A Study of Dimple Characteristics On Golf Ball Drag [PDF]

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ScienceDirect Procedia Engineering 147 (2016) 87 – 91

11th conference of the International Sports Engineering Association, ISEA 2016

A study of dimple characteristics on golf ball drag Harun Chowdhury*, Bavin Loganathan, Yujie Wang, Israt Mustary and Firoz Alam School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Melbourne, VIC 3083, Australia

Abstract Dimples on the golf ball have significant effect on its aerodynamic properties as well as the flight trajectory. The aerodynamic of golf ball is still not fully understood in spite of a significant number of published data in the open literature. Most studies were conducted using the wind tunnel testing and Computational Fluid Dynamics (CFD) simulation. This paper examines the aerodynamic effect of dimple depth on golf balls. 3D printing technology was used to manufacture 11 balls with varied dimple depth. RMIT Aero Wind Tunnel was used to measure the drag forces over a range of wind speeds. It was found that the drag coefficient of golf ball varied significantly due to varied dimple geometry. The results indicate that the increase of the dimple depth ratio or surface roughness of the golf ball can shift the transition to a lower Reynolds number and increase the drag coefficient in transcritical regime. The results also established a positive linear correlation between relative roughness and drag coefficient.

© Publishedby byElsevier ElsevierLtd. Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Authors. Published (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ISEA 2016 Peer-review under responsibility of the organizing committee of ISEA 2016 Keywords: Golf ball; dimple; drag; wind tunnel; Aerodynamics.

1. Introduction The aerodynamics of golf ball is of great concern not only for the golf ball manufactures but also for the golf players as the types of golf ball used may greatly affect the performance of players. The flight trajectory is influenced by the aerodynamic forces exerted on the ball especially due to the variation in dimple geometry. Most commercially manufactured golf ball dimple not only vary in the numbers (between 250 and 500) but also in their size, shape and depth as stated by Alam et al. [1]. Several widely published studies have been conducted by Smits et al. [23], Smith et al. [4] and Ting et al. [5] on golf ball aerodynamics under spinning and non-spinning conditions. Choi et al. [6] conducted a detailed study of how surface dimpling can trigger the turbulent flow around a golf ball and reduced the drag significantly. The surface dimpling shifts the critical region to a much lower Reynolds number and at critical region, the drag coefficient reduced by almost 50% compared to the smooth ball. After the critical region, the drag coefficient increases with the increase of the Reynolds number. They also found that the critical Reynolds number at which drag coefficient is minimal may depend on the dimple size, depth and shape. The depth ratio of the golf ball used by Choi et al. was 0.4 × 102, and the critical Reynolds number was found to be 0.9 × 105. Choi et al. conjectured that the increase of dimple depth may shift the critical region to a lower Reynolds number while increasing the minimum drag coefficient value. However, their conjecture has not been validated with further study. In this context, the primary objective of this study is to evaluate the aerodynamic properties especially drag of a series of golf balls with varied dimple characteristics. In this study, the effect of dimple depth on golf ball drag was evaluated using wind tunnel environment.

* Corresponding author. Tel.: +61 3 99256103; fax: +61 3 99256108. E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ISEA 2016

doi:10.1016/j.proeng.2016.06.194

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Harun Chowdhury et al. / Procedia Engineering 147 (2016) 87 – 91

Nomenclature A CD FD k d ε Re V μ ρ

projected frontal area (m2) drag coefficient (dimensionless) aerodynamic drag force (N) dimple depth or roughness height (m) diameter of the golf ball (m) relative roughness parameter Reynolds number (dimensionless) wind speed (m/s) dynamic viscosity of air (Pa.s) air density (kg/m3)

2. 2. Methodology 2.1. CAD Models In order to conduct the wind tunnel experiments, 11 full-scale golf balls which have uniformly distributed dimples (total 336) were modelled by using CATIA a popular computer aided design (CAD) software. The diameter (42.67 mm) and dimple size (3.5 mm) of the model golf balls were kept constant. However, the depth of each dimple was varied from 0.5 to 1.5 mm with an increment of 0.1 mm. To compare the dimpled balls, a smooth ball was also modelled using the same diameter. Fig.1 shows an example of the 3D CAD model with dimple parameters of the golf ball.

