Sports Engineering

, Volume 16, Issue 3, pp 137–154 | Cite as

A review of recent research into aerodynamics of sport projectiles

Invited paper

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.

Keywords

Aerodynamics Archery Arrow Badminton Baseball Basketball CFD Computational fluid dynamics Cricket Discus Drag Football Golf Hammer throw Ice hockey Javelin Lift Rugby Sepaktakraw Shuttlecock Ski jumping Sport Soccer Tennis Trajectory analysis Volleyball Whiffle ball Wind tunnel 

References

  1. 1.
    Daish CB (1972) The physics of ball games. The English Universities Press Ltd, LondonGoogle Scholar
  2. 2.
    Mehta RD (1985) Aerodynamics of sports balls. Ann Rev Fluid Mech 17:151–189CrossRefGoogle Scholar
  3. 3.
    Frohlich C (2011) Resource Letter PS-2: Physics of Sports. Am J Phys 79:565–574CrossRefGoogle Scholar
  4. 4.
    White C (2011) Projectile dynamics in sport. Routledge, AbingdonGoogle Scholar
  5. 5.
    Wolfson R (2012) Essential University Physics, 2nd edn. Addison-Wesley, San Francisco, p 40Google Scholar
  6. 6.
  7. 7.
    Thornton ST, Marion JB (2004) Classical dynamics of particles and systems, 5th edn. Thomson Brooks/Cole, Belmont, p 59Google Scholar
  8. 8.
    Goff JE (2004) Heuristic model of air drag on a sphere. Phys Educ 39:496–499CrossRefGoogle Scholar
  9. 9.
    Adair RK (2002) The physics of baseball, 3rd edn. Perennial/Harper Collins, New YorkGoogle Scholar
  10. 10.
    White FM (2011) Fluid mechanics, 7th edn. McGraw-Hill Higher Education, New YorkGoogle Scholar
  11. 11.
    Wesson J (2002) The science of soccer. Institute of Physics Publishing, London, p 168Google Scholar
  12. 12.
    Goff JE, Carré MJ (2009) Trajectory analysis of a soccer ball. Am J Phys 77:1020–1027CrossRefGoogle Scholar
  13. 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 YorkGoogle Scholar
  14. 14.
    Nathan AM (2008) The effect of spin on the flight of a baseball. Am J Phys 76:119–124CrossRefGoogle Scholar
  15. 15.
    de Mestre N (1990) The mathematics of projectiles in sport. Cambridge University Press, CambridgeGoogle Scholar
  16. 16.
    Anderson Jr JD (2005) Ludwig Prandtl’s Boundary Layer. Phys Today 58:42–48CrossRefGoogle Scholar
  17. 17.
    Achenbach E (1972) Experiments on the flow past spheres at very high Reynolds numbers. J Fluid Mech 54:565–575CrossRefGoogle Scholar
  18. 18.
    Goff JE (2010) Power and spin in the beautiful game. Phys Today 63:62–63CrossRefGoogle Scholar
  19. 19.
    Bearman PW and Harvey JK (1976) Golf Ball Aerodynamics. Aeronautical Quarterly 27:112–122Google Scholar
  20. 20.
    Achenbach E (1974) The effects of surface roughness and tunnel blockage on the flow past spheres. J Fluid Mech 65:113–125CrossRefGoogle Scholar
  21. 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 221:789–806CrossRefGoogle Scholar
  22. 22.
    Koonin SE, Meredith DC (1990) Computational physics. Addison-Wesley, Boston Chapter 6Google Scholar
  23. 23.
    Huebner KH (2001) The finite element method for engineers, 4th edn. Wiley-Interscience, New YorkGoogle Scholar
  24. 24.
    Beer G, Smith I, Duenser C (2008) The boundary element method with programming: for engineers and scientists. Springer, New YorkGoogle Scholar
  25. 25.
    Hanna RK (2012) CFD in Sport – a Retrospective; 1992–2012. Proc Eng 34:622–726CrossRefGoogle Scholar
  26. 26.
    Chung TJ (2010) Computational fluid dynamics, 2nd edn. Cambridge University Press, CambridgeGoogle Scholar
  27. 27.
  28. 28.
