Andrew Dominijanni, Sc.B. Student, Materials Science and Engineering, Brown University.
Project Summary
I designed a golf putter to impart topspin to the golf ball, unlike most putters. Topspin on a putt decreases the period of skid, and promotes stable rolling earlier, thus increasing accuracy. My design utilizes a directionally compliant hosel to enhance the vertical gear effect between the impacting bodies (club head and ball). The design is successful in imparting topspin, as quantified by the "roll ratio". Furthermore, the roll ratios agree reasonably with theoretical predictions based on mass properties of the clubhead. Qualitative tests demonstrate that the putter functions just as a standard putter, and results in a smoother roll. The putter conforms to all USGA regulations on clubhead design.
Introduction
Golfers of all ages and abilities know that the most important club in the bag is the putter. Unlike any other club, the putter is used on virtually every hole in a round. In fact, when establishing par for a given hole, two strokes are automatically allotted for putting. Thus over an 18 hole, par 72 golf course, 50% of the strokes are expected to be putts. Contrast this with a driver, which is realistically only a maximum of 19% of strokes, and likely less. In 2010, 5 of the top 15 players on the PGA tour in terms of scoring average (strokes per round) were also in the top 15 of putting average (putts per hole).
Here's the problem: when a putt is struck by a traditional putter, backspin is imparted to the ball. This results in the ball skidding along the first several feet of its path, until friction with the ground causes it to begin rolling forward. This initial skidding is a period of instability for the ball, which achieves much better directional stability when it begins to roll coherently. The putt can shift directions during this period, resulting in inaccurate putts. For instance, on a perfectly level 10 foot putt, there is only a 2 degree margin for error in aiming. See diagram (not to scale).
Figure 1. Aim Angle Diagram
On a real golf course, and indeed even in controlled situations, a putt is never perfectly straight. A rolling golf ball is extremely sensitive to contours on a putting surface, resulting in curved paths, or what golfers call "break". Thus, the success of a putt is a combination of putt aim, and putt distance. Obviously, the ball must reach the hole to go in, which sets the lower limit of speed. The upper limit of speed is set by the velocity where the ball will skip over the hole rather than going in.
Figure 2. Putt Aim-Speed Diagram
A putt breaks less on a putt that is struck hard, whereas more break must be played on slowly struck putts. There is a limited set of combinations of direction and speed that will result in the ball going into the hole. Consequently, the golfer would like to be able to control his aim and putt speed as much as possible. Skid can adversely affect both of these factors, especially speed.
For these reasons, I am designing a putter that will impart topspin, thus decreasing skid and resulting in more accurate, consistent putting. Golfers of all abilities will benefit from this technology and make more putts!
Background
Many designs exist which claim to improve putting. Indeed most focus on rolling characteristics as the key to accurate putts. Some claim that hitting the ball with a slight downward trajectory (due to a high putter center of gravity) will result in more friction with the ground thus initiating roll more quickly. The following picture shows such a design.(1)
Figure 3. T-Roll Diagram
Neglecting the questionable physics of the centers of gravity themselves directly causing a negative launch angle, there are other problems with this hypothesis. First is the fact that a golf ball sits in a slight depression and a positive launch angle is desirable to overcome this. Additionally, a negative launch angle drives the ball into the ground, resulting in a series of bounces, which is worse than skid for putts. Major clubmakers do not utilize this design, a good indication that this idea does not work in reality.
Almost all major clubmakers (e.g. Nike, Odyssey, Ping, Cleveland, Titleist) design their putters to have low and deep centers of gravity (i.e. close to the ground and as far back away from the ball as possible), and high moments of inertia about the vertical axis. The legitimate physics behind these decisions is the gear effect.
The gear effect is a result of bodies impacting at angles or with misaligned centers of mass (i.e. the point of impact does not lie along the line connecting the two bodies' centers of mass). The following two diagrams illustrate one facet of the gear effect with three stages of impact between a ball and a block. Center of gravity is denoted by the black and white quartered circle.
Figure 4. Basics of Gear Effect
When the ball impacts the block away from its center of gravity, the block rotates slightly clockwise during impact. As a result of static friction, the two bodies are temporarily engaged like gears, and the golf ball gains counter-clockwise spin. The ultimate result is that the ball rebounds at a slight angle to the right and with counter clockwise spin.
