不同高爾夫球桿面對推桿表現之影響

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(1)國立臺灣師範大學運動與休閒學院體育學系博士論文. 不同高爾夫球桿面對推桿表現之影響 The Effects of Different Faces on Golf Putting Performance. 研究生：吳彥磊指導教授：黃長福. 中華民國 109 年 8 月.

(2) 不同高爾夫球桿面對推桿表現之影響 2020 年 08 月研究生：吳彥磊指導教授：黃長福. 摘. 要. 高爾夫球市場伴隨龐大高爾夫球運動器材市場與商機，尤其以球具功能重要。高爾夫球器材廠商持續導入先進製程與設計，持續球具的研發、開發與設計以幫助高爾夫參與者達最佳表現。研究目的針對使用不同高爾夫球桿面對於推桿表現之影響，針對其推桿動作與球滾動之運動學參數。受試對象為 22 名受過高爾夫球運動專項訓練的體育系男性，並進行兩公尺與四公尺距離測試。本研究使用超聲波儀器 (Puttlab 6, Science & Motion Sports, GmbH, Flörsheim, Germany, 70Hz *3)進行推桿運動數據蒐集。球滾動參數使用高速攝影機 (BlackFly, FLIR Systems, Virginia, USA, 120Hz)，以橫狀面座標校正後進行捕捉與分析。本研究針對市場推桿表面加工參數之推桿進行進球率、推桿與球滾動運動學蒐集並進行單因子變異數分析(α = .05)，如達差異則利用 LSD 法進行事後比較。接者針對水平出球角度、球初速度與球滾動距離進行多元迴歸分析。結果發現桿面有加工的進球率不管是兩公尺與四公尺都較高。加工深度會影響滑度比例與滾動比例，但不一定會降地球滾動距離。多元迴歸結果顯示推桿桿面為影響出球角度最主要因子。桿頭速度為影響出球速度最主要因素，上擊球角度未增加出球速度。出球速度、速度比例與滾動比例為影響球滾動距離最主要因素。. i.

(3) 研究結果對於未來推桿設計上很有幫助並且可應用在推桿教學應用。未來研究可針對不同果嶺速度、距離與果嶺坡度進行資料蒐集，並加入更多運動生物力學參數分析。. 關鍵字 : 運動器材設計、高爾夫球運動、推桿運動學、球滾動運動學. ii.

(4) The Effects of Different Faces on Golf Putting Performance Author: Wu, Yen-Lei Advisor: Huang, Chen-Fu. Abstract. The golf market is accompanied by vast golf equipment and business opportunities, especially the advancement in the golf equipment performance and function. Golf equipment manufacturers consistently introduce advanced manufacturing processes, R&D, designs, and continue to develop and help golf participants achieve their best performance. There have been very few researches on human using different face milling putters. Most research used mechanical or simulation as the primary analysis method and did not collect the kinematic parameters of putter and ball rolling. Twenty-two healthy males were conducted as subjects with experiment distances from two and four-meters distances. The study used the ultrasonic instrument (Puttlab 6, Science&Motion Sports, GmbH, Flörsheim, Germany, 70Hz *3) to collect putting kinematic data. The ball rolling parameters are captured and analyzed using a high-speed camera (BlackFly, FLIR Systems, Virginia, USA, 120Hz) positioned on the transverse plane above the intended line of putt. The face geometries that were tested were the mainstream face milling parameters. ANOVA variance analysis (α = .05) was performed to analyze between face geometries and putter-ball kinematic data, and the LSD method was used for post-hoc analysis. Multiple regression analysis was implemented to determine critical predictors for the horizontal angle of the ball, the initial ball velocity, and the ball rolling distance. The study concludes that putter face milling can enhance putting performance. Deep. iii.

(5) milling may increase roll ratio but does not loss of ball distance. The putter face angle is the main predictor for horizontal launch angle, and roll ratio is predictive for horizontal launch angle from four meters. Putter velocity is the main predictor of ball velocity. A positive rise angle does not enhance ball velocity. Ball velocity and roll ratio are two main predictors to roll distance. Findings will be beneficial for future putter equipment design and putter coaching. Future studies can add biomechanical data along with different green speed, distance, and slope.. KEYWORDS: Sports Equipment Design, Golf Sport, Putter Kinematics, Ball Roll Kinematics. iv.

(6) TABLE OF CONTENTS. 摘要 ............................................................................................................................... i Abstract .......................................................................................................................... iii TABLE OF CONTENTS ............................................................................................... v LIST OF FIGURES ....................................................................................................... ix LIST OF TABLES .......................................................................................................... x. Chapter One - Introduction ........................................................................................... 1 1.1. Introduction ........................................................................................................................ 1 1.2. Research Hypothesis .......................................................................................................... 3 1.3. Research Limitation and Delimitation ............................................................................... 3. Chapter Two Literature Review .................................................................................... 5 2.1. Golf Equipment .................................................................................................................. 5 2.1.1. Golf club types of equipment ....................................................................................... 5 2.1.2. Science of putting ........................................................................................................ 6 2.1.3. Importance of putting ................................................................................................ 10 2.2. Putting Stroke Kinematics ................................................................................................ 13 2.2.1. Putting Stroke ............................................................................................................ 13 2.2.2. Performance index putting stroke kinematics ........................................................... 14 2.2.3. Relation of putting stroke kinematics parameters to ball kinematics ........................ 16 2.3. Ball Kinematics ................................................................................................................ 16. v.

(7) 2.3.1. Definition ball kinematics ......................................................................................... 16 2.3.2. Essential ball kinematics to performance ................................................................. 20 2.4. Putter Equipment and Ball ............................................................................................... 21 2.4.1. Background of Golf Equipment ................................................................................. 21 2.4.2. Golf Equipment Design and ruling ........................................................................... 23 2.4.2. Manufacturing and processing.................................................................................. 24 2.4.4. The Role of Friction Coefficient in the Putter/Ball Interaction ................................ 27 2.4.5. Putter specification on performance ......................................................................... 28 2.4.6. Putter Face material and milling .............................................................................. 29 2.5. Putting Testing Apparatus ................................................................................................ 30 2.6. Summary .......................................................................................................................... 33. Chapter Three - Methodology ..................................................................................... 35 3.1. Methodology .................................................................................................................... 35 3.1.1. Participants ............................................................................................................... 35 3.1.2. Experiment setting ..................................................................................................... 35 3.1.3. Equipment setup ........................................................................................................ 36 3.2. Experiment Procedure ...................................................................................................... 39 3.2.1. Experiment Setup....................................................................................................... 39 3.2.2. Equipment.................................................................................................................. 39 3.3. Apparatus and calculations............................................................................................... 40 3.3.1. Putting Performance ................................................................................................. 41 3.3.2. Putting Kinematics .................................................................................................... 41 3.3.3. Ball Launch Acquisition ............................................................................................ 44 3.4. Statistical Analysis ........................................................................................................... 45. vi.

