Senior Experience in Engineering Design Program /Capstone Design I and II Project Waiver and Release of Liability for Sale/Donation

Transcription

1 School of Engineering, Votey Hall Senior Experience in Engineering Design Program /Capstone Design I and II Project Waiver and Release of Liability for Sale/Donation In consideration of the University of Vermont selling or donating: (Insert detailed name of equipment or design here) the undersigned agrees to: 1) Accept the equipment as is; 2) Take full responsibility to safely remove the equipment from University of Vermont premises at: (Insert location where equipment is currently located, including the building name and room number) 3) Indemnify, defend and hold harmless UVM, their agents, and employees from any and all liability, claims, and causes of action or demands of any kind and nature which may arise from use of this equipment. Signed by Receiving Person: Print Name: Title: Company Name: Address: City, State: Signature Date: i U VM

2 To Whom It May Concern, Enclosed is the summary of all work done by the BombTech Innovative Golf Putter team on the BombTech Grenade Putter. Outlined in the first two sections is the main problem statement for the project and an overview of the final design. Following these sections is the objective and functional analyses and the development and specifications of the final design. Finally, a description and justification of the performed tests as well as test results are presented with a formal conclusion summarizing what the data showed. In the appendix, the budget, bill of materials, final schedule, and test plans are provided. Lastly, an Engineering and Design Overview document is provided for use on BombTech Golf s website. Speaking for all members of the design team, also known as The Dream Team, we would like to extend a huge thank you to BombTech Golf s founder Tyler Sullivan for enabling this project to be a part of our engineering experience at the University of Vermont. We would also like to thank everyone who helped us along the way with this project, especially John Novotny for all his hard work in guiding us through the entire process. Thank you,, aka The Dream Team Cody Jackson Jeff Keenan Victoria Thacher Corey Tillson Official Document When Signed ii U VM

3 BombTech Golf Innovative Golf Putter Final Design Report Client: Tyler Sullivan, BombTech Golf Mentor: Dr. John Novotny Corey Tillson B.S. Mechanical Engineering Victoria Thacher B.S. Mechanical Engineering Design Team: Jeffery Keenan B.S. Mechanical Engineering Cody Jackson B.S. Mechanical Engineering iii U VM

4 Section Title Page Report 1 Final Problem Statement 3 2 Design Overview Objective Analysis USGA Conforming Improved Performance Improved Accuracy and Consistency Smoother Ball Roll Stroke Stability Manufacturability Aesthetically Pleasing Function Analysis Generate Topspin Maintain Stability at Contact Ease Alignment Maintain Stability in Stroke Generate Pleasant Sound Generate Pleasant Feel Decrease Ball Loft Design Details Individual Features The Material Mass Configuration and Dimensions Alignment Cues Face Details Clubhead Sole Shaft Configuration Specifications P age

5 Design Analysis Pendulum Motion Analysis Analysis of Moment of Inertia Effect on Off Center Shots Material Analysis Coefficient of Restitution Analysis Testing and Results Consistency Testing Analysis of Initial Roll Characteristics Pilot and Qualitative Testing Conclusion 38 Appendices A1 Budget 41 A2 Bill of Materials 43 A3 Final Schedule 44 A4 A4.1 A4.1.1 A4.1.2 A4.1.3 A4.2 A4.2.1 A4.2.2 A4.2.3 A4.3 A4.3.1 A4.3.2 A4.3.3 A4.4 A5 A6 Testing Plans and Procedures Consistency Testing Test Boundaries Required Resources Test Method Analysis of Initial Roll Characteristics Test Boundaries Required Resources Test Method Pilot and Qualitative Testing Test Boundaries Required Resources Test Method Assumptions, Constraints and Risks Engineering and Design Overview References P age

6 1) Final Problem Statement BombTech Golf is looking for a putter designed to improve any golfer's short game performance. The primary objective of the project is to design the head of the putter. All aspects of the club design should contribute to producing a smooth pendulum motion in the swing and smooth ball roll. The putter must comply with USGA regulations, specifically Appendix II, 1, 2, 4, and 5. It should improve the overall accuracy and consistency of the putts by lowering the deviation of ball spread from the hole. This can be done by maximizing the moment of inertia about the z-axis (MOIz approaching USGA limit of 5900 g-cm2) through the design geometry and distribution of weight. The putter should also promote a smooth initial ball roll, by promoting topspin and minimizing the backspin and initial lofting upon impact. This will be accomplished by designing the club head to have the majority of its mass on the outer edges of its geometry and by lowering the club head s center of mass (preferably <8 mm above club bottom and >15 mm behind the clubface). The putter should promote a firm and stable stroke to minimize wandering of the club during the swing. This will be accomplished by designing the head to be heavier (approximately 400g-450g) than most putter heads on the market. There should be visual alignment cues to assist the golfer in lining up shots, which will be in the form of lines of contrasting colors. The design should also generate a pleasant sound and feel for the putter through the selection of materials that will produce a desirable sound and minimize vibration. The putter shall also be designed with machinability in mind so as to keep production costs to a minimum. Lastly, the club should be aesthetically pleasing to the consumer and keep with BombTech Golf s matte black and neon green color scheme. 3 P age

7 2) Design Overview The final revision of the putter can be seen below in Figure 2a. The design chosen is a mallet putter by definition with an above average mass of 445 grams. It has most of this weight on the outside of the club to maximize the moment of inertia about the z-axis as shown in Figure 2b. Keeping with the MOIz constraint given by the USGA, the design pushes the limit at 5850 g/cm 3. The hole in the rear of the club was used for weight management and reassignment. The shaft is center mounted keeping the moment arm on off-center shots about the shaft small. Figure 2a shows the final revision of the putter shown with green painted alignment cues. The putter was milled out of 12l14 steel at Stephen s Precision Milling in Bradford, VT. 12L14 steel was chosen due to its machinability and how it has similar properties to that of 1018 carbon steel. The green alignment cues provide high contrast lines spaced a golf ball s diameter apart for user alignment during a game of golf. Figure 2b shows the 3D printed prototype putter with simulated axis for reference. 4 P age

8 The face of the club was placed at a relatively neutral angle of 2.5 degrees from vertical as shown in figure 2c. This helps lift the ball out of its divot while helping to minimize the back spin. Market research determined that the average clubface lofting was between 2 and 3 degrees from vertical. Figure 2d below, shows the rounded bottom which prevents the toe or heel from digging into the ground during a swing on an uneven green. In addition, it allows the club s lie angle to be adjusted by ±3º from the original 69º lie angle for a more comfortable stance. Figure 2c shows the side view of final design displaying the loft angle. Figure 2d shows the face and sole view of final design. 5 P age

9 3) Objective Analysis BombTech Golf Putter USGA Conforming Improved Perfermance Manufacturability Aesthetically Pleasing Figure 3a shows the Primary Objective Tree Figure 3a shows the four primary objectives that were identified for the design and production of the Grenade. Each objective serves the purpose of accomplishing one of the goals set forth by the Final Problem Statement. The primary objectives are that the putter must conform to USGA Regulations, it must improve the putting performance of the user, it must be designed such that it can be manufactured at a reasonable cost and process, and that the putter must be aesthetically pleasing visually, acoustically, and in terms of feel to the user. 3.1) USGA Conforming One of the primary constraints was that the putter must conform to USGA regulations, primarily those set forth in Appendix II: Design of Clubs. Amongst the many limitations, those that directly impacted the clubhead design were that the club must be plain in shape, must not have multiple hitting surfaces, cannot incorporate electronic devices, and must conform to the set dimensional limits. These dimension limits state that the distance between the heel and toe must be greater than or equal to 2/3 rd the distance from front to back, that the width of the club must not exceed 7 inches, and that the distance from the sole to the top of the club is less than or equal to 2.5 inches. The MOIz of the clubhead must also stay within the USGA defined upper limit of 5900 g-cm 2. To achieve and abide by these constraints, the Grenade was designed to have a simple shape and conforming dimensions. Section 5 details the overall dimensions of the clubhead. The distance from the heel to toe is 4 inches, and the distance from front to back is 3 inches. The overall height is 1 inch. These are consistent and compliant with the regulations described in Appendix II. 6 P age

