RELATED APPLICATIONS INFORMATION The application claims the benefit under 35 U.S.C. 119(e) to U.S. Provisional Patent Application Ser. No. 60/543,764, filed Oct. 5, 2011, entitled “A Kit for a Driver and Golf Ball That Provides Optimum Performance,” which is incorporated herein by reference in its entirety as if set forth in full.
This application is also related to U.S. patent application Ser. No. 12/765,762, filed Apr. 22, 2010, entitled “A Low Lift Golf Ball,” and is also related to U.S. patent application Ser. No. 13/423,028, filed Mar. 16, 2012, entitled “Anti-Slice Golf Ball Construction,” and is also related to U.S. patent application Ser. No. 13/097,013, filed Apr. 28, 2011, entitled “A Nonconforming Anti-Slice Ball,” all of which are incorporated herein by reference in their entirety as if set forth in full.
BACKGROUND 1. Field of the Invention
The embodiments described herein relate generally to golf balls and are specifically concerned with a kit for a driver and a golf ball to create desired flight characteristics.
2. Related Art
Golf ball dimple pattern design has long been considered a critical factor in ball flight distance. A golf ball's velocity, launch angle, and spin rate is determined by the impact between the golf club and the golf ball, but the ball's trajectory after impact is controlled by gravity and aerodynamics of the ball. Dimples on a golf ball affect both drag and lift, which in turn determine how far the ball flies.
The aerodynamic forces acting on a golf ball during flight may be determined according to well-understood laws of physics. Scientists have created mathematical models so as to understand these laws and predict the flight of a golf ball. Using these models along with several readily determined values such as the golf ball's weight, diameter and lift and drag coefficients, scientists have been able to resolve these aerodynamic forces into the orthogonal components of lift and drag. The lift coefficient relates to the aerodynamic force component acting perpendicular to the path of the golf ball during flight while the drag coefficient relates to the aerodynamic force component acting parallel to the flight path. The lift and drag coefficients vary by golf ball design and are generally a function of the speed and spin rate of the golf ball and for the most part do not depend on the orientation of the golf ball on the tee for a spherically symmetrical or “conforming” golf ball.
The maximum height a golf ball achieves during flight is directly related to the lift generated by the ball, while the direction that the golf ball takes, specifically how straight a golf ball flies, is related to several factors, some of which include spin and spin axis orientation of the golf ball in relation to the golf ball's direction of flight. Further, the spin and spin axis are important in specifying the direction and magnitude of the lift force vector. The lift force vector is a major factor in controlling the golf ball flight path in the x, y and z directions. Additionally, the total lift force a golf ball generates during flight depends on several factors, including spin rate, velocity of the ball relative to the surrounding air and the surface characteristics of the golf ball. A golf ball that is not hit squarely off the tee will tend to drift off-line and disperse away from its intended trajectory. This is often the case with recreational golfers who impart a slice or a hook spin on the golf ball when striking the ball.
In order to overcome the drawbacks of a hook or a slice, some golf ball manufacturers have modified the construction of a golf ball in ways that tend to lower the spin rate. Some of these modifications include utilizing hard two-piece covers and using higher moment of inertia golf balls. Other manufacturers have resorted to modifying the ball surface to decrease the lift characteristics on the ball. These modifications include varying the dimple patterns in order to affect the lift and drag on the golf ball.
Some prior golf balls have been designed with non-conforming or non-symmetrical dimple patterns in an effort to offset the effect of imperfect hits, so that the unskilled golfer can hit a ball more consistently in a straighter path. Although such balls do not conform to the United States Golf Association (USGA) Rules of Golf, they are very helpful for the recreational golfer in making the shots fly straighter and the game more fun. One such ball is described in U.S. Pat. No. 3,819,190 of Nepela et al. This ball is also known as a Polara™ golf ball, and has regions with different types and numbers of dimples or no dimples. A circumferential band extending around the spherical ball has a plurality of dimples, while polar areas on opposite sides of the band have more shallow, fewer or no dimples at all. For this asymmetric golf ball, the measured lift and drag coefficients are strongly influenced by the orientation of the rotating golf ball. This is evidenced by the fact that the trajectory of the golf ball is strongly influenced by how the golf ball is oriented on the tee. For this ball to work properly, it must be placed on the tee with the poles of the ball oriented such that they are in the plane that is pointed in the intended direction of flight. In this orientation, the ball produces the lowest lift force and thus is less susceptible to hooking and slicing.
U.S. patent application Ser. Nos. 12/765,762 (the '762 application), 13/423,028 (the '028 application), and 13/097,013 (the '013 application) each describe a golf ball that creates low lift relative to conventional golf balls in order to help golfers address the problems of hooking and slicing and can be included in the kits described herein. The '762 application describes a low lift conforming golf ball, while the '028 and '013 applications each describe a low lift, nonconforming golf ball design. Golf balls designed in accordance with the techniques described in these applications have been demonstrated to reduce hooks and slices; however, because such balls exhibit low lift, they tend to not fly as far as a normal golf ball struck with a normal club, such as a conventional driver. It should be noted that it has been demonstrated that certain of these balls will fly as far or even further than a conventional golf ball when hit with certain clubs, but almost uniformly these balls do not fly as far when hit with the driver. Driver distance is something most golfers, even amateur and high handicap players are very sensitive to and in general providing the maximum distance, while correcting hooks and slices to the greatest degree possible is desirable.
In golf, the club that is usually used on the tee for par 4 and 5 holes is the driver club. Drivers were once made of wood, but today they are made of metal or are a composite of metal and other materials. Standard driver golf clubs for men in the USA are generally labeled 8-12 degrees loft, with the majority of driver lofts being labeled by the manufacturer as being in the range of 9.5-10.5 degrees loft. However, these drivers are actually higher loft than they are labeled because the golf industry is aware that many golfers aspire to use the same equipment that professional golfers use, which are drivers with a loft of <9 degrees so the manufacturers purposely mislabel the actual loft on a driver. Still, drivers with conventional lofts, e.g., 9-12 degrees, will often result in shorter distance off the tee when used with a low lift golf ball, such as those described in the '762, '028, and '013 applications.
But much of the distance lost due to the low loft of such balls can be reclaimed if a driver with the appropriate loft is used. But most golfers have no idea how to determine the best fit of golf ball and golf club, or golf club parameters. Moreover, e.g., conventional drivers may not provide the needed loft, as conventional clubs are designed for conventional or high lift balls and are marketed to appeal to a golfer's desire to be like the pros.
SUMMARY Certain embodiments as disclosed herein provide for a kit comprising a golf club and a golf ball where the golf club loft is selected in order to improve or optimize the distance that the golf ball travels when hit.
In one aspect, the kit comprises a golf club with predetermined club loft based on a golfer's swing and a golf ball which is designed to have a lower flight trajectory than other golf balls, as a result of lower lift, higher drag, higher weight, smaller size, or any combination of factors that cause the golf ball to have a lower flight trajectory.
In one aspect, the golf ball has a dimple pattern which has reduced or no dimple volume in a selected circumferential band around the ball and more dimple volume in other regions of the ball. This causes the ball to have a “preferred” spin axis because of the weight differences caused by locating different volume dimples in different areas across the ball. This in turn reduces the tendency for dispersion of the ball to the left or right (hooking and slicing) during flight. In one example, the circumferential band of lower dimple volume is around the equator with more dimple volume in the polar regions. This creates a preferred spin axis passing through the poles. The dimple pattern is also designed to exhibit relatively low lift when the ball spins in the selected orientation around its preferred spin axis. This golf ball is nonconforming or non-symmetrical under United States Golf Association rules.
A golf ball's preferred or selected spin axis may also be established by placing high and low density materials in specific locations within the core or intermediate layers of the golf ball, but has the disadvantage of adding cost and complexity to the golf ball manufacturing process.
Where a circumferential band of lower or zero dimple volume is provided about the equator and more dimple volume is provided in the polar regions, a ball is created which has a large enough moment of inertia (MOI) difference between the poles horizontal (PH) orientation and other orientations that the ball has a preferential spin axis going through the poles of the ball. The preferred spin axis extends through the lowest weight regions of the ball. If these are the polar regions, the preferred axis extends through the poles. If the ball is oriented on the tee so that the “preferred axis” or axis through the poles is pointing up and down (pole over pole or POP orientation), it is less effective in correcting hooks and slices compared to being oriented in the PH orientation when struck.
The lower volume dimples do not have to be located in a single circumferential band to create a preferred spin axis. The lower volume dimples can be located outside the one or more bands, planes or regions, so long as the presence of the lower volume dimple bands, regions or planes are situated such that the ball in one rotational orientation has a higher MOI than in any other rotational orientations. In some of the designs described above and below, the dimple design results in a ball which has a highest MOI in one rotational orientation and a lower and nearly equal MOI in the two other rotational orientations that are orthogonal to the highest MOI rotational orientation. For clarification purposes and for example, the 3 orthogonal axes of rotation would be geometrically similar to the x-y-z axes in a three dimensional Cartesian coordinate system where any two axes are perpendicular to each other. So in the example where the ball has a lower or zero dimple volume provided about the equator and more dimple volume provided in the polar regions, which results in a ball which has a large enough moment of inertia (MOI) difference between the poles horizontal (PH) orientation and other orientations that the ball has a preferential spin axis going through the poles of the ball—this axis going through the poles could be named the x-axis and the MOI when the ball rotated about the x-axis would be higher than when it rotated about the y or z axes. In this particular design the MOI rotating about the y and z axes would be the same. The volume of the dimples could also be controlled so that the ball has a higher MOI in one orientation and a lower MOI in one of the other orthogonal axes of rotation and an even lower MOI in the third orthogonal axis of rotation. The preferred spin axis is still the highest MOI rotational configuration of all the possible rotational orientations.
In another aspect, the ball may have no dimples in a band about the equator (a land area) and deep dimples in the polar regions. The dimple-less region may be narrow, like a wide seam, or may be wider, i.e. equivalent to removing one or more rows of dimples on each side of the equator.
By creating a golf ball with a dimple pattern that has less dimple volume in a band around the equator and by removing more dimple volume from the polar regions adjacent to the low-dimple-volume band, a ball can be created with a large enough moment of inertia (MOI) difference between the poles-horizontal (PH) and other orientations that the ball has a “preferred” spin axis going through the poles of the ball and this preferred spin axis tends to reduce or prevent hooking or slicing when a golfer aligns the ball in the PH orientation on the tee (poles pointing right and left and the equatorial plane aligned in the intended direction of flight) and then hits the ball in a manner which would generate other than pure backspin on a normal symmetrically designed golf ball. In other words, when this ball is hit in manner which would normally cause hooking or slicing in a symmetrical or conforming ball, the ball tends to rotate about the selected spin axis and thus not hook or slice as much as a symmetrical ball with no selected or “preferred” spin axis. In one embodiment, the dimple pattern is designed so that it generates relatively low lift when rotating in the preferred spin axis PH orientation. The resulting golf ball displays enhanced hook and slice correcting characteristics.
The low volume dimples do not have to be located in a continuous band around the ball's equator. The low volume dimples could be interspersed with higher volume dimples, the band could be wider in some parts than others, the area in which the low volume dimples are located could have more land area (lack of dimples) than in other areas of the ball. The high volume dimples located in the polar regions could also be inter-dispersed with lower volume dimples; and the polar regions could be wider in some spots than others. The main idea is to create a higher moment of inertia for the ball when it is rotating in one configuration and to do this by manipulating the volume of the dimples across the surface of the ball. This difference in MOI then causes the ball to have a preferred spin axis. The golf ball is then placed on the tee so that the preferred spin axis is oriented approximately horizontally and perpendicular to the intended direction of flight so that when the ball is hit with a hook or slice action, the ball tends to rotate about the initial horizontal spin axis orientation and thus not hook or slice as much as a symmetrical ball with no preferred spin axis would hook or slice. In some embodiments, the preferred spin axis is the PH orientation.
Another way to create the preferred spin axis would be to place two or more regions of lower volume or zero volume regions on the ball's surface and make the regions somewhat co-planar so that they create a preferred spin axis. For example, if two areas of lower volume dimples were placed opposite each other on the ball, then a dumbbell-type weight distribution would exist. In this case, the ball has a preferred spin axis equal to the orientation of the ball when it is rotating end-over-end with the “dumbbell areas”.
The ball can also be oriented on the tee with the preferred spin axis tilted up to about 45 degrees to the right and then the ball still resists slicing, but does not resist hooking as much. If the ball is tilted 45 degrees to the left it reduces or prevents hook dispersion, but does not reduce or prevent slice dispersion as much. This may be helpful for untrained golfers who tend to hook or slice a ball. When the ball is oriented so that the preferred axis is pointing up and down on the tee (POP orientation for a preferred spin axis in the PH orientation), the ball is much less effective in correcting hooks and slices compared to being oriented in the PH orientation.
In other cases, the kit may include a conforming ball with no preferred spin axis but with first and second areas of dimples of different dimensions designed to exhibit relatively low lift. Or the kit may include a ball that exhibits relatively low lift because of the design of the dimple characteristics such as depth, shape, diameter, edge radius and their arrangement on the golf ball.