(8) Chapter Four - Results ................................................................................................. 46 4.1. Putting performance and kinematics ................................................................................ 46 4.2. Ball Direction putter-ball kinematics ............................................................................... 47 4.2.1. Ball direction putter-ball kinematics from two metres .............................................. 47 4.2.2. Ball direction putter-ball kinematics from four metres ............................................. 48 4.3. Ball distance-related putter-ball kinematics ..................................................................... 49 4.3.1. Ball initial velocity putter-ball kinematics from two metres ..................................... 49 4.3.2. Ball initial velocity putter-ball kinematics from four metres .................................... 49 4.3.3. Ball distance relation to putter-ball kinematics from two metres ............................. 50 4.3.4. Ball distance relation to putter-ball kinematics from four metres ............................ 50 4.3. Regression Model for Horizontal Launch Angle ............................................................. 51 4.3.1. Horizontal launch angle variability from two meters ............................................... 51 4.3.2. Horizontal launch angle variability from four meters .............................................. 52 4.4. Regression Model for Ball Velocity................................................................................. 53 4.4.1. Ball initial velocity variability from two meters ........................................................ 53 4.4.2. Ball initial velocity variability from four meters ....................................................... 53 4.5. Regression Model for Ball Distance ................................................................................ 54 4.5.1. Distance variability from two meters ........................................................................ 54 4.5.2. Distance variability from four meters ....................................................................... 55. Chapter Five - Discussion ............................................................................................ 57 5.1. Comparison of putting performance and direction........................................................... 57 5.2. Putting Stroke Kinematics................................................................................................ 58 5.3. Ball Roll kinematics ......................................................................................................... 59. vii.

(9) 5.4. Direction variability model .............................................................................................. 60 5.5. Ball velocity variability model ......................................................................................... 62 5.6. Distance variability model ............................................................................................... 63. Chapter Six - Conclusion ............................................................................................. 65 6.1. Conclusion........................................................................................................................ 65 6.2. Future Recommendations ................................................................................................. 66. References...................................................................................................................... 67 APPENDICES............................................................................................................... 75 APPENDIX A ......................................................................................................................... 75 APPENDIX B ......................................................................................................................... 80 APPENDIX C ......................................................................................................................... 81 APPENDIX D ....................................................................................................................... 125. viii.

(10) LIST OF FIGURES Figure 2.1. Figure 2.2. Figure 2.3. Figure 2.4. Figure `. Theoretical golf ball model---------------------------------------------Backspin rate versus loft angle/club for FE and empirical oblique impact data.---------------------------------------------------------------Speed ramp for green speed STIMPMETER from USGA. --------“World-class model”----------------------------------------------------The primary forces on a golf ball rolls on putting green.------------. Figure 2.6.. 6 7 8 12 16. Comparison of the height of the centre of gravity (CG) and loft on Metal-Wood, Iron and Putter.------------------------------------------Figure 2.7. Putter Design Ruling.----------------------------------------------------Figure 2.8. Groove volume, depth, width and pitch design.---------------------Figure 2.9. Golf club Groove inspection gauge and fixture.---------------------Figure 2.10. An interaction golf putter-golf ball taken using high-speed photography from the side-camera.------------------------------------Figure 2.11. Golf putting data capture taken using high-speed photography from the top-camera.-----------------------------------------------------Figure 3.1. Experimental Setup orientation with Putting Turf and Apparatus.Figure 3.2. Putter specification.-------------------------------------------------------. 22. Figure Figure Figure Figure. 39 41 42 44. 3.3. 3.4. 3.5. 3.6.. Experimental setup, equipment and apparatus calibration. --------Definition of various axis and relation to the target.----------------Putter kinematics parameters.------------------------------------------Experiment setup for Ball Roll Kinematics.--------------------------. ix. 23 25 26 30 31 35 37.

(11) LIST OF TABLES Table 2.1. Summary of Friction Coefficient Data.----------------------------------Holing percentage from PGA, “World-class model” and by Table 2.2. Norwegian elite players.---------------------------------------------------Summary of commercially available golf putters, the face material Table 2.3. used, face milling type, groove type and pattern.----------------------Table 2.4. Summary of putter material and milling of the putter face.-----------Table Table Table Table. 2.5. 3.1. 3.2. 3.3.. Past research on putter specifications and ball roll kinematics.------Summary of the four putter’s Inertial Properties and specifications-Summary of the four putters used for face geometries testing.-------Definition of putter kinematics parameters.-----------------------------The putter used for testing in the study. The putter are defined by Table 3.4. three letters code. The loft angle given along with surface treatment.Table 3.5. Definition of ball roll kinematics parameters.--------------------------Means and standard deviations of putting kinematics among face Table 4.1. geometry from two-meters about putter-ball temporal and displacement.----------------------------------------------------------------Means and standard deviations of putting kinematics among face Table 4.2. geometry from four-metres concerning putter-ball temporal and displacement.----------------------------------------------------------------Means and standard deviations of putting kinematics among face Table 4.3. geometry from two-meters in relation to ball direction (°).-----------Means and standard deviations of putting kinematics among face Table 4.4. geometry from four-metres about ball direction (°).-------------------Means and standard deviations of putter-ball kinematics among face Table 4.5. geometry from two-meters about ball launch speed (m/s).-----------Means and standard deviations of putter-ball kinematics among face Table 4.6. geometry from four-metres with ball launch speed (m/s).------------Means and standard geometry from two Means and standard Table 4.8. geometry from four Table 4.7.. deviations of putting kinematics among face meters with ball distance (m).-------------------deviations of putting kinematics among face meters with ball distance (m).-------------------. x. 8 11. 24 29 35 37 38 41 42 43 46. 46. 47 47 48 49 49 50.

(12) Table 4.9.. Table 4.10.. Table 4.11. Table 4.12.. Linear regression model among predictors and kinematics variable horizontal launch angle R2 and standardized coefficients from twometers.-----------------------------------------------------------------------Linear regression model among predictors and kinematics variable horizontal launch angle R2 and standardized coefficients from fourmetres.-----------------------------------------------------------------------Linear regression model among predictors and kinematics variable ball velocity R2 and standardized coefficients from two-meters.----Linear regression model among predictors and kinematics variable ball velocity R2 and standardized coefficients from four-metres.----. Linear regression model among predictors and kinematics variable Table 4.13. ball roll distance R2 and standardized coefficients from two meters.-----------------------------------------------------------------------Linear regression model among predictors and kinematics variable Table 4.14. ball roll distance R2 and standardized coefficients from four meters.------------------------------------------------------------------------. xi. 51. 51 52 53. 54. 55.

(13) Chapter One – Introduction. 1.1. Introduction The origin of golf dates back hundreds of years and has become ever popular with Tiger Woods and introduction to Olympics in 2016 RIO. The performance of golf is determined by having the least strokes to finish the ball in the hole cup, which requires many different techniques, from “long-game” driving, iron-play, “short-game” for pitching, chipping and putting. The putting stroke is the smallest amplitude of all, but it represents an estimated 43% of the strokes per round (Pelz, 2000). Putting technique is considered one of the essential skills determining factors on the Professional Golf Association (PGA) (Alexander & Kern, 2005). Elite golfers are required to incorporate a good “green reading” skill, putter face aim, and sufficient putting stroke consistency, i.e., accurate face angle, putter path, and impact point (Karlsen, Smith and Nilsson, 2008a). Proficiency of golf performance skills (driving, chipping or putting) can be evaluated based from either direct data, i.e., ball displacement, accuracy, holing; or secondary data, i.e., face angle, path, angle of approach (Pelz, 2000), impact spot (Karlsen et al., 2008a; Pelz, 2000 Wiren, 1990), attack angle (rise), stroke displacement and temporal stroke data (Marquardt, 2007). Karlsen & Nilsson (2008b) have categorized putting performance into green consistency, putter aim, and putting stroke. The putting kinematics variables were found to be a significant predictor for skill level variance, from face angle, path, stroke temporal, displacements, and directional accuracy (Delay et al., 1997; Karlsen et al., 2008a; Marquardt, 2007; Sim & Kim, 2010; Wu, Huang, Marquardt, and Wang, 2020). Higher competency players exhibit a longer downswing amplitude and slower velocity at impact and a shorter time to peak velocity; 1.