Dimple size 3.5

Golf ball D 42.67 0.5-1.5

Dimple

Dimple depth

Fig.1. (a) Example of a CAD model Golf ball; (b) Parameters (in mm) of the golf ball dimple

2.2. Definition of the Dimple Characteristics There are two ways to define the dimple characteristics. One is dimple depth ratio which has been mentioned by Choi et al. [6]. The formula is: k (1) Dimple depth ratio d

Where, k is dimple depth and d is the diameter of the golf ball. Another way to express the dimple characteristics of golf ball is with its surface roughness parameter as studied by Chowdhury [7] and Achenbach [8] and it is defined by the following formula: k (2) H d

It can be noted that both the formulae are similar is nature. Table 1 shows the model golf balls with their dimple characteristic parameters used in this study: Table 1. Model golf balls with their dimple characteristics Golf Ball Model#

#1

#2

#3

#4

#5

#6

#7

#8

#9

#10

#11

Smooth

Dimple Depth (mm)

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0

0.012

0.014

0.016

0.019

0.021

0.023

0.026

0.028

0.030

0.033

0.035

0

Relative Roughness (H)

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Harun Chowdhury et al. / Procedia Engineering 147 (2016) 87 – 91

2.3. Experimental Models For this study, 12 solid models (in full scale) (see Table 1) were manufactured using a 3D printer and resin material. Each ball was printed using the same material and printing process. After the printing process, all 3D solid models were heat treated to harden the surface so that the deformation during the wind tunnel test can be minimised. Each model was printed with a cylindrical hole to fit the mounting rod onto the load cell for force measurement. Fig.2 shows the solid 3D printed smooth sphere and a dimpled golf ball.

Fig.2. Example of solid 3D printed model of golf ball: (a) Smooth sphere; (b) Dimpled ball

2.4. Aerodynamic Measurements In order to measure the aerodynamic drag acting on the solid models, a mounting system made of a steel sting was developed to hold all the test models onto the force sensor in the wind tunnel test section. A closed return circuit aero wind tunnel with 1 m2 octagonal test section and maximum speed of approximately 150 km/h was used to measure the aerodynamic forces of each ball experimentally. An aerodynamic fairing was used to reduce the effect of any force acting on the mounting system. Fig. 3 shows the experimental setup in the wind tunnel. A multi-axis force sensor (made by JR3 Inc., USA) connected to a data acquisition system was used to record drag force data over a range of wind speeds (20120 km/h) with an increment of 10 km/h at zero yaw angle. Each set of data was recorded for 30 seconds time average with a frequency of 20 Hz. Furthermore, multiple data sets were collected at each speed tested and the results were averaged to minimise possible errors in the experimental data. The repeatability of the measured forces was within ±0.01 N and the wind velocity was less than ±0.5 km/h. The measured aerodynamic drag force (FD) was converted to dimensionless parameter: drag coefficient (CD) and Reynolds number (Re) defined as: (3) FD CD

Re

1 UV 2 A 2

UVD P

(4)

Fig. 3. RMIT Aero Wind Tunnel including the data acquisition system and experimental setup (inset)

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3. Results and Discussion The air flow transition (from laminar to turbulent) was observed with 11 model golf balls with varied dimple depth. A smooth surfaced sphere with the same diameter was also tested. Drag coefficient as a function of Reynolds number for all model balls including the smooth sphere is shown in Fig. 4. The results show that the transitional effects vary differently depending on the surface profile of the dimpled golf ball over a range of Re (2 u 104  4 u 104). It was observed that the golf balls with higher degree of roughness trigger the flow separation earlier than those with relatively lower value of roughness parameter. However, no flow transition from the laminar to turbulent was observed with the smooth surfaced sphere within the Re range tested.

0.80 #1 #4 #7 #10

0.70

Drag Coefficient (CD)

0.60

#2 #5 #8 #11

#3 #6 #9 Smooth

0.50 0.40

0.30 0.20 0.10 0.00 0.00

1.00

2.00

3.00 4.00 5.00 6.00 Reynolds Number, Re × 104

7.00

8.00

9.00

10.00

Fig. 4. The variation of drag coefficient (CD) with Reynolds number (Re)

It was observed that the surface roughness parameter triggered the flow transition effect earlier or later based on their magnitude. For example, the Model#11 (H = 0.035) underwent the flow transition earlier at Re = 2 u 104 compared to all other samples. On the other hand, the Model#1 (H = 0.012) with comparatively less surface roughness value underwent flow transition at Re = 4 u 104. It is also evident that as the surface roughness increases, the critical Reynolds number (Recrit) decreases. Previous study by Achenbach in 1974 [8] indicated that as the surface roughness increases, the critical Reynolds number (Recrit) decreases and the minimal coefficient of drag (CDmin) increases. This investigation also found similar trend with the published data by Choi et al. [6], Chowdhury [7] and Achenbach [8]. The minimal CD values at the critical Reynolds number (Recrit) for each model are plotted separately as a function of Relative roughness (see Fig. 5). 7