Gear effect is used in other golf clubs, especially drivers, to reduce backspin and also to correct for an off center hit. Most putters' high MOI about the vertical axis are to minimize this effect on off center hits and keep putts rolling straight. This is qualitatively described as increasing the size of the "sweet spot".
The following link further explains the gear effect in relation to golf (Part 5):
In relation to putters, the gear effect can help to promote forward roll from impact, thus minimizing skid. The following diagram illustrates the concept.
Figure 5. Gear Effect Promoting Topspin
N.M. Lindsay has explored the gear effect in relation to putters in the following paper:
To summarize the key results in a useful form for my purposes:
Figures 6,7. Center of Mass Parameters and Axis Definitions
where hi is the height from the bottom of the putter to the impact point, hc is the height from the bottom of the putter to the center of mass, and p is the distance from the face of the putter to the center of mass. Kx is the radius of gyration about the heel-toe x-axis (out of the plane) and M is the mass of the putterhead. Note that Kx^2=Ix/M. is the loft angle of the clubface. For reasons to be explained below, the loft angle of my putters will be 0. Thus the equation reduces to:
Some early conclusions can be made from this model. First of all, the maximum value of hi is 0.84 inches, or half a golf ball's diameter. Thus the positioning of the center of mass through parameters hc and p is key. Lowering the center of mass results in an increase in Roll Ratio, as does, up to a certain point, moving the center of mass away from the face. Increasing the mass of the putter head decreases the Roll Ratio, as does increasing the radius of gyration about the x-axis. Note that the radius of gyration is used because it is independent of the mass of the body.
Of particular interest is the effect of the shaft's stiffness on the vertical gear effect. The concern is that the putter head will not act as a free body with the shaft opposing rotation about the x-axis.
Existing Solutions
As mentioned previously, most modern putters are designed with a low center of gravity. Additionally, they are designed with "heel-toe" weighting, meaning that weight is distributed toward the ends of the clubhead. This is purported to increase impact stability and make for a larger "sweet-spot". We know know that this means the horizontal gear effect is minimized. I will now explore 2 examples of putters which claim to impart topspin upon impact.
The Nike Golf METHOD putter "provides a faster, positive forward roll at impact for the kind of accuracy and consistency Tour professionals demand". It does this by utilizing "polymetal groove technology".
Figure 8. Nike METHOD
The patent for the Nike METHOD claims that the typical loft angle of the METHOD putter is 2 degrees rather than the standard 4 degrees, but that the soft polymeric material "grips" the ball and helps to pop it out of its depression. This fact is difficult to verify, but it is known that higher loft angle imparts backspin (by another manifestation of the gear effect). Thus, by decreasing the loft angle, Nike has inherently reduced backspin, to say nothing of the effects of the polymer. The video on Nike's online animation illustrates an earlier transition to rolling, but they do not disclose the specifications of the "traditional putter" nor does the putter appear to impart topspin. Rather it appears to impart very little spin initially while also launching at a lower angle. The fact that this test is performed in the presence of ground friction means that the initial spin characteristics are difficult to determine. There are claims of further high-tech testing, but quantitative results are not immediately available. Furthermore, this putter retails for $299.99.
Norman Lindsay, the author of the previously discussed paper, designed a putter based on the vertical gear effect. The putter is designed to have a low and deep center of gravity, and claims to have a "high-compliance hosel". The hosel is where the shaft connects to the putter head. The flexible hosel would seemingly allow the head to act as a free body, thus enhancing the gear effect.
Figure 9. Linday All-TS
The patent for golf clubs of this type can be found here. From the patent information and photos, it appears as the though the hosel is compliant in all directions. This means that in addition to enhancing the vertical gear effect, it also enhances the horizontal gear effect. This would result in directional inaccuracy. The Lindsay website shows photos of other putters imparting backspin, but does not show photos of its own putters imparting topspin. "We show in our Spin Measurements page how simple direct measurements prove that putter we have tested from several other manufacturers fail to deliver on their topspin claims." Their methods are quite simple and demonstrative, however it is somewhat suspect that they do not show analysis of their own putters.