(14) accurate putter face aim (Marquardt, 2007; Wu et al., 2020); higher holing rate from 1~5 meters (Tierney & Coop, 1998). Ball kinematics has been a critical topic to understand distance control and ball roll consistency. Hurrion and Hurrion (2002) promoted less backspin will cause less skid for better distance control. However, most ball roll researches used mechanical arm (Pelz, 2000; Pope, James, Wood & Henrikson, 2014), simulation (Drane, Fourier, Sherwood & Breed, 2014) and lacked human participants. Thus, no research has explored the putter kinematics with ball roll kinematics with human golfers. Golf club design has improved dramatically since the implementation of computer-aided design and manufacturing for higher precision machining. Milling face geometries started to For years, golf equipment designs have been researched technological break-through to improve golf performance through engineering, manufacturing and designs. Wood equipment has been implementing materials, face configurations, and design to enhance ball velocity and distance. Wedge equipment development has have been focused on face milling grooves configurations, to optimize spin and trajectory. Putter equipment has been focused mainly on head types, length, loft, centre-of-gravity (CG) and moment of inertia (MOI). Contradict researches results on face milling with ball roll kinematics had yet to determine performance benefits of face geometry, seen in the wood and wedge equipment. Nevertheless, validating the putter face milling settings and patterns, on putting kinematics, ball direction, velocity and distance variance is critical to determine putting performance. The purpose of the research is to compare two and four-meter putting performance and putter-ball kinematics among four putter face geometries. Additionally, the study hopes to identify critical predictors for key putting performance variables with elite players.. 2.

(15) 1.2. Research Hypothesis. The research questions hypothesis of this thesis are to examine the following: 1. It is hypothesized that the putter face milling variance influence is putting performance. 2. It is hypothesized that putter face milling variance influence putter-ball kinematics. 3. It is hypothesized that the putter face milling variance will affect different predicting models to horizontal launch angle. 4. It is hypothesized that the putter face milling variance will affect different predicting models to initial ball velocity. 5. It is hypothesized that the putter face milling variance will affect different predicting models to ball distance.. 1.3. Research Limitation and Delimitation This research is limited to elite male golfers and does not apply to other skill levels, age groups and genders golfers. Putter equipment is limited to the test setting with head type, mass, lie angle, loft angle, length and MOI (butt) specifications. The face milling configuration is limited to milling settings, patterns, and surface roughness to this research and does not apply to other milling, patterns or materials. Testing results are limited to two and four meters on artificial turf Stimp 10 and do not apply different speed or natural turf. Research results to level green and do not apply to slope green. The delimitation of this study is determined by the researcher to clarify the research hypothesis best. The putter face selection of Face 1 has been the most-win putter on tour；Face two has been used by the most-win player in the history of golf, and Face 3 and 4 are two the. 3.

(16) most iconic face milling & pattern. Putting distances of two and four-meters was chosen based on its critical indication for putting performance, direction and distance.. 4.

(17) Chapter Two Literature Review. 2.1. Golf Equipment. 2.1.1. Golf club types of equipment Golf has become ever popular with Tiger Woods and introduction to Olympics in 2016 RIO. Golf performance depends on skills in wood play, iron play, short game and putting. Putting is considered one of the most crucial skills and is one of the determining factors for earning on the Professional Golf Association (PGA) (Alexander & Kern, 2005). Putting is the most static of all the golf swings and represents about 43% of the strokes in a golf game (Pelz, 2000). There are fourteen clubs in a set of golf equipment, divided into three main categories, wood, iron, and putter. The putter is used for rolling the ball on the green. The putter equipment design is smallest in dimension, shortest in length, most substantial in mass, with a flat striking loft-angle face, an upright lie angle. Putter equipment has specific design requirements, i.e., such as bent shafts, non-circular grips, and positional guides (R&A, 2009). The putter equipment evolved from iron-club like design, into L-shaped putters and “PING Anser” putter, which was the first putter with peripheral weighting, cavity back and low CG. Since then, the putter equipment evolved with seen an increase in distribution using investment casting, forging, milling manufacturing to CG, MOI, and face design for optimizing putting performance. With an emphasis on advancement in milling and manufacturing methods to enhance putter-ball interactions. Hurrion and Hurrion (2002) was one of the first studies to research the difference in the no-milled face compared with a particular type of putter face 5.

(18) milling patterns and its effects on ball roll kinematics using a high-speed camera. Lindsay, (2003) research focused on putter equipment CG, MOI, loft angle, hosel design and relationship to ball roll kinematics, i.e., vertical gear effect. Brouillette (2010) compared the ball roll ratio, rpm, and ball distance, with different materials like aluminium, delprhin, and steel groove face. Lambeth, Brekke, & Brunski, J. (2018) compared the same tool cutter with different geometries designs and influence on ball speed change on off-centre horizontal mis-hits.. 2.1.2. Science of putting Oblique Modelling Various investigations, including those of Mindlin and Deresiewicz (1954) and Maw, Barber, and Fawcett (1976; 1981) have been built on Hertz's work in the modelling typical impacts by adding various tangential parameters to attempt to model the oblique impact of elastic spheres. While these models provide the scientific community with a good starting point into the modelling of an oblique impact, the materials used to construct golf balls behave viscoelastically, meaning that the material behaviour will vary at different strains and strain rates. The golf ball can deform by up to 25 % (Ujihashi, 1994), depending on the impact speed. As such, assumptions such as 'the coefficient of restitution is unity' (Maw et al., 1976) make the models difficult to modify for use in a golfing context where approximately 20% energy is lost in the ball following a high-speed (40 ms-1) standard impact (Lemons, 2002). The presence of a tangential component would only enhance the reduction in post-impact speed, through energy used to generate backspin (Lieberman & Johnson, 1994). Jones (2002) used the Hertzian theory to model the typical impact of a golf ball. However, the model could only replicate deformation at low inbound speeds (4 ms-1) and failed to take into account the energy loss in the ball material at increased speed. Chou et al. (1994) determined that during oblique impact in the golf ball, energy loss was explained by hysteresis 6.

(19) as well as friction by calculation from force/time histories of real, oblique impacts at 45°. These indicated that the maximum force of the impact was well below the yield stress of the materials used to construct golf balls. This energy loss during oblique impact has been defined subsequently as having two different components, motion within the ball relative to the centre of gravity and elastic strain energy displacement within the material. Maw et al. (1976, 1981) and attempted to model the oblique impact of an elastic golf ball theoretically. The analogy chosen was that shown in Figure 2.1. they were modelling the ball as a series of concentric circles where slip occurred between each layer throughout the impact. FT is the direction of the tangential force, FN, the direction of the reasonable force.. FN (a). FT. (b). (c). Figure 2.1. Theoretical golf ball model. (a) The annul positions immediately before oblique impact, (b) The annuli positions immediately on oblique impact, (c). Source: Maw et al. (1981) Chou et al. (1994) used experimental data to verify FE models simulating oblique impact. The impact speeds of Chou et al. (1994) were comparable to that following contact with a metalwood (45 ms-1), using a professional golfer to swing clubs from metal-wood (driver) through to a nine iron and pitching equipment (loft angle around 55°) at swing speeds of around 30 ms1. . The fit from both papers, between experimental and FE backspin/loft angle data, is. reproduced in Figure 2.2.. 7.