Other features and advantages will become more readily apparent to those of ordinary skill in the art after reviewing the following detailed description and accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS The details of the present embodiments, both as to structure and operation, may be gleaned in part by study of the accompanying drawings, in which like reference numerals refer to like parts, and in which:
FIG. 1 is a perspective view of one hemisphere of a first embodiment of a golf ball cut in half through the equator, illustrating a first dimple pattern designed to create a preferred spin axis and low lift, the opposite hemisphere having an identical dimple pattern;
FIG. 2 is a perspective view similar to FIG. 1 illustrating a second embodiment of a golf ball with a second, different dimple pattern;
FIG. 3 is a perspective view illustrating one hemisphere of a compression molding cavity for making a third embodiment of a golf ball with a third dimple pattern;
FIG. 4 is a perspective view similar to FIGS. 1 and 2 illustrating a fourth embodiment of a golf ball with a fourth dimple pattern;
FIG. 5 is a perspective view similar to FIGS. 1, 2 and 4 illustrating a fifth embodiment of a golf ball with a fifth dimple pattern;
FIG. 6 is a perspective view similar to FIGS. 1, 2, 4 and 5 illustrating a sixth embodiment of a golf ball having a different dimple pattern;
FIG. 7 is a perspective view similar to FIGS. 1, 2, and 4 to 6 illustrating a seventh embodiment of a golf ball having a different dimple pattern;
FIG. 8 is perspective view similar to FIG. 1 but illustrating a modified dimple pattern with some rows of dimples around the equator removed;
FIG. 9 is a diagram illustrating the relationship between the chord depth of a truncated and a spherical dimple in the embodiments of FIGS. 1 to 7;
FIG. 10 is a graph illustrating the average carry and total dispersion versus the moment of inertia (MOI) difference between the minimum and maximum orientations for balls having each of the dimple patterns of FIGS. 1 to 7, and a modified version of the pattern of FIG. 1, compared with a ball having the dimple pattern of the known non-conforming Polara™ ball and the known TopFlite XL straight ball;
FIG. 11 is a graph illustrating the average carry and total distance versus MOI difference between the minimum and maximum orientations for the same balls as in FIG. 10;
FIG. 12 is a graph illustrating the top view of the flights of the golf balls of FIGS. 1, 2 and 3 and several known balls in a robot slice shot test, illustrating the dispersion of each ball with distance downrange;
FIG. 13 is a side view of the flight paths of FIG. 12, illustrating the maximum height of each ball;
FIGS. 14 to 17 illustrate the lift and drag coefficients versus Reynolds number for the same balls which are the subject of the graphs in FIGS. 12 and 13, at spin rates of 3,500 and 4,500, respectively, for different ball orientations;
FIG. 18 is a diagram illustrating a golf ball configured in accordance with another embodiment;
FIG. 19 is a chart illustrating the golf ball trajectory model results for a PRO V1 golf ball at 90 mph, 3,000 rpm and various launch angles;
FIG. 20 shows interval plots of the vertical launch angle for 8 cases (3 clubs, 3 tee heights) using the Polara Ultimate Straight golf ball in the Poles Horizontal (PH) orientation;
FIG. 21 shows the resulting carry distance for the cases of FIG. 20;
FIG. 22 is a chart illustrating the data for the vertical launch for the ProV1 and Polara Ultimate Straight golf balls;
FIG. 23-26 are charts illustrating the results of a player hitting several groups of shots using a 9 deg loft driver and a 16 deg loft driver with the ProV1 and Polara Ultimate Straight golf balls;
FIGS. 27 and 28 are charts illustrating summaries of the results of even more player testing showing the average trajectory for various tee heights and clubs when hitting the Polara Ultimate Straight golf balls;
FIG. 29 is a perspective view of another golf ball with a dimple pattern which may be used in accordance with another embodiment of a kit comprising a low loft golf ball and a golf club of predetermined loft angle;
FIG. 30 is a top-view schematic diagram of a golf ball with a cuboctahedron pattern in accordance with another embodiment of the kit, with the golf ball in the poles-forward-backward (PFB) orientation;
FIG. 31 is a schematic diagram showing the triangular polar region of another embodiment of the golf ball with a cuboctahedron pattern of FIG. 30;
FIG. 32 is a graph of the total spin rate and Reynolds number for the TopFlite XL Straight golf ball and a B2 prototype ball, configured in accordance with one embodiment, hit with a driver club using a Golf Labs robot;
FIG. 33 is a graph or the Lift Coefficient versus Reynolds Number for the golf ball shots shown in FIG. 32;
FIG. 34 is a graph of Lift Coefficient versus flight time for the golf ball shots shown in FIG. 32;
FIG. 35 is a graph of the Drag Coefficient versus Reynolds Number for the golf ball shots shown in FIG. 32;
FIG. 36 is a graph of the Drag Coefficient versus flight time for the golf ball shots shown in FIG. 32;
FIG. 37 is a diagram illustrating the relationship between the chord depth of a truncated and a spherical dimple in accordance with one embodiment of a low lift, symmetric golf ball;
FIG. 38 is a graph illustrating the max height versus total spin for all of a 172-175 series golf balls, configured in accordance with certain embodiments, and the Pro V1® when hit with a driver imparting a slice on the golf balls;
FIG. 39 is a graph illustrating the carry dispersion for the balls tested and shown in FIG. 38;
FIG. 40 is a graph of the carry dispersion versus initial total spin rate for a golf ball with the 172 dimple pattern and the ProV1® for the same robot test data shown in FIG. 38;
FIG. 41 is a graph of the carry dispersion versus initial total spin rate for a golf ball with the 173 dimple pattern and the ProV1® for the same robot test data shown in FIG. 38;
FIG. 42 is a graph of the carry dispersion versus initial total spin rate for a golf ball with the 174 dimple pattern and the ProV1® for the same robot test data shown in FIG. 38;
FIG. 43 is a graph of the carry dispersion versus initial total spin rate for a golf ball with the 175 dimple pattern and the ProV1® for the same robot test data shown in FIG. 38;
FIG. 44 is a graph of the wind tunnel testing results showing Lift Coefficient (CL) versus DSP for the 173 golf ball against different Reynolds Numbers;
FIG. 45 is a graph of the wind tunnel test results showing the CL versus DSP for the Pro V1 golf ball against different Reynolds Numbers;
FIG. 46 is picture of a golf ball with a dimple pattern in accordance with another embodiment of the kit;
FIG. 47 is a graph of the lift coefficient versus Reynolds Number at 3,000 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and a 273 dimple pattern in accordance with certain embodiments;
FIG. 48 is a graph of the lift coefficient versus Reynolds Number at 3,500 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and 273 dimple pattern;
FIG. 49 is a graph of the lift coefficient versus Reynolds Number at 4,000 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and 273 dimple pattern;
FIG. 50 is a graph of the lift coefficient versus Reynolds Number at 4,500 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and 273 dimple pattern;
FIG. 51 is a graph of the lift coefficient versus Reynolds Number at 5,000 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and 273 dimple pattern;
FIG. 52 is a graph of the lift coefficient versus Reynolds Number at 4000 RPM initial spin rate for the 273 dimple pattern and 2-3 dimple pattern balls of Tables 10 and 11;
FIG. 53 is a graph of the lift coefficient versus Reynolds Number at 4500 RPM initial spin rate for the 273 dimple pattern and 2-3 dimple pattern balls of Tables 10 and 11;
FIG. 54 is a graph of the drag coefficient versus Reynolds Number at 4000 RPM initial spin rate for the 273 dimple pattern and 2-3 dimple pattern balls of Tables 10 and 11; and
FIG. 55 is a graph of the drag coefficient versus Reynolds Number at 4500 RPM initial spin rate for the 273 dimple pattern and 2-3 dimple pattern balls of Tables 10 and 11.
FIG. 56 is a graph illustrating the optimum driver loft for a given swing speed and ball type;
FIG. 57A is a cross-sectional view taken through the poles of a first embodiment of a golf ball having a non-spherical core;
FIG. 57B is a cross-sectional view on the lines 1B-1B of FIG. 1A, taken through the equatorial plane of the ball;
FIG. 58 is a front elevation view of the core of the ball of FIGS. 57A and 57B;
FIG. 59A is a cross-sectional view taken on an x-axis through the equatorial plane of a second embodiment of a golf ball with an non-spherical core;
FIG. 59B is a cross-sectional view of the ball of FIG. 59A taking along the orthogonal y-axis in the equatorial plane;
FIG. 60 is a front elevation view of the core of the ball of FIGS. 59A and 59B;
FIG. 61 is a cross-sectional view through the poles of a third embodiment of a golf ball having a non-spherical inner and outer core;
FIG. 62 is a cross-sectional view through the poles of a fourth embodiment of a golf ball which has narrow banded inner core and a banded outer core or mantle layer;
FIG. 63 is a cross sectional view of a fifth embodiment of a golf ball with an oblong core;
FIG. 64 is a cross-sectional view of a sixth embodiment of a golf ball which has a less elongated core than the embodiment of FIG. 63;
FIG. 65 is a cross-sectional view of a seventh embodiment of a golf ball with a non-spherical core;
FIG. 66 is a front elevation view of the core of the golf ball of FIG. 65;
FIG. 67 is a cross sectional view through the poles of an eighth embodiment of a golf ball with a modified non-spherical core;
FIG. 68 is a front perspective view of the core of the golf ball of FIG. 67;
FIG. 69 is a cross-sectional view through the poles of a golf ball according to another embodiment;
FIG. 70 is a front elevation view of the core of the golf ball of FIG. 69;
FIG. 71 is a front elevation view similar to FIG. 70 but illustrating a modified core;
FIG. 72 is a front elevation view similar to FIGS. 70 and 71 but illustrating another modified core;
FIG. 73 is a cross sectional view through the poles of another embodiment of a golf ball with a modified non-spherical core;
FIG. 74 is a front elevation view of the core of the golf ball of FIG. 73;
FIG. 75 is a front elevation view similar to FIG. 74 but with a modified core;
FIG. 76 is a front elevation view similar to FIGS. 74 and 75 but illustrating a modified core;
FIG. 77 is a cross-sectional view of a golf ball with the core of FIG. 76;
FIG. 78 is a front elevation view of a core similar to FIG. 76 but with flattened areas a the poles;
FIG. 79 is a front elevation view of the non-spherical core of another embodiment of a golf ball;
FIG. 80 is a cross-sectional view of a golf ball incorporating the core of FIG. 79;
FIG. 81 is a perspective view of a golf ball with dimples which may have the core of any of the embodiments of FIGS. 57A to 80;
FIG. 82 is a perspective view of another embodiment of a golf ball with a different dimple pattern from FIG. 81, which may have the core of any of the embodiments of FIGS. 57A to 80;
FIG. 83 is a perspective view of another embodiment of a golf ball with another different dimple pattern which may have the core of any of the embodiments of FIGS. 57A to 80;
FIG. 84 is a perspective view of another embodiment of a golf ball with a different dimple pattern which may have the core of any of the embodiments of FIGS. 57A to 80;
FIG. 85 is a perspective view of another embodiment of a golf ball with a different dimple pattern which may have the core of any of the embodiments of FIGS. 57A to 80; and
FIG. 86 is a front elevation view similar to FIGS. 70 and 71 but illustrating a modified core.
DETAILED DESCRIPTION After reading this description it will become apparent to one skilled in the art how to implement the embodiments in various alternative implementations and alternative applications. Further, although various embodiments will be described herein, it is understood that these embodiments are presented by way of example only, and not limitation. As such, this detailed description of various alternative embodiments should not be construed to limit the scope or breadth of the appended claims.
The embodiments described herein involve a series of drivers with lofts ranging from about 12 to 24.5 degrees. However, the ideas and technology described here could be used for drivers of lower or higher loft than the range of lofts actually produced and shown here. The USGA has set limits driver specification, including size (less than or equal to 460 cc), coefficient of restitution (0.83), characteristic time (256 micro seconds). Certain of the clubs described herein were designed to have increased volume that will improve several playability characteristics for certain golfers. The larger size can enable the drivers to be made more forgiving for off-center hits, for example. Further, the drivers can have a coefficient of restitution higher than that of the USGA limits.
The embodiments described herein are directed to a combination or kit of a low lift, symmetric or asymmetric ball that reduces hooks or slices and combined with a driver of high loft, increased volume add high spring-like effect to maximize distance, wherein the driver and the ball are paired to produce the best results, i.e., maximum distance and control for a specific golfer. In order to select the correct kit, the golfer's swing must be characterized. Accordingly, systems and methods for characterizing golfer's swing are also disclosed.
Overall, the kits described herein are a combination of a driver and ball to maximize distance and game improvement reduction of hooks and slices. As noted, lower lift golf balls have the advantage that they are less prone to hook or slice when mishit, but due to their lower lift they can also end up flying shorter distance off shots with the driver. To overcome the disadvantage of shorter distance, a higher loft driver is needed to maximize distance with low lift golf balls. The exact loft depends on several factors including the lift and drag characteristics of the ball and the golfers swing speed. Descriptions of example low lift golf balls, including lift and drag characteristic information are provided below.
In one embodiment, the kit will include drivers having a loft range of 12 degrees to 25 degrees. In order to match a driver and a low lift golf ball to a player, a fitting scheme will be employed. Players with slower swing speeds in the 70 to 80 mph range will be fitted to drivers with higher lofts. Conversely, players with faster swing speeds will need drivers with not quite as much loft. Overall, swing speed is the major factor in determining driver loft for a given golf ball and swing speed is considered a macro-adjustment.
But, e.g., another factor influencing the driver loft selected is the natural ball flight tendencies of shots hit by the player. Players with higher ball flights (often caused by higher backspin or higher launch angle) will tend to be fitted with slightly lower driver lofts and players with lower ball flights will be fitted with slightly higher driver lofts.
A third factor influencing the driver loft is the golf ball selected. The present invention is a kit for a driver and golf ball combination. A low lift ball such as the Polara Ultimate Straight or the 28-1, described below, are low flying balls that develop low lift and exhibit excellent hook and slice reducing characteristics. A higher driver loft is needed for this low-lift type of ball. For a slightly higher lift golf ball such as the Polara XD, which does not correct hooks and slices as much as the Polara Ultimate Straight or the 28-1, a slightly lower loft driver will be selected than would be used by the same player for the Polara Ultimate Straight golf ball for example.
