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The aerodynamics of golf balls is considerably more complex than that of many other spherical balls. The surface roughness in the form of dimples intensifies the level of complexity and three-dimensionality of air flow around the golf ball. Prior studies have revealed that golf ball aerodynamics is still not fully understood due to the varied dimple size, shape, depth and pattern. The current study experimentally measured drag coefficients of a range of commercially available golf balls, under a range of wind speeds. It was found that the drag coefficients of these balls varied significantly due to varied dimple geometry.
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5
th
Asia-Pacific Congress on Sports Technology (APCST)
A study of golf ball aerodynamic drag
Firoz Alam
*
, Tom Steiner, Harun Chowdhury, Hazim Moria, Iftekhar Khan,
Fayez Aldawi, Aleksandar Subic
School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Melbourne, Victoria 3083, Australia
Received 8 April 2011; revised 15 May 2011; accepted 16 May 2011
Abstract
The aerodynamics of golf balls is considerably more complex than that of many other spherical balls. The surface
roughness in the form of dimples intensifies the level of complexity and three-dimensionality of air flow around the
golf ball. Prior studies have revealed that golf ball aerodynamics is still not fully understood due to the varied dimple
size, shape, depth and pattern. The current study experimentally measured drag coefficients of a range of
commercially available golf balls, under a range of wind speeds. It was found that the drag coefficients of these balls
varied significantly due to varied dimple geometry.
© 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of RMIT University
Keywords: Aerodynamics; golfball; wind tunnel; drag coefficient
1. Introduction
The player’s performance can significantly be enhanced if the aerodynamic behavior of the golf ball is
understood and the potential benefit exploited intelligently. A wide variety of commercially manufactured
golf balls are available to suit individual golfer’s style of play. Of particular relevance to this work is the
variation in dimple geometry. The flight trajectory is influenced by the aerodynamic forces exerted on the
ball, which are significantly dependent on the physical features of the dimples. Most commercially
manufactured golf balls have between 250 and 500 dimples, however these dimples vary in size, shape
and depth. Golf ball manufacturers often claim superior aerodynamic performance of their balls, however
* Corresponding author. Tel.: +61-3-9925-6103; fax: +61-3-9926-6108.
E-mail address: firoz.alam@rmit.edu.au.
1877–7058 © 2011 Published by Elsevier Ltd.
doi:10.1016/j.proeng.2011.05.077
Procedia Engineering 13 (2011) 226–231
Firoz Alam et al. / Procedia Engineering 13 (2011) 226–231
227
there is an absence of detailed aerodynamic data available in the public domain. This hampers
verification of claims, and also intelligent selection of balls by players.
A golf ball usually moves at a speed that is sufficiently high to reduce its’ drag to about half that of a
smooth sphere. This favorable reduction in drag is caused by the dimples on the golf ball surface which
trigger the boundary layer to transition from laminar to turbulent flow. Several widely published studies
have been conducted by Smits et al. [8-9], Bearman and Harvey [6], Choi et al. [7], Smith et al. [10] and
Ting et al. [11] on golf ball aerodynamics under spinning and non-spinning conditions. Despite this work
the mechanisms through which the dimpled surface influence the boundary layer transition have not been
fully understood to the extent that accurate force and trajectory prediction would be possible [4-5, 7-10].
Studies conducted by commercial golf ball manufacturers are generally kept “in-house” as confidential
information in a highly competitive market, and consequently very little information is available in the
public domain on development and the current performance of golf balls. In this context the primary
objective of this research is to experimentally evaluate the aerodynamic properties, especially drag, of a
series of commercially available golf balls with varied dimple characteristics, which are widely used in
professional and amateur/recreational golf.
2. Experimental Procedure
2.1. Description of balls
Eight brand new commercially available golf balls that are widely used in major tournaments around the
world were selected for this study. Each of these balls has different dimple characteristics. The average
diameter and mass of the golf ball is around 42.7 mm and 45.5 g. The balls’ retail prices vary significantly
from 2.5 to 7.0 Australian dollars. The commercial brand name and their physical characteristics (diameter,
cost and dimple shapes) are shown in Table 1. The pictorial dimple shapes are shown in Figure 1.
Table 1. Balls’ dimple types
Ball Name Dimple Shape
1 Titleist Pro V1 Circular
2 TaylorMade Circular
3 Srixon Circular
4 Callaway Hexagonal
5 Nike PD2 Circular (smaller and large)
6 Wilson Staff Circular flat
7 Top Flite Circular within Circular
8 MaxFli Circular shallow
Figure 1 shows the dimple configuration of each ball used in this study. The dimple shape and size are
quite different from each other; none of these eight balls have the same dimple size and configuration.