(20) Figure 2.2. Backspin rate versus loft angle/club for FE and empirical oblique impact data. Chou et al. (1994) fitted parameters for coefficients of friction and viscosity to consider friction in more detail. Chou et al. (1994) yielded an agreement with backspin magnitudes up to a loft angle of 30° (backspin magnitudes of 1500-8500 rpm). This was also encountered by Johnson (1998) in their attempts to model oblique impact using numerical methods and experimentally determined friction coefficients. It appears that the measurement of sliding and rolling friction coefficients between putterball interaction, has to this point not been comparable with the tangential force magnitude, and the relationship is generated at loft angles of above 40°. The accuracy of the FE results compared to the real force/time data (determined by firing the modelled ball at an instrumented, rigid oblique (45°) target), decreased with an increase in the impact speed, particularly in the unloading of the golf ball from the clubface. This indicates that polymer viscoelasticity may not have been fully taken into account when the material parameters were selected for the model. This is a problem with the 'black-box' nature of FE modelling as it is hard to take into account changes in material behaviour with strain rate, particularly if the role of the various ball components (core, cover, and mantle) during deformation changes at different speeds (Cochran & Farrally, 2002). Coefficient of Friction The friction properties between the turf and ball affect the ball slide (skid) and roll and how ball speed changes. Drane, Duffy, Fournier, Sherwood and Breed (2014) have indicated 8.

(21) the static coefficient of between artificial turf conditions by incline with horizontal (θ) and Equation to calculate Coefficient numbers as below (2-1) and friction of coefficient of sliding, dynamic and incline angle for rolling (Drane et al., 2014) in Table 2.1. tan. (2-1). (𝜃) = 𝜇. Table 2.1. Summary of Friction Coefficient Data. Test Conditions Static Coefficient of Sliding Friction Dynamic Coefficient of Sliding Friction Incline Angle to Initiate Rolling. μ. Incline Angle(θ). 0.3. 16.8. 0.26. 14.5. -. 5.2. Source: Drane, Duffy, Fournier, Sherwood and Breed (2014) The method to measure the friction and coefficient between the ball and the green is called The Stimpmeter. The Stimpmeter is thirty-six inches long with a groove about notch with 30 inches from the tapered end (USGA). The ball sits on the notch at the starting position, lying flat on the ground; when the user lifts the other end of the Stimpmeter to an angle of about 22 degrees, gravity influence the ball from the notch (Yun, 2013). The average Stimp of top professional tours like PGA/ LPGA ranges from 10~12ft, as illustrated in Figure 2.3.. Figure 2.3. Speed ramp for green speed STIMPMETER from USGA. Source: Yun (2013) 9.

(22) 2.1.3. Importance of putting Proficiency of golf performance (driving, chipping or putting) can be evaluated based from either direct data, i.e., ball displacement, accuracy, or secondary data, i.e., face, path, angle of approach (Pelz, 2000) and impact spot (Karlsen et al., 2008a). Literature suggests that the putting stroke has a minor effect with directional accuracy and that adopting an invariant pattern of movement that is easy to replicate could be more beneﬁcial (Karlsen et al., 2008a). Many coaches advocate a putting stroke where the putter has positive acceleration at impact (DeGunther, 1996; Pelz, 2000). Better competency players show a longer downswing amplitude and a slower velocity at impact (Delay et al., 1997) and a shorter time to peak velocity. The direction, also known as aim, has been less researched has been 1.3% PGA veterans (Tierney & Coop, 1998) and 1.8% (Karlsen, 2003). Past studies have compared various skill levels on putting (Delay, Nougier, Orliaguet, & Coello, 1997; Coello, Delay, Nougier, & Orliaguet, 2000; Paradisis & Rees, 2000; Carnahan, 2002; Fairweather, 2002; Sim & Kim, 2010). Variation in proficiency levels can be identified by kinematics in backswing amplitude (Sim & Kim, 2010) downswing amplitude (Delay et al., 1997), impact velocity, stroke-ratio (Sim & Kim, 2010) and variability in movement and velocity (Paradisis & Rees, 2002; Kenny et al., 2008). According to Wiren (1990), success in a short game like putting correlates to grip type, impact, point of contact. Ball displacement and club velocity inputting can be increased by downswing amplitude (Delay et a., 1997). According to Pelz (2000), the face angle determines 83% while 17% relates to the path while Karlsen et al. (2008a) found 83% faces, 15% is the path, and 3% is impact spot. Delay et al. (1997) found downswing time in expert players to be 261 – 289 ms on putts of 1 – 4 m. Karlsen (2003) found no differences in downswing time on putts of 2 m (305 ms), 8 m (312 ms), and 25 m (297 ms) for elite players. Researches (Karlsen & Nilsson, 2002) has suggested the elite player face angle, path and impact spot variability at 0.5°, 0.8° and 2.9mm impact spot 10.

(23) respectively. However, club setup, shaft lean, aim relative to target has not been addressed. Karlsen and Nilsson (2008b) result showed that face rotation in the downswing of 1° open to 4° closing, face change less than ±1.5° and downswing time 270ms to 370ms is considered acceptable. However, this study tested environments, and too many putts were tested 18.3 (s=5.31), which alters the reliability of the test. Research by Karlsen and Nilsson (2008b) has suggested that elite players have less variability and stroke itself has limited influence on the number of the putts holed. Putting is considered one of the most critical skills in golf, and the foremost factor in predicting competition results. Putting holing rate is directly correlated to the proficiency of golf performance (driving, chipping or putting) can be evaluated based from either direct data, i.e., ball displacement, accuracy, or secondary data, i.e., face, path, angle of approach (Pelz, 2000), impact spot (Wiren, 1990) and impact spot (Karlsen et al., 2008a). Literature suggests that the stroke has minor influence directional accuracy and that adopting an invariant pattern of movement that is easy to replicate could be more beneﬁcial (Karlsen et al., 2008a). Golf coaches advocate a putting stroke where the putter has positive acceleration at impact (DeGunther, 1996; Pelz, 2000). Better competency players show longer DS amplitude and slower velocity at impact (Delay et al., 1997) and a shorter time to peak velocity. The direction, also known as aim, has been less researched has been 1.3% PGA veterans (Tierney & Coop, 1998) and 1.8% (Karlsen, 2003). Past studies have compared various skill levels on putting (Delay, Nougier, Orliaguet, & Coello, 1997; Coello, Delay, Nougier, & Orliaguet, 2000; Paradisis & Rees, 2000; Carnahan, 2002; Fairweather, 2002; Sim & Kim, 2010). Variation in proficiency levels can be identified by kinematics in backswing amplitude (Sim & Kim, 2010) downswing amplitude (Delay et al., 1997), impact velocity, stroke-ratio (Sim & Kim, 2010) and variability in movement and velocity (Paradisis & Rees, 2002; Kenny et al., 2008). According to Wiren (1990), success in a short game, like putting correlations to grip type, impact, point of contact. Ball displacement and club velocity inputting can be increased by downswing amplitude (Delay et a., 1997). 11.

(24) According to Pelz (2000), the face angle determines 83%, while 17% relates to the path while Karlsen et al. (2008a) found 83% faces, 15% is the path, and 3% is impact spot. Delay et al. (1997) found that expert golfers' downswing time ranges from 261 – 289 ms from 1-4meter putts. Karlsen (2003) found that elite players no differences between distances with downswing time from 2 meters (305 ms), 8 meters (312 ms), and 25 meters (297 ms). Research (Karlsen & Nilsson, 2008b) has suggested the elite players’ face angle, path, and impact spot variability at 0.5°, 0.8°, and 2.9mm impact spot, respectively. However, club setup, shaft lean, aim relative to target has not been addressed. Research (Karlsen et al., 2008a) showed that face rotation in the downswing of 1° open to 4° closing, face change less than ±1.5° and downswing time 270ms to 370ms is considered acceptable. However, this study tested environments, and too many putts were tested 18.3 (s=5.31), which alters the reliability of the test. Research by Karlsen and Nilsson (2008b) has suggested that elite players have less variability and stroke itself has limited influence on the number of the putts holed. Putting is considered one of the essential skills in golf and the primary factor in predicting competition results. Putting the holing rate is directly correlated to the distance to the hole. Karlsen et al. (2008a) found done collective study of past research and tour professional rate of sunk putts versus distance, listed in Table 2.2. Karlsen et al. (2008a) found done collective study of past research and tour professional rate of sunk putts versus distance, listed in Table 2.2. Holing rate for 1putt is listed in Figure 2.4. Table 2.2. Holing percentage from PGA, “World-class model” and by Norwegian elite players Putting Distances PGA Tour top-10 putters 1-meter 93.10% 2-meters 64.20% 3-meters 43.90% 4-meters 30.70% 5-meters 22.60%. World-class model 92.00% 65.00% 45.30% 31.50% 22.40%. Source: Tierney and Coop (1998) 12. Norwegian elite players 89.70% 56.90% 37.30% 25.10% 11.50%.