10 Through the use of SolidWorks, the MOIz was determined to be 5850 g-cm 2, which also abides by the limits set forth by the USGA. In terms of design shape and appearance, the Grenade can be considered conforming as well. Only one putting surface was designed into the club, and the overall shape was determined to be plain in shape by the design team, Dr. John Novotny, and BombTech Golf due to the lack of any extravagant or unnecessary design features. 3.2) Improved Performance As described in the Problem Statement, the principal goal of the project was to design a putter that would improve a golfer s short game. Qualitative determination of improvement was split up into three different sub-objectives: Improved consistency and accuracy, smoother ball roll, and stroke stability. A detailed design analysis is described in section 7 to statistically show that the Grenade met the defined qualitative and quantitative objectives and requirements ) Improved Accuracy and Consistency Improvement in the consistency can be defined as lowering the deviation of putts from the desired target on off-center shots. Through research [1,2,3,4,5] it was determined that strategic placement of the mass, and thus the increased MOIz, theoretically decreases the dispersion of offcenter shots. Approximately 50% of the total mass of the Grenade was designed into the outer 30% of the clubhead. This increased the MOIz to 5850 g-cm 2 as previously described. The design also focused on moving mass toward the bottom of the club to lower the center of mass (COM). The final design s COM is located 7 mm above the sole of the club and 17 mm behind the clubface, which increases the sweet spot and satisfies the requirements set forth in the Problem Statement. To improve the accuracy of the putter, contrasting alignment cues were incorporated into the design. Due to accuracy being more influenced by the skill of the golfer rather than the features of the putter, only simple alignment lines were chosen to accomplish this objective. Bright green lines, spaced the width of a golf ball, and aligned with the center of the club, are used to assist the golfer with proper alignment. 7 P age

11 3.2.2) Smoother Ball Roll Smooth ball roll is vital when determining the quality of a putt. If a putter imparts initial backspin or skipping then the ball will have a tendency to bounce or deviate from its intended path. To decrease the initial backspin and skipping, the COM was designed to be located lower and deeper on the club. As stated above, the COM is located 7 mm above the sole of the club and 17 mm behind the clubface. These dimensions cause the club to impart a force closer to the center of the ball and in an orientation nearly parallel to the ground, thus theoretically reducing the chance of backspin and skipping. A loft of 2.5 was chosen as an optimal loft angle, such that initial lofting is reduced while still imparting some upward direction to the ball to lift it out of its static indentation. Both of these metrics were initially going to be used to calculate a roll ratio, as described by N.M. Lindsay [1], but due to questions about the metric s validity and the difficulty in accurately obtaining some of the parameters needed to calculate the ratio, the use of the roll ratio to quantify the performance of the initial roll was discarded. Many companies claim that grooves affect the roll of the ball, potentially decreasing backspin by adding friction to the initial contact. Based on the analysis described by N.M. Lindsay, it was determined that the face grooves make no impact on the ball roll. Despite this, face grooves were included as part of the putter s appearance and to appeal to golfers who prefer face grooves ) Stroke Stability The stability of a golfer s stroke is a major aspect of a golfer s short game. A stroke that wanders from a straight path will result in misaligned and off-center shots. To decrease this wandering, the clubhead was designed to have a heavy than average weight. The final clubhead weight is 445 grams, roughly 100 grams heavier than the average putter. As shown in section 6, the heavier head promotes a pendulum-like motion, stabilizing the golfer s stroke leading to better putts. 3.3) Manufacturability Because the Grenade is being sold on the open market by BombTech Golf, the design needed to be simple and not too elaborate so that machining and manufacturing costs were kept at a minimum. This was achieved with the help of Stephens Precision s engineers who helped advise and tweak the final design to minimize the total cost. Through consulting, 12l14 carbon steel was 8 P age

12 decided as the putter material due to its ease in machining and similar qualities to harder steels such as stainless and 1018 carbon steel. Minimizing cost was also done by reducing the amount of cuts and tool changes that would be needed to complete the clubhead. In addition to reducing cost, the Grenade was required to be durable and weather resistant. Due to the 12l14 carbon steel s lack of rust resistance, a coating was necessary to prevent unwanted aging. An electroplated nickel coating was chosen to achieve this and for aesthetic purposes. 3.4) Aesthetically Pleasing Not only must the putter perform well quantitatively, it must also be qualitatively acceptable. To do so, the Grenade was designed to have a high quality appearance, feel, and sound. The quality appearance was accomplished through multiple rounds of designing and consulting with BombTech to produce a putter that they felt confident selling. The overall appearance had to include consideration for how BombTech s color scheme could be incorporated into the design. A simple theme was decided upon, using the matte metallic finish as the primary feature and the BombTech green as highlights in the form of alignment cues. The quality of the feel and sound were driven by the material selection. Top of the line putters that are considered the best in terms of sound and feel are CNC milled, which is the process that was chosen for manufacturing. It wasn t until testing, described in section 7, that these metrics were confirmed. 9 P age

13 4) Function Analysis Figure 4a shows the expanded functional analysis chart. Most functions result in multiple positive outputs for the project. They are all closely linked and work together to produce a good overall putter. Figure 4a shows the expanded graphical functional analysis of the workings of the Grenade putter. Due to the simplicity of the putter, some functions control the performance of multiple different parameters. This is why it was important to optimize each function so that the overall performance of the putter is ideal. Each function specifically made an impact on the quality of the putter and the ability to meet the requirements set forth in the Problem Statement. 4.1) Generate Topspin This makes the ball have a smoother rolling motion. Initially the loft of the club will create a backspin, but the goal was to minimize the backspin. Generating topspin helps the ball roll in a more perfect manner and prevent skipping. To achieve optimal topspin, the COM was desired to be located <8 mm above the sole and >15 mm behind the clubface. These requirements were met in our design, where the COM was located 7 mm above the sole and 17 mm behind the face. This resulted in improved topspin and decreased skipping. 4.2) Maintain Stability at Contact This sub function will enhance the resultant putt in a number of ways. It prevents the club head from torqueing around the ball at the moment of impact and will result in a straighter shot. Stability at contact also greatly enhances the feel of the club which may turn out to be the most important factor to golfer satisfaction. A maximum MOIz was desired to achieve this goal. The 10 P age

14 final design has a MOIz of 5850 g-cm 2, only 50 g-cm 2 less than the upper limit set by the USGA. The large MOIz can be attributed to the location of the majority of the mass. The initial requirement was for the majority (>50%) of the mass located on the outer 15% of the club. In the end, 50% of the mass was assigned to the outer 30% of the club. This change can be attributed to the limitations of the design in regards to producing an aesthetically acceptable putter and mass constraints 4.3) Ease Alignment This function helps the golfer aim the putt in the direction that he/she chooses. Every putt has an alignment, and optimizing the alignment cues further helps the golfer line up their putt. This function influences the ball velocity, ball loft, feel, and sound outputs in various primary or secondary ways. In the final design, the alignment cues are two bright green lines spaced a golf ball width apart. This allows the golfer to easily align the golf ball on the center of the face, increasing the chances of an ideal putt. 4.4) Maintain Stability in Stroke This function creates topspin on the ball by providing a cleaner stroke. Stability in the stroke also helps to keep the ball velocity and direction on the right path. This function is also involved in eliminating ball loft. A shaky stroke can cause the ball to do unwanted things. Stability is crucial in overall feel of the club and sound. To alleviate any instability in the golfer s stroke, the clubhead has a mass of 445 grams, which is 20 grams higher than previously desired. The increased weight further adds to the stability of the golfer s stroke. 4.5) Generate Pleasant Sound This function is important to the overall enjoyment of the club. It has little influence on the other outputs except for the feel and sound outputs. To achieve a pleasant sound, CNC milled carbon steel was chosen as the machining material and process. Machining a putter out of a single piece of steel eliminates any material property changes commonly found in the forging and casting processes. These changes decrease the quality of the sound upon impact. 11 P age