More specifically, referring to the table below it can be seen that a player with a 77 mph swing speed, using a low lift golf ball such as the Polara Ultimate Straight will be fitted with a driver with 22 degrees loft in order to maximize the overall distance the player hits the ball. A 24.5 degree driver would be needed to maximize the total carry distance for this same player-ball combination.
Conversely, if a player with a 77 mph swing speed wants to optimize total distance using a high lift golf ball like the Titleist Pro V1, then this golfer would choose a 12 degree driver and would choose an 18 degree driver to maximize carry distance.
The optimum driver loft for different combinations of balls and player swing speeds can bee seen in the table and chart in FIG. 56. Accordingly, if a golfer has already selected a certain ball, then by simply measuring the golfer's swing speed a fairly accurate determination can be made of the correct driver loft the golfer should use, e.g., using the chart below; however, golfers often do not know what ball they should be using. Accordingly, it is important to be able to identify the correct ball and club, i.e., kit for a golfer that does not know what ball to play to improve his game.
In order to identify the correct kit, several aspects of the golfer's game can first be determined. For example, it can be determined how far the golfer hits his driver. This can be determined by asking the golfer; however, most golfers over estimate how far they hit the ball generally and specifically overestimate how far they hit their driver. Accordingly, it is preferable to measure, e.g., using a launch monitor how far the golfer can hit his or her driver. It should be noted that distance is not the only issue, as ball flight or trajectory can play an important role as well. Thus, preferably, the ball flight information would be measured as well.
If it is not possible to measure driver distance, then other determinations relating to what club the golfer uses from certain distances can be made. For example, if the golfer normally hits an 8 iron from 150 yards, then this is an indication that they have a relatively high swing speed and high trajectory. Whereas, if they hit a 4 iron, then they likely have a relatively low swing speed and trajectory.
It is also important to determine whether the golfer normally hooks or slices and by how much.
The above information can then be correlated with swing speed, launch angle, and spin rate, which can then be used to identify a correct kit. For example, if a golfer slices significantly, then they will tend to have a higher launch angle and a higher spin rate if they use a conventional golf ball such as the ProV1. Accordingly, a very low lift ball such as the Polara Ultimate Straight may be selected. But this will significantly reduce the maximum trajectory height and carry distance of the ball. Tables such as that below can be used to determine what the relative maximum trajectory heights and carry distances may be if the golfer were to use the Polara Ultimate Straight and then this information used to select the correct club or kit.
TABLE 1
Specifies the Club Loft that
Club Ball Max Maximizes Carry or Total
Club Speed, Speed, VLA, Spin, Height DR, Max Carry Dist, Total Dist, Distance with this particular
Loft Ball mph mph deg rpm yds Height, yds yds yds ball and swing speed.
10 ProV1 77.5 115.8 8.6 2483 88 10 152 191
12 ProV1 76.6 114.4 12.2 2681 97 16 167 194 TOTAL Distance
14.5 ProV1 76.9 115.4 11.8 2846 100 16 169 192
18 ProV1 76.4 113.4 15.4 3803 103 23 170 187 CARRY Distance
22 ProV1 76.7 110.6 17.8 4895 97 26 162 172
24.5 ProV1 76.2 108.7 19.6 5306 93 27 157 165
10 Polara Ultimate Straight 77.4 115.6 8.9 2246 59 6 110 170
12 Polara Ultimate Straight 76.4 113.8 12.5 2334 70 10 129 174
14.5 Polara Ultimate Straight 76.6 114.9 11.9 2514 71 10 130 174
18 Polara Ultimate Straight 76.0 112.5 16.0 3380 85 16 151 177
22 Polara Ultimate Straight 76.0 110.1 18.1 4480 92 20 162 182 TOTAL Distance
24.5 Polara Ultimate Straight 76.6 108.1 19.6 5187 94 23 165 179 CARRY Distance
10 Polara XD 77.7 116.0 8.8 2353 74 8 132 185
12 Polara XD 76.4 114.3 12.4 2510 85 13 151 186
14.5 Polara XD 77.1 115.6 11.9 2641 88 13 154 187 TOTAL Distance
18 Polara XD 76.3 113.4 15.6 3565 97 19 168 187 CARRY Distance
22 Polara XD 76.4 110.5 17.9 4689 98 24 167 178
24.5 Polara XD 76.5 108.5 19.2 5575 95 26 161 171
10 ProV1 102.3 149.5 10.3 2955 156 26 245 270
12 ProV1 102.4 151.4 10.2 3176 161 27 248 272 Total Distance and Carry Distance
14.5 ProV1 101.4 150.0 12.0 3866 159 35 244 261
18 ProV1 101.3 149.1 13.5 4923 150 41 230 241
22 ProV1 102.9 145.2 17.8 6517 135 48 211 219
24.5 ProV1 103.9 142.0 19.1 7612 126 49 198 201
10 Polara Ultimate Straight 101.7 148.0 10.3 2616 103 13 181 239
12 Polara Ultimate Straight 102.0 149.7 10.3 2871 108 13 189 237
14.5 Polara Ultimate Straight 101.1 148.7 12.2 3499 125 19 212 248 TOTAL Distance
18 Polara Ultimate Straight 101.0 147.6 13.4 4690 142 26 229 246
22 Polara Ultimate Straight 103.0 144.0 17.4 6582 147 41 232 242 CARRY Distance
24.5 Polara Ultimate Straight 103.8 142.2 18.6 7469 139 45 218 225
10 Polara XD 102.4 149.9 10.2 2742 138 20 228 264
12 Polara XD 102.3 151.5 10.2 3017 146 21 236 275 TOTAL
14.5 Polara XD 101.2 150.6 12.0 3708 156 30 248 274 CARRY
18 Polara XD 101.7 149.4 13.6 5065 156 39 242 254
22 Polara XD 102.6 145.3 17.4 6804 140 47 218 228
24.5 Polara XD 103.8 142.6 18.9 7639 131 50 207 214
FIG. 56 is a graph illustrating the optimum driver loft for a given swing speed and ball type. It should be noted that if other balls are going to be used, then information for these balls can be derived by comparing the lift and drag characteristics of those balls to the characteristics of the balls in the graph of FIG. 56 and represented in Table 1. It should be noted that the recommended lofts are significantly higher for the most part for the Polara balls than for the ProV1.
Computer modeling capability using a golf ball trajectory model, as well as measurement capabilities using a Trackman™ Net System™ to measure actual golf shots allows one to better understand the effect between club loft, ball spin, and carry distance.
Using the trajectory model, pre-determined launch conditions can be set up and evaluated in order to understand the effect of varying club loft on the resultant trajectory. A first series of tests used the following initial launch parameters: ball speed=200 fps (simulating approximately a 90 mph swing speed), initial spin=3000 rpm. The vertical launch angle was varied from 5 to 45 degrees and the resultant overlaid trajectories are shown in FIG. 19.
The maximum height and carry distance both vary as the launch angle in increased. But while the maximum height simply increases with increasing vertical launch angle, the carry distance starts out relatively short (5 deg launch=approx 170 yds carry), reaches a maximum (20 & 25 deg vertical launch=approx 195 yds carry), and then the carry actually decreases as the vertical launch continues to be increased. At 40 deg vertical launch, the carry is actually shorter than at 5 deg vertical launch, at about 165 yds.
Clearly there is an “optimal” trajectory that maximizes carry distance. In the simulated trajectories of FIG. 19, the optimal trajectory would be between 20 and 25 degrees vertical launch angle. Flying either above this trajectory (higher launch angle) or below it (lower launch angle) will result in a loss of carry distance
In general, golf companies label a driver with 11-12 or greater loft as a “High Loft” or “High Trajectory” driver. Several companies make drivers labeled as 13.5 degrees loft. There is one company named Thomas Golf that makes degree labeled “16 degree”. The USGA has set limits driver specification, including size (less than or equal to 460 cc), coefficient of restitution (0.83), characteristic time (256 micro seconds). As a golfer' club head speed slows, and with all other things being constant, the golf ball needs to launch higher in order to maintain distance. Similarly with backspin—as the club head speed slows, a higher backspin is desired.
It should also be noted that the kits described herein can include non-conforming golf balls, as noted, as well as non-conforming clubs. Parameters such as club length, club head size, shaft flex, etc., will also affect distance and accuracy. Because the kits described herein include equipment that a typical golfer has never used and for which there is not significant data available, it is even more important to provide a method for fitting a golfer with the correct kit.
Conventional USGA conforming drivers are all designed to be 460 cc in volume or less. However, increasing the volume can improve several playability characteristics for certain golfers so it is anticipated that the drivers could easily be made over 500 cc and even as high as 600 cc or even 700 cc or higher. The larger size will enable the driver to be made more forgiving for off-center hits, for example. Making the driver larger volume will also enable the driver to be made with a larger breadth (dimension E in attached diagram). The USGA restricts the breadth to be less than the width. For some of the drivers described herein, the breadth is greater than the width for all models. Making the ratio of breadth to width even larger will also benefit the playability of the driver. For the current models the breadth/width is 1.04 (12 degree loft) to 1.136 (24.5 degree loft). The breadth-width ratio could be increased to 1.3 or even as high as 1.6 in order to improve the playability for the golfer.
The loft of the driver is important in getting the ball to launch higher in the air. Even though the highest loft made was 24.5 degrees, tests show that many golfers like the 24.5 degree driver and could further benefit from even higher loft drivers. Especially for golf balls like the Polara Ultimate Straight (has about half the lift of a normal golf ball) a higher lofted club is required for getting the ball to fly higher and thus maximize the carry distance. Thus a driver loft of up to 40 degree would be useful, even as high as 55 degrees would be useful for some golfers, especially those with very slow swing speeds.
The face of these clubs can comprise beta-titanium (Beta-Ti). This can be done to increase the CT and COR. Beta Ti is stronger than normal titanium alloy so the face can be made thinner and thus have a higher “spring effect”. It should also be noted that as the driver loft is increased the face thickness is decreased because the direct force on the face decreases. This allows the face to have a higher COR than would be found with a standard club design. In certain embodiments, the thinnest face can be 2.3 mm. This lower limit can be selected to cause the face to have a certain level of strength. In other embodiments, however, the face can be even thinner, especially for golfers with a lower swing speed. The face can be made less than 2 mm, lower than 1.9 mm and even as low as 1.5 mm for slower swing speed golfers and lofts greater than 12 degrees.
In certain embodiments, the face height for the clubs can be 56 mm. In larger volume versions the face can be even higher (greater than 56 mm tall). Even for similar volume versions the face can be higher by making the rear portion of the club less voluminous. The face width can be increased to over 119 mm and this would improve the performance for off-center hits. Making the face width 25-75% greater would help improve performance for some golfers.
In certain embodiments, the shafts used on the drivers can all be cut to 45.75″. Because some of the drivers are higher loft and are designed to be more forgiving w/ slice and hook shots than a normal driver, the shaft length can be longer and adding 0.25-6.0 inches should help golfers generate considerably more club head velocity and thus more ball distance. Adding even 6-12 inches would even be possible and with the higher loft (>12 degrees) the mis-hits would be lessened because of the fact that the higher backspin caused by the higher loft would prevent the spin axis on slices and hooks from being as tilted to the right or left as would be the case with a lower loft driver (<12 degrees). The shafts were made by UST-Mamiya and were their model “6000 series”. The shafts were in flexes stiff, regular, A (senior) and L (ladies)
In certain embodiments, the drivers use variable face thickness. For example, the entire face can be very thin (2.3-2.6 mm thickness), but can include “ramps” on the lower portion of the face escalate from 2.3 mm to 2.9 mm. For comparison, most constant conforming face thicknesses are in the range of 2.9-3.1 mm thick depending on the face size and head volume (for 6-4 titanium). These drivers have beta-Ti (15-3-3-3) faces and use 2.9 mm ramps to help reinforce the strength of the face. The ramps or reinforcement bars are variable width—wider at the base than at the top. The following Table 2 illustrates some example club characteristics that include such ramps.
TABLE 2
Loft General Face Thickness Ramp Max
12 2.6 mm 2.9 mm
14.5 2.5 mm 2.9 mm
18 2.4 mm 2.9 mm
22 2.3 mm 2.9 mm
24.5 2.3 mm 2.9 mm
To look at the effect that increased launch angle has on the carry distance for the Polara Ultimate Straight, several tests were performed. These tests involved expert golfers hitting balls while data was recorded with the Trackman™ Net System™. The Appendix attached hereto includes data garnered from these and other tests.
For the first test (see complete report attached as Appendix A) the only parameters varied were club type and tee height (ball impact club face location). Three clubs were used: 8.5 deg driver, 11.5 deg driver, 13 deg 3-wood. For each club, 3 groups of shots (all using the Polara Ultimate Straight in the Poles Horizontal orientation) were hit with a mid-level tee-height (standard position, center of club face), a low tee height (approx 1 cm lower), and a high tee height (approx 1 cm higher). Typically the face of a driver or any of the woods such as the 3-wood, is not perfectly flat. These clubs have faces that are convex (bulging outward) and thus the upper portion of the club face has an effectively higher loft than the middle section, which in turn is higher loft than the lower section. The objective of this test was to vary only the launch angle (spin would also be expected to vary) while keeping the golf swing (per club) itself unchanged. In this way, the primary effect of launch angle on carry distance could be observed. The results of this test are shown in FIG. 20.
These results clearly showed that for all 3 clubs increasing the vertical launch angle resulted in increased carry distance for all cases. The chart in FIG. 20 shows interval plots of the vertical launch angle for 8 cases (3 clubs, 3 tee heights) for the Polara Ultimate Straight golf ball tested in the PH orientation. The achieved result of increased vertical launch angle with increasing tee-height is evident. The chart of FIG. 21 shows the resulting carry distance for these cases.