(25) Figure 2.4. “World-class model”, predicting 1-putt probability, 3-putt probability and expected numbers of putts taken from a different distance by a world-class putter. Source: Tierney and Coop (1998). 2.2. Putting Stroke Kinematics. 2.2.1. Putting Stroke The putting technique requires skills like green reading, control of ball distance, accurate aim, and excellent ball roll kinematics (Hurrion & Hurrion, 2002). Brooks (2002) described three types of putting strokes recommended for golf instruction, about the target line, which are, the straight back to straight through, inside to inside, and inside to straight through. After examining the strokes using mathematical models, Brooks (2002) did not arrive at a conclusion to which stroke is best. However, a putting stroke was during the backswing the putter head moves inside the aim line and where the putter face is square to the putter path, which means the putter face is open to the aim line at the end of the backswing was endorsed. Pelz (2000) advocates a different type of putting stroke, where the path is linear, and the putter face is square to the path throughout the stroke. Pelz (2000) recommends this type of. 13.

(26) stroke with the putter face square, as there may be timing limitations, resulting in the inability to square the clubface precisely at impact. The main argument against what was proposed by Pelz (2000) is that the straight stroke is more biomechanically complex 19 than it first seems, as it relies on a fully horizontal axis of rotation for the putter, and muscle activity that will compensate for the deviation from the horizontal axis (Karlsen et al. 2008a). Neal and Wilson (1985) modelled the golf putt as a double-pendulum system composed of two arms and the putter. It was described that the shoulder is meant to roll in an up-and-down fashion, and the two hands hold the putter, moving back and forth in a symmetrical pattern (Neal & Wilson, 1985).. 2.2.2. Performance index putting stroke kinematics Delay, Nougier, Orliaguet, and Coello (1997) observed novices showing the normal pendulum motion while expert players did not. Expert players demonstrated an asymmetrical pattern where a longer follow-through was observed (Delay et al. 1997; Sim & Kim, 2010). Sim and Kim (2010) analyzed the differences between expert's and novice's accuracy in golf, putting in regards to impulse variability. Schmidt, Zelaznik, Hawkins, Frank, and Quinn (1979) developed an impulse variability model to send a ball close to the target, the magnitude of the impulse applied to the ball by the putter needs to be precise. Inputting, the moment of impact is extremely brief. Therefore, the putter's velocity at impact becomes extremely important in achieving accuracy (Sim & Kim, 2010). Research has demonstrated that movement at impact is not decided upon the moment of impact, but that movement is attuned and planned from initiation of the movement (Bootsma & van Wieringen, 1988; Coello, Delay, Nougier & Orliaguet, 2000) and through the period of swinging up to impact referred to as downswing (Müller & Abernethy, 2006). Delay et al. (1997) suggest that movement control may not be complete at impact. Sim and Kim (2010) results showed that expert players had a lower level 14.

(27) of velocity than the novice group; the experts also achieved increased accuracy; Delay et al. (1997) reported the same results. The question raised from both of these sets of results is how the expert group reached the target with a lower velocity. Delay et al. (1997) suggested that energy produced by novices might not entirely be transferred to the ball, with more energy loss at the moment of impact. Sim and Kim (2010) support this claim as it was observed that expert players maximum velocity occurred after impact, which means the ball gained stronger impulse when it left the putter face rather than at the moment of impact. A second explanation was provided by Delay et al. (1997), which concerned the ball roll. During experimentation, it was observed that the novice players ball often bounced during rolling, whereas the experts' ball glided smoothly. Sim and Kim (2010) further this theory of different types of ball roll; they suggest expert players achieve greater energy efficiency by striking the ball with the putter during the rising phase of the stroke during increasing velocity so that it rolls rather than slides towards the target. This would explain how the 20 expert players reached the target with reduced impact velocity as a ball will lose less kinetic energy when it rolls in comparison to when it slides (Sim & Kim, 2010). MacKenzie and Sprigings (2005) state that several elements are needed to hit a successful putt. The first being that the golfer must correctly read the green, to determine the correct target line and establish the optimal speed to impact on the golf ball to project it towards the target (hole). During the putting stroke, the putter should only demonstrate horizontal velocity in the direction of the decided target line, reducing elements of velocity in other directions, which would be undesirable. This will ensure the plane of the putter face with be perpendicular to the original putting line (MacKenzie & Sprignings, 2005). A technique that can be used to read the green is the plumb-bob method; this is where the golfer stands behind the ball, straddling an imaginary line that bisects the hole (MacKenzie & Sprignings, 2005). The golfer then suspends the putter at an arm's length in front of the face allowing gravity to pull the shaft into a correct 15.

(28) vertical alignment (Foston, 1992). Although it has been proven successful in individual professionals, Mackenzie and Sprigings (2005) deem it to be an unreliable method to determine the intended target line due to the high sensitivity of the plumb-bob method to confounding factors. 2.2.3. Relation of putting stroke kinematics parameters to ball kinematics Karlsen et al. (2008a) examined the golf, putting stroke, and determined three main determinants of direction variability. These were putter face angle that was accountable for 80% of the variability, putter path accounted for 17% variability, and the horizontal impact point on the putter face accounted for 3% (Karlsen et al., 2008a). Pelz (2000) only considered two factors that contribute to direction variability, firstly, putter face angle (83%) and putter path (17%). Therefore, the putter face angle may be the most critical club head kinematic variable regarding golf ball direction variability, as highlighted by Karlsen et al. (2008a) and Pelz (2000). To date, no study has examined body movements' effect on the putter face and performance variability.. 2.3. Ball Kinematics. 2.3.1. Definition ball kinematics Adding topspin to the ball is an essential factor in achieving putting accuracy. The object is to minimize initial skidding of the ball on the green after putter contact, deceleration force is high, and the ball will often skid. During skidding, the ball loses linear momentum while gaining angular momentum as its rolling motion increases. The skidding ends with pure rolling motion when no further skidding occurs. Past studies (Lindsay, 2000) impact-face surface properties, impact-face loft, and putter-head mass distribution.. 16.

(29) N. V μmg. mg. Figure 2.5. The primary forces on a golf ball rolls on putting green. If a golf ball is struck by a putter to produce no initial spin, it will skid for a distance (xt) until the frictional torque increases its angular velocity, finally achieving the pure rollingwithout-skidding condition. ω= Vcm. (2-2). R Currently, to formulate golf ball models are formulated to predict what will happen to a golf ball when subjected to a given set of impact conditions. It appears that no single model of golf ball impact currently can be incorporated, either for typical impacts, or oblique, which can predict the dynamic performance of different types of golf ball construction under every set of impact conditions. Modelling visco-elastic, multi-component golf balls involve complex calculations and numerous assumptions before a model can be incorporated. The run of a golf ball consists of the bounce phase and the subsequent rolling after landing. In the case of a drive, golfers will typically want a long run, while for shots on the green, limiting the bounce and skid of the golf ball are ideal. Several researchers (Daish, 1972; Penner, 2002) have presented models of golf balls bouncing on turf. In the case of Daish (1972), the general behaviour of a bouncing ball on a rigid surface is modelled, with the golf ball used as an example. Daish considers two specific cases. First, is the case where the ball slides over the surface throughout the impact, which, for the typical impact of a golf ball on the turf, will result in the golf ball retaining some of its backspin as it bounces from the surface. 17.