Here is a list of things that I think are good and bad about these designs:
Good
Bad
Nike METHOD
- Ostensibly backed by testing
- Adopted by Tour professionals
- Catchy marketing
- Attractive form
- Expensive
- Technology not explained
Lindsay All-TS
- Technology basics explained well
- Multiple technologies
- Hosel compliant in all directions
- Unconventional form
- Seemingly unavailable
- Not proven
Design
My Proposed Solution:
A new approach would be to create a putter to enhance the vertical gear effect while minimizing horizontal gear effects. The putter will be designed with a compliant hosel (junction between the shaft and clubhead). The hosel will allow the putter head to behave more as a free body as far as rotation about x-axis, but not the z-direction. The head will be allowed to rotate slightly more than standard rigid hosel putters, thus enhancing the vertical gear effect and promoting topspin. This flexible hosel will allow a standard form heel-toe weighted putter to impart topspin. The putter will have 0 degrees of loft, eliminating the tendency to produce topspin. This can be done because the vertical gear effect imparts both topspin and a positive launch angle.
Requirements:
My putter will:
Impart a "roll ratio" of >0 to the golf ball upon impact.
Impart a consistent "roll ratio" to the ball under real conditions.
Pass qualitative testing by a skilled and experienced golfer.
Constraints:
The putter will conform with all USGA regulations for golf putter design and function (general club as well as putter face specific).
The putter will not require a special stroke to achieve the requirements above.
The putter will look like a traditional blade putter (i.e. depth to width ratio no more than 0.4)
Evaluation Criteria
Roll Ratio (percentage) = (Initial Spin Rate)/(Initial Horizontal Velocity)*100 in the absence of ground friction.
Standard Deviation of Roll Ratio (percentage) < 1%
Putter should feel solid, should not feel as though the ball is being "popped up" or driven into ground. Side by side comparison to standard putter favors new design.
How to Evaluate:
Crayon Test: The following diagram illustrates the simple crayon test for Roll Ratio. The red stripe is a piece of paper with crayon rubbed on one side and taped to a hard vertical surface (wall).
Figure 10. Crayon Test Diagram
The ball is placed at the edge of a surface (table) and hit towards the crayon paper. The absence of surface friction after impact means that I can safely assume the ball is at a constant horizontal velocity and spin rate in the short amount of time until impact with the paper. There are no significant forces acting on the ball until it strikes the wall. Thus, with this method, I am able to analyze the impact characteristics independent of ground friction. When the ball strikes the crayon at point B, a mark is left on the ball. An equator is initially placed horizontally, such that the arc length along the circumference between point A and B is the rotation distance. This distance is measured using a string, from the center of the equator line to the center of the mark (mark is often ~2-3 mm in diameter due to surface dimples). With the distance D measured beforehand, the roll ratio can be calculated extremely easily by the following equation:
An initial trial of 24 putts was performed with the baseline putter.
I feel that the crayon method provides great "value" results, that is to say, the amount of information obtained for the amount of setup and analysis time. I also like the distribution because it accounts for actual human conditions that occur on a golf course, thus representing the whole set of possible outcomes of a stroke. The testing of the prototypes will be telling as to whether more precise methods are needed to distinguish the putters. Figure 11 shows that the crayon test can be reasonably represented by a normal distribution, characterized by mean and standard deviation. These normal distribution curves will be used to compare the designs. Additionally, the crayon test can be made more reliable by using a sheet of carbon paper in place of the crayon rub.
A xenon strobe light (set to 1400 flashes per minute) was used to image the ball in flight and visually confirm the spin rate. Spin angle is calculated in photoshop using a line drawn over the marked equator and the free transform tool to determine angle to horizontal. The scale in the back is used to calculate the number of pixels per inch. This is then used to determine the travel distance. Roll Ratio is calculated by dividing the spin distance (fractions of a rotation)*(circumference)/(travel distance).
Figures 13,14. Baseline Strobe Images
From Figures 13 and 14, the Roll Ratio is calculated to be 2.05%, but more importantly, it shows clearly that backspin is imparted to the ball by the Cleveland putter.
This method is more accurate for any given individual putt than the crayon method, but it takes much more time to perform and analyze the data. It is not practical to perform a set of 24 putts as in the crayon method. I believe the 24 putt test set is very informative in terms of real performance. For these reasons, I will characterize all iterations of my design using the crayon method to obtain a distribution and average, as well as a pair of strobe images to visually confirm the spin.
First Prototype:
My design is a 3-part putter system. Most putters have 2 parts, the shaft and the club head. The two are rigidly joined using strong epoxy. My design will incorporate a third piece between the shaft and the head. This piece will have a "tongue" that fits into a slot cut in the head. The tongue (blue) will fit in the slot (white) tightly in the x direction not allowing rotation about the z-axis, but there will be room in the y direction to allow rotation about the x-axis.