15 4.6) Generate Pleasant Feel This function is also important to the overall enjoyment of the club. Perceived feel is what putting is mainly about. The effects from the other functions will not improve the game of a terrible golfer by substantial amounts, but feel can still make that golfer happy. To achieve a pleasant feel, CNC milled carbon steel was chosen as the machining material and process. Machining a putter out of a single piece of steel eliminates any material property changes commonly found in the forging and casting processes. These changes decrease the quality of the feel upon impact. 4.7) Decrease Ball Loft Ball loft creates skipping which can cause putts to overshoot or undershoot their target. By decreasing loft, topspin is increased. This creates a more preferred roll and should result in more consistent ball velocities. The final design has a loft of 2.5º, which is within the limits set in the requirements. This loft angle helped reduce skipping and backspin, producing purer putts. 12 P age

16 5) Design Details The Grenade putter was designed for simplicity while still being able to greatly improve a golfer s game. This means that the putter is a single piece of CNC milled 12l14 steel, unlike many of the newer putters on the market which are an assembly of multiple components. This gives the Grenade several key features and advantages over its competitors. The individual features and specifications are detailed below. 5.1) Individual Features Figure 5a shows the top and bottom view of the Grenade 5.1.1) The Material The material for the Grenade putter was initially chosen to be a carbon steel alloy. Through consulting with BombTech and Stephens Precision, the 12l14 carbon steel alloy was chosen as the final material. There are several key advantages to using 12l14 carbon steel, with the main benefit being its favorable machinability. The 12l14 alloy has at most 0.35% [6] lead by molar weight which makes the alloy comparable to aluminum in terms of ease of machining. This in turn reduces the cost of machining significantly compared to other carbon steel options, such as 1018 and stainless, that were considered. While the 12l14 carbon steel is easier to machine than other carbon steels, it maintains similar physical characteristics as the other alloys. Its density is 7.87 g/cm 3 which is the average density for carbon steels. It also has similar Brinell and Rockwell Hardness ratings, elastic modulus, Poisson s ratio, and tensile strength as 1018 carbon steel [6], a very common steel used in 13 P age

17 putters. All of these similarities mean that the putter can be machined at nearly half the cost of other materials and still maintain the excellent sound and feel that comes with a CNC milled putter. The only disadvantage to 12l14 compared to other carbon steels is its susceptibility to rust. Without a coating, the putter would begin to rust within a week. To alleviate this issue, an electroplated nickel coating is used to coat the putter head to prevent rusting and to give it a clean, professional, and sharp appearance ) Mass Configuration and Dimensions The main focus of the design was on where to put the majority of the mass. To achieve a large MOIz the mass needed to be positioned on the outer portions of the club. Figure 5b shows that the bulk of the mass is on the outsides, leaving a cavity like region in the middle with a smaller percentage of the total mass. Figure 5b shows the back view of the Grenade The final design places approximately 50% of the weight on the outer 30% of the club. By using an oval cutout, as also seen in Figure 5b, more mass could be concentrated on the outside of the putter. Doing so increases the MOIz and increases performance, as detailed in sections 6 and 7. A large MOIz reduces torqueing and optimizes energy transfer on off-center shots. In addition to expanding the mass configuration towards the outside, mass was focused towards the bottom of the club. By moving the COM lower and lower, the club s tendency to impart skipping and backspin on a ball is proportionally reduced. Figure 5c shows the location of the COM. 14 P age

18 Figure 5c shows the location of the COM As seen in the schematic, the COM is positioned 7 mm above the bottom of the club. As mentioned in section 4, this and the location with respect to the face, creates a larger sweet spot, ensuring that shots off the center of the face are more accurate and consistent. Figure 5d shows the overall dimensions of the Grenade. Figure 5d shows the dimensions of the Grenade 5.1.3) Alignment Cues Putting requires a fair deal of skill and accuracy to ensure minimal putts and consequently lower round scores. While aiming is very subjective to the golfer s style, alignment cues can be used to assist a golfer in the aiming process. On the Grenade putter, the alignment cues are two bright green lines, spaced a ball width apart, and oriented with the center of the club. Figure 5e shows the configuration of the alignment cues. Figure 5e shows the configuration and coloring of the alignment cues 15 P age

19 The key to the Grenade s alignment cues are its contrasting color scheme and the location of the lines. The alignment cues themselves are BombTech Golf s signature bright green. They are set on a matte nickel background so they are staunchly noticeable and distinguished. By having the cues centered and spaced a ball diameter apart, it promotes the alignment of the ball with the center of the face. Therefore, this feature encourages sweet spot shots which will result in truer and smoother putts 5.1.4) Face Details The development of the face was kept to a simple grooved design. The possibility of using inserts or a second material were explored, but regular grooves were ultimately agreed upon. While research suggests that grooved putter faces make no difference in the roll of the ball, the grooves were added to appease those consumers who prefer a grooved face as opposed to a smooth face. The grooves were cut using the CNC mill running at a low speed and feed rate. In addition to the face grooves, the face loft angle was set at 2.5. This angle was decided upon based on the industry standard loft angle of 2-3. Figure 5f shows the face with grooves. Figure 5f shows the face with grooves ) Clubhead Sole The underside of the club head required several design considerations as well. The sole of the putter needed to be rounded to alloy for golfers to adjust the club to fit their putting stance and style. To account for this requirement, the sole has a curved bottom that can be used to adjust the lie angle (set at 69 ) by ±3. This alloys the clubhead to rock from toe to heel depend on the golfer s preference. The rounded bottom also prevents the edges from digging into the ground if the golfer s stroke impacts the ground during the downswing. All of the edges have been rounded and softened to further prevent this possibility. Figure 5g shows the curved bottom and engravings. 16 Page

20 Figure 5g shows the curved bottom and engravings ) Shaft Configuration The location of the shaft was another area of discussion during the design process. BombTech Golf requested that a center shaft be used based on the consumer demand that they had experienced. To accommodate the demand, research was conducted to determine if there was an advantage or disadvantage to shaft location. N.M. Lindsay [1] determined that by placing the shaft in the center of the club, the torque and twisting on off-center shots are reduced based on a smaller moment arm with respect to the shaft location. The lie angle of the shaft is 69. Figure 5g shows the location and angle of the shaft 5.2) Specifications BombTech Golf Grenade Putter Head Weight 445g MOIz 5850 g-cm^2 Loft Angle 2.5 Lie Angle 69 ± 3 COM Location 7 mm above Sole, 17 mm behind Face Toe Hang Face Balanced Shaft Straight Center Offset 0 Shaft Material 12l14 Carbon Steel Coating E-Nickel Type High MOI Mallet Table 5a shows the final specifications for the Grenade 17 P age

21 6) Design Analysis 6.1) Pendulum Motion Analysis There were many assumptions made when analyzing the putter s swing in space. The first assumption was that the swing of a putt replicates the motion of a single pendulum. This assumption can be made because it is most generally understood that the ideal method of putting is one that follows a pendulum. This putting style focuses on locking the golfer s wrists and elbows, eliminating the double pendulum-like swing of other clubs (drivers, irons, etc.), and causing the hands, arms, and shoulders to act as an extension of the pendulum. A visual representation of this model can be seen in Figure 6a. Figure 6a: Pendulum Motion [1] From the analysis of the pendulum model and how it relates to putting, it was determined that a shorter pendulum length will be easier to control and have less swing variability. Therefore, raising the center of pendulum s mass should increase putting consistency. To simplify the pendulum model further, each segment of the pendulum is assumed to be of uniform density. The segments and their relative locations can be seen in Figure 6b. Figure 6b shows the segments used to calculate the overall center of mass. 18 P age