(30) In the second case, the frictional force between the ball and the surface is significant enough to check the backspin and to have the ball bouncing out of the impact with topspin. Daish determined that the minimum value of the coefficient of kinetic friction, µmin, between the ball and the surface, required to check the backspin, is given by where vix and viy are the impact velocity components, r is the radius of the ball, ωi is the backspin of the impacting ball, and e is the coefficient of restitution between the ball and the surface. Daish used this model to compute the runs for several different golf shots. In general, however, this value would depend on the impact speed. Penner (2002) measured the dependence of the coefficient of restitution for standard impact on the impact speed of the golf ball and found that although the value of e was approximately 0.5 at low impact speeds, less than one ms−1, for higher impact speeds the value of e decreased, approaching a value of 0.12 as impact speeds approached 20 ms−1. Putting is the most common shot in the game of golf. Several researchers have considered the motion of a golf ball as well as the interaction between the golf ball and the hole. The golf ball's initial motion is dependent on how the golfer strikes the ball. Daish (1972) found, from high-speed films, that most golfers putt the ball ‘on the up.’ For these cases, the golf ball is projected into the air and will make a series of bounces before it begins rolling along the green. For putts that are not projected upwards, the golf ball will initially skid along the turf. Both Daish, and Cochran and Stobbs (1968), state that the golf ball will be in a state of pure rolling after the ball has travelled approximately 20% of the total length of the putt. Lorensen and Yamrom (1992), Alessandrini (1995), and Penner (2002) have presented models of the motion of a rolling golf ball over a green. The primary difference between the models is how the frictional force acting on the golf ball is handled. Lorensen and Yamrom use two different constant coefficients of friction, one to model an initial sliding phase, and the other to model the rolling phase. This model was used as the basis for visualizing trajectories, using computer graphics and golf balls travelling over piecewise-planar models of real greens. 18.

(31) Alessandrini treats a putt as a two-point boundary value problem and determines the initial conditions required that would allow the trajectory to terminate at the hole with zero velocity. In this model, the frictional force is kept constant over the total length of the putt. Penner (2002) treats the golf ball as being in a state of rolling throughout the putt. In this model, the retarding force acting on the golf ball is taken to be that which constrains the ball to roll. Using this model, Penner (2002) determined that golf balls' trajectories roll on the flat, uphill, downhill, and sideways-sloped greens. Penner (2002) determined the launch conditions required for a successful putt by determining which golf ball trajectories along the green would lead to allowable impact speeds and parameters as determined by Holmes’ ball capture model. As with Mahoney, it was found that the probability of making a downhill putt can be significantly higher than the probability of making an equally distant uphill putt. For this downhill putt, an off-line trajectory will tend to converge back towards the target line, while the reverse occurs for uphill putts. This somewhat surprising result must be tempered by the consequences of a missed putt, as a missed downhill putt will, in general, stop much further from the hole than an equivalent uphill putt. For most golfers, this would result in a preference for uphill putts. Penner (2002) also determined the range of allowable launch speeds and angles for putts across the slope of a green. It was found that taking a slower uphill path, as opposed to a faster, more direct path, would increase the probability of success. Werner and Greig (2000) did a detailed analysis of several aspects of putting. They looked at hit patterns on a putter and the stop patterns around the hole for golfers of various handicaps. They used these results, along with a model of the putt, to determine what is the ideal distance beyond the hole that a golfer should be aiming for. For example, for a ten-foot putt on a flat green, they found that a golfer should strike the golf ball so it would stop a distance of approximately 20–40 cm, depending on the golfer's handicap and the green speed, past the position of the hole. 19.

(32) Lemons, Stanczack, Beasley and Cocharn (1999) looked at the effects of ball construction on both putting distance and break amounts. They found that the cover hardness played the most crucial role in the distance the ball rolls. For example, using a putting mechanical arm, they found that for the same putter head speed, a hard-covered two-piece ball rolled approximately 3–5% farther than either a soft covered three-piece or soft covered two-piece ball. It was also found that the ball construction played no part in the break of the putt. Hubbard and Alaways (1999) considered several aspects of the interaction between a golf ball and a green. They measured surface viscoelastic properties of the turf by experimentally dropping balls onto a green and measuring their resulting accelerations and positions. Peak accelerations of about 50g were measured, and several bounces were observed from small drop heights (2 cm). They also measured the variation of the coefficient of rolling friction over the length of a putt. They found that the rolling friction increased by about 10% throughout a 4.3 m putt. This would indicate that the coefficient of rolling friction increases with decreasing velocity. 2.3.2. Essential ball kinematics to performance Lindsay (2013) presented a theoretical and experimental study showing the selection of centre-of-gravity (CG) and moment of inertia (MOI) of the putter head around the heel-toe axis could minimize and even eliminate the initial skidding phase of a putt. In the past, putter design has mainly focused on the inertia properties of the golf equipment, putting kinematics whereas putter kinematics like face angle, putter path and horizontal impact spot has been key to successful putting skills (Karlsen et al., 2008a; Pelz, 2000). Putter designs have been focussed on to maximize the performance on mis-hits like horizontal off-centre impact (Lambeth et al., 2018) and skid distance, roll efficiency (Hurrion and Hurrion, 2002), as well as polymer inserts on the forward spin (Brouillette & Valade, 2008). Putter design has been interested in examining how inertia properties of the clubhead in the horizontal plane, as well 20.

(33) as facial treatments, on off-centre heel-toe impacts. Interests in improving the performance of the putter in the vertical plane, reducing skidding distance. Pure rolling earlier in the putt trajectory, conceptually producing more stable putts via the spin stabilization effect (Karnopp, 2004).. 2.4. Putter Equipment and Ball. 2.4.1. Background of Golf Equipment Golf equipment has been evolving over hundreds of years, with the introduction of modern technology and manufacturing method from handcrafting, forging, casting, CNC, to CAD and CAM. The formability and machinability of the material concerning the aesthetics of the club, and add face insert such as a polymer, some makers polish or CNC the face to ensure flatness, some are adding grooves into the impact area, milling of the area between grooves and the deposition of particles via shot-blasting will affect the choice of material. Titanium-based alloys such as Ti-6Al-4V typically used to produce metal-woods may have a hardness of 300 HV20 (Faulkner, Otto, & Strangewood, 2002). Age hardened aluminium-based alloys approach hardness values of 70 HV5 (LePort-Samzun, Trepleton, Strangewood, 2002). The lower price compared titanium-based alloys mean that steel is more commonly seen as a putter material when wear resistance is considered as a design criterion. Finally, the cost difference between materials and manufacturing will affect the choice made by the manufacturer. Most common putters on the market are stainless steel, carbon steel, aluminium and polymer. The primary objective of a shot with a putter is not to strike the ball with a considerable distance, instead, to increase the accuracy and control of distance. The putter hardness may also affect the magnitude of surface roughness introduced through shot-blasting or milling. Putter design is the most versatile all of the golf equipment due to golf rule regulations. Putter head design is divided into three main categories, with related CG in both x-axis and z-axis and MOI 21.