    Klopsteg PE (1943) Physics of Bows and Arrows. Am J Phys 11:175–192CrossRefGoogle Scholar
  29. 29.
    Denny M (2011) Their arrows will darken the sun: the evolution and science of ballistics. The Johns Hopkins University Press, BaltimoreGoogle Scholar
  30. 30.
    French K and Kirk T (2005) Measuring the flight of an arrow using the Acoustic Doppler Shift. Mech Sys and Sig Proc 21:1188–1191CrossRefGoogle Scholar
  31. 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 225:8–21Google Scholar
  32. 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)Google Scholar
  33. 33.
    Park JL (2011) The aerodynamic drag and axial rotation of an arrow. Proc Inst Mech Eng Part P J Sports Eng and Tech 225:199–211CrossRefGoogle Scholar
  34. 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)Google Scholar
  35. 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 34:455–460CrossRefGoogle Scholar
  36. 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 226:114–122Google Scholar
  37. 37.
    Chen LM, P YH, Chen YJ (2009) A study of shuttlecock’s trajectory in badminton. J Sports Sci and Med 8:657–662Google Scholar
  38. 38.
    Alam F, Chowdhury H, Theppadungporn C, and Subic A (2010) Measurements of Aerodynamic Properties of Badminton Shuttlecocks. Proc Eng 2:2487–2492CrossRefGoogle Scholar
  39. 39.
    Chan CM, Rossmann JS (2012) Badminton shuttlecock aerodynamics: synthesizing experiment and theory. Sports Eng 15:61–71CrossRefGoogle Scholar
  40. 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 34:104–109CrossRefGoogle Scholar
  41. 41.
    Texier BD, Cohen C, Quéré D, and Claneta C (2012) Shuttlecock dynamics. Proc Eng 34:176–181CrossRefGoogle Scholar
  42. 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 27:589–596MATHCrossRefGoogle Scholar
  43. 43.
    Alawys LW, Hubbard M (2001) Experimental determination of baseball spin and lift. J Sports Sci 19:349–358CrossRefGoogle Scholar
  44. 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 71:1152–1162CrossRefGoogle Scholar
  45. 45.
    McBeath MK, Nathan AM, Bahill AT, Baldwin DG (2008) Paradoxical pop-ups: Why are they difficult to catch? Am J Phys 76:723–729CrossRefGoogle Scholar
  46. 46.
    www.sportvision.com/baseball/pitchfx. Accessed Jan 2013Google Scholar
  47. 47.
    Nathan AM (2012) Analysis of knuckleball trajectories. Proc Eng 34:116–121CrossRefGoogle Scholar
  48. 48.
    Meyer ER, Bohn JL (2008) Influence of a humidor on the aerodynamics of baseballs. Am J Phys 76:1015–1021CrossRefGoogle Scholar
  49. 49.
    Nathan AM, Cantakos J, Kesmna R, Mathew B, Lukash W (2012) Spin of a batted baseball. Proc Eng 34:182–187CrossRefGoogle Scholar
  50. 50.
    McGinnis RS, Perkins NC, King K (2012) Pitcher training aided by instrumented baseball. Proc Eng 34:580–585CrossRefGoogle Scholar
  51. 51.
    Fontanella JJ (2006) The physics of basketball, The Johns Hopkins University Press, BaltimoreGoogle Scholar
  52. 52.
    Huston RL, Grau CA (2003) Basketball shooting strategies – the free throw, direct shot and layup. Sports Eng 6:49–64CrossRefGoogle Scholar
  53. 53.
    Okubo H, Hubbard M (2012) Defense for basketball field shots. Proc Eng 34:730–735CrossRefGoogle Scholar
  54. 54.
    Mehta RD (2005) An overview of cricket ball swing. Sports Eng 8:181–192CrossRefGoogle Scholar
  55. 55.
    James DM, Carré MJ, and Haake SJ (2004) The playing performance of country cricket pitches. Sports Eng 7:1–14CrossRefGoogle Scholar
  56. 56.
    James D, MacDonald DC, and Hart J (2012) The effect of atmospheric conditions on the swing of a cricket ball. Proc Eng 34:188–193CrossRefGoogle Scholar