22 Each segment was represented by point mass placed at its center of gravity. From these point masses, the overall center of mass location for the pendulum system was calculated using Equation 1. L = m r + m r + + m r m + m + + m (1) To obtain the final length of pendulum values, many assumptions were made about the weights and lengths of the segments. For example, human body masses and lengths were assumed to be that of the average male in the United States (a height of meters and a mass of 88.3 kilograms) [2,3]. The weights of each of the putter s segments were accurately obtained from product pages, measurements, and SolidWorks data. Unfortunately, the product pages for the Nike Drone and Odyssey Tank did not include the lengths of each segment. As a result, the values for both the Drone and the Tank were estimated from pictures using the given total lengths. The Ping Anser was available to be measured, and the center of gravity was found by determining its balancing point. Table 6a shows the mass, length, and center of gravity values used in determining the pendulum lengths. 19 P age

23 Segment Mass(kg) Length(m) COG Location w/ respect to Segment (from ground) COG Location w/ respect to ground Blade Ping Anser Whole Putter Odyssey Tank Counter Weight Grip Shaft Head Totals N/A N/A Belly Putter Nike Drone Grip Shaft Head Totals NA N/A Our Initial Design Whole Putter Our Initial Design with an Added Counterbalance Putter Counterbalance Totals N/A N/A Body Segments Upper Arm Varies Fore Arm Varies Hands Varies Table 6a: Mass, length, and center of gravity values used for each segment 20 P age

24 Table 6b shows the calculated pendulum length values for a blade putter (Ping Anser), a belly putter (Nike Drone), a putter mimicking a belly putter (Odyssey Tank), the initial design, and the initial design with an added counterbalance. Putter Length of Pendulum (m) Blade Ping Anser Odyssey Tank 0.4 Belly Putter Nike Drone Initial Design Add in Counterbalance (100g) Table 6b: Pendulum Lengths It can be first noticed that the belly putter, contrary to what was expected, has the longest pendulum length. This is most likely due to the assumption that the pivot point in for normal style putters is directly between the shoulder blades. That is an idealized putt. In reality, any swaying motion in the hips will project the pivot point farther behind the shoulder blades, drastically increasing the length of the pendulum. Another factor that has been overlooked during this analysis is that traditional style putters are free, which inherently reduces stability. Belly putters, in addition to a short pendulum length, have the increased stability from the anchoring. The initial design for the putter as well as the initial design with an added counterbalance have a pleasingly far shorter pendulum length than the other analyzed putters. If further improvements are desired, the geometry and weights would need to be altered to raise the center of mass of the pendulum system away from the club head. Increasing the weight of the shaft, grip, or counterbalance in the design will accomplish a smaller pendulum length. If desired, reassessing the value of a heavy head and considering decreasing its mass in exchange for a higher center of mass could be beneficial. However, since the heavy head is currently central to the design, this is not something that should be altered. 21 P age

25 6.2) Analysis of Moment of Inertia Effect on Off Center Ball Hits The point of this analysis is to demonstrate mathematically that increasing the moment of inertia about the z-axis (MOIz) will result in better transfer of forward velocity to the ball and prevent energy loss in the contact region. For this analysis, the Z-axis was set to come up out of the face of the putter towards the golfer, and the X-axis was set to run along the face of the putter. The Y-axis runs perpendicular to the X-axis and parallel with the ground. The MOIz can be increased by increasing the amount of material away from the Z-axis which will be shown in the second part of this analysis. Starting with the model of the kinetic energy before and after the contact with the ball and knowing that energy is conserved in this problem, the sum of the energies before and after the contact should be equal. Also noting that; m v f v i 2 = I z (w f w i ) 2 m = Mass v f = Velocity Final v i = Velocity Initial I z = Mass Moment of Inertia about Z Axis w f = Angular Velocity Final w i = Angular Velocity Inital F = ma T = FL = I z α a = Acceleration F = Force of the ball hitting the clubface L = Moment arm Dividing the initial equation by the time of the impact; 22 P age

26 m v f v i 2 s = I z(w f w i ) 2 s And further noting that; v f v i s = a w f w i s = α Leads; ma 2 = I z α 2 Which upon dividing by acceleration and substituting in from above gives; ma = F2 L 2 I z ( 1 a ) Now remembering the formula for acceleration and substituting that back in as well as the equation for force; Which can be solved for final velocity; F = F2 L 2 s ( ) I z v f v i v f = v i FL2 s I z (2) Equation 2 shows that final velocity in the linear direction is diminished as F, L, and s increase. It also demonstrates that the MOIz will counteract those other parameters and help maintain the final velocity as high as possible. If it is assumed that the collision of the clubface with the ball was purely elastic then all the final velocity would be transferred to the ball. Therefore increasing the MOIz will help to maintain linear velocity even with the ball being struck off center. This should help to keep golfers from coming up short on putts that are hit off center. Figure 6c below shows increasing MOIz and the resultant final velocity after an initial velocity of 10 m/s. It is clear that increasing the MOIz will result in less deviation of the club head under miss hit conditions. 23 P age

27 Final Velocity Final Velocity Final Velocity (m/s) MOIz (kg/m^2) Figure 6c shows that as the MOI increases there is a trend toward maintain the initial velocity of the impact Putter Type MOI z (kg/m^2) Percentage of Wing Type Blade % Mallet % Wing Type % Table 6c shows the percentage less that each different type of possible head would in general produce for a MOI The current prototype design falls under the wing type category of putters. The values found in Table 6c are found in SolidWorks on a single design in each of the respective categories. The percentage is just a tool for visualizing the gains to be had in using a wing type putter head. Generally there is a line in the industry between obtaining a high MOIz and centering the weight low and behind the putter s sweet spot. It is believed that with a low centered wing type putter the optimal putter will be designed. 24 P age

28 6.3) Material Analysis When designing a golf club, the material selection is a vital process. The material defines the weight, feel, and look of the club. For putters, the material selection is even more important, as it affects every physical and engineering aspect of the club. Many different materials have been used for putters, from metals to composite plastics. This analysis was done to determine which material would be best suited for the primary material for our putter. Table 6d displays different materials considered for use. Through research and data gathered [6] about common metals used for golf clubs, several alloys of carbon steel, stainless steel, aluminum, beryllium copper, and titanium were analyzed. Beryllium copper and titanium were not considered as potential usable materials due to potential hazards and cost associated with manufacturing the stated materials. 630 Steel was also found to be non-ideal due to its high cost of production. The most important factors taken into consideration were the materials tensile strength, hardness, machinability, and cost. The putter will ideally be CNC or hand milled, so the material s machinability proved to be one of the deciding factors. Based on the data collected, 1018 steel, 303 and 304 stainless steel, 350 maraging steel, and T6 aluminum were found to be the materials best suited for use. All of the metals (excluding 304 stainless steel) had machinability of 68% and above. All are also low cost in terms of cost/lb. and in machinability. Aluminum and the two stainless steels were the most commonly referenced putter materials found during background research. Through discussion with BombTech, 1018 steel was initial chosen as the material to be used for the putter. BombTech stated that the quality of the steel and the market appeal of a milled steel putter were the driving factors in choosing the harder and more expensive steel over aluminum. After the final design was created and decided on, 12L14 steel was chosen as the material. This was due to a discussion with the machine shop about the machinability of the design. 12L14 has the same mechanical properties as 1018 but can be milled at faster rates which would reduce machining cost. 25 P age

29 Tensile Strength Hardness Elongation Elastic Modulus Corrosion Resistant? Temperature Resistant? Machinability Density Cost Carbon Steel ksi 126 HB 15% 30,000 ksi Yes Yes 65% 0.28 lb/in 3 Mid-high ksi 197 HB 27% 30,000 ksi Yes Yes 78% 0.28 lb/in 3 Mid-high 12L ksi 163 HB 10% ~29,000 ksi No Yes 175% 0.28lb/in 3 mid Stainless Steel ksi 363 HB 15% 28,000 ksi Yes Yes 45% 0.28 lb/in 3 High ksi 360 HB 16% 28,000 ksi Yes Yes 45% 0.28 lb/in 3 Mid-high ksi 201 HB 30% 28,000 ksi Yes Yes 45% 0.29 lb/in 3 Mid ksi 228 HB 35% 28,000 ksi Yes Yes 78% 0.29 lb/in 3 Mid 17-4 PH 190 ksi 388 HB 10% 28,000 ksi Yes Yes 48% 0.28 lb/in 3 Mid-high 15-5 PH 160 ksi 388 HB 12% 28,000 ksi Yes Yes 48% 0.28 lb/in 3 Mid-high Maraging Metal ksi 530 HB 15% 30,500 ksi Yes Yes 80% 0.29 lb/in 3 Low Aluminum T6 18 ksi 95 HB 15% 10,200 ksi Yes Yes Excellent 0.10 lb/in 3 Low Beryllium Copper Basic 80 ksi 362 HB 23% 18,500 ksi Yes Yes Hazardous 0.30 lb/in 3 High Titanium ksi 334 HB 14% 16,500 ksi Yes Yes Extremely Difficult 0.16 lb/in 3 High Table 6d: Material Properties Table Key Metal chosen for use by BombTech Metals that were considered by design group, but considered not ideal Metals that should not be used or considered

