Sports Engineering

, Volume 21, Issue 2, pp 95–102 | Cite as

Investigation of toppling ball flight in American football with a mechanical field-goal kicker

  • Chase M. Pfeifer
  • Timothy J. Gay
  • Jeff A. Hawks
  • Shane M. Farritor
  • Judith M. Burnfield
Original Article


A mechanical field-goal kicking machine was used to investigate toppling ball flight in American football place-kicking, eliminating a number of uncontrollable impact variables present with a human kicker. Ball flight trajectories were recorded using a triangulation-based projectile tracking system to account for the football’s 3-dimensional position during flight as well as initial launch conditions. The football flights were described using kinematic equations relating to projectile motion including stagnant air drag and were compared to measured trajectories as well as projectile motion equations that exclude stagnant air drag. Measured football flight range deviations from the non-drag equations of projectile motion corresponded to deficits between 9 and 31%, which is described by a football toppling compound drag coefficient of 0.007 ± 0.003 kg/m. Independent variables including impact location and impact angle orientation resulted in 15 impact conditions. We found that an impact location of 5.5 cm from the bottom of the ball maximized trajectory height and distance. At the 5.5-cm impact location, alterations in impact angle produced minimal change in football trajectory, including launch angle (range = 1.96 deg), launch speed (range = 1.06 m/s), and range (range = 0.94 m).


Kicking Football Drag Place-kicking American football Trajectory 



This research greatly benefited from the help of our research assistants, Andrew Palmesano, Margret Clay, and Jesse Lin. We would also like to acknowledge the Nebraska Athletic Performance Lab and the Athletics Department at the University of Nebraska-Lincoln for providing the laboratory space necessary for performing this study. This work was supported in part by the National Science Foundation through award PHY-1505794(TJG).

Compliance with ethical standards

Conflict of interest

The authors have no conflict of interest.


  1. 1.
    Goff JE (2013) A review of recent research into aerodynamics of sport projectiles. Sports Eng 16(3):137–154CrossRefGoogle Scholar
  2. 2.
    Watts RG, Moore G (2003) The drag force on an American football. Am J Phy 71(8):791–793CrossRefGoogle Scholar
  3. 3.
    Rae WJ, Streit RJ (2002) Wind-tunnel measurements of the aerodynamic loads on an American football. Sports Eng 5(3):165–172CrossRefGoogle Scholar
  4. 4.
    Rae WJ (2003) Flight dynamics of an American football in a forward pass. Sports Eng 6(3):149–163CrossRefGoogle Scholar
  5. 5.
    Cunningham J, Dowell L (1976) The effect of air resistance on three types of football trajectories. Res Quarterly Am Alliance Health Phys Educ Recreat 47(4):852–854Google Scholar
  6. 6.
    Brancazio PJ (1985) The physics of kicking a football. Phys Teach 23(7):403–407CrossRefGoogle Scholar
  7. 7.
    Gay T (2004) Football physics: the science of the game. Rodale, Harlan, pp 129–165Google Scholar
  8. 8.
    Lee WM, Mazzoleni AP, Zikry MA (2013) Aerodynamic effects on the accuracy of an end-over-end kick of an American football. Sports Eng 16(2):99–113CrossRefGoogle Scholar
  9. 9.
    Tipler PA, Mosca G (2007) Physics for scientists and engineers. Macmillan, BasingstokeGoogle Scholar
  10. 10.
    Pfeifer CM (2015) Biomechanical investigation of elite place-kicking. Dissertation, University of Nebraska-LincolnGoogle Scholar
  11. 11.
    Pfeifer CM, Burnfield JM, Twedt MH, Cesar GM, Hawks JA (2016) Video capture and post processing technique for approximating 3D projectile trajectory. Sports Tech. doi: 10.1080/19346182.2016.1248974 Google Scholar
  12. 12.
    Rouse H (2011) Dover books on physics: elementary mechanics of fluids. Dover, Mineola, New YorkGoogle Scholar
  13. 13.
    Alam F, Smith S, Chowdhury H, Moria H (2012) Aerodynamic drag measurement of American footballs. Proc Eng 34:98–103CrossRefGoogle Scholar
  14. 14.
    Asai T, Seo K, Kobayashi O, Sakashita R (2007) Fundamental aerodynamics of the soccer ball. Sports Eng 10(2):101–109CrossRefGoogle Scholar
  15. 15.
    Bearman PW, Harvey JK (1976) Golf ball aerodynamics. Aeronaut Quart 27(2):112–122CrossRefGoogle Scholar
  16. 16.
    Djamovski V, Rosette P, Chowdhury H, Alam F, Steiner T (2012) A comparative study of rugby ball aerodynamics. Proc Eng 34:74–79CrossRefGoogle Scholar

Copyright information

© International Sports Engineering Association 2017

Authors and Affiliations

  • Chase M. Pfeifer
    • 1
  • Timothy J. Gay
    • 2
  • Jeff A. Hawks
    • 3
  • Shane M. Farritor
    • 3
  • Judith M. Burnfield
    • 1
  1. 1.Institute for Rehabilitation Science and EngineeringMadonna Rehabilitation HospitalLincolnUSA
  2. 2.Physics & AstronomyUniversity of NebraskaLincolnUSA
  3. 3.Department of Mechanical and Materials EngineeringUniversity of Nebraska-LincolnLincolnUSA

Personalised recommendations