(34) on the z-axis of the head (Lindsay, 2003). Cochran and Farrally (2002) present results comparing the loss in yardage of shots struck using a golf mechanical arm 19 mm off-centre for a bladed compared to a perimeter-weighted five iron. The blade loses 2 yards more than the perimeter-weighted club, although the overall distance travelled by the ball was not given, nor was the extent of the peripheral weighting. Perimeter weighted in putters can be described as being more 'forgiving' to the golfer for an offcentre hit; in other words, the ball may still travel an appreciable, although total distance. This is easier to achieve with a bladed club than a perimeter weighted club due to the lower moment of inertia, hence the persistence of bladed irons and putter within the modern game. Past researchers have compared the performance of different putter designs, whereas head types have found to have significantly improved in alignment (Karlsen & Nilsson, 2008b). Putters have been made from iron-based alloys or steels and remained one of the unchanged product designs in the bag. While metal-woods have evolved by technology transfer from the aerospace industry to materials such as titanium-based alloys through processing routes like investment casting, the same transfer has not been applied to the manufacture of irons and putter. The latter club types are robust in construction, and distance gain is not the primary design criterion. The higher density of steels compared to lighter alloys such as titanium- and aluminium-based alloys reduce the twisting force that the clubhead is subjected on the downswing and at impact through an increase in the moment of inertia acting on the clubhead during the golfer's swing (Chou et al., 1995). Also, the higher density of steel enables the manufacturer to keep the head narrow. This keeps the 'sweet spot' of the head point close to the centre of gravity (CG) of the clubhead (Cochran & Stobbs, 1968; Sato, 1995). The sweet spot is the area on a line perpendicular to the face from the centre of gravity (CG) which the golfer should be aiming to present to the ball at impact in a square orientation relative to the swing direction and the line of aim (Cochran & Stobbs, 1968). The reduction in the height of the sweet spot and the smaller distance from the CG to the 22.

(35) impacting surface will minimize any twisting of the head through impact (Cochran & Stobbs, 1968), which will make it easier to present the ball square to the ball. The putter is the last stroke hitting towards the hole, and is the only products that hit from the ground with limited launch time and where the ball interacts with turf with limited skid, before rolling with the centre of gravity low and centre for maximizing accuracy listed Figure 2.6.. (a) Metal-wood. (b) Iron. loft. (c) Putter. loft. loft. Figure 2.6. Comparison of the height of the centre of gravity (CG) and loft on Metal-Wood, Iron and Putter.. 2.4.2. Golf Equipment Design and ruling As part of the rule-making process, the governing bodies of the game impose limits on the golf ball and the golf equipment. There are two main areas of legislation that are pertinent to the potential performance of golf equipment, specifically the putter. The groove design (depth, width and ratio), groove geometry (i.e. raised lip design are non-conforming) are listed in Appendix A and surface roughness of the club are also limited in Appendix A by R&A (2009). The standard steel face can have a maximum surface roughness magnitude (Ra parameter) of 4.82 um with a 15% tolerance. The hardness of the putter face material, the grooves of the. 23.

(36) club are restricted by certain geometric features, the details of which, along with the surface roughness constraints, are given in Appendix A. Size and dimensions According to R&A (2016), putter size and dimension distance from heel to toe are less than or equal to 177.8mm; the height of the golf equipment is less than or equal to 63.5mm, as illustrated in Figure 2.7.. Figure 2.7. Putter Design Ruling (R&A, 2009). The big moment of inertia (MOI) clubhead can still maintain the proximity of the CG to the sweet spot to minimize sidespin. With this in mind, the iron and putter design used by amateur and some professional golfers has evolved over the last 30 years. The introduction of more significant, cavity-backed, perimeter-weighted irons in the 1980s has made the game easier to play for the amateur golfer through an increased moment of inertia, which increases resistance to twisting (Chou et al., 1995).. 2.4.2. Manufacturing and processing Computer numerical controlled (CNC) milling has become increasingly popular for the production of high-end putters due to the dimensional tolerances and the flatness of the putter face. Golf equipment manufacturers have moved towards CNC milling on the face of putters and irons to ensure flatness, which is not achievable through the purely through casting or forging process. CNC milling as a surface engineering process and technique for controlling 24.

(37) surface texture on the face of clubs to increase the spin rate of the golf ball after impact, significantly affected by groove and milling pattern and surface roughness. List of commercially available putters, face materials, milling, and grooves are listed in Table 2.3 as below. Table 2.3. Summary of commercially available golf putters, the face material used, face milling type, groove type and pattern. Club Maker. Model. Head Type. Material. Milling. Depth. Pattern. PING Titleist Titleist Areso Golf Areso Golf Wilson Envroll. Sigma SC SC C30 E71 Infinite ER-1. Blade Blade Blade Blade Blade Blade Blade. SS 17-4 SS 303 SS 303 SC1025 SS303 SS 17-4 SS303. Groove Groove Groove Groove Ridge Groove Ridge. Deep Light Deep Deep Deep Light Deep. Circular Circular Circular Circular Circular Circular Straight. 1025 C-Mn steel – 0.18~0.23C 0.30/0.60 Mn 303SS C-Mn Steel – 0.18~0.23C 0.30/0.60 Mn. Types of Manufacturing Method Golf clubs today are made either from forging, investment casting, or metal block of material. The difference is mainly related to the design, cost, and quality requirements of the intended golf equipment. A hollow design like a driver is mostly made from casting and forging; irons and putters can be made from three types of the manufacturing method. Face milling and processing Modern golf equipment manufacturing requires having the face blasted, polished, or milled for a flat surface to ensure performance. Golf club design rules require golf equipment maker to comply with surface roughness, groove design, and surface roughness. By using computer-aided design, CAM can control the flatness of the putter face surface, groove depth, width, pitch, milling designs, milling patterns and surface roughness of the putter face. 25.

(38) Grooves depth and configurations Atypical distance grooves pitch of 3.5 mm (R&A, 2009) which the golf ball will come into contact with several grooves during impact at high speed (30 to 45 ms -1). Grooves may, therefore, have a bearing on the interaction mechanics. In 1987, Frank Thomas of the USGA undertook a study on the effects of grooves on launch characteristics. The general conclusion concerning grooves was that the spin rate of three different types of a two-piece golf ball (balata- and ionomer- covered) increased with a reduction in the spacing between grooves at a loft angle of 55°. This would appear to indicate that the presence of grooves on the face influences the magnitude of spin imparted. Putter equipment starting to implement the same concept to control spin. Putter equipment has 2-4° of the loft, which will also impart slight backspin with impact (Drane et al., 2014). Cochran and Stobbs (1968) provide calculation using the formula which is not revealed, showing sample graph showing an (unspecified) relationship for a loft angle/inbound speed/ball type combination is given confirming that backspin decreases with an increase in the measured launch angle of the shot. This is an erroneous assumption as the polymeric nature of the golf ball materials will mean that there will be additional energy losses associated with viscoelasticity. The grooves geometries mostly commonly were straight grooves with V- and U-shaped. This classification refers to the shape at the base of the groove, illustrated in Figure 2.8. It shows an example of width, depth, pitch, and lip angle, which are legislated for in the Rules of Golf (R&A, 2009) and listed Appendix A. Grooves are designed into the golf equipment to improve performance.. Figure 2.8. Groove volume, depth, width and pitch design. Source: R&A (2009) 26.

(39) The regulations, gauge and testing apparatus for equipment grooves are illustrated in Figure 2.9. Details of putter groove regulations limits at 0.5mm deep and width regulate to pitch ratio is 1:1. Unlike wood or iron equipment, putter equipment has not limited to the pattern of the groove configuration, details listed in Appendix A.. Figure 2.9. Golf club Groove inspection gauge and fixture. Source: R&A (2009). 2.4.4. The Role of Friction Coefficient in the Putter/Ball Interaction The parameters introduced in vertical angle deviation (loft), surface roughness, grooves, and ball construction would be expected to combine to affect the coefficient of friction and, therefore, launch characteristics such as launch conditions such as launch angle, velocity, and backspin magnitude during impact. In common, general oblique interactions seen in the putter and ball, which are comprised of different components. These are principally sliding and rolling of the ball on the (putter) face, and ball deformation (Maw et al., 1976; 1981). In the pioneering scientific study into the mechanics of golf impacts. Cochran and Stobbs (1968) stated that while the ball is still in contact with the clubface; it reaches its maximum speed of spinning at the point at which it completely stops sliding and begins to roll. This was observed using highspeed photography of impacts and capturing the ball trajectory. The effect that the coefficient of friction between putter and ball will translate into ball velocity translate into ball and turf launch conditions. The magnitude of the tangential force 27.