30 6.4) Coefficient of Restitution Analysis The second set of analysis done was a comparison of coefficients of restitution (CoR) between the two types of metal to be considered for the putter: aluminum and steel. A block of each, 1½ thick, were retrieved and used to perform a simple CoR test. The blocks were placed securely on the floor with a ruler situated behind. A golf ball (Titleist NXT Tour S) was dropped from 10 inches above the block and the resultant bounce height was measured via video and the results tabulated. The CoR was then found using the derivation below. [4] v 1 v mv 2 0 mgh 0 v 0 2gh 0 v 1 2gh 1 v 0 2gh 0 2gh 1 2gh 0 h 1 h 0 (3) Steel-Golf Ball (10" Drop) Aluminum-Golf Ball (10" Drop) Drop Number Rebound Height (h 1) 1 6.6" 4.5" 2 7.0" 4.3" 3 7.1" 4.7" 4 6.9" 4.8" Avg = 6.9" Avg = 4.6" ε = (h 1/h 0) ε = 0.83 ε = 0.68 Table 6e shows the raw and calculated coefficient of restitution data It should be known that the results for both materials don t necessarily serve as direct representatives for the ideal materials initially chosen. The purpose was to compare the CoR of general aluminum and general steel, seeing as they are two vastly different metals. The final results do provide valuable insight. As shown in Table 6e, the steel CoR was 0.83, right around the constraint of 0.90 for putters defined by the USGA. The aluminum CoR was a more modest Even though these numbers are just a baseline, they show that the steel is an appropriate choice as a putter material. The higher CoR will provide a better transfer of energy from the putter to the ball, ensuring minimal loss in velocity on off-center hits. 27 UVM

31 7) Testing and Results 7.1) Consistency Testing One of the most important features of a golf putter is its ability to manage miss-hits. When a putter strikes a ball off of its sweet spot, the ball should have the highest possible velocity for that particular input. In other words, at that point, the energy transfer from the club to the ball is at a maximum. When the impact point travels away from the sweet spot, it is expected that the ball will lose some of that energy. Thus, the ball will travel a shorter distance. Part 1 of this test was aimed at determining how much distance is lost when the ball is impacted at specific points in the x-direction across the face of the club. The distances of the balls across many trials were analyzed to determine the club s overall consistency. Furthermore, the BombTech Grenade was compared to two other market putters, the TaylorMade Rossa and the Odyssey Rossie. For each club, the sweet spot distance is immediately specified. This value represents the average distance the ball traveled when hit directly off the club s sweet spot. Because this is the location where energy transfer is at a maximum, it is considered the ideal distance travelled. The sweet spot distance was determined by finding the average location for a series of balls hit directly off the center of the club. All other clubface locations and respective distances were measured as a radial distance in relation to the ideal sweet spot location. The testing process/plan is described in further detail in the appendix, section A4. Tables 7a, 7b, and 7c show the respective test results for the BombTech Grenade, TaylorMade Rossa, and Odyssey Rossie. 28 UVM

32 BombTech Grenade (Sweet spot Distance: 360 inches) Face Location (cm off face) Average Radial Dispersion (in) Standard Deviation (in) R Dispersion/D SweetSpot Heel Heel Heel Heel Center Toe Toe Toe Toe Table 7a shows the consistency data for the BombTech Grenade TaylorMade Rossa (Sweet spot Distance: 359 inches) Face Location (cm off face) Average Radial Dispersion (in) Standard Deviation (in) R Dispersion:/D SweetSpot Heel Heel Heel Heel Center Toe Toe Toe Toe Table 7b shows the consistency data for the TaylorMade Rossa 29 UVM

33 Odyssey Rossie (Sweet spot Distance: 348 inches) Face Location (cm off face) Average Radial Dispersion (in) Standard Deviation (in) R Dispersion/D SweetSpot Heel Heel Heel Heel Center Toe Toe Toe Toe Table 7c shows the consistency data for the Odyssey Rossie All the data shows an expected, similar trend. As the impact location travels away from the sweet spot, the radial dispersion increases drastically. To compare the radial dispersion of each face location between each of the putters, a one-way analysis of variance (ANOVA) was performed. The one-way ANOVA was performed using a predetermined level of significance of.05. The null hypothesis is that all mean dispersion ratios are statistically equal. The alternate hypothesis is that all the mean dispersion ratios are statistically different. The one-way ANOVA was performed using MATLAB software. The results of the one-way ANOVA can be seen in Table 7d. 30 UVM

34 Analysis of Variance (One-Way ANOVA) of Normalized Consistency Test Data Face Location (cm off face) BombTech Grenade TaylorMade Rossa Odyssey Rossie R Dispersion/D Sweetspot Standard Deviation R Dispersion/D Sweetspot Standard Deviation R Dispersion/ D Sweetspot Standard Deviation Level of Significance (α=0.05) Heel *10-36 Heel *10-20 Heel *10-18 Heel *10-5 Center Toe Toe *10-5 Toe *10-8 Toe *10-17 Table 7d shows the One-was ANOVA of the normalized consistency test data The one-way ANOVA shows that the consistency test results showing the BombTech Grenade to have reduced dispersion are statistically significant except for the face location of 1 cm towards the toe. At this location the level of significance was found to be.103, which is greater than the predetermined value of.05. Further testing would need to be performed to statistically prove the BombTech results for this face location to be superior to the TaylorMade Rossa and Odyssey Rossie. The one-way ANOVA also showed that the standard deviations among the BombTech Grenade and TaylorMade Rossa were statistically comparable, while the BombTech Grenade showed a significant reduction in standard deviation when compared to the Odyssey Rossie. A graph showing the radial dispersion vs. club face location for each of the putters can be seen in Figure 7a. For clarity, the standard deviations are not shown in the graph. In the graph, it can be seen that the BombTech Grenade shows clear reduction in dispersion across the entire face of the club. The largest reduction in dispersion can be seen at 4 cm towards the heel of the club. At this location the BombTech Grenade experiences almost four times the reduction in dispersion when compared to the Odyssey Rossie. 31 UVM

35 Ratio of Radial Dispersion to Ideal Distance From Starting Point Radial Dispersion Vs. Club Face Location Distance from Center of Club Face: Heel to Toe (cm) BombTech Odyssey TaylorMade Figure 7a displays the graph showing radial dispersion versus club face location for the BombTech Grenade, Odyssey Rossie, and TaylorMade Rossa 7.2) Analysis of Initial Roll Characteristics An important factor for quantifying the performance of the Grenade putter versus that of other putters was the initial ball motion off the face of the club. Quick generation of topspin and low distance of skipping were desired from the objectives set forth beforehand. To test this parameter, the automated pendulum swing rig was used to hit balls while recording with a high definition high speed camera. The camera was able to record at 500 frames per second allowing for analysis of the video post swing to determine certain features of the roll. For this testing, three putters were used: the BombTech Grenade, the TaylorMade Rossa, and the Odyssey Rossie. Each putter was recorded hitting the ball five times and the data was analyzed in QuickTime Movie Player. Each frame of the video was equal to a time step of two milliseconds so important parameters could be monitored as they played out over the first few milliseconds of ball contact. Table 7e and 7f below shows the pure data compiled from the high speed videos. 32 UVM