As can be seen, there appears to be a direct correlation of increasing carry distance with increasing vertical launch angle for the Polara Ultimate Straight, PH orientation. The increased scatter for low tee height with the 3-wood and 8.5 deg driver was due to the fact that for these clubs, lowering the tee height from standard position resulted in a more challenging shot to hit solidly for the golfer.
Data for another on-course player test shows very clearly that increasing driver club loft results in significant improvement in the carry distance of the Polara Ultimate Straight, PH orientation while actually decreasing the carry distance of a more traditional ball, in this case the Titleist™ ProV1. This is due to the combination of the higher lofted club and the unique aerodynamic performance of the Polara Ultimate Straight golf ball.
The player hit several groups of shots using a 9 deg loft driver and a 16 deg loft driver. Balls were randomly mixed between ProV1 and Polara Ultimate Straight (PH orientation). Data was recorded with the Trackman™ Net System™ and some results are presented below. (See full report, Appendix B). The data for the vertical launch angles is illustrated in the chart of FIG. 22. With the 9 deg driver the launch angles for both the ProV1 and Polara Ultimate Straight are approximately 14.5 degrees, and increase to 18-19 degrees with the 16 deg lofted driver. The data for initial ball spin is shown in FIG. 23.
The spin has increased dramatically for both balls using the 16 deg lofted driver relative to the 9 deg. Since the ProV1 is a relatively high-lift ball, this increased spin would generate even more lift. Even though the Polara Ultimate Straight is a much lower lift ball under comparable spin conditions compared to the Pro V1, the increased lift generated by the increased spin and the increased vertical launch angle would still be expected to increase maximum height and flight time. The combination of the higher spin and higher vertical launch angle is what is observed in the trajectory data illustrated in the charts of FIG. 24 and FIG. 25.
At 9 deg driver loft, the maximum height for the ProV1 is about 36 yds, while the Polara Ultimate Straight is only about 21 yds. When the loft is increased to 16 degrees, the maximum height for the ProV1 has increased to about 52 yds, while the Polara Ultimate Straight has increased to a maximum height of about 40 yds. This effect on flight time is similar and is illustrated in the chart of FIG. 25.
With a 9 deg loft, the Polara Ultimate Straight is in the air a full 2 seconds shorter than ProV1, while with the 16 deg loft, the difference has dropped to 1 second. Also, the flight time for the Polara Ultimate Straight with 16 deg loft is very similar to the flight time for the ProV1 at 9 deg loft. Carry distance in yards is shown in the chart of FIG. 26.
Of interest here is that the carry distance for the ProV1 decreased dramatically (by about 30 yards) when going from the 9 deg lofted driver to the 16 deg lofted driver, while the carry for the Polara surprisingly increased 30 yards by going to the higher lofted driver.
Here is the data from above summarized in table form:
TABLE 3
Horizontal
Club Ball Launch Launch Spin
Driver Speed, Speed, Smash Angle, Angle, Spin, Axis,
Loft Ball mph mph Factor deg deg rpm deg
9 ProV1 103.1 154.0 1.49 14.5 4.4 2447 −11.6
9 Ult Str 102.4 152.4 1.49 14.6 5.1 2173 −12.0
16 ProV1 101.6 149.3 1.47 18.4 4.9 3973 −8.0
16 Ult Str 103.3 151.3 1.46 19.3 4.3 4155 −5.9
Vertical Landing
Max Carry Carry Landing Ball
Dr Ht DR, Max Ht, Dist, Disp, Angle, Speed, Flight
Loft yds yds yds yds deg mph Time, s
9 168.3 35.6 265.4 −12.3 −39.6 72.9 6.6
9 124.7 20.6 214.0 11.3 −26.5 82.8 4.5
16 157.0 51.8 236.9 −0.8 −54.0 75.0 7.4
16 151.7 39.9 245.8 11.3 −42.8 75.2 6.4
The above data suggests that the higher lofted club is resulting in shorter carry for the ProV1 because the higher spin generate by the higher loft club, combined with the relatively high lift of the ball and the higher launch angle, cause the ball to “balloon” above it's optimal trajectory, and carry distance is lost.
However, for the Polara Ultimate Straight ball (in PH orientation), the increased spin resulting from the higher lofted club gives extra lift to the relatively low lift Polara, and this combined with the higher launch angle causes the ball to climb higher as it attempts to reach it's optimal trajectory, and carry distance is gained.
One distinction should be made between a higher lofted driver and a 3 wood. Although a 3 wood club usually has a loft of approximately 15 degrees, it also has a lower volume and lower mass head. The 3 wood also has a shorter shaft. These mass, volume and length characteristics contribute to shorter distance and thus when a higher lofted driver is recommended for use with the Polara Ultimate Straight golf ball, it is preferred that the higher lofted driver have a club head size and mass that is at least that of typical modern drivers (460 cc limit by USGA). Another preferred driver design is to make a driver with a loft greater than 10.5 degrees and to have the head larger than the USGA limit of 460 cc and to also exceed the USGA COR (coefficient of restitution) and CT (Characteristic Time) limits. A driver with these criteria included in its design would deliver even longer golf ball flight distance.
FIGS. 27 and 28 are charts illustrating summaries of the results of even more player testing showing the average trajectory for various tee heights and clubs when hitting the Polara Ultimate Straight golf balls. These results show a direct comparison between average trajectories for the 8.5 and 11.5 deg drivers at each tee height. Note that the 8.5 deg driver on high tee has nearly identical trajectory as 11.5 deg driver on mid tee. In FIGS. 27 and 28, the low tee height positions are represented by the green line, mid tee height positions are the red line and high tee height positions are the blue line. In FIGS. 27 and 28 the top line is the blue line, the middle line is the red line and the bottom line is the green line.
Armed with these data, a kit can be assembled that matches a driver, or other club or clubs, with certain parameters, in particular loft, with a golf ball such as the Polara Ultimate Straight golf ball based on the swing characteristics of a certain golfer. For example, this can be as simple as producing a kit with a driver that has, e.g., a 16 degree loft to be sold with a golf ball such as described above that is for golfers with swing speeds under 90 mph, or 80 mph, or basically whatever the data shows. Kits can then also be produced pairing, e.g., drivers with lower lofts with golf balls such as those described above for golfers with higher swings speeds. For example there may be kits for golfers with swing speeds under 80 mph, between 80 and 90 mph, between 90 and 100 mph, and over 100 mph.
More variations can also be produced, to provide more granularity. In addition, other parameters, such as angle of attack, smash factor, spin rate, etc., can also be taken into account when producing kits. Thus, a salesperson can measure a few parameters related to a golfer's swing and then quickly identify the correct kit, i.e., club and ball pairing.
Appendices A-C include the results of various tests performed in order to obtain data to verify the above. Appendix A is a summary of data for tests performed using a Trackman™ where the tee heights were varied for various lofted clubs. Appendix B is a summary of data for tests performed using a Trackman™ where 9 degree and 16 degree drivers were used with various golf balls. Appendix C is a summary of data for tests performed using a Trackman™ where the tee height were varied or clubs with 10.5 degree and 8.5 degree lofted drivers were used.
The very different aerodynamics of the Polara Ultimate Straight golf ball are so different from normal golf balls that they have never been extensively studied before and until the new Polara Ultimate Straight golf ball was introduced people did not have the occasion to even study a ball with this range of aerodynamic performance. So it is not a surprise that nobody until this time has demonstrated the benefits or ever recommended using a higher lofted driver than normal with a ball that exhibits lower lift than normal. Balls with similar aerodynamic performance to the Polara Ultimate straight that exhibit low lift will similarly benefit from the use of a higher lofted driver—generally greater than 10.5 degrees loft, for example balls with symmetrical dimple patterns which are also designed for a lower flight trajectory, as described in detail below, as well as other golf balls which have lower than normal flight trajectories, such as golf balls with higher drag, higher weight, or smaller size. A kit can be assembled in a similar matter to that described above for the Polara Straight golf ball, using any of the conforming or symmetrical low lift or low trajectory golf balls described below in connection with FIGS. 29 to 55, or with other balls having similar aerodynamic performance.
Thus, a low lift ball does not have to have an asymmetric dimple pattern, like the Polara Ultimate Straight, in order to benefit from the higher lofted driver. Any golf ball with an asymmetrical or symmetrical dimple pattern that flies lower than another golf ball benefits in general from a higher lofted driver as compared to a driver that provides the optimum distance for a higher lift golf ball. It should also be mentioned that a ball with higher drag also exhibits shorter distance than a ball with lower drag, when all other factors are equal. So in this case, the ball with the higher drag also benefits from the higher lofted driver because it helps the ball stay in the air longer and fly faster than it could roll on the ground.
FIGS. 1 to 8 illustrate several embodiments of non-conforming or non-symmetrical balls having different dimple patterns which may be used in embodiments of a kit comprising one of the non-conforming balls and a driver of predetermined high loft angle, as described in more detail below. In each case, one hemisphere of the ball (or of a mold cavity for making the ball in FIG. 3) cut in half through the equator is illustrated, with the other hemisphere having an identical dimple pattern to the illustrated hemisphere. In each embodiment, the dimples are of greater total volume in a first area or areas, and of less volume in a second area. In the illustrated embodiment, the first areas, which are of greater dimple volume, are in the polar regions of the ball while the second area is a band around the equator, designed to produce a preferred spin axis through the poles of the ball, due to the larger weight around the equatorial band, which has a lower dimple volume, i.e. lower volume of material removed from the ball surface. Other embodiments may have the reduced volume dimple regions located in different regions of the ball, as long as the dimple pattern is designed to impart a preferred spin axis to the ball, such that hook and slice dispersion is reduced when a ball is struck with the spin axis in a horizontal orientation (PH when the spin axis extends through the poles).
In the embodiments of FIGS. 1-8, the preferred spin axis goes through the poles of the ball. It will be understood that the design of FIGS. 1-8 can be said to then have a gyroscopic center plane orthogonal to the preferred spin axis, i.e., that goes through and is parallel with the equatorial band. Thus, the designs of FIGS. 1-8 can be said to have a region of lower volume dimples around the gyroscopic center plane. It should also be recognized that in these embodiments, the gyroscopic center plane does not go through all regions, i.e., it does not go through the regions with greater dimple volume.
It should also be understood that the terms equator or equatorial region and poles can be defined with respect to the gyroscopic center plane. In other words, the equator is in the gyroscopic center plane and the preferred spin axis goes through the poles.
In fact it has been determined that making dimples more shallow within the region inside the approximately 45 degree point 1803 on the circumference of the ball 10 with respect to the gyroscopic center plane 1801, as illustrated in FIG. 18, further increases the MOI difference between the ball rotating in the PH and pole-over-pole (POP) orientations as described below. Conversely, making dimples deeper inside of the approximately 45 degree point 1803 decreases the MOI difference between the ball rotating in the PH and pole-over-pole (POP) orientations. For reference, the preferred spin axis 1802 is also illustrated in FIG. 18.
FIG. 1 illustrates one hemisphere of a first embodiment of a non-conforming or non-symmetrical golf ball 10 having a first dimple pattern, hereinafter referred to as dimple pattern design 28-1, or “28-1 ball”. The dimple pattern is designed to create a difference in moment of inertia (MOI) between poles horizontal (PH) and other orientations. The dimple pattern of the 28-1 ball has three rows of shallow truncated dimples 12 around the ball's equator, in each hemisphere, so the ball has a total of six rows of shallow truncated dimples. The polar region has a first set of generally larger, deep spherical dimples 14 and a second set of generally smaller, deep spherical dimples 15, which are dispersed between the larger spherical dimples 14. There are no smaller dimples 15 in the two rows of the larger spherical dimples closest to the band of shallow truncated dimples 12. This arrangement removes more weight from the polar areas of the ball and thus further increases the MOI difference between the ball rotating in the PH and pole-over-pole (POP) orientations.
Shown in Table 1 are the dimple radius, depth and dimple location information for making a hemispherical injection molding cavity to produce the dimple pattern 28-1 on one hemisphere of the ball, with the other injection molding cavity being identical. As illustrated in Table 1, the ball has a total of 410 dimples (205 in each hemisphere of the ball). The truncated dimples 12 are each of the same radius and truncated chord depth, while the larger and smaller spherical dimples are each of three different sizes (Smaller dimples 1, 2 and 3 and larger dimples 5, 6, 7 in Table 1 of the '013 application). The locations of the truncated dimples and each of the different size spherical dimples on one hemisphere of the ball are illustrated in detail in Table 1 of the '013 application.
As seen in FIG. 1 and Table 1 of the '013 application, the first, larger set of spherical dimples 14 include dimples of three different radii, specifically 8 dimples of a first, smaller radius (0.067 inches), 52 dimples of a second, larger radius (0.0725 inches) and 16 dimples of a third, largest radius (0.075 inches). Thus, there are a total of 76 larger spherical dimples 14 in each hemisphere of ball 10. The second, smaller set of spherical dimples, which are arranged between the larger dimples in a region closer to the pole, are also in three slightly different sizes from approximately 0.03 inches to approximately 0.04 inches, and one hemisphere of the ball includes 37 smaller spherical dimples. The truncated dimples are all of the same size and have a radius of 0.067 inches (the same as the smallest spherical dimples of the first set) and a truncated chord depth of 0.0039 inches. There are 92 truncated dimples in one hemisphere of the ball. All of the spherical dimples 14 have the same spherical chord depth of 0.0121 inches, while the smaller spherical dimples 15 have a spherical chord depth of 0.008 inches. Thus, the truncated chord depth of the truncated dimples is significantly less than the spherical chord depth of the spherical dimples, and is about one third of the depth of the larger spherical dimples 14, and about one half the depth of the smaller dimples 15.
