls. Proc Eng 34:152–157

    Article  Google Scholar 

  119. Barber S, Chin SB, Carré MJ (2009) Sports ball aerodynamics: a numerical study of the erratic motion of soccer balls. Comput Fluids 38:1091–1100

    Google Scholar 

  120. Barber S, Carré MJ (2010) Soccer ball aerodynamics. In: Peters M (ed) Computational fluid dynamics for sport simulation. Springer, Berlin

  121. Lees A, Asai T, Andersen TB, Nunome H, Sterzing T (2010) The biomechanics of kicking in soccer: A review. J of Sports Sci 28:805–817

    Article  Google Scholar 

  122. Asai T, Carré MJ, Akatsuka T, Haake SJ (2002) The curve kick of a football I: impact with the foot. Sports Eng 5:183–192

    Article  Google Scholar 

  123. Hong S, Kazama Y, Nakayama M, Asai T (2012) Ball impact dynamics of knuckling shot in soccer. Proc Eng 34:200–205

    Article  Google Scholar 

  124. Cross R, Lindsey C (2004) Technical tennis: racquests, strings, balls, courts, spin, and bounce. USRSA, Duluth

  125. Mehta RD, Alam F, Subic A (2008) Aerodynamics of tennis balls – a review. Sports Tech 1:1–10

    Article  Google Scholar 

  126. Goodwill SR, Chin SB, Haake SJ (2004) Aerodynamics of a spinning and non-spinning tennis balls. J Wind Eng 92:935–958

    Google Scholar 

  127. Djamovski V, Pateras J, Chowdhury H, Alam F, Steiner T (2012) Effects of seam and surface texture on tennis balls aerodynamics. Proc Eng 34:140–145

    Article  Google Scholar 

  128. Kelley J, Choppin SB, Goodwill SR, Haake SJ (2010) Validation of a live, automatic ball velocity and spin rate finder in tennis. Proc Eng 2:2967–2972

    Article  Google Scholar 

  129. Cairns TW, Van Lierop K (2000) Volleyballs and Aerodynamics: A Review. Int J Volleyball Res 3:8–14

    Google Scholar 

  130. Cairns TW (2004) Modeling lift and drag forces on a volleyball. In: Hubbard M, Mehta RD, Pallis JM (eds) The engineering of sport 5, vol 1, pp 97–103

  131. Asai T, Ito S, Seo K, Hitotsubashi A (2010) Aerodynamics of a New Volleyball. Proc Eng 2:2493–2498

    Article  Google Scholar 

  132. Rossmann Jenn, Rau A (2007) An experimental study of Whiffle ball aerodynamics. Am J Phys 75:1099–1105

    Article  Google Scholar 

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Acknowledgments

I thank Matt Carré for providing me with some pertinent articles. I also thank Jay Gerlach for providing me with journal access at his university. Thanks to Matthew Jones and Michael Solontoi for reading an early draft and offering helpful comments. I am also grateful to reviewers for valuable suggestions.

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Goff, J.E. A review of recent research into aerodynamics of sport projectiles. Sports Eng 16, 137–154 (2013). https://doi.org/10.1007/s12283-013-0117-z

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