36 Putter Grenade Trial Number Total Time (ms) Time for 1/4 turn (ms) Skipping Time (ms) Time from end of 1/4 turn till off screen (ms) Means Odyssey Means TaylorMade Means Table 7e shows the data computed from high speed roll analysis footage. 33 UVM

37 Putter Grenade Trial Number ω (total) ω (rest) V(1/4) Distance of Skip Distance for 1/4 turn Means Odyssey Means TaylorMade Means Table 7f shows the data computed from high speed roll analysis footage. The testing provided quantitative results for the skipping, angular rotation, angular velocity, and translational velocity seen in the first few seconds of ball contact. These parameters were measured and the means are shown in Tables 7e and 7f. For a true comparison, the data was normalized for some parameters. In Figure 7b below, the time parameter was normalized for the time of skipping divided by the time required to complete a one-quarter turn from vertical. This normalization shows the ratio of how long the ball hesitates before beginning the top spin motion. 34 UVM

38 Figure 7b shows the normalized time parameter for initial ball contact for three different clubs. The normalization in Figure 7b demonstrates that the Grenade putter imparts top spin motion almost immediately compared to the other two tested putters. In the footage this was even more visible from the amount of skipping that the other two clubs produced. Figure 7c below presents another normalization of the roll analysis data. This normalization involves taking the angular velocity of the first quarter turn and dividing it by the translational velocity of the first quarter turn. This is essentially a comparison of the rotational and linear velocity to see if there is any excessive over-spinning or under-spinning of the ball on contact. Figure 7c shows the normalized velocity parameter determined from the high speed roll footage. 35 UVM

39 Figure 7c shows that for all the clubs there was not excessive over or under-spinning. These results also demonstrate that for all tests the ball was spinning angularly faster than it was translating across the screen. Figure 7d shows the normalized distance parameter for the roll analysis data. Figure 7d shows the normalized distances measured in the roll analysis. This normalization is dividing the skip distance by the distance required for the first quarter turn to complete. This was a demonstration of how the club was imparting a skipping motion versus a spinning motion. Many golfers believe that the key to excellent putts is found in limiting distance of skipping and maximizing the rolling aspect of the ball contact. Figure 7d shows that the Grenade putter and the Rossa putter share very similar ratios of skipping distance versus quarter turn distance. This is still a good result as it shows that the Grenade performs as well as market putters even if it does not exceed their results as the other analyses show. 7.3) Pilot and Qualitative Testing A final round of testing was performed to gain qualitative data for the BombTech Grenade putter. The putter was brought to display on the University of Vermont campus, and students, faculty, and other people passing by were invited to test out the putter on a fake putting green. The pilot testing generated about fifty surveys, of which only 10 were used for final data comparison. Many surveys were discarded for a variety of reasons such as lack of clarity or the person being surveyed had never golfed on a full course. An additional, undocumented visit to Dick s Sporting 36 UVM

40 Goods allowed for the gathering of comments and feedback from their golf section s employees. Figure 7e shows a picture taken from each of these events. Figure 7e shows golfers demoing the Grenade Each collected survey asked the user to rate the sound, feel, and appearance of the BombTech Grenade, TaylorMade Rossa, and Odyssey Rossie. It is important to note that the study was not blind and there were few useable surveys. Therefore, the data should be observed as a starting trend for the putter and not a full statistical analysis. The resulting data is presented in Table 7g. Results of Head to Head User Testing (n=10) Rating Out of 10 BombTech Grenade TaylorMade Rossa Odyssey Rossie Sound 8.28± ± ±1.38 Feel 8.50± ± ±1.57 Appearance 8.29± ± ±1.90 Table 7g shows head to head user testing results In addition to the data presented in the table, many of the users offered feedback that could be helpful in gauging what users may want from a future putter design such as, a heel shafted or blade putter. 37 UVM

41 8) Conclusions The four main objectives of the project were to produce a putter that was USGA conforming in design, improved performance over other market putters, be manufacturable in mass quantities, and finally, to be aesthetically pleasing. The grenade putter meets all known USGA requirements for club design. The rules as set forth in Appendix II: Design of Clubs dictate that the club must be plain in shape, must not have multiple hitting surfaces, must be free of electronic devices, and conform to the required dimensional parameters. The USGA also dictates that the width of the club may not exceed seven inches and the distance from the heel to the toe must exceed two-thirds the distance from the front to the back of the club. The club may only be at a maximum of two and a half inches high and the moment of inertia about the z-axis may not exceed 5900 grams per centimeter cubed. To the farthest extent of the rules, the Grenade putter should be accepted by the USGA for use in professional golf. This approval process is still being reviewed but the club should fall within their guidelines. The Grenade was designed to maximize the moment of inertia available within the guidelines of the USGA for improvement of consistency. This effort was to reduce the deviation of ball velocity from what a perfect hit would enact on the ball on off center impacts. The consistency testing conducted clearly shows that the Grenade putter was far better at reducing radial spread than the other two putters tested. This result completely signifies that the Grenade met this this performance objective with flying colors. Another objective of enhanced performance was to provide a smoother ball roll off impact. The roll analysis testing demonstrated that the grenade putter minimized skipping distance in favor of inducing roll earlier in the post impact time frame. The Grenade was also expected to increase stroke stability. The final weight was on the higher side of most other putters on the market. While this objective was not directly tested with a quantitative test, the user feedback received seemed to suggest that the club felt solid and smooth in the hands. The club head is heavier than most other putters on the market which theoretically diminishes the jittery motion that is seen in human putts. This objective cannot be proven directly but in theory it was met. The ability to be manufactured was always a prime objective of the project as the Grenade is, at its heart, a consumer product. The Grenade was recently pushed into mass production so this 38 UVM

42 objective was clearly met. The putter was designed with a milling process in mind and the knowledge that every second of milling required an increase in the final putter price. Aesthetically pleasing was the final objective to be met in the project. This is largely based on individual preference but based on user feedback in our short demo times, the Grenade is at least somewhat appealing to the masses. It was also chosen by our client as being his favorite and he was offered three other sharp looking putters. The Grenade is a pretty complete product in general, but a few things did come up after production was completed on the first prototypes. The material resistance to wear and corrosion is questionable as the 12L14 is not rust resistant. The steel is also rather soft allowing for impacts to dent and scratch the club head. The putter was electro nickel plated to increase corrosion resistance but that solution is not an end all solution to the corrosion problem. Specifically, the team is worried about the putter rusting if the final coating is scratched. Another shortcoming of the design is that the putter is not heel shafted and there has been feedback requesting a heel shafted putter. When designing the putter it was generally accepted that a center shaft would suffice, but when seeing the final product, it limits the alignment cues on the top of the club and seems a little out of place. There was also hope for counterbalancing to be standard in all Grenade putter grips but that idea is still in the concept phase and not a reality for the putter at this time. Overall, the Grenade putter has exceeded expectations for improvement of performance and the other outlined objectives. Looking forward, the client has expressed interest in developing a heel shafted revision and a blade style putter that is similar in shape to the Grenade to add to the club lineup available to consumers. This project started as an idea on a UVM engineering webpage and has resulted in a successfully built and produced product. In that sense, it is an impressive accomplishment and a total success. 39 UVM

43 Appendices 40 U VM

44 A1) Budget BombTech Golf took care of finding a machine shop and raw material purchasing out of concern for their company s image and due to the end goal of the project being a new putter brought to market. The cost associated with machining the putter design was the only concern for the team, which was to be minimize to meet the clients price point. The design team was giving no real budget since the only purchases needed were that for the test rig and the client trusted team to keep that cost low. Below in Table A1a the budget from the Preliminary Design Report is displayed. The final budget changed drastically due to opportunities and choices made by the team to save money. Part Quantity Unit Cost Price IMF prototype 1 $900/prototype PVC pipe 20' $0.35/ft bolts 1 box $9/box nuts 1 box $9/box golf balls 36 $12/dozen shafts 1 per head $15/shaft grip 1 per head $15/grip man hours 150 hours $15/hour $ $ 7.00 $ 9.00 $ 9.00 $ $ $ $ 2, Total $3, Table A1a: Initial SEED Budget 41 U VM