  57. 57.
    Fuss FK, Smith RM, Subic A (2012) Determination of spin rate and axes with an instrumented cricket ball. Proc Eng 34:128–133CrossRefGoogle Scholar
  58. 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 11–19Google Scholar
  59. 59.
    Hubbard M, Cheng KB (2007) Optimal discus trajectories. J Biomech 40:3650–3659CrossRefGoogle Scholar
  60. 60.
    Frohlich C (1981) Aerodynamic and mechanical forces in discus flight. Am J Phys 49:1125–1132CrossRefGoogle Scholar
  61. 61.
    Goff JE (2010) Gold medal physics: the science of sports. The Johns Hopkins University Press, Baltimore, Chapter 8Google Scholar
  62. 62.
    Seo K, Shimoyama K, Ohta K, Ohgi Y, Kimura Y (2012) Aerodynamic behavior of a discus. Proc Eng 34:92–97CrossRefGoogle Scholar
  63. 63.
    Crowther WJ, Potts JR (2007) Simulation of a spin-stabilised sports disc. Sports Eng 10:3–21CrossRefGoogle Scholar
  64. 64.
    Lissaman P, Hubbard M (2010) Maximum range of flying discs. Proc Eng 2:2529–2535CrossRefGoogle Scholar
  65. 65.
    Gay T (2005) The physics of football. HarperCollins, New YorkGoogle Scholar
  66. 66.
    Goff JE (2010) Gold medal physics: the science of sports. The Johns Hopkins University Press, Baltimore, Chapter 3Google Scholar
  67. 67.
    Rae WJ (2003) Flight dynamics of an American football in a forward pass. Sports Eng 6:149–163CrossRefGoogle Scholar
  68. 68.
    Rae WJ, Steit RJ (2002) Wind-tunnel measurements of the aerodynamic loads on an American football. Sport Eng 5:165–172CrossRefGoogle Scholar
  69. 69.
    Alam F, Smith S, Chowdhury H, and Moria H (2012) Aerodynamic drag measurements of American footballs. Proc Eng 34:98–103CrossRefGoogle Scholar
  70. 70.
    Watts RG, Moore G (2003) The drag on an American football. Am J Phys 71:791–793CrossRefGoogle Scholar
  71. 71.
    Jorgensen TP (1999) The physics of golf, 2nd edn. Springer, New YorkGoogle Scholar
  72. 72.
    Davies JM (1949) The Aerodynamics of Golf Balls. J Appl Phys 20:821–828CrossRefGoogle Scholar
  73. 73.
    Choi J, Jeon WP, Choi H (2006) Mechanism of drag reduction by dimples on a sphere. Phys Fluids 18:041702Google Scholar
  74. 74.
    Penner AR (2001) The physics of golf: The optimum loft of a driver. Am J Phys 69:563–568CrossRefGoogle Scholar
  75. 75.
    Penner AR (2001) The physics of golf: The convex face of a driver. Am J Phys 69:1073–1081CrossRefGoogle Scholar
  76. 76.
    Parviz M, Kim J (1997) Tackling Turbulence with Supercomputers. Sci Am 276:62–68Google Scholar
  77. 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 2:3249–3254CrossRefGoogle Scholar
  78. 78.
    Dapena J, Gutiérrez-Dávila G, Soto VM, Rojas FJ (2003) Prediction of distance in hammer throwing. J Sports Sci 21:21–28CrossRefGoogle Scholar
  79. 79.
    Haché A (2002) The physics of hockey. The Johns Hopkins University Press, BaltimoreGoogle Scholar
  80. 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 10:75–86CrossRefGoogle Scholar
  81. 81.
    Hubbard M, Rust HJ (1984) Simulation of Javelin Flight Using Experimental Aerodynamic Data. J Biomech 17:769–776CrossRefGoogle Scholar
  82. 82.
    Hubbard M (1984) Optimal Javelin Trajectories. J Biomech 17:777–787CrossRefGoogle Scholar
  83. 83.
    Hubbard M, Alaways LW (1987) Optimum Release Conditions for the New Rules Javelin. Int J Sport Biomech 3:207–221Google Scholar
  84. 84.
    Hubbard M, Bergman CD (1989) Effect of Vibrations on Javelin Lift and Drag. Int J Sport Biomech 5:40–59Google Scholar