With this dimple arrangement, significantly more material is removed from the polar regions of the ball to create the larger, deeper spherical dimples, and less material is removed to create the band of shallower, truncated dimples around the equator. In testing described in more detail below, the 28-1 dimple pattern of FIG. 1 and Table 1 was found to have a preferred spin axis through the poles, as expected, so that dispersion is reduced if the ball is placed on the tee in a poles horizontal (PH) orientation. This ball was also found to generate relatively low lift when the ball spins about the preferred spin axis.
FIG. 2 illustrates one hemisphere of a second embodiment of a ball 16 having a different dimple pattern, hereinafter referred to as 25-1, which has three rows of shallow truncated dimples 18 around the ball's equator in each hemisphere and deep spherical dimples 20 in the polar region of the ball. The deep dimples closest to the pole also have smaller dimples 22 dispersed between the larger dimples. The overall dimple pattern in FIG. 2 is similar to that of FIG. 1, but the total number of dimples is less (386). Ball 16 has the same number of truncated dimples as ball 10, but has fewer spherical dimples of less volume than the spherical dimples of ball 10 (see Table 2 of the '013 application). Each hemisphere of ball 16 has 92 truncated dimples and 101 spherical dimples 20 and 22. The main difference between patterns 28-1 and 25-1 is that the 28-1 ball of FIG. 1 has more weight removed from the polar regions because the small dimples between deep dimples are larger in number and volume for dimple pattern 28-1 compared to 25-1, and the larger, deeper dimples are also of generally larger size for dimple pattern 28-1 than the larger spherical dimples in the 25-1 dimple pattern. The larger spherical dimples 20 in the ball 16 are all of the same size, which is equal to the smallest large dimple size in the 28-1 ball. The truncated dimples in FIG. 2 are of the same size as the truncated dimples in FIG. 1, and the truncated dimple radius is the same as the radius of the larger spherical dimples 20.
The dimple radius, depth and dimple location information for making an injection molding cavity to produce the dimple pattern 25-1 of FIG. 2 are illustrated in detail in Table 2 of the '013 application. Such a ball 25-1 has only two different size smaller spherical dimples 22 in the polar region (dimples 1 and 2 which are the same size as dimples 1 and 2 of the 28-1 ball), and only one size larger spherical dimple 20, i.e. dimple 4 which is the same size as dimple 5 of the 28-1 ball. Thus, the 28-1 ball has some spherical dimples, specifically dimples 6 and 7 in Table 1, which are of larger diameter than any of the spherical dimples 20 of the 25-1 ball.
FIG. 3 illustrates a mold 23 having one hemisphere of a compression molding cavity 24 designed for making a third embodiment of a ball having a different dimple pattern, identified as dimple pattern or ball 2-9. The cavity 24 has three rows of raised, flattened bumps 25 designed to form three rows of shallow, truncated dimples around the ball's equator, and a polar region having raised, generally hemispherical bumps 26 designed to form deep, spherical dimples in the polar region of a ball. The resultant dimple pattern has three rows of shallow truncated dimples around the ball's equator and deep spherical dimples 2 in the polar region of the ball in each hemisphere of the ball. As illustrated in FIG. 3 and shown in Table 3 of the '013 application, there is only one size of truncated dimple and one size of spherical dimple in the 2-9 dimple pattern. The truncated dimples are identified as dimple #1 in Table 3 of the '013 application, and the spherical dimples are identified as dimple #2 in Table 3 of the '013 application. The 2-9 ball has a total of 336 dimples, with 92 truncated dimples of the same size as the truncated dimples of the 28-1 and 25-1 balls, and 76 deep spherical dimples which are all the same size as the large spherical dimples of the 25-1 ball. Thus, about the same dimple volume is removed around the equator in balls 28-1, 25-1 and 2-9, but more dimple volume is removed in the polar region in ball 28-1 than in balls 25-1 and 2-9, and ball 2-9 has less volume removed in the polar regions than balls 28-1 and 25-1.
It will be understood that a similar type of mold, or set of molds, is used for all of the embodiments described herein, and that mold 23 is shown by way of example only.
Table 4 of the '013 application lists dimple shapes, dimensions, and coordinates or locations on a ball for a dimple pattern 28-2 which is very similar to the dimple pattern 28-1 and is therefore not shown separately in the drawings. The ball with dimple pattern 28-2 has three larger spherical dimples of different dimensions, numbered 5, 6 and 7 in Table 4 of the '013 application, and three smaller spherical dimples of different dimensions, numbered 1, 2 and 3, and the dimensions of these dimples are identical to the corresponding dimples of the 28-1 ball in Table 1 of the '013 application, as are the dimensions of truncated dimples numbered 4 in Table 4 of the '013 application. The dimple pattern 28-2 is nearly identical to dimple pattern 28-1, except that the seam that separates the two hemispheres of the ball is wider in the 28-2 ball, and the coordinates of some of the dimples are slightly different, as can be determined by comparing Tables 1 and 4 of the '013 application.
The dimple coordinates for pattern 28-2 are illustrated in detail in Table 4 of the '013 application.
FIGS. 4 to 6 illustrate hemispheres of three different balls 30, 40 and 50 with different dimple patterns. The dimple patterns on balls 30, 40 and 50 are hereinafter referred to as dimple patterns 25-2, 25-3, and 25-4. Dimple patterns 25-2, 25-3 and 25-4 are related in that they have basically the same design except that each has a different number of rows of truncated dimples surrounding the equator. The dimple dimensions and positions for the balls of FIGS. 4 to 6 are provided below in Tables 5, 6 and 7, respectively of the '013 application.
Ball 30 or 25-2 of FIG. 4 has two rows of shallow truncated dimples 32 adjacent the equator in each hemisphere (i.e., a total of four rows in the complete ball), and spherical dimples 34 in each polar region. As indicated in Table 5 of the '013 application, there are two different sizes of spherical dimples 34, and two different sizes of truncated dimple 32.
Ball 40 or 25-3 of FIG. 5 has four rows of shallow, truncated dimples 42 adjacent the equator in each hemisphere (i.e. a circumferential band of eight rows of shallow truncated dimples about the equator), and deep spherical dimples 44 in each polar region. As illustrated in FIG. 5 and indicated in Table 6 of the '013 application, the truncated dimples 42 are of three different sizes, with the largest size dimples 42A located only in the third and fourth rows of dimples from the equator (i.e. the two rows closest to the polar region). Ball 40 also has spherical dimples with slightly different radii, as indicated in Table 6 of the '013 application.
Ball 50 or 25-4 of FIG. 6 has three rows of shallow, truncated dimples 52 on each side of the equator (i.e. a circumferential band of six rows of dimples around the equator) and deep spherical dimples 54 in each polar region. Ball 50 has spherical dimples of three different radii and truncated dimples which are also of three different radii, as indicated in Table 7 of the '013 application. As illustrated in FIG. 6 and indicated in Table 7 of the '013 application, the third row of truncated dimples, i.e. the row adjacent to the polar region, has some larger truncated dimples 52A, which are three of the largest truncated dimples identified as Dimple #5 in Table 7 of the '013 application. The adjacent polar region also has some larger spherical dimples 54A arranged in a generally triangular pattern with the larger truncated dimples, as illustrated in FIG. 6. Dimples 54A are three of the largest spherical dimples identified as Dimple #6 in Table 7 of the '013 application. As seen in Table 7 of the '013 application, there are twelve total large truncated dimples #5 and twelve total large spherical dimples #6, all with a radius of 0.0875 inches. FIG. 6 illustrates the triangular arrangement of three large truncated dimples and three large spherical dimples at one location. Similar arrangements are provided at three equally spaced locations around the remainder of the hemisphere of the ball illustrated in FIG. 6.
As indicated in Tables 5, 6, and 7 of the '013 application, the balls 25-2 and 25-3 each have three different sizes of truncated dimple in the equatorial region and two different sizes of spherical dimple in the polar region, while ball 25-4 has three different sizes of truncated dimple as well as three different sizes of spherical dimple. The polar region of dimples is largest in ball 25-2, which has four rows of truncated dimples (two rows per hemisphere) in the equatorial region, and smallest in ball 25-3, which has eight rows of truncated dimples in the equatorial region. In alternative embodiments, balls may be made with a single row of truncated dimples in each hemisphere, as well as with a land area having no dimples in an equatorial region, the land area or band having a width equal to two, four or more rows of dimples, or with a band having regions with dimples alternating with land regions with no dimples spaced around the equator.
Dimple patterns 25-2, 25-3 and 25-4 are similar to pattern 2-9 in that they have truncated dimples around the equatorial region and deeper dimples around the pole region, but the truncated dimples in patterns 25-2, 25-3 and 25-4 are of larger diameter than the truncated dimples of patterns 28-1, 25-1 and 2-9. The larger truncated dimples near the equator mean that more weight is removed from the equator area. With all other factors being equal, this means that there is a smaller MOI difference between the PH and POP orientations for balls 25-2, 25-3 and 25-4 than for balls 28-1, 28-2, 25-1 and 2-9.
FIG. 7 illustrates one hemisphere of a golf ball 60 according to another embodiment, which has a different dimple pattern identified as dimple pattern 28-3 in the following description. Dimple pattern 28-3 of ball 60 comprises three rows of truncated dimples 62 on each side of the equator, an area of small spherical dimples 64 at each pole, and an area of larger, deep spherical dimples 65 between dimples 64 and dimples 62. Table 8 of the '013 application indicates the dimple parameters and coordinates for golf ball 60. As illustrated in Table 8 of the '013 application, ball 28-3 has one size of truncated dimple, four sizes of larger spherical dimples (dimple numbers 2, 3, 5 and 6) and one size of smaller spherical dimple (dimple number 1) in the polar regions.
As indicated in Table 8 of the '013 application and FIG. 7, the small spherical dimples 64 at the pole are all of the same radius, and there are thirteen dimples 64 arranged in a generally square pattern centered on the pole of each hemisphere. There are four different larger spherical dimples 65 (dimple numbers 2 to 6 of Table 8) of progressively increasing radius from 0.075 inches to 0.0825 inches. The ball with dimple pattern 28-3 also has a preferred spin axis through the poles due to the weight difference caused by locating a larger volume of dimples in each polar region than in the equatorial band around the equator.
The dimple parameters and coordinates for making one hemisphere of the 28-3 ball are illustrated in detail in Table 8 of the '013 application.
In one example, the seam widths for balls 28-1, 28-2, and 28-3 was 0.0088″ total (split on each hemisphere), while the seam widths for balls 25-2, 25-3, and 25-4 was 0.006″, and the seam width for ball 25-1 was 0.030″.
Each of the dimple patterns described above and illustrated in FIGS. 1 to 7 has less dimple volume in a band around the equator and more dimple volume in the polar region. The balls with these dimple patterns have a preferred spin axis extending through the poles, so that slicing and hooking is resisted if the ball is placed on the tee with the preferred spin axis substantially horizontal. If placed on the tee with the preferred spin axis pointing up and down (POP orientation), the ball is much less effective in correcting hooks and slices compared to being oriented in the PH orientation. If desired, the ball may also be oriented on the tee with the preferred spin axis tilted up by about 45 degrees to the right, and in this case the ball still reduces slice dispersion, but does not reduce hook dispersion as much. If the preferred spin axis is tilted up by about 45 degrees to the left, the ball reduces hook dispersion but does not resist slice dispersion as much.
FIG. 8 illustrates a ball 70 with a dimple pattern similar to the ball 28-1 of FIG. 1 but which has a wider region or land region 72 with no dimples about the equator. In the embodiment of FIG. 8, the region 72 is formed by removing two rows of dimples on each side of the equator from the ball 10 of FIG. 1, leaving one row of shallow truncated dimples 74. The polar region of dimples is identical to that of FIG. 1, and like reference numbers are used for like dimples. Rows of truncated dimples may be removed from any of the balls of FIGS. 2 to 7 in a similar manner to leave a dimple-less region or land area about the equator. The dimple-less region in some embodiments may be narrow, like a wider seam, or may be wider by removing one, two, or all of the rows of truncated dimples next to the equator, producing a larger MOI difference between the poles horizontal (PH) and other orientations.
FIG. 9 is a diagram illustrating the relationship between the chord depth of a truncated and a spherical dimple as used in the dimple patterns of the golf balls described above. A golf ball having a diameter of about 1.68 inches was molded using a mold with an inside diameter of approximately 1.694 inches to accommodate for the polymer shrinkage. FIG. 9 illustrates part of the surface 75 of the golf ball with a spherical dimple 76 of spherical chord depth of d2 and a radius R represented by half the length of the dotted line. In order to form a truncated dimple, a cut is made along plane A-A to make the dimple shallower, with the truncated dimple having a truncated chord depth of d1, which is smaller than the spherical chord depth d2. The volume of cover material removed above the edges of the dimple is represented by volume V3 above the dotted line, with a depth d3. In FIG. 9,
V1=volume of truncated dimple,
V1+V2=volume of spherical dimple,
V1+V2+V3=volume of cover removed to create spherical dimple, and
V1+V3=volume of cover removed to create truncated dimple.
For dimples that are based on the same radius and spherical chord depth, the moment of inertia difference between a ball with truncated dimples and spherical dimples is related to the volume V2 below line or plane A-A which is removed in forming a spherical dimple and not removed for the truncated dimple. A ball with all other factors being the same except that one has only truncated dimples and the other has only spherical dimples, with the difference between the truncated and spherical dimples being only the volume V2 (i.e. all other dimple parameters are the same), the ball with truncated dimples is of greater weight and has a higher MOI than the ball with spherical dimples, which has more material removed from the surface to create the dimples.
The approximate moment of inertia can be calculated for each of the balls illustrated in FIGS. 1 to 7 and in Tables 1 to 8 of the '013 application (i.e. balls 2-9, 25-1 to 25-4, and 28-1 to 28-3). In one embodiment, balls having these patterns were drawn in SolidWorks® and their MOI's were calculated along with the known Polara™ golf ball referenced above as a standard. SolidWorks® was used to calculate the MOI's based on each ball having a uniform solid density of 0.036413 lbs/in̂3. The other physical size and weight parameters for each ball are given in Table 4 below.