(40) dictates the friction coefficient, FT, in this case, coefficient of friction is comprised of the coefficient of static friction, the coefficient of sliding friction and the coefficient of rolling friction. The friction of the ball and turf affects how the ball slides and rolls, which is how ball velocity change over time (Pope, James, Wood, & Henrikson, 2014). 2.4.5. Putter specification on performance Long game research like Cochran and Stobbs (1968) had observed that face grooves made little difference to the backspin magnitude when the loft angle of the club was comparable to that of a five iron and a nine iron (30° and 45° loft angles respectively). Putting unlike the long game, where kinematic data are related to the ground, whereas influence putter loft angle to have a negative effect on roll ratio (Pope et al., 2014). Karlsen and Nilsson (2008b) focused on the shaft weight influence on putter kinematics and found lightest shaft have longer putting distance (2.1%). Karlsen and Nilsson (2008b) evaluated the aiming accuracy and consistency among commercially available putter head types (mainly blade and mallet), where blade-type putters were found to be more accurate. Wu, Huang, Marquardt, Yu and Lee (2012) researched putter head weighting configuration, changing mass distribution between toe-heel will change the putting kinematics. Sherwin and Kenny (2013) evaluated the difference between standard length putter with belly, and long putters, and found anchoring styled putter doesn’t have a performance advantage over the traditional style of putting. Wu, Huang, Liu and Marquardt (2013) evaluated putting grip sizes on putting kinematics; results suggested shorten total rotation, timing and rhythm. Wu, Huang, Liu, Marquardt, and Chen (2014) evaluated the counter-balance grip design influences on putting kinematics and found that it alters temporal in backswing and downswing. Pope et al., (2014) compared different loft angle with the “PING Anser” and suggested that negative loft can increase roll ratio. Lambeth et al. (2018) focused on matching momentum (MOI) of the putter and comparing to ball velocity loss on horizontal miss-centre on putter face, whereas the larger the MOI (5000 g/cm2) has, the 28.

(41) less distance loss from 30mm. 2.4.6. Putter Face material and milling The contemporary of putter face designs started the evolution from the “PING Anser” in the 70s with mass distribution and has the most wins on the professional tour. The next evolution came around the millennium where the new materials in face insert were introduced, i.e. copper (Scotty Cameron, Tel 3 with Teryllium) and Odyssey Putter (white polymer insert). As advancement in the manufacturing method, i.e. computer-aided-design (CAD) and computer-aided-manufacturing (CAM), there has been significantly advanced implementation into golf equipment design. The golf equipment manufacturing started to using investment casting to CNC milling. Monk, Davis, Otto & Strangwood (2015) researched in material and surface effect with ball spin and launch angle with wedge iron club. However, such extensive research on putter was limited. The first study on putter face geometry was Hurrion and Hurrion (2002) comparing professional golfers own putters versus face milling putter and found a significant reduction in skid distance. Lindsay (2003) presented a theoretical study showing that selection of centre-of-gravity (CG) and moment of inertia (MOI) of the putter around toe-heel axis can eliminate the skid phase of a putt. Brouillette and Valader (2008) perform an experimental study on commercially available putters, all equipped with polymer insert or face grooves, and show that this face treatment has minimal effect on skidding phase. Brouillette (2010) compared face material aluminium milling and polymer face, findings suggest that softer materials and grooves decreases COR and ball velocity but will not effect roll ratio. Richard et al. (2017) experimental approach with a test plot of commercially available putters and golf ball to evaluate dimple effect on horizontal launch deviation, where they found that the dimple effect has minimal influence. Lambeth et al. (2018) evaluated various deep milling pitch while using the same cutter and pattern. Findings suggest that matching horizontal miss-hits with MOI will lessen ball velocity and distance. However, these researches have laid the foundations for 29.

(42) putter-ball interaction on ball roll kinematics. There has been a lack of clarity and consistency between researches due to the availability of face geometry configurations. Thus, it limits the translation of the knowledge of how putter faces geometries influences putting performances. Contemporary putter face is mostly steel material due to its anti-corrosion, durability and machinable properties. Putter face geometries are primarily milled with either grooves or ridge pattern with either circular or square pattern. Circular is most popular as it can milling flatness of the flat as well as control the depth with accuracy. The most common types of putter face geometries are listed in Table 2.4. Table 2.4. Summary of putter material and milling of the putter face. Picture. Material. Surface. SS 17-4. Flat. SS303. Grooves. Depth. Pattern. None. None. None. Milling. Groove. Light. Circular. SS303. Milling. Groove. Deep. Circular. SS303. Milling. Ridge. Deep. Circular. 2.5. Putting Testing Apparatus Past putting researches focus on putting kinematics or ball roll kinematics. Putter kinematics studies (Marquardt, 2007; Karlsen et al., 2008; Wu et al., 2012) used ultrasonic device (Puttlab) to capture putter kinematics and have proven to have accurate measurements for human putting stroke kinematics. Past studies used a high-speed camera to verify ball roll kinematics (Drane et al., 2014; Hurrion & Hurrion, 2002; Richardson, Mitchell & Hughes,. 30.

(43) 2018). An interaction between a putter-golf ball, taken using high-speed photography, can be observed in Figure 2.10.. Figure 2.10. An interaction golf putter-golf ball taken using high-speed photography from the side-camera. Source: Quintic Golf.com. The side-camera have been popular in ball roll kinematics studies (Drane et al., 2014; Hurrion & Hurrion, 2002; Richardson et al., 2018) to capture ball velocity, backspin and skid distance. However, the photography area from the side view is limited to 0.5-0.6 meters which calculates remain of the putting distances and ball roll kinematics. There are radar-based ball roll measuring devices used for golf putting which positioned behind the ball. Due to the radar location, it is ideal for golf ball flight trajectory rather than ball roll on turf. There is no research on doppler radar on ball roll kinematics. The top-camera setting can better calibrate XY-plane. Calibration process first to identify the intended putting area, mainly from starting position to finish position, Ball tracking setup, how is make putts and missed putts calculated. Benefits of the to-camera compared with the side-camera is that one can capture the full horizontal ball trajectory where the ball stops. In order to monitor putting performance, the best position to capture from top-camera.. 31.

(44) Figure 2.11. Golf putting data capture taken using high-speed photography from the top-camera. Source: Science&Motion Sports GmbH. Many studies used putting mechanical arm has been with pendulum rig to produce the excellent reliability testing apparatus for impact spot, backswing amplitude and distance control (Karlsen & Nilsson, 2008b; Mackenzie & Evans, 2010; Pope et al., 2014). Richardson et al. (2018) have found the difference between mechanical and human on putting kinematics. Human putting studies (Delay et al., 1997; Marquardt, 2008; Wu et al., 2020) found significant differences in putting kinematics between proficiency levels. Most ball roll kinematics researches use horizontal high-speed cameras to capture ball roll kinematics (Hurrion & Hurrion, 2002; Brouillette, 2010; Pope et al., 2014; Lambeth et al., 2018) however, this method limit the capture area for under 50 cm and lack the data for horizontal ball roll trajectory, velocity and position which are the key for ball roll kinematics. Past ball roll kinematics researchers are illustrated in Table 2.5.. 32.