  85. 85.
    Hubbard M, Laport S (1997) Damping of Javelin Vibrations in Flight. J Appl Biomech 13:269–286Google Scholar
  86. 86.
    Maryniak J, Ladyźyńska-Kozdraś E, Golińska E (2009) Mathematical Modeling and Numerical Simulations of Javelin Throw. Hum Dev 10:16–20Google Scholar
  87. 87.
    Maszczyk A, Zając A, Ryguła I (2011) A neural network model approach to athlete selection. Sports Eng 13:83–93CrossRefGoogle Scholar
  88. 88.
    Lipscombe TD (2009) The physics of rugby. Nottingham University Press, NottinghamGoogle Scholar
  89. 89.
    Seo K, Kobayashi O, Murakami M (2006) Flight dynamics of the screw kick in rugby. Sports Eng 9:49–58CrossRefGoogle Scholar
  90. 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, BerlinGoogle Scholar
  91. 91.
    Djamovski V, Rosette P, Chowdhury H, Alam F, Steiner T (2012) A comparative study of rugby ball aerodynamics. Proc Eng 34:74–79CrossRefGoogle Scholar
  92. 92.
    Taha Z, Sugiyono (2009) Effect of diameter on the aerodynamics of sepaktakraw balls, a computational study. Int J Sports Sci Eng 3:17–21Google Scholar
  93. 93.
    Seo K, Watanabe I, Murakami M (2004) Aerodynamic force data for a V-style ski jumping flight. Sports Eng 7:31–39CrossRefGoogle Scholar
  94. 94.
    Seo K, Murakami M, Yoshida K (2004) Optimal flight technique for V-style ski jumping. Sports Eng 7:97–104CrossRefGoogle Scholar
  95. 95.
    Nørstrud H, Øye IJ (2010) On CFD simulation of ski jumping. In: Peters M (ed) Computational fluid dynamics for sport simulation. Springer, BerlinGoogle Scholar
  96. 96.
    McNeil JA, McNeil JB (2009) Dynamical analysis of winter terrain park jumps. Sports Eng 11:159–164CrossRefGoogle Scholar
  97. 97.
    McNeil JA, Hubbard M, Swedberg AD (2012) Designing tomorrow’s snow park jump. Sports Eng 15:1–20CrossRefGoogle Scholar
  98. 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 30:53–61CrossRefGoogle Scholar
  99. 99.
    Goff JE (2010) Gold medal physics: the science of sports. The Johns Hopkins University Press, Baltimore, Chapter 7Google Scholar
  100. 100.
    Carré MJ, Asai T, Akatsuka T, Haake SJ (2002) The curve kick of a football II: flight through the air. Sports Eng 5:193–200CrossRefGoogle Scholar
  101. 101.
    Goff JE, Carré MJ (2010) Soccer ball lift coefficients via trajectory analysis. Euro J Phys 31:775–784CrossRefGoogle Scholar
  102. 102.
    Barber S, Carré MJ (2010) The effect of surface geometry on soccer ball trajectories. Sports Eng 13:47–55CrossRefGoogle Scholar
  103. 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)Google Scholar
  104. 104.
    Bray K, Kerwin DG (2003) Modelling the flight of a soccer ball in a direct free kick. J Sports Sci 21:75–85CrossRefGoogle Scholar
  105. 105.
    Cook BG, Goff JE (2006) Parameter space for successful soccer kicks. Euro J Phys 27:865–874CrossRefGoogle Scholar
  106. 106.
    Asai T, Seo K, Kobayashi O, Sakashita R (2007) Fundamental aerodynamics of the soccer ball. Sports Eng 10:101–110CrossRefGoogle Scholar
  107. 107.
    Goff JE, Smith WH, Carré MJ (2011) Football boundary-layer separation via dust experiments. Sports Eng 14:139–146CrossRefGoogle Scholar
  108. 108.
    Goff JE, Carré MJ (2012) Investigations into soccer aerodynamics via trajectory analysis and dust experiments. Proc Eng 34:158–163CrossRefGoogle Scholar
  109. 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 219:657–666CrossRefGoogle Scholar
  110. 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 222:195–205CrossRefGoogle Scholar