The dimple shape and size are quite different from each other as none of these 8 balls that have the
exactly same dimple size and configuration.
Each of these balls was tested in the RMIT Industrial Wind Tunnel using a six-component force
balance over a range of representative wind speeds (40 km/h to 140 km/h in increments of 20 km/h).
228 Firoz Alam et al. / Procedia Engineering 13 (2011) 226–231
(a) Titleist Pro V1
(b) TaylorMade TP/Red LDP
(c) Top Flite D2 Distance
(d) Wilson Staff DX2
Distance
(e) Callaway Big Bertha
(f) Nike PD 2
(g) MaxFli
(h) Srixon AD333
Fig. 1. Range of golf balls used in this study.
2.2. Experimental set up
The study was conducted in the RMIT Industrial Wind Tunnel, which is a closed return circuit wind
tunnel with a turntable to enable study of cross wind effects. The maximum speed of the wind tunnel is
approximately 150 km/h, with a turbulence intensity of 1.8%. The wind tunnel test section has a
rectangular cross-section; dimensions of the test section are 3 m wide, 2 m high and 9 m long. Further
details about the tunnel can be found in Alam et al. [3]. The wind tunnel was calibrated before conducting
the experiments relevant to this present work, and the air speeds were measured via a modified NPL
ellipsoidal-head Pitot-static tube located at the same station as the golf ball, connected to a MKS Baratron
pressure sensor through flexible tubing.
A mounting stud was manufactured to hold the ball and was mounted on a six component force
balance (type JR-3) as shown in Figure 2. The 1
st
set up shown in Figure 2(a) was used for the initial
measurement however the interference drag was found to be very high compared the drag of the golf ball.
The 2
nd
set up, shown in Figure 2(b), was developed later and found to be more suitable for this study.
Computer software developed in-house was used to acquire load data from the force balance, and
compute all six forces and moments (drag, side, and lift forces, and yaw, pitch, and roll moments), and
then calculate their non-dimensional coefficients.
Firoz Alam et al. / Procedia Engineering 13 (2011) 226–231
229
(a) Setup A
(b) Setup B (improved, and used to obtain data presented here)
Fig. 2. Two experimental setups that have been used in this study shown here
The aerodynamic properties (drag, lift and side force and their corresponding moments) were
measured at wind speeds of 40 km/h to 140 km/h. The aerodynamic forces acting on the balls alone were
determined by subtracting the forces acting on the supporting gear only (with no ball attached) from the
combined force determined for balls attached to the supporting gear (mounting stud).
3. Results and Discussion
The output data from the wind tunnel computer data acquisition system comprised three forces (drag,
lift, and side force) and three moments (yaw, pitch, and roll). The drag coefficient (C
D
) and Reynolds
number (Re) were calculated by using the following formulae:
AV
D
C
D
2
2
1
ρ
=
and
μ
ρ
Vd
Re =
; where,
D,
ρ
, V, d, μ and A are respectively the drag force, air density, wind velocity, ball diameter, absolute
dynamic viscosity of air, and projected frontal area of the ball.
The data shows significant variation between balls as far as C
D
is concerned, with the greatest variation
amongst most balls being evident at lower Reynolds numbers for the range tested. The aerodynamic
behaviour of a squash ball (with relatively smooth surface to replicate a smooth sphere) was also
measured to compare the findings with the smooth sphere data obtained by Achenbach [1]. The C
D
value
for the squash ball is also shown in Figure 3 for benchmarking purpose with the published data. The C
D
of
each golf ball varies significantly with Reynolds numbers, and the drag coefficient for all the balls
exhibits similar broad behaviours. The transition from the sub-critical region to the critical region is
complete at a Reynolds number of approximately 1×10
5
for all golf balls. At this Reynolds number, the
C
D
for each ball has decreased to its minimum value. In the data presented in Figure 3, only the Maxfli
golf ball has similar drag behaviour to that shown in Bearman and Harvey [7]. After the transition, the
Maxfli has a minimum C
D
value of approximately 0.25. Although most other golf balls also undergo
transition and have minimum values at around, their minimum C
D
value is significantly higher (between
25% and nearly 50%) compared to the Maxfli golf ball. The variation in C
D
values among the golf balls is
believed to be primarily due to the differences in boundary layer separation generated by different dimple
230 Firoz Alam et al. / Procedia Engineering 13 (2011) 226–231
numbers, shapes, sizes, depths and patterns. The significant variation in drag coefficient between balls
with superficially similar dimpling suggests that even subtle differences in dimpling can produce
substantial changes in flow separations which consequently affect pressure drag.