TABLE 4
surface
density, mass, volume, area,
Ball lbs/in{circumflex over ( )}3 mass, lbs grams inch{circumflex over ( )}3 inch{circumflex over ( )}2
Polara 0.03613 0.09092 41.28 2.517 13.636
2-9 0.03613 0.09064 41.15 2.509 13.596
25-1 0.03613 0.09060 41.13 2.508 13.611
25-2 0.03613 0.09024243 40.97 2.4979025 13.560402
25-3 0.03613 0.09028772 40.99 2.4991561 13.575728
25-4 0.03613 0.09026686 40.98 2.4985787 13.568852
28-1 0.03613 0.09047 41.07 2.504 13.609
28-2 0.03613 0.09047 41.07 2.504 13.609
28-3 0.03613 0.09053814 41.1 2.5060878 13.556403
The MOI for each ball was calculated based on the dimple pattern information and the physical information in Table 4. Table 5 shows the MOI calculations.
TABLE 5
% MOI
% delta
(Pmax- relative
Px, lbs X Py, lbs X Pz, lbs X MOI Delta = Pmin)/ to
Ball inch{circumflex over ( )}2 inch{circumflex over ( )}2 inch{circumflex over ( )}2 Pmax Pmin Pmax-Pmin Pmax Polara
Polara 0.025848 0.025917 0.025919 0.025919 0.025848 0.0000703 0.271% 0.0%
2-9 0.025740 0.025741 0.025806 0.025806 0.025740 0.0000665 0.258% −5.0%
25-1 0.025712 0.025713 0.025800 0.025800 0.025712 0.0000880 0.341% 25.7%
25-2 0.02556791 0.02557031 0.02558386 0.0255839 0.0255679 1.595E−05 0.062% −77.0%
25-3 0.0255822 0.02558822 0.02559062 0.0255906 0.0255822 8.42E−06 0.033% −87.9%
25-4 0.02557818 0.02558058 0.02559721 0.0255972 0.0255782 1.903E−05 0.074% −72.6%
28-1 0.025638 0.025640 0.025764 0.025764 0.025638 0.0001254 0.487% 79.5%
28-2 0.025638 0.025640 0.025764 0.025764 0.025638 0.0001258 0.488% 80.0%
28-3 0.02568461 0.02568647 0.02577059 0.0257706 0.0256846 8.598E−05 0.334% 23.0%
With the Polara™ golf ball as a standard, the MOI differences between each orientation were compared to the Polara golf ball in addition to being compared to each other. The largest difference between any two orientations is called the “MOI Delta”, shown in table 5. The two columns to the right quantify the MOI Delta in terms of the maximum % difference in MOI between two orientations and the MOI Delta relative to the MOI Delta for the Polara ball. Because the density value used to calculate the mass and MOI was lower than the average density of a golf ball, the predicted weight and MOI for each ball is relative to each other, but not exactly the same as the actual MOI values of the golf balls that were made, robot tested and shown in Table 5. Generally a golf ball weighs about 45.5-45.9 g. Comparing the MOI values of all of the balls in Table 5 is quite instructive, in that it predicts the relative order of MOI difference between the different designs, with the 25-3 ball having the smallest MOI difference and ball 28-2 having the largest MOI difference.
Table 6 shows that a ball's MOI Delta does strongly influence the ball's dispersion control. In general as the relative MOI Delta of each ball increases, the dispersion distance for a slice shot decreases. The results illustrated in Table 6 also include data obtained from testing a known TopFlite XL straight ball, and were obtained during robot testing under standard laboratory conditions, as discussed in more detail below.
TABLE 6
% MOI
difference Avg Avg Avg Avg
between C-DISP, C-DIST, T-DISP, T-DIST,
Ball Orientation orientations ft yds ft yds
28-2 PH 0.488% 9.6 180.6 7.3 201.0
28-1 PH 0.487% −2.6 174.8 −7.6 200.5
TopFLite XL random 0.000% 66.5 189.3 80.6 200.4
Straight
25-1 PH 0.341% 7.4 184.7 9.6 207.5
28-3 PH 0.334% 16.3 191.8 23.5 211.8
Polara PFB 0.271% 29.7 196.6 38.0 214.6
2-9 PH 0.258% 12.8 192.2 10.5 214.5
25-4 PH 0.074% 56.0 185.4 71.0 197.3
25-2 PH 0.062% 52.8 187.0 68.1 199.9
25-3 PH 0.033% 63.4 188.0 75.1 197.9
As illustrated in Table 6, balls 28-3, 25-1, 28-1 and 28-2 all have higher MOI deltas relative to the Polara, and they all have better dispersion control than the Polara. This MOI difference is also shown in FIGS. 10 and 11, which also includes test data for the TopFlite XL Straight made by Callaway Golf.
The aerodynamic force acting on a golf ball during flight can be broken down into three separate force vectors: Lift, Drag, and Gravity. The lift force vector acts in the direction determined by the cross product of the spin vector and the velocity vector. The drag force vector acts in the direction opposite of the velocity vector. More specifically, the aerodynamic properties of a golf ball are characterized by its lift and drag coefficients as a function of the Reynolds Number (Re) and the Dimensionless Spin Parameter (DSP). The Reynolds Number is a dimensionless quantity that quantifies the ratio of the inertial to viscous forces acting on the golf ball as it flies through the air. The Dimensionless Spin Parameter is the ratio of the golf ball's rotational surface speed to its speed through the air.
The lift and drag coefficients of a golf ball can be measured using several different methods including an Indoor Test Range such as the one at the USGA Test Center in Far Hills, N.J. or an outdoor system such as the Trackman™ Net System™ made by Interactive Sports Group in Denmark. The test results described below and illustrated in FIGS. 10 to 17 for some of the embodiments described above as well as some conventional golf balls for comparison purposes were obtained using a Trackman™ Net System.
For right-handed golfers, particularly higher handicap golfers, a major problem is the tendency to “slice” the ball. The unintended slice shot penalizes the golfer in two ways: 1) it causes the ball to deviate to the right of the intended flight path and 2) it can reduce the overall shot distance. A sliced golf ball moves to the right because the ball's spin axis is tilted to the right. The lift force by definition is orthogonal to the spin axis and thus for a sliced golf ball the lift force is pointed to the right.
The spin-axis of a golf ball is the axis about which the ball spins and is usually orthogonal to the direction that the golf ball takes in flight. If a golf ball's spin axis is 0 degrees, i.e., a horizontal spin axis causing pure backspin, the ball does not hook or slice and a higher lift force combined with a 0-degree spin axis only makes the ball fly higher. However, when a ball is hit in such a way as to impart a spin axis that is more than 0 degrees, it hooks, and it slices with a spin axis that is less than 0 degrees. It is the tilt of the spin axis that directs the lift force in the left or right direction, causing the ball to hook or slice. The distance the ball unintentionally flies to the right or left is called Carry Dispersion. A lower flying golf ball, i.e., having a lower lift, is a strong indicator of a ball that has lower Carry Dispersion.
The amount of lift force directed in the hook or slice direction is equal to: Lift Force*Sine (spin axis angle). The amount of lift force directed towards achieving height is: Lift Force*Cosine (spin axis angle).
A common cause of a sliced shot is the striking of the ball with an open clubface. In this case, the opening of the clubface also increases the effective loft of the club and thus increases the total spin of the ball. With all other factors held constant, a higher ball spin rate in general produces a higher lift force and this is why a slice shot often has a higher trajectory than a straight or hook shot.
The table 7 below shows the total ball spin rates generated by a golfer with club head speeds ranging from approximately 85-105 mph using a 10.5 degree driver and hitting a variety of prototype golf balls and commercially available golf balls that are considered to be low and normal spin golf balls:
TABLE 7
Spin Axis, degree Typical Total Spin, rpm Type Shot
−30 2,500-5,000 Strong Slice
−15 1,700-5,000 Slice
0 1,400-2,800 Straight
+15 1,200-2,500 Hook
+30 1,000-1,800 Strong Hook
FIG. 10 illustrates the average Carry and Total Dispersion versus the MOI difference between the minimum and maximum orientations for each dimple design (random for the TopFlite XL, which is a conforming or symmetrical ball under USGA regulations), using data obtained from robot testing using a Trackman™ System as referenced above. Balls 25-2, 25-3, and 25-4 of FIG. 10 (also illustrated in FIGS. 4 to 6) are related since they have basically the same dimple pattern except that each has a different number of rows of dimples surrounding the equator, with ball 25-2 having two rows on each side, ball 25-3 having four rows, and ball 25-4 having three rows. The % MOI delta between the minimum and maximum orientation for each of these balls obtained from the data in FIG. 10 is indicated in Table 8 below.
TABLE 8
Rows of truncated around the
Design # equator (per hemisphere) % MOI Delta
25-2 2 0.062%
25-3 4 0.033%
25-4 3 0.074%
FIG. 11 shows the average Carry and Total Distance versus the MOI difference between the Minimum and Maximum orientations for each dimple design.
Table 9 below illustrates results from slice testing the 25-1, 28-1, and 2-9 balls as well as the Titleist ProV1 and the TopFlite XL Straight balls, with the 25-1, 28-1 and 2-9 balls tested in both the PH and POP orientations. In this table, the average values for carry dispersion, carry distance, total dispersion, total yards, and roll yards are indicated. This indicates that the 25-1, 28-1 and 2-9 balls have significantly less dispersion in the PH orientation than in the POP orientation, and also have less dispersion than the known symmetrical ProV1 and TopFlite balls which were tested.
TABLE 9
Results from 4-15-10 slice test
Average Values for TrackMan Data
Carry Carry Total Total
Ball Orien- Dispersion, Distance, Dispersion, Distance, Roll,
Name tation ft yds ft yds yds
25-1 PH 11 197 17 224 25
28-1 PH -8 194 −5 212 18
2-9 PH 15 202 22 233 30
25-1 POP 39 198 54 215 18
28-1 POP 47 202 62 216 14
2-9 POP 65 194 79 206 13
ProV1 POP 66 197 74 204 7
TopFlite POP 50 196 69 206 10
Golf balls 25-1, 28-1, 2-9, Polara 2p 4/08, Titleist ProV1 and TopFlite XL Straight were subjected to several tests under industry standard laboratory conditions to demonstrate the better performance that the dimple patterns described herein obtain over competing golf balls. In these tests, the flight characteristics and distance performance of the golf balls 25-1, 28-1 and 2-9 were conducted and compared with a Titleist Pro V1® made by Acushnet and TopFlite XL Straight made by Callaway Golf and a Polara 2p 4/08 made by Pounce Sports LLC. Also, each of the golf balls 25-1, 28-1, 2-9, Polara 2p 4/08, were tested in the Poles-Forward-Backward (PFB), Pole-Over-Pole (POP) and Pole Horizontal (PH) orientations. The Pro V1® and TopFlite XL Straight are USGA conforming balls and thus are known to be spherically symmetrical, and were therefore tested in no particular orientation (random orientation). Golf balls 25-1 and 28-1 were made from basically the same materials and had a DuPont HPF 2000 based core and a Surlyn™ blend (50% 9150, 50% 8150) cover. The cover was approximately 0.06 inches thick.
The tests were conducted with a “Golf Laboratories” robot and hit with the same Taylor Made® driver at varying club head speeds. The Taylor Made® driver had a 10.5° R9 460 club head with a Motore 65 “S” shaft. The golf balls were hit in a random order. Further, the balls were tested under conditions to simulate an approximately 15-25 degree slice, e.g., a negative spin axis of 15-25 degrees.
FIGS. 12 and 13 are examples of the top and side view of the trajectories for individual shots from the Trackman™ Net System™ when tested as described above. The Trackman™ trajectory data in FIGS. 12 and 13 clearly shows the 28-1, 25-1 and 2-9 balls in PH orientation were much straighter (less dispersion) and lower flying (lower trajectory height). The maximum trajectory height data in FIG. 13 correlates directly with the lift coefficient (CL) produced by each golf ball. The results indicate that the Pro V1® and TopFlite XL straight golf ball generated more lift than the 28-1, 25-1 or 2-9 balls in the PH orientation.
Lift and Drag Coefficient Testing & Results, CL and CD Regressions FIGS. 14-17 show the lift and drag coefficients (CL and CD) versus Reynolds Number (Re) at spin rates of 3,500 rpm and 4,500 rpm respectively, for the 25-1, 28-1 and 2-9 dimple designs as well as for the TopFlite® XL Straight, Polara 2p and Titleist Pro V1®. The curves in each graph were generated from the regression analysis of multiple straight shots for each ball design in a specific orientation.
The curves in FIGS. 14-17 depict the results of regression analysis of many shots over the course of testing done in the period from January through April 2010 under a variety of spin and Reynolds Number conditions. To obtain the regression data shown in FIGS. 14 to 17, a Trackman™ Net System™ consisting of 3 radar units was used to track the trajectory of a golf ball that was struck by a Golf Labs robot equipped with various golf clubs. The robot was set up to hit a straight shot with various combinations of initial spin and velocity. A wind gauge was used to measure the wind speed at approximately 20 ft elevation near the robot location. The Trackman™ Net System™ measured trajectory data (x, y, z location vs. time) which were then used to calculate the lift coefficients (CL) and drag coefficients (CD) as a function of measured time-dependent quantities including Reynolds Number, Ball Spin Rate, and Dimensionless Spin Parameter. Each golf ball model or design was tested under a range of velocity and spin conditions that included 3,000-5,000 rpm spin rate and 120,000-180,000 Reynolds Number. A 5-term multivariable regression model for the lift and drag coefficients as a function of Reynolds Number (Re) and Dimensionless Spin Parameter (W) was then fit to the data for each ball design: The regression equations for CL and CD were:
CLRegression=a1*Re+a2*W+a3*Rê2+a4*Ŵ2+a5*ReW+a6
CDRegression=b1*Re+b2*W+b3*Rê2+b4*Ŵ2+b5*ReW+b6
Where ai with i=1-6 are regression coefficients for Lift Coefficient and
-
- bi with i=1-6 are regression coefficients for Drag Coefficient
Typically the predicted CD and CL values within the measured Re and W space (interpolation) were in close agreement with the measured CD and CL values. Correlation coefficients of 96-99% were typical.