  111. 111.
    Alam F, Chowdhury H, Moria H, Fuss FK (2010) A comparative study of football aerodynamics. Proc Eng 2:2443–2448Google Scholar
  112. 112.
    Alam F, Chowdhury H, Moria H, Fuss FK, Khan I, Aldawi F, Subic A (2011) Aerodynamics of contemporary FIFA soccer balls. Proc Eng 13:188–193CrossRefGoogle Scholar
  113. 113.
    Asai T, Ito S, Seo K, Koike S (2012) Characteristics of modern soccer balls. Proc Eng 34:122–127CrossRefGoogle Scholar
  114. 114.
    Alam F, Chowdhury H, Stemmer M, Wang Z, Yang J (2012) Effects of surface structure on soccer ball aerodynamics. Proc Eng 34:146–151Google Scholar
  115. 115.
    Hong S, Chung C, Nakayama M, Asai T (2010) Unsteady Aerodynamic Force on a Knuckleball in Soccer. Proc Eng 2:2455–2460CrossRefGoogle Scholar
  116. 116.
    Asai T, Kamemoto K (2011) Flow structure of knuckling effects in footballs. J Fluids Struc 27:727–733CrossRefGoogle Scholar
  117. 117.
    Murakami M, Seo K, Kondoh M, Iwai Y (2012) Wind tunnel measurement and flow visualisation of soccer ball knuckle effect. Sports Eng 15:29–40CrossRefGoogle Scholar
  118. 118.
    Ito S, Kamata M, Asai T, Seo K (2012) Factors of unpredictable shots concerning new soccer balls. Proc Eng 34:152–157CrossRefGoogle Scholar
  119. 119.
    Barber S, Chin SB, Carré MJ (2009) Sports ball aerodynamics: a numerical study of the erratic motion of soccer balls. Comput Fluids 38:1091–1100Google Scholar
  120. 120.
    Barber S, Carré MJ (2010) Soccer ball aerodynamics. In: Peters M (ed) Computational fluid dynamics for sport simulation. Springer, BerlinGoogle Scholar
  121. 121.
    Lees A, Asai T, Andersen TB, Nunome H, Sterzing T (2010) The biomechanics of kicking in soccer: A review. J of Sports Sci 28:805–817CrossRefGoogle Scholar
  122. 122.
    Asai T, Carré MJ, Akatsuka T, Haake SJ (2002) The curve kick of a football I: impact with the foot. Sports Eng 5:183–192CrossRefGoogle Scholar
  123. 123.
    Hong S, Kazama Y, Nakayama M, Asai T (2012) Ball impact dynamics of knuckling shot in soccer. Proc Eng 34:200–205CrossRefGoogle Scholar
  124. 124.
    Cross R, Lindsey C (2004) Technical tennis: racquests, strings, balls, courts, spin, and bounce. USRSA, DuluthGoogle Scholar
  125. 125.
    Mehta RD, Alam F, Subic A (2008) Aerodynamics of tennis balls – a review. Sports Tech 1:1–10CrossRefGoogle Scholar
  126. 126.
    Goodwill SR, Chin SB, Haake SJ (2004) Aerodynamics of a spinning and non-spinning tennis balls. J Wind Eng 92:935–958Google Scholar
  127. 127.
    Djamovski V, Pateras J, Chowdhury H, Alam F, Steiner T (2012) Effects of seam and surface texture on tennis balls aerodynamics. Proc Eng 34:140–145CrossRefGoogle Scholar
  128. 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 2:2967–2972CrossRefGoogle Scholar
  129. 129.
    Cairns TW, Van Lierop K (2000) Volleyballs and Aerodynamics: A Review. Int J Volleyball Res 3:8–14Google Scholar
  130. 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 97–103Google Scholar
  131. 131.
    Asai T, Ito S, Seo K, Hitotsubashi A (2010) Aerodynamics of a New Volleyball. Proc Eng 2:2493–2498CrossRefGoogle Scholar
  132. 132.
    Rossmann Jenn, Rau A (2007) An experimental study of Whiffle ball aerodynamics. Am J Phys 75:1099–1105CrossRefGoogle Scholar

Copyright information

© International Sports Engineering Association 2013

Authors and Affiliations

  1. 1.Department of PhysicsLynchburg CollegeLynchburgUSA

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