Experimental Verification of Trajectory Analysis of Golf Ball under Atmospheric Boundary Layer

  • Takeshi Naruo
  • Taketo Mizota


Aerodynamic forces and torque acting on the ball were measured under various flight conditions in a wind tunnel. Using the aerodynamic force coefficients, mathematical calculation of flight trajectory was made by time integral calculus. Three-dimensional flight trajectory, changes in velocity as well as rotation velocity were obtained. Furthermore the logarithmic law was applied to trajectory formation of a golf ball in order to include influence of atmospheric boundary layer. Moreover, an experiment was conducted in order to verify the logarithmic law and the trajectory formulation. Wind velocity distribution in the vertical direction was measured. As a result, the measured result almost matched the logarithmic law. Golf balls were hit under various initial launch conditions by a professional golfer using various golf clubs. Initial launch conditions of the golf balls were measured and wind velocity distribution in the golf ball direction was also measured. The golf ball trajectory under atmospheric boundary layer was calculated by using measured initial launch conditions and wind velocity distribution. The calculated drop positions by trajectory analysis agreed with the actual measured results.


Wind Direction Wind Velocity Atmospheric Boundary Layer Aerodynamic Force Trajectory Analysis 
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  1. Bearman P.W. and Harvey J.K. (1976) Golf ball aerodynamics. Aeronautical Quarterly, 27, pp.112–122.Google Scholar
  2. Naruo, T. and Mizota, T. (2005) Trajectory analysis of golf ball under atmospheric boundary layer. The Impact on Technology on Sport, Melbourne, pp. 253–260.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Takeshi Naruo
    • 1
  • Taketo Mizota
    • 2
  1. 1.Mizuno CorporationOsakaJapan
  2. 2.Fukuoka Institute of TechnologyFukuokaJapan

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