45 The team and client chose to not use IMF for a prototype due to the high cost and that the 3-D printer in UVM s FabLab was made available at no cost. This allowed multiple prototypes to be made for use in deciding on a final design. As mentioned above the shafts and grips were taken care of by the client and the golf balls were not purchased but rather gathered from the team members personal golf bags eliminating the need to purchase them. The man hours were an estimate of what the team put in to the project for the first semester and would roughly double to include the second one. This cost was omitted from final budget due to it not actual being a cost to the client. The final budget can be seen in the following Bill of Materials section. 42 U VM

46 A2) Bill of Materials Bill of Materials Description Quantity Unit Cost ($) Cost 1/4" x 2.5" Bolts $2.50 1/4" nuts $4.80 1/4"x3/4"x2-1/2" U-bolt $ /16"x1-3/4"x2-1/2" U-bolt $ /2" steel rod $ /4" x 10' PCV pipe $11.58 T fitting $ fitting $ fitting $7.28 End caps $3.44 Coupler fitting $0.77 PCV cement $8.27 Bearings $11.86 Total : $85.90 Table A2a shows the Bill of Materials for the entire project 43 U VM

47 A3) Final Schedule 44 U VM

48 A4) Testing Plans and Procedures A4.1) Consistency Testing A4.1.1) Test Boundaries One of the most important features of a golf putter is its ability to manage miss-hits. When a putter strikes a ball off of its sweet spot, the ball should have the highest possible velocity for that particular input. When the impact point travels away from the sweet spot, it is expected that the ball will lose some of that velocity. Part 1 of this test was aimed at determining how much of this velocity is lost when the ball is impacted at specific points in the x-direction across the face of the club; both the distance and direction of the ball were analyzed to determine the club s overall consistency. The scope of this test did not include the testing of angular or vertical adjustments to the clubface impact point. A4.1.2) Required Resources Apparatus: In this study, a test apparatus used to standardize and mimic a pendulum-like swing for each of the evaluated swings. The apparatus, shown in Figure A4a, consisted of a PVC frame, a free to rotate steel bar, and a custom plate used to attach each putter at the desired heights and angles. Figure A4a shows the testing apparatus: SolidWorks design and completed product 45 U VM

49 Putters: The putters tested were the BombTech Grenade, TaylorMade Rossa, and Odyssey Rossie. Putting Green: A surface was used to ensure the ball replicated a consistent path. This required that the surface was flat, consistent (free of mounds, bumps, and divots), and had a speed that is somewhat similar to that of a putting green. The testing process was performed on carpet in the Dudley H. Davis Center located at the University of Vermont. Golf Balls: Ten new, USGA conforming golf balls were used in all parts of the testing process. These golf balls had distinct markings (X) on its side that were used to monitor the placement of the ball. Measurement Tools: Many measurement tools were needed for this test. The first, a plumb bob, was used to measure and constrain the height of the backswing. Another measuring tool was used to measure distances of the stopped ball from its point of impact. A final measurement tools, was very precise and used to measure out the placement of the ball off the center of the face. A4.1.3) Test Method Before beginning this test, the exact placement of the test apparatus was noted. This ensured putting green consistency among trials if the test was performed in multiple sittings. The following procedures were used for each of the putters being tested. This procedure tested the distribution of velocity transfer across the clubface. 1. Attach the putter to the test rig so that it is held firmly in the holding apparatus. The placement angle should be chosen to match the shaft angle of the club. Adjust the height of the rig so that the base of the club head barely sweeps the putting green as it crosses the vertical plane. 2. A plumb bob is used to control the height of the swing. Determine a swing height to be used by trying out different heights and examining the impact each one has on the ball. The final distance of sweetspot hits should range inches. However, it is not necessary for the distances found for each club to be the same. 3. Place the golf ball at the point where the club head reaches the vertical axis, dead center with respect to the clubface. This will generate the distance for the club s sweet spot, determining an ideal distance value. Perform swings at this spot. It is important that these measurements be accurate because the further measurements taken in Part 1 will be with respect to an ideal value found by averaging these values. 4. In step 4, the starting spot of the golf ball will be moved across the face of the club in specific increments. Begin with 1 cm from the sweet spot and travel in 1 cm increments until reaching 46 U VM

50 the 4 cm. These measurements will be taken from both sides of the sweet spot, towards the toe and heel. 20 swings and respective measurements will be performed at each location for each club. Each measurement is a radial measurement taken with respect to the ideal distance found in step 3. A4.2) Analysis of Initial Roll Characteristics A4.2.1) Test Boundaries Topspin transfer to the ball from the club is preferred for producing a smooth ball roll. The BombTech Grenade was designed with the intention to produce increased topspin through strategic weighting. This test determined the topspin of the ball produced by the club swing. In every section of this test, the results of the BombTech putter prototype were compared with two popular putters available on market today. It was expected that the prototype would perform well in comparison to the competitors because of its strategic weighting and optimized MOI z among other features specified in its design. A4.2.2) Required Resources Putters: The putters tested were the BombTech Grenade, TaylorMade Rossa, and Odyssey Rossie. Putting Green: This testing process were performed on a fake putting green placed in Votey Hall, located at the University of Vermont. Golf Balls: Many new, USGA conforming golf balls were used in all parts of the testing process. These golf balls had distinct markings (X) on its side that were used to monitor the placement and rotation of the ball. High-Speed Camera: A high-speed camera was used to record the ball movement resulting from each swing during the testing process. The high-speed camera (500 frames/second) was able to differentiate between small angular movements happening at fairly high speeds. Measurement Tools: Many measurement tools were needed for this test. The first, a plumb bob, was used to measure the distance of the putting backswing. Topspin and lofting was measured using a 3- inch length scale located in the cameras frame. 47 U VM

51 A4.2.3) Test Method Before beginning this test, the exact placement of the test apparatus was noted. This ensured putting green consistency among trials if the test was performed in multiple sittings. The following procedures were used for each of the putters being tested. This procedure tested and analyzed the ball topspin produced by the swing. 1. Attach the putter to the test rig so that it is held firmly in the holding apparatus. The placement angle should be chosen to match the shaft angle of the club. Adjust the height of the rig so that the base of the club head barely sweeps the putting green as it crosses the vertical plane. 2. Set up the camera to record at least 18 inches of the balls path beyond where the ball is expected to have loft. Set up the camera frame to include the impact and potential lofting. Take note of the exact placement of the camera to use in further trails. 3. Determine a preferable swing height by trying out different heights and examining the impact each one has on the ball. 4. Place the golf ball at the point where the club head reaches the vertical axis. Make sure to have the X marking centered on the side of the ball facing the camera. Record this location on the green for control of ball placement in future trials. 5. Record 5 swings from the chosen height. 6. Load the footage onto the computer. Determine and record the translational and angular velocities as well as time values and distance values for each trial. The velocity and time ratios can be determined by measuring the velocity of the ball s center as it compares to the speed of its surface, and doing the same with respect to time A4.3) Pilot and Qualitative Testing A4.3.1) Test Boundaries A final test was performed to gain qualitative feedback for the BombTech Grenade putter. This test was used to assess the perceived sound, feel, and appearance of the BombTech Grenade in comparison to other putters. 48 U VM