As shown in Figure 3, although there is significant variation in C
D
values one ball, the Maxfli, has drag
characteristics that are distinctly different from all the other balls tested. Close examination of the dimple
geometry of the Maxfli showed that these dimples were shallow but not flat, and there was a significant
angle between the edge of dimples and the outer “spherical envelope”. Other balls appeared to have
somewhat smoothed profiles where the dimples merged into the outer “spherical envelope” which
reduced the angle in these areas. The data supports a conjecture that this relative “sharpness” opposed to
“smoothing” is a critical factor for drag reduction.
C
D
versus Re
0.20
0.30
0.40
0.50
0.60
0.70
0.80
6.E+04 7.E+04 8.E+04 9.E+04 1.E+05 1.E+05 1.E+05
Reynolds number, Re
Drag Coefficient, C
D
CBBD (Callaway)
MAX (Ma xfi )
NPD (Nike)
SR (W Staff)
SRN (Srixon)
T0M (TaylorMade 0)
T1F (Top Flite)
TPVX (Titleist Pro VX)
Squash ball
Fig. 3. Drag coefficient as a function of Reynolds Number for balls tested
4. Conclusions
The following conclusions were made from this work:
The dimple characteristics have significant effects on aerodynamic drag of golf balls.
Price did not correlate with performance for the balls purchased and tested.
The variation of drag coefficient among the current production golf balls has found to be as large as
40% due to dimple characteristics.
Data obtained supports a conjecture that the profile of the region where the dimple merges into the
outer “spherical envelope” has a strong influence on drag.
Firoz Alam et al. / Procedia Engineering 13 (2011) 226–231
231
5. Future Work
Work is underway to characterize the dimples and relate them to aerodynamic properties. The effects
of spin on aerodynamic properties especially on drag and lift will be analysed.
Thorough flow visualization around a golf ball will be made.
A comparative study of CFD and EFD of golf ball aerodynamic properties is currently being
undertaken.
Acknowledgements
The authors are highly grateful to Mr. Danny Spasenoski, Mr. Dinh Le and Mr. Mustafa Salehi, School
of Aerospace, Mechanical and Manufacturing Engineering, RMIT University for their assistance with the
wind tunnel data acquisition and processing.
References
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The present work is concerned with the flow past spheres in the Reynolds number range 5 × 104 [less-than-or-eq, slant] Re [less-than-or-eq, slant] 6 × 106. Results are reported for the case of a smooth surface. The total drag, the local static pressure and the local skin friction distribution were measured at a turbulence level of about 0·45%. The present results are compared with other available data as far as possible. Information is obtained from the local flow parameters on the positions of boundary-layer transition from laminar to turbulent flow and of boundary-layer separation. Finally the dependence of friction forces on Reynolds number is pointed out.
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In order to understand the role of surface dimpling on the flow over a golf ball, direct numerical simulations (DNS) are conducted within the framework of an immersed boundary approach for two physical regimes. Computations of the flow over a non-rotating golf ball are reported for a subcritical flow at a Reynolds number of 2.5 × 104 and a supercritical case at a Reynolds number of 1.1 × 105. Grid refinement studies for both Reynolds numbers indicated that characteristics of the subcritical flow could be captured using a mesh of 337 × 106 points, and for the supercritical case using a grid with 1.2 × 109 points. Flow visualizations reveal the differences in separation characteristics between the two Reynolds numbers. Profiles of the mean velocity indicate that the flow detaches completely at approximately 84° in the subcritical case (measured from the stagnation point at the front of the ball), while in the supercritical regime there are alternating regions of reattachment and separation within dimples with complete detachment around 110°. Energy spectra highlight frequencies associated with vortex formation over the dimples prior to complete detachment in the supercritical regime. Reynolds stresses quantify momentum transport in the near-wall region, showing that the axial stress increases around 90° for the subcritical case. In the supercritical regime these stress components alternately increase and decrease, corresponding to local separation and reattachment. Prediction of the drag coefficient for both Reynolds numbers is in reasonable agreement with measurements.