Science and Golf II: Proceedings of the 1994 World Scientific Congress of Golf

By A. J. Cochran; M. R. Farrally | Go to book overview

52

A new aerodynamic model of a golf ball in flight

A.J. Smits

Princeton University, Princeton, NJ, USA


and D.R. Smith

IMST, Marseille, France

Abstract

A new aerodynamic model of a golf ball is proposed based on recent wind tunnel measurements. The primary features of the model are the inclusion of a spin rate decay law, and a non-linear dependence of the drag on Reynolds number. This term is necessary to represent accurately the decrease in drag coefficient observed at Reynolds numbers greater than about 200,000.

Keywords: Golf ball, Aerodynamics.


1 Introduction

Accurate measurements of the lift and drag characteristics of golf balls are necessary to predict the golf ball trajectory and its point of impact The first comprehensive measurements of the lift and drag of a spinning golf ball were made by Davies (1949) who measured the aerodynamic forces acting on the ball by dropping it through the horizontal air stream of a wind tunnel. By measuring the point of impact of the ball on the tunnel floor, and by repeating this measurement for balls with clockwise and counterclockwise spin, the lift and drag could be determined. The spin rate was varied up to 8000 rpm (corresponding to a spin rate parameter W=ωr/V of 0.089), but only one tunnel speed was used (105 ft/s, corresponding to a Reynolds number R=2Vr/v of about 94,000). Davies also presented some trajectory calculations using the measured lift and drag information, but, as he stated: “Neither the manner in which L and D vary with translational speed nor the time rate of change of rotational speed are known.”

The next major contribution was made by Bearman and Harvey (1976), who suspended a large model of a golf ball in a wind tunnel using fine wire supports. The ball could be spun in either direction using a motor mounted inside the ball. The interference due to the support wires was determined by reference to previous results for spinning smooth spheres, and it was found that when the ratio of the support wire diameter to the ball diameter was less than about 0.005 the interference effects were negligible. Results were obtained for Reynolds numbers between 0.4×105 and 2.5×105 (equivalent golf ball velocities of 46 and 289 ft/s respectively), and spin rate parameters of 0.02 to 0.3. No information was obtained on the time rate of change of rotational speed.

More recently, Aoyama (1990) adapted Davies method for finding lift and drag from drop tests by recording the trajectory of the ball as it fell using short exposure video techniques. This approach can give more accurate results for lift and drag since there is no need for simplifying assumptions regarding the trajectory shape, the equations of motion or the relative velocity differences between the ball and the airstream. Lift and drag coefficients were presented for ball velocities of 100 to 250 ft/s, and spin rates from 1000

Science and Golf II: Proceedings of the World Scientific Congress of Golf. Edited by A.J. Cochran and M.R. Farrally. Published in 1994 by E & FN Spon, London. ISBN 0 419 18790 1

-340-

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