0.25

6 5

0.2

0.15 0.1

0.05 0 0.000

y = 4.9278x + 0.0621 R² = 0.7897 0.010 0.020 0.030 Relative Roughness (H)

0.040

Critical Re u 104

Min Drag Coefficient (CD)

0.3

4 3 2

y = -100.16x + 6.4554 R² = 0.7281

1 0 0.000

0.010 0.020 0.030 Relative Roughness (H)

Fig. 5. Relative roughness as a function of: (a) minimum drag coefficient; (b) Critical Reynolds number

0.040

Harun Chowdhury et al. / Procedia Engineering 147 (2016) 87 – 91

The figure clearly demonstrates nearly a linear relationship from ε = 0.012 to 0.035. The linear equation which fits the data is relative roughness, ε = 4.9278 u CDmin + 0.0621 with the correlation coefficient, R² = 0.7897. The standard regression value indicates a linear correlation between the relative roughness (ε) and the CDmin. With the increase of surface roughness, the magnitude of CDmin value generally increases, agreeing with findings of Achenbach, 1974 [8] which examined the surface roughness of solid spheres. Figure 5 also depicts a relationship of relative roughness (ε) and Recrit based on CDmin values obtained. The relationship is linear from ε = 0.012 to 0.035. The linear equation which fits the data is relative roughness, ε = 100.16 u Recrit u 104 + 6.4554 with the correlation coefficient, R² = 0.7281. The standard regression value indicates a linear correlation between the relative roughness and the Recrit. Drag coefficient in transcritical regime has been further analyzed to correlate the surface roughness with drag coefficient. The CD values at 100 km/h (Re = 7 u 104) were plotted as shown in Fig. 6. The data show a positive linear correlation with 94% R2 value. The data indicate that at 100 km/h the drag coefficient increases with increase of relative roughness. Therefore, it can be concluded that the golf ball with shallower dimples can travel further than that with deeper dimples at 100 km/h and over.

0.35 Drag Coefficient (CD)

0.30 0.25 0.20 0.15 0.10

0.05 0.00 0.000

y = 5.7395x + 0.0694 R² = 0.9437 0.010 0.020 0.030 Relative Roughness (H)

0.040

Fig. 6. Drag coefficient as a function relative roughness at 100 km/h

4. Conclusions Results show that the drag coefficient of golf ball varied significantly due to varied dimple geometry. The results indicate that the increase of the dimple depth ratio or surface roughness of the golf ball can shift the transition to a lower Reynolds number and increase the drag coefficient in transcritical regime. The results also established a positive linear correlation between relative roughness and drag coefficient. References [1] Alam F, Chowdhury H, Moria H, Steiner T and Subic A. A Comparative Study of Golf Ball Aerodynamics. Proceedings of the 17th Australasian Fluid Mechanics Conference (AFMC) 2010; 5-9 December, Auckland. [2] Smits AJ and Ogg S. Golf Ball Aerodynamics. In: J.M. Pallis, R. Mehta, M. Hubbard, Editors, Proceedings 5th International Sports Engineering Conference, 2004. [3] Smits AJ. and Smith DR. A new aerodynamics model of a golf ball in flight. Science and Golf 1994;340-347. [4] Smith CE, Beratlis N, Balaras E, Squires K and Tsunoda M. Numerical investigation of the flow over a golf ball in the subcritical and supercritical regimes. International Journal of Heat and Fluid Flow 2010;31:262–273. [5] Ting LL. Effects of dimple size and depth on golf ball aerodynamic performance. In: 4th ASME-JSME Joint Fluids Engineering Conference 2004. [6] Choi J, Jeon W, Choi H. Mechanism of drag reduction by dimples on a sphere. Physics of Fluids 2006;18:1-4. [7] Chowdhury M. Aerodynamics of sports fabrics and garments. PhD Thesis. RMIT University, Melbourne, Australia, 2012. [8] Achenbach E. The effects of surface roughness and tunnel blockage on the flow past spheres. J Fluid Mech 1974;65:113–25.

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