Figure 15. Design Concept
The space in the slot that is not occupied by the tongue will be filled with a polymeric material to join the pieces and allow flexibility. The first prototype will be constructed from 6061 aluminum alloy. The SolidWorks model and drawings are shown below.
The mass properties of the first prototype are as follows (from SolidWorks mass properties):
Ix
0.0566 lb*in^2
Iz
0.4528 lb*in^2
M
0.2506 lb
hc
0.3987 in
hi
0.8400 in
p
0.5091 in
Table 1. First Prototype Properties
The cavity in the back of the putter results in the low center of gravity desired for the vertical gear effect. The center of gravity is 0.3987 inches up from the bottom of the putter, while the putter face is 1 inch tall. The highest the club can impact the equator of the ball is, by definition, half of the diameter of the golf ball, 0.84 inches. Assuming the center of gravity of the golf ball is the center of the sphere, this means that the impact between the two bodies can be up to 0.4413 inches eccentric. The cavity leaves material at the heel and toe of the putter, to maintain as high a moment of inertia about the z-axis as possible. This is a basic heel-toe weighted blade design which is utilized by most major club manufacturers and is based originally on the PING Anser. I am using this design as a kind of template, to test the compliant hosel, and because I personally find this form to give me the most confidence on the green.
The polymer used in construction is SmoothOn PMC-744 urethane rubber with a Shore hardness of 44 A. It was mixed in the 2:1 proportion and then poured into the slot. The hosel was then placed into the slot and the rubber allowed to cure. Prior to assembly, the end surfaces of the slot and tongue were roughened with 100 grit sandpaper to ensure that the rubber would adhere to both pieces. The shaft is a TrueTemper stepless steel shaft, purchased from GolfSmith.com and assembled using TourVan shafting epoxy. I use 3 tennis overgrips as a substitute for a golf club grip, but this will be an easy addition to the ultimate prototype.
Figure 19. Urethane Mixing Kit
Figure 20. First Prototype Analysis
Figure 20 shows the distribution for Prototype 1 (PT1) as compared with the baseline. The mean is 9.13% and the standard deviation is 2.73. The first protoype successfully imparts topspin on the golf ball, however it is very inconsistent, as seen by the broad bell curve. This means that the putter is imparting inconsistent spin rates, especially when compared to the baseline putter. Inputting the numbers from Table 1 in the Roll Ratio equation yields 11.4%, higher than the mean, but within the range of the data.
Qualitatively, the putter does seem to roll the ball. The audible skid is much less than with the baseline putter. Despite the flexible material, the impact is crisp and solid. The concern was that the polymeric joint would cause the impact to feel "longer" more like a tennis racquet than a golf club. The club head is too light to be a finished product, as most golfers prefer heavier swing weight. Additionally, the "sweet spot" is too close to the heel, I would like it to be closer to the middle of the clubhead.
Second Prototype:
The second prototype is the same assembly as the first, but with weight added in strategic locations to address some of the problems from the first prototype. One gram strips of lead tape were used. 3 grams were added to the bottom of the club on the heel side, 5 on the bottom on the toe side, 7 on the vertical face at the toe, and 2 on the back side of the striking face. The extra weight toward the heel and toe increases the moment of inertia about the z-axis, which should make the roll ratio more consistent on slightly off center hits. More weight is added to the toe than the heel to move the sweet spot to the middle of the clubface. A total of 17 grams is added. The hope is that that the added weight will create a narrower bell curve with approximately the same roll ratio. Figure 21 shows the modifications.
Figure 21. Second Prototype
Figure 22. Second Prototype Analysis
Figures 23,24. Second Prototype Strobe Images
The mean for PT2 is 8.94% and the standard deviation is 1.41. The mean stays about the same, and the standard deviation is almost cut in half. The second prototype is more consistent than the first, while still imparting topspin. Figures 23 and 24 clearly illustrate the topspin that is imparted at impact, but also the desired slightly positive launch angle that results from the gear effect. Though the added weight improves the performance, the putter still feels too light. The sweet spot is effectively moved closer to the middle of the clubhead, allowing for a more normal setup. Another aspect that I do not like about the first and second prototypes is the position of the shaft in relation to the clubface. Figure 18 shows that the shaft comes out of the middle of the clubhead, about 3/4" back from the face. Traditionally, putter shafts are flush with the club face or even one half to a whole shaft diameter ahead (as in the Portofino, known as whole shaft offset). I would prefer a 0 shaft offset, that is, for the front edge of the shaft to be flush with the striking face.