52 A4.3.2) Required Resources Putters: The putters tested were the BombTech Grenade, TaylorMade Rossa, and Odyssey Rossie. Putting Green: This testing process were performed on a fake putting green between the Bailey-Howe Library and the Dudley H. Davis Center, located at the University of Vermont. Golf Balls: Many new, USGA conforming golf balls were used in all parts of the testing process. Survey: A survey was created to gather feedback on the Grenade s sound, feel, and appearance in comparison to the other putters provided for testing. A4.3.3) Test Method Before beginning this test, the exact placement of the test apparatus was noted. This ensured putting green consistency among trials if the test was performed in multiple sittings. The following procedures were used for each of the putters being tested. This procedure tested the perceived feel, sound, and appearance of the putter. 1. Set up a play putting green and stand at the University of Vermont. 2. Allowed golfers to use the three putters being compared. 3. Asked the golfers to assess clubs using the surveys provided. A4.4) Assumptions, Constraints and Risks This test is based on the assumption that the swing of a putt replicates the motion of a single pendulum. This assumption can be made because it is most generally understood that the ideal method of putting is one that follows a pendulum. The test apparatus used to control the swing was built with this assumption in mind. The produced swing will have no angular offset when coming into contact with the ball, which also assumes and ideal swing. The data produced in this test was expected to vary only slightly between trials and clubs. Therefore, the accuracy of the data was assumed to be heavily reliant on the reproducibility of the test and the abilities of the testing equipment. If the data was too similar, statistical analysis may have proven that more trials needed to be conducted. It is expected that the consistency test will show more substantial value difference, but it was still important to maintain reproducibility. The pilot test will not be performed as a blind study, and therefore, there may be bias present among users. 49 U VM

53 50 U VM

54 A5) Engineering and Design Overview Because a User Manual isn t truly necessary for a putter, it has been substituted for an engineering and design overview that will be featured on BombTech Golf s website. The following write up is a first draft and will be reviewed and revised with the help of BombTech Golf. Why Design a Putter? After the success of the Grenade driver, BombTech Golf s founder Tyler Sully Sullivan returned to UVM looking for a group of engineering seniors to lead a new project the design and production of BombTech s first putter. This is when the Dream Team was born. The primary objective of the project was to design, engineer, and oversee production of a putter that could improve the average golfer s short game. Similarly to driving, putting is heavily influenced by the golfer s mentality and confidence so there was only a small window in which we could focus our efforts. This limited the extent to which we could explore and produce innovations but it also helped to produce a putter that was exclusively designed for excellent performance and to live up to the aesthetic standards set forth by the Grenade driver. A big issue with golfers is a stable putting stroke. When the putter head wanders, the likelihood of a mishit is increased. We learned that by increasing the weight of the clubhead, it would promote a pendulum style swing path. We believed that increasing the clubhead mass will keep golfers from mishitting putts and subsequently raising their score. But what happens if you have a perfectly stable stroke and still hit the ball a distance off the sweet spot? If the putter mass is large and strategically placed, the putter s moment of inertia can be optimized to be highly efficient. The term moment of inertia gets thrown around often, but not many golfers may know what it truly signifies. When a putter has a high moment of inertia, it will resist the urge to rotate when a force is applied to its heel or toe. This resistance theoretically lowers the distance that a putt will miss the desired target. So on a shot of the toe with a high MOI putter, the golfer could be 3 feet from the hole rather than 7 feet, which could be make a huge difference. Finally, the putter material selection was a major factor in our design considerations. Current top market companies utilize a single piece of carbon steel and a computer numerical controlled (CNC) milling process to create products that lead the competition in terms of qualitative feel, sound, and performance. BombTech Golf s mission is to release premium products that can compete with the big names. For this reason, we decided that the putter would be milled out of a single piece of low carbon steel. On top of this, the entire milling and finishing process takes place here in Vermont! Design Process The first phase of the design after determining the desired metrics, was the prototyping phase where we designed nearly thirty clubs and prototyped about ten that would achieve all the goals we had for performance. We utilized a 3D-printer to rapid prototype clubs straight from computer modeling software. In the software we were able analyze properties of each club head and compare them side by side. 51 U VM

55 From the prototyping phase arose one club that hit every design goal and that had a great look to it. That club was nearly what you see today as the BombTech Golf Grenade Putter. We worked with Stephen s Precision Milling in Bradford, VT who helped to develop the final product that the club is today. 3D printed prototype of the final design With freshly cut putter in hand, we began testing it with a standardized putter testing rig. We proceeded to test nearly one thousand ball impacts to gather the data on the performance. We then used statistical analysis software to provide hard hitting evidence that the Grenade was the real deal. Design Details The putter was developed mainly to be a forgiving club and to prevent human error while putting. This was achieved by pursuing a high moment of inertia about the z-axis. Moment of inertia is the clubs resistance to being torqued by an off-center impact. The grenade putter clocks in at a stomping 5850 grams per centimeter squared. This as will be shown in the consistency test makes the sweet spot on the club head huge compared to other putters. This allows for slight errors in swing path to influence the end result less. Many of the geometry features in the club are designed to maximize this moment of inertia (MOI). The center cut hole is there for weight management to ensure the best feel and allow for weight to be moved into other areas. This is also why we chose a mallet putter over a blade putter design. It allows for more movement of mass and contributes to a much higher moment of inertia. Our efforts to increase the moment of inertia paid off as in our testing our club performed significantly better at minimizing ball dispersion on off-center hits. 52 U VM

56 The club is heavy. At 445 grams it is one of the heaviest putters on the market. This was intended as well. The increased weight prevents psychological factors like nerves from overcoming your swing and influencing the swing path. We encourage the user to not fight the weight but let it guide the hands through the motion. Research has shown that putter head velocity shakes around as the swing is executed. The heavier head stabilizes the jittery velocity and forces the transitions to be more fluid. We also chose a loft angle of 2.5 degrees to promote pure roll. Slow motion analysis of club impacts shows that the ball pops off the ground and does not begin rolling for quite some distance. The grenade putter minimizes this distance and gets the ball rolling almost twice as fast as comparable putters. We also chose our material very carefully. Since this putter is completely milled from one piece of solid steel the material properties were crucial. 12l14 steel is a modern composite that has recently begun being used in many applications but was rather exotic just a few years ago. While 12l14 is still a steel alloy that can withstand pulling forces upwards of 60,000 psi, it is as soft as aluminum. This tough as nails and humble material is what gives the putter that solid pleasant feel and sound that makes the Grenade putter feel like a thousand bucks. Engineered Results So how does the Grenade putter perform compared to other putters? To determine this, we subjected the putter to three different sets of tests. The first test looked at the Grenade s consistency and accuracy, the second test analyzed its initial roll characteristics, and the third test was a qualitative assessment, where the Grenade was given to local golfers who gave their feedback and opinion on the putter. Since the primary objective of putting is to put the ball in the cup, the first test we conducted was a consistency and accuracy test. We hit numerous balls off different face locations, ranging from the heel to the toe, and measured the radial distance the resultant putt was from the determined distance of a putt of the center. The radial distance was compared to the optimal center distance to produce a metric that could be used to compare the three putters we tested. Below are the results of the experiment. Radial Dispersion Vs. Club Face Location Ratio of Radial Dispersion to Ideal Distance From Starting Point BombTech Odyssey TaylorMade Distance from Center of Club Face: Heel to Toe (cm) 53 U VM

57 What this graph shows is the relationship between off-center shots and a dispersion ratio. The dispersion ratio is essentially a percentage that a shot is away from the hole. For example, a 30 putt with a dispersion ratio of 0.2 means you are 20% of the 30 away from the hole leaving you with a 6 putt to the hole. The above graph shows that the Grenade putter has a dispersion ratio ranging from to (1-5 dispersion on a 30 putt). This is an average 54% improvement over the tested Odyssey Rossie and an average 40% improvement over the tested TaylorMade Rossa! Statistical analysis further supports our data, showing the clear improvement. The second test was an analysis of the Grenade s initial roll characteristics compared to the other two clubs tested. Using a high-speed camera, we were able to record how each club imparted spin on the ball in high definition. As evident in the video (linked below), the Grenade produces topspin almost immediately, while the balls off TaylorMade Rossa and Odyssey Rossie don t start spinning until 6 inches and 8 inches (respectively) into their roll path! This reduction in skipping and promotion of topspin directly leads to truer ball roll which results in less missed putts and more birdies. In addition to these quantitative tests, we displayed the finished Grenade putter and allowed local golfers to try it out. The initial feedback was very positive, with emphasis put on the Grenade s soft and responsive feel, stable stroke, and highly satisfying impact sound. We now invite you to pull the pin and give the Grenade putter a shot! Make more putts, guaranteed! 54 U VM