Below in Tables 10A and 10B are the regression constants for each ball shown in FIGS. 14-17. Using these regression constants, the Drag and Lift coefficients can be calculated over the range of 3,000-5,000 rpm spin rate and 120,000-180,000 Reynolds Number. FIGS. 14 to 17 were constructed for a very limited set of spin and Re conditions (3,500 or 4,500 rpm and varying the Re from 120,000 to 180,000), just to provide a few examples of the vast amount of data contained by the regression constants for lift and drag shown in Tables 10A and 10B. The constants can be used to represent the lift and drag coefficients at any point within the space of 3,000-5,000 rpm spin rate and 120,000-180,000 Reynolds Number.
TABLE 10A
Lift Coefficient regression equation coeficient
Ball Design# Orientation a4 a3 a5 a2 a1 a6
25-1 PH −0.030201 −3.98E−12 −8.44E−07 0.867344 1.37E−06 −0.087395
25-1 PFB −2.20008 −3.94E−12 −4.28E−06 2.186681 1.61E−06 −0.129568
28-1 PFB −1.23292 −6.02E−12 −3.02E−06 1.722214 2.26E−06 −0.177147
28-1 PH −0.88888 −4.65E−12 −3.49E−06 1.496342 2.15E−06 −0.22382
Polara 2p 4/08 PH −0.572601 −2.02E−11 −6.63E−06 1.303124 6.1E−06 −0.231079
Polara 2p 4/08 PFB −1.396513 −7.39E−12 −2.82E−06 1.612026 2.34E−06 −0.140899
Titleist ProV1 na −0.996621 −4.01E−12 −1.83E−06 1.251743 1.08E−06 0.018157
2-9-121909 PFB −0.564838 −2.73E−12 8.44E−07 0.592334 1.78E−07 0.161622
2-9-121909 PH −3.198559 −8.57E−12 −8.56E−06 2.945159 3.57E−06 −0.349143
TopFlite XL-Str NA −0.551398 1.48E−12 1.76E−06 0.61879 −1.08E−06 0.222013
TABLE 10B
Drag Coefficient regression equation coeficient
Ball Design# Orientation b4 b3 b5 b2 bl b6
25-1 PH 0.369982 −3.16E−12 −1.81E−07 0.278718 9.28E−07 0.139166
25-1 PFB −0.149176 −1.64E−12 3.04E−07 0.66705 5.35E−07 0.126985
28-1 PFB 0.431796 −1.62E−12 8.56E−07 0.25899 2.76E−07 0.200928
28-1 PH 0.84062 −2.23E−12 8.84E−07 −0.135614 4.23E−07 0.226051
Polara 2p 4/08 PH −1.086276 4.01E−12 −2.33E−06 1.194892 −2.7E−07 0.157838
Polara 2p 4/08 PFB −0.620696 −3.52E−12 −1.3E−06 0.965054 1.2E−06 0.043268
Titleist ProV1 na −0.632946 2.37E−12 7.04E−07 0.761151 −7.41E−07 0.195108
2-9-121909 PFB −0.822987 1.57E−13 2.61E−06 0.509 −4.46E−07 0.224937
2-9-121909 PH 2.145845 −3.66E−12 −8.88E−07 −0.110029 1.14E−06 0.130302
TopFlite XL-Str NA −0.373608 −1.38E−12 1.85E−07 0.663666 3.5E−07 0.14574
As can be determined from FIGS. 14 to 17, the lift coefficient for balls 25-1, 28-1 and 2-9 in a pole horizontal (PH) orientation is between 0.10 and 0.14 at a Reynolds number (Re) of 180,000 and a spin rate of 3,500 rpm, and between 0.14 and 0.20 at a Re of 120,000 and spin rate of 3,500, which is less than the CL of the other three tested balls (Polara 2p 0408 PH and PFB, Titleist ProV1 and TopFlite XL random orientation). The lift coefficient or CL of the 28-1, 25-1 and 2-9 balls in a PH orientation at a spin rate of 4,500 rpm is between 0.13 and 0.16 at an Re of 180,000 and between 0.17 and 0.25 at an Re of 120,000, as seen in FIG. 15. Drag Coefficients (CD) for the 28-1, 2-9 and 25-1 balls in PH orientation at a spin rate of 3,500 rpm are between 0.23 and 0.26 at an Re of 180,000 and between about 0.24 and 0.27 at an Re of 120,000 as illustrated in FIG. 16. CDs for the same balls at a spin rate of 4,500 rpm (FIG. 17) are about 0.28 to 0.29 at an Re of 120,000 and about 0.23 to 0.26 at an Re of 180,000.
Under typical slice conditions, with spin rates of 3,000 rpm or greater, the 2-9, 25-1, 28-1 in PH orientation and the Polara 2p in PFB orientation exhibit lower lift coefficients than the commercial balls: ProV1 and TopFlite XL Straight. Lower lift coefficients translate into lower trajectory for straight shots and less dispersion for slice shots. Balls with dimple patterns 2-9, 25-1, 28-1 in PH orientation have approximately 10-40% lower lift coefficients than the ProV1 and TopFlite XL Straight under Re and spin conditions characteristics of slice shots.
Tables 11-13 are the Trackman™ Report from the Robot Test. The robot was set up to hit a slice shot with a club path of approximately 7 degrees outside-in and a slightly opened club face. The club speed was approximately 98-100 mph, initial ball spin ranged from about 3,800-5,200 rpm depending on ball construction and the spin axis was approximately 13-21 degrees.
TABLE 11
Vert. Horiz.
Club Attack Club Swing Swing Dyn. Face
Shot Ball ID w Speed Angle Path Plane Plane Loft Angle
No Orientation ball Design orient [mph] [deg] [deg] [deg] [deg] [deg] [deg]
153 903PH 2-9 H 95.8 −6.1 −6.8 55.7 −11.0 10.5 −4.6
156 902PH 2-9 H 95.1 −6.6 −6.9 55.9 −11.4 10.7 −3.3
158 908PH 2-9 H 99.1 −6.1 −7.0 56.7 −11.0 10.5 −3.7
173 908H 2-9 H 101.9 −6.5 −7.3 56.7 −11.6 10.2 −4.2
175 907H 2-9 H 99.7 −5.5 −7.6 56.4 −11.2 10.4 −3.5
179 902H 2-9 H 96.7 −5.6 −6.5 56.9 −10.2 10.3 −4.4
185 907H 2-9 H 98.7
191 908H 2-9 H 98.2 −5.9 −7.7 54.9 −11.8 9.8 −3.7
155 904POP 2-9 POP 96.8 −5.7 −7.6 55.6 −11.5 10.2 −4.0
157 906POP 2-9 POP 99.2 −6.0 −7.7 55.4 −11.8 10.6 −4.6
159 905POP 2-9 POP 98.9 −5.6 −7.7 55.5 −11.5 10.3 −5.0
177 902POP 2-9 POP 98.8 −5.2 −6.8 57.3 −10.1 10.1 −3.9
178 906POP 2-9 POP 99.4 −6.0 −7.6 55.0 −11.8 10.3 −3.7
187 901POP 2-9 POP 98.5 −5.9 −7.8 55.3 −11.8 10.2 −2.7
188 906POP 2-9 POP 101.1 −6.4 −7.4 54.0 −12.1 10.2 −4.5
196 904POP 2-9 POP
142 505PH 25-1 H 100.1 −6.6 −7.7 54.4 −12.5 10.9 −4.0
143 502PH 25-1 H
145 506PH 25-1 H 100.3 −5.6 −8.0 55.8 −11.8 10.7 −3.4
149 501PH 25-1 H 98.9 −5.7 −7.5 56.2 −11.3 10.3 −4.9
160 502H 25-1 H 100.0 −6.0 −7.7 55.2 −11.8 10.7 −4.1
163 506H 25-1 H
165 501H 25-1 H 99.0 −5.7 −7.8 55.9 −11.7 10.1 −4.7
170 505H 25-1 H 100.7 −5.3 −7.9 55.7 −11.5 10.2 −4.3
184 506H 25-1 H 98.8 −5.6 −7.7 55.6 −11.5 10.3 −3.3
186 502H 25-1 H 99.1 −5.7 −7.9 54.7 −11.9 10.4 −4.1
193 502H 25-1 H 98.7 −5.8 −7.5 55.0 −11.6 10.0 −4.3
197 501PH 25-1 H
224 516H 25-1 H 99.0 −5.7 −7.6 55.4 −11.5 10.5 −4.4
192 503PFB 25-1 PFB 99.6 −5.7 −7.9 54.6 −11.9 10.3 −4.6
141 503POP 25-1 POP 98.9 −5.8 −7.7 56.2 −11.6 11.0 −3.1
144 505POP 25-1 POP 98.8 −5.7 −7.8 55.8 −11.7 11.1 −3.3
150 508POP 25-1 POP 98.8 −5.6 −7.9 56.3 −11.6 10.3 −3.1
151 507POP 25-1 POP 98.9 −5.7 −7.8 55.9 −11.7 11.2 −3.3
161 508POP 25-1 POP 99.5 −5.5 −7.9 54.8 −11.8 10.1 −4.3
162 507POP 25-1 POP 99.1 −5.5 −7.6 55.4 −11.4 10.7 −4.2
166 504POP 25-1 POP 99.0 −5.6 −7.8 55.9 −11.6 10.9 −3.5
171 503POP 25-1 POP 99.0 −5.7 −7.8 56.3 −11.6 10.9 −4.1
182 504P 25-1 POP 98.9 −5.8 −7.8 55.3 −11.8 10.5 −3.4
183 507POP 25-1 POP 98.9 −5.7 −7.8 55.8 −11.7 10.2 −3.5
189 508POP 25-1 POP 99.1 −5.7 −7.5 54.7 −11.6 10.7 −3.3
169 802F 28-1 F 98.3 −5.1 −8.2 56.4 −11.6 10.6 −3.4
231 814F 28-1 F 98.9 −5.7 −7.8 56.0 −11.7 10.9 −3.5
146 803PH 28-1 H 99.2 −5.8 −7.9 56.0 −11.8 10.7 −3.2
167 803H 28-1 H 99.0 −5.4 −7.6 56.0 −11.3 10.4 −3.8
195 803H 28-1 H 98.8 −5.6 −7.7 55.6 −11.5 8.8 −4.0
199 812H 28-1 H 98.8 −6.2 −7.4 54.5 −11.8 9.4 −3.8
208 815H 28-1 H 98.8 −5.9 −7.5 54.9 −11.7 10.5 −4.0
233 811H 28-1 H 99.3 −6.1 −7.4 55.8 −11.6 11.1 −3.6
194 801PFB 28-1 PFB 98.7 −5.5 −7.9 55.0 −11.7 10.4 −4.0
147 802POP 28-1 POP
148 801POP 28-1 POP 98.8 −5.7 −7.9 56.0 −11.8 10.9 −3.4
164 801POP 28-1 POP 97.6 −6.5 −7.1 55.0 −11.6 10.8 −4.0
181 802POP 28-1 POP 98.5 −5.2 −8.0 56.2 −11.5 10.4 −2.7
205 V140 Titleist ProV1 na 98.8 −5.7 −7.5 54.7 −11.6 10.2 −4.4
212 V92 Titleist ProV1 na 98.8 −5.6 −7.7 54.7 −11.6 10.4 −4.5
219 V95 Titleist ProV1 na 99.3 −5.8 −7.5 54.4 −11.7 10.4 −4.6
237 V76 Titleist ProV1 na 98.9 −6.1 −8.1 54.9 −12.4 10.6 −3.5
241 V180 Titleist ProV1 na 97.6 −5.7 −7.0 56.5 −10.8 11.0 −4.4
243 V97 Titleist ProV1 na 99.3 −5.6 −7.8 56.1 −11.5 10.5 −4.2
198 224 TopFlite XL Straight na 99.3 −6.3 −7.0 53.4 −11.7 10.3 −4.7
207 225 TopFlite XL Straight na 98.7 −6.1 −7.6 55.3 −11.8 10.4 −3.6
215 223 TopFlite XL Straight na 96.5 −5.2 −7.6 56.5 −11.0 10.4 −4.2
222 227 TopFlite XL Straight na 98.8 −6.2 −6.9 54.1 −11.4 10.2 −4.7
236 185 TopFlite XL Straight na 98.8 −4.6 −8.7 56.1 −11.8 10.2 −3.3