Third Prototype:
The third prototype was machined out of 303 stainless steel. This makes the swing weight more pleasing and also inherently increases the moment of inertia about the z-axis, which should further increase the roll consistency (narrower peak). Another major change is the hosel piece. The third prototype's hosel accomplishes the 0 shaft offset, simply by adding some material and shifting the shaft bore towards the face (see pictures). Note that the hosel is still made of 6061 aluminum alloy. The third change is increasing the length of the slot and tongue in the y direction. The additional mass removed from the heel to make the slot bigger positions the sweet spot in the correct location. Other minor cosmetic changes were made, such as fillets on some edges.
Figure 25. Third Prototype SolidWorks Model
Figure 26. Third Prototype Back
Figure 27. Third Prototype Top
Ix
0.1644 lb*in^2
Iz
1.3025 lb*in^2
M
0.7289 lb
hc
0.3945 in
hi
0.8400 in
p
0.5069 in
Table 2. Third Prototype Properties
Figure 28. Third Prototype Analysis
Figures 29, 30. Third Prototype Strobe Images
The mean roll ratio for the third prototype is 5.27% with a standard deviation of 0.63. The reason for this is the increase in mass of the clubhead. Assuming that the radius of gyration remains the same due to the similar head shape, the extra mass opposes rotation about the y-axis and thus reduces the gear effect. From Figure 28, it is clear that the roll is very consistent, much more so than for the first two prototypes. However, the tradeoff is that less topspin is imparted, this is to be expected from the theory. The roll ratio for this prototype is actually greater than that predicted by the roll ratio equation. The data in Table 2 predicts a roll ratio of 4.52%. Figures 29 and 30 once again illustrate the topspin, with a roll ratio of 5.0% calculated from the images. The following video gives a shot-after-shot comparison of the iterations of the design.
I will now evaluate the third prototype in terms of the design requirements.
1.i. The putter satisfies this requirement, imparting topspin upon impact with the golf ball.
1.ii. The standard deviation for the third prototype is less than 1, satisfying this requirement.
1.iii. The putter does seem to diminish audible skid, but does not drive the ball into the ground. The impact feels slightly softer and "slower" but not unreasonably so.
The putter also satisfies all of the constraints. It is within USGA regulations for putters, produces topspin with a normal putting stroke, and has a traditional form. Since the putter satisfies all of the design requirements and is within the constraints, I consider the project to be a success. Perhaps the best indication is the fact that I would feel confident putting this putter in play in a competitive round. I feel it would be particularly beneficial on short-medium length putts, from about 5-15 feet. I am very happy with the results of this project, because, although there are many putters on the market that claim to impart topspin, none of them have any concrete proof. I have to believe that if companies had this kind of visual evidence for the function of their products, they would show it. I was able to definitively show topspin from my putters through strobe photography. My design is a functional and effective prototype but it is nowhere near a polished product.
I am confident that this design can be improved. If I were able to devote more time and resources to developing this as a commercial product I would continue to tweak a number of things. I would tweak the aesthetics of the club and possibly develop other putter forms beside the heel-toe weighted blade based on the same hosel technology (mid-mallet, mallet, etc). Primarily, I would experiment with the polymeric fill material, trying different thermoplastic elastomers and thermosetting polymers, both softer and harder, to study their effects on performance and durability. I would also like to use other materials such as bronze, nickel, magnesium, etc. Combinations of these materials in the putter head can be used to affect the mass properties. Obviously a long term test must be performed to make sure the properties of the putter, specifically the polymer fill, do not degrade over a reasonable putter lifetime, ~10 years. I believe that a roll ratio of 10% with consistency (standard deviation) as good or better than the baseline putter is easily achievable in a mass-production model. Experimenting with different face inserts would also be interesting, to see if the contact surface has any impact on gear effect. Using tungsten plugs to play with weight distribution would also be interesting and could lower the center of gravity further with the same club head shape. I would also put a real grip on it!
Figure 15. Design Concept
Figure 16. Prototype 1 Model
Figure 20. First Prototype Analysis
Figure 22. Second Prototype Analysis
Figure 25. Third Prototype SolidWorks Model
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