Trajectory analysis of a soccer ball

American Journal of Physics

Volumn 77, Issue 11, 2009, Pages 1020-1027

  Goff, John Eric ^a   Carŕ, Matt J ^b  

^a LYNCHBURG COLLEGE   (United States)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350026271     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.3197187     Document Type: Article

References (39)

1. Lyman J. Briggs, " Effects of spin and speed on the lateral deflection (curve) of a baseball; and the Magnus effect for smooth spheres.," Am. J. Phys. 0002-9505 27, 589-596 (1959). 10.1119/1.1934921
2. E. Achenbach, " Experiments on the flow past spheres at very high Reynolds numbers.," J. Fluid Mech. 0022-1120 54, 565-575 (1972). 10.1017/S0022112072000874
3. E. Achenbach, " The effects of surface roughness and tunnel blockage on the flow past spheres.," J. Fluid Mech. 0022-1120 65, 113-125 (1974). 10.1017/S0022112074001285
4. Robert G. Watts and Eric Sawyer, " Aerodynamics of a knuckleball.," Am. J. Phys. 0002-9505 43, 960-963 (1975). 10.1119/1.10020
5. Robert G. Watts and Ricardo Ferrer, " The lateral force on a spinning sphere: Aerodynamics of a curveball.," Am. J. Phys. 0002-9505 55, 40-44 (1987). 10.1119/1.14969
6. P. W. Bearman and J. K. Harvey, " Golf ball aerodynamics.," Aeronaut. Q. 0001-9259 27, 112-122 (1976).
7. S. J. Haake, S. G. Chadwick, R. J. Dignall, S. Goodwill, and P. Rose, " Engineering tennis-Slowing the game down.," Sports Eng. 1369-7072 3, 131-144 (2000). 10.1046/j.1460-2687.2000.00040.x
8. R. D. Mehta and J. M. Pallis, " Sports ball aerodynamics: Effects of velocity, spin and surface roughness.," in Materials and Science in Sports, edited by, F. H. Froes, and, S. J. Haake, (TMS, Warrendale, PA, 2001), pp. 185-197.
9. M. J. Carŕ, S. R. Goodwill, and S. J. Haake, " Understanding the effect of seams on the aerodynamics of an association football.," J. Mech. Eng. Sci. 0022-2542 219, 657-666 (2005).
10. T. Asai, K. Seo, O. Kobayashi, and R. Sakashita, " Fundamental aerodynamics of the soccer ball.," Sports Eng. 1369-7072 10, 101-110 (2007).
11. Sarah Barber, " The aerodynamics of association footballs.," Ph.D. thesis, University of Sheffield, July 2007.
12. M. A. Passmore, S. Tuplin, A. Spencer, and R. Jones, " Experimental studies of the aerodynamics of spinning and stationary footballs.," J. Mech. Eng. Sci. 0022-2542 222, 195-205 (2008).
13. M. J. Carŕ, T. Akatsuka, and S. J. Haake, " The curve kick of a football: II. Flight through the air.," Sports Eng. 1369-7072 5, 193-200 (2002). 10.1046/j.1460-2687.2002.00109.x
14. John Wesson, The Science of Soccer (Institute of Physics, Bristol, 2002).
15. K. Bray and D. G. Kerwin, " Modelling the flight of a soccer ball in a direct free kick.," J. Sports Sci. 0264-0414 21, 75-85 (2003). 10.1080/0264041031000070994 (Pubitemid 36244952)
16. Brandon G. Cook and John Eric Goff, " Parameter space for successful soccer kicks.," Eur. J. Phys. 0143-0807 27, 865-874 (2006). 10.1088/0143-0807/27/4/017 (Pubitemid 43932817)
17. John Eric Goff, Gold Medal Physics (Johns Hopkins U. P., Baltimore, MD, 2010), Chap..
18. Joseph M. Zayas, " Experimental determination of the coefficient of drag of a tennis ball.," Am. J. Phys. 0002-9505 54, 622-625 (1986). 10.1119/1.14519
19. Antonin Štěpánek, " The aerodynamics of tennis balls-The topspin lob.," Am. J. Phys. 0002-9505 56, 138-142 (1988). 10.1119/1.15692
20. LeRoy W. Alaways and Mont Hubbard, " Experimental determination of baseball spin and lift.," J. Sports Sci. 0264-0414 19, 349-358 (2001). 10.1080/02640410152006126 (Pubitemid 32433036)
21. Alan M. Nathan, " The effect of spin on the flight of a baseball.," Am. J. Phys. 0002-9505 76, 119-124 (2008). 10.1119/1.2805242
22. Frank M. White, Fluid Mechanics, 6th ed. (McGraw-Hill, New York, 2008), p. 27.
23. Reference, pp. 476-480.
24. We used a standard 32-panel soccer ball manufactured by Umbro, model X III 250.
25. D. J. Tritton, Physical Fluid Dynamic, 2nd ed. (Clarendon, Oxford, 1988), pp. 159-161.
26. The programs at 〈 http://goff-j.web.lynchburg.edu/MathematicaAJP. html 〉 are free for readers to download and modify as they wish.
27. Robert L. Zimmerman and Fredrick I. Olness, MATHEMATICA for Physics, 2nd ed. (Addison-Wesley/Prentice-Hall, San Francisco, 2003).
28. See 〈 www.hawkeyeinnovations.co.uk 〉 for more information.
29. CINE VIEWER by Phantom may be downloaded for free at 〈 www.visionresearch.com/index.cfm?page=software 〉. Note that a "cine" is simply a motion picture.
30. Our in-house software was developed by Richard Dignall and Simon Goodwill at the University of Sheffield. There are other commercially available software packages that allow one to analyze trajectories from videos. A good one sold primarily in the U.S. is VIDEOPOINT.
31. John H. Mathews, Numerical Methods for Computer Science, Engineering, and Mathematics (Prentice-Hall, London, 1987), p. 284.
32. Kendall E. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1989), p. 317.
33. See, for example, R. D. Mehta, " Aerodynamics of sports balls.," Annu. Rev. Fluid Mech. 0066-4189 17, 151-189 (1985). 10.1146/annurev.fl.17.010185.001055
34. See, for example, Neville De Mestre, The Mathematics of Projectiles in Sports (Cambridge U. P., Cambridge, 1990).
35. Reference, p. 39.
36. Reference, p. 105.
37. Reference, p. 106. Note that we write the cross product in the opposite way that De Mestre does.
38. See, for example, Ref., pp. 281-283, and Ref. pp. 318-320.
39. David James and Steve Haake, " The spin decay of sports balls in flight.," in The Engineering of Sport 7, edited by, M. Estivalet, and, P. Brisson, (Springer, Paris, 2008), Vol. 2, pp. 165-170.