248 222 TopFlite XL Straight na 98.9 −7.0 −6.5 56.1 −11.2 10.8 −3.6
TABLE 12
Ball Smash Vert. Horiz. Drag Lift Spin Spin Max Max Max
Shot Speed factor Angle Angle Coef. Coef. Rate Axis Height x Height y Height z
No [mph] [] [deg] [deg] [] [] [rpm] [yds] [yds] [yds] [yds]
153 142.8 1.49 7.6 5.0L 0.26 0.19 4212 21.0 129.9 17.6 0.5L
156 141.2 1.48 8.0 4.0L 0.24 0.16 4048 12.6 129.4 15.9 3.9L
158 141.8 1.43 7.8 4.3L 0.23 0.15 4013 16.1 132.1 15.7 3.5L
173 143.3 1.41 7.4 4.6L 0.27 0.21 4105 19.7 132.6 20.3 2.6R
175 142.0 1.42 7.4 4.4L 0.26 0.18 4459 16.9 132.3 18.1 0.1L
179 141.4 1.46 7.5 5.1L 0.24 0.16 4017 19.3 128.3 15.2 3.0L
185 141.3 1.43 7.7 3.9L 0.25 0.16 3922 16.4 126.7 15.1 2.2L
191 142.5 1.45 7.3 4.3L 0.26 0.17 3899 18.4 131.4 17.1 0.8R
155 143.0 1.48 7.1 4.7L 0.29 0.22 4472 22.1 128.2 19.7 4.9R
157 143.0 1.44 7.9 5.1L 0.28 0.20 3943 22.4 127.6 19.8 3.6R
159 142.4 1.44 7.5 5.5L 0.26 0.21 4063 23.0 130.0 19.7 3.9R
177 142.6 1.44 7.2 4.5L 0.29 0.22 4246 16.9 132.5 22.2 3.5R
178 143.6 1.44 7.3 4.5L 0.30 0.22 4410 23.6 127.8 19.6 6.3R
187 142.0 1.44 7.5 3.6L 0.28 0.21 4142 14.9 136.7 21.9 2.2R
188 142.8 1.41 7.4 5.0L 0.29 0.22 3974 21.2 132.5 22.7 6.4R
196 141.8 7.2 4.4L 0.28 0.23 4190 22.0 131.6 22.5 9.9R
142 144.7 1.45 7.5 4.9L 0.26 0.15 5019 16.0 124.4 14.7 4.1L
143 146.5 7.4 4.3L 0.26 0.16 4903 16.4 127.4 15.7 1.8L
145 146.0 1.46 7.4 4.4L 0.25 0.16 5020 18.7 128.3 15.5 1.8L
149 146.6 1.48 7.2 5.5L 0.27 0.19 4929 16.9 137.1 20.8 0.7L
160 145.5 1.46 7.7 4.9L 0.26 0.14 4644 13.5 122.2 14.3 5.5L
163 145.8 7.1 4.6L 0.25 0.15 4930 16.9 125.6 13.9 3.4L
165 147.0 1.49 7.1 5.4L 0.26 0.18 4717 17.6 139.0 19.7 2.1L
170 146.2 1.45 7.0 5.2L 0.26 0.16 4962 16.2 127.6 15.0 3.7L
184 145.7 1.47 7.0 4.5L 0.27 0.15 4926 15.9 122.4 14.0 2.9L
186 146.1 1.47 7.3 5.0L 0.26 0.14 4628 11.2 119.9 13.4 6.5L
193 146.8 1.49 6.8 5.0L 0.29 0.18 4775 17.7 130.0 17.0 2.1L
197 145.6 7.1 4.9L 0.26 0.17 4612 16.0 135.3 18.4 0.5L
224 146.6 1.48 7.2 5.4L 0.29 0.16 4816 16.5 125.4 15.7 4.7L
192 145.7 1.46 7.0 5.3L 0.29 0.20 4834 16.5 133.2 21.4 1.8R
141 146.9 1.48 7.5 4.1L 0.31 0.21 5169 18.0 132.5 22.1 3.8R
144 145.9 1.48 7.8 4.2L 0.28 0.20 4897 17.6 133.5 21.5 4.0R
150 147.0 1.49 7.1 4.2L 0.30 0.21 4938 14.5 133.5 22.0 1.5R
151 146.1 1.48 7.8 4.4L 0.28 0.19 5122 14.7 134.7 21.2 0.4L
161 146.0 1.47 6.9 5.1L 0.28 0.20 4813 21.3 133.7 19.3 2.4R
162 146.4 1.48 7.3 5.0L 0.29 0.21 5020 17.2 134.5 21.4 1.0R
166 146.8 1.48 7.6 4.6L 0.30 0.20 4993 11.8 133.3 21.6 0.5L
171 147.1 1.48 7.6 4.9L 0.29 0.21 5069 18.9 133.7 21.8 2.9R
182 146.3 1.48 7.3 4.3L 0.28 0.20 4779 19.5 135.3 21.3 6.8R
183 146.1 1.48 7.1 4.3L 0.30 0.21 4871 13.9 136.3 22.8 1.6R
189 145.5 1.47 7.6 4.4L 0.29 0.19 4573 12.5 129.4 19.4 1.9L
169 145.8 1.48 6.9 4.7L 0.31 0.21 5582 20.8 129.5 20.2 5.6R
231 147.2 1.49 7.4 4.5L 0.32 0.22 5353 15.2 130.3 23.5 1.8R
146 146.7 1.48 7.5 4.2L 0.27 0.15 4996 15.1 120.5 14.1 3.5L
167 146.1 1.48 7.3 4.8L 0.28 0.14 4786 16.7 114.3 12.8 4.2L
195 145.6 1.47 7.4 4.5L 0.28 0.14 4612 17.0 109.2 11.8 3.7L
199 145.5 1.47 8.0 4.3L 0.29 0.14 4513 9.8 114.1 13.8 5.6L
208 146.6 1.48 7.3 4.9L 0.29 0.15 4960 12.6 117.0 14.0 5.5L
233 146.5 1.48 7.6 4.5L 0.30 0.16 5181 16.7 119.7 15.1 3.1L
194 146.8 1.49 7.0 4.9L 0.32 0.22 5172 14.7 129.9 23.1 1.4R
147 146.8 7.2 4.0L 0.30 0.19 5045 15.0 132.8 20.3 1.2R
148 146.8 1.49 7.6 4.3L 0.29 0.20 4915 19.8 133.9 21.2 5.5R
164 146.6 1.50 7.5 4.6L 0.28 0.18 4812 15.8 134.9 19.1 0.0R
181 145.4 1.48 7.2 3.8L 0.28 0.19 4748 16.9 131.9 18.8 2.4R
205 144.9 1.47 7.3 5.0L 0.27 0.22 4388 16.6 143.1 26.0 5.2R
212 145.3 1.47 7.3 5.1L 0.28 0.22 4618 15.1 142.7 26.6 3.3R
219 145.1 1.46 7.3 5.2L 0.30 0.23 4534 14.1 139.0 26.4 0.3R
237 145.9 1.48 7.7 4.3L 0.29 0.23 4400 14.3 140.8 28.1 5.5R
241 144.7 1.48 7.9 5.0L 0.29 0.22 4546 18.4 141.3 27.0 8.5R
243 145.4 1.46 7.3 5.0L 0.30 0.24 4834 17.8 139.3 28.0 8.0R
198 145.0 1.46 7.6 5.1L 0.28 0.22 3925 16.4 139.6 26.1 3.3R
207 145.4 1.47 7.6 4.3L 0.29 0.21 4254 14.6 138.9 24.7 4.4R
215 144.5 1.50 7.4 4.9L 0.30 0.23 4412 17.5 139.7 26.4 6.0R
222 145.3 1.47 7.3 5.2L 0.29 0.23 4362 13.3 140.0 27.3 1.0R
236 145.0 1.47 7.4 4.5L 0.29 0.23 4523 13.0 142.9 27.8 4.2R
248 145.3 1.47 7.9 4.1L 0.30 0.24 4424 12.0 138.7 31.0 4.5R
TABLE 13
Spin Vert. Ball Spin Flight
Shot Length X Side Height Rate Time Length X Side Angle Speed Rate Time
No [yds] [yds] [yds] [yds] [rpm] [s] [yds] [yds] [yds] [deg] [mph] [rpm] [s]
153 198.4 198.3 5.6R −0.2 5.13 198.1 198.0 5.5R −31.3 59.7 5.12
156 203.3 203.3 1.1L −0.3 5.05 202.8 202.8 1.2L −27.4 60.0 5.02
158 204.4 204.4 1.7L −0.2 3180 5.08 204.1 204.1 1.7L −27.7 59.5 3182 5.07
173 197.6 197.3 10.7R −0.3 3292 5.35 197.2 196.9 10.7R −36.1 59.2 3295 5.33
175 197.3 197.2 6.7R −0.2 5.30 197.0 196.9 6.6R −33.2 56.9 5.28
179 201.6 201.6 0.7R −0.2 4.90 201.2 201.2 0.7R −26.1 63.2 4.89
185 194.3 194.3 0.4R −0.1 4.88 194.1 194.1 0.4R −28.2 60.2 4.87
191 190.6 190.4 8.3R −0.1 3076 5.19 190.6 190.4 8.3R −35.3 54.4 3076 5.19
155 189.7 188.8 18.3R 0.2 3714 5.21 190.0 189.1 18.3R −36.1 58.8 3713 5.23
157 191.1 190.2 17.6R −0.3 3164 5.18 190.7 189.9 17.5R −35.3 60.2 3166 5.17
159 190.1 189.0 20.2R 0.0 3247 5.17 190.1 189.0 20.2R −36.6 60.5 3247 5.17
177 191.7 191.2 14.6R −0.5 3397 5.53 191.2 190.6 14.5R −41.0 58.3 3401 5.50
178 190.6 189.4 21.2R 0.1 3598 5.21 190.8 189.6 21.3R −35.5 58.5 3597 5.21
187 198.5 198.2 10.8R −0.4 3262 5.72 198.1 197.8 10.7R −40.7 54.1 3264 5.70
188 187.2 185.9 22.1R 0.0 3116 5.65 187.2 185.9 22.1R −43.9 53.8 3115 5.65
196 186.2 184.0 28.2R 0.2 5.65 186.4 184.2 28.3R −43.3 54.3 5.66
142 192.7 192.7 1.4L −0.2 4.80 192.3 192.3 1.4L −27.0 59.7 4.78
143 195.0 194.9 4.0R −0.3 4.91 194.4 194.4 3.9R −28.8 59.6 4.89
145 196.9 196.8 2.8R −0.2 4.93 196.4 196.4 2.7R −28.1 59.4 4.91
149 199.0 198.9 6.8R −0.3 3934 5.56 198.6 198.5 6.8R −37.7 56.4 3936 5.54
160 192.6 192.6 4.9L −0.2 3702 4.68 192.3 192.2 4.9L −25.6 61.8 3704 4.66
163 196.3 196.3 0.1L −0.2 4.74 195.9 195.9 0.2L −25.2 60.6 4.73
165 203.3 203.3 2.3R −0.5 3709 5.60 202.7 202.7 2.3R −36.1 53.7 3712 5.57
170 196.4 196.4 0.5R −0.2 3956 4.85 196.0 196.0 0.5R −27.3 60.5 3958 4.83
184 188.8 188.8 0.3R −0.2 4.68 188.5 188.5 0.3R −26.7 58.5 4.67
186 189.2 189.1 7.2L −0.3 3703 4.50 188.6 188.4 7.3L −25.0 62.4 3707 4.48
193 192.8 192.8 1.3R −0.2 5.19 192.5 192.5 1.2R −33.3 53.4 5.18
197 190.8 190.7 6.8R −0.2 3587 5.54 190.6 190.4 6.7R −39.4 49.9 3588 5.53
224 189.9 189.8 4.2L −0.2 3777 5.00 189.5 189.5 4.2L −30.9 53.1 3779 4.98
192 187.0 186.3 16.0R −0.5 3777 5.70 186.5 185.8 15.8R −43.2 50.7 3781 5.67
141 195.0 194.3 16.7R −0.2 4093 5.63 194.8 194.1 16.6R −38.6 55.5 4095 5.62
144 196.4 195.5 19.0R 0.4 3950 5.58 197.0 196.1 19.1R −37.0 54.4 3948 5.60
150 198.0 197.6 12.6R −0.5 3920 5.58 197.4 197.0 12.5R −37.6 56.8 3925 5.55
151 201.0 200.8 8.1R −0.4 4011 5.65 200.4 200.3 8.0R −36.6 53.6 4016 5.62
161 196.3 195.8 14.7R −0.3 3854 5.38 195.9 195.3 14.6R −35.2 56.8 3856 5.36
162 200.6 200.3 10.4R −0.4 4008 5.52 200.0 199.8 10.3R −36.3 58.0 4011 5.50
166 196.2 195.9 9.7R −0.3 3934 5.62 195.8 195.6 9.6R −38.4 53.4 3936 5.60
171 200.0 199.4 16.0R −0.3 4006 5.54 199.7 199.0 16.0R −37.1 56.3 4009 5.53
182 192.9 191.3 25.5R 0.4 3714 5.69 193.4 191.6 25.7R −40.1 51.7 3710 5.72
183 193.3 192.9 12.9R −0.3 3829 5.79 193.0 192.6 12.8R −42.8 53.8 3831 5.77
189 189.4 189.3 4.9R −0.1 3545 5.41 189.3 189.2 4.9R −38.1 49.9 3546 5.40
169 188.3 186.9 22.4R 0.4 4376 5.46 188.8 187.4 22.6R −37.7 52.7 4371 5.48
231 183.7 183.3 12.7R −0.2 4123 5.91 183.5 183.1 12.7R −46.6 46.7 4124 5.90
146 188.9 188.9 1.6L −0.2 3978 4.55 188.4 188.4 1.7L −26.2 61.5 3981 4.54
167 178.8 178.7 3.1L 0.2 3846 4.29 179.1 179.1 3.1L −25.3 61.2 3844 4.30
195 171.5 171.5 1.5L 0.1 4.10 171.7 171.7 1.5L −24.5 60.5 4.11
199 176.1 175.9 8.1L 0.0 3524 4.49 176.0 175.8 8.1L −28.8 54.9 3524 4.49
208 178.2 178.1 6.1L −0.1 3935 4.56 178.2 178.1 6.1L −29.6 55.2 3935 4.56
233 180.1 180.1 1.0L 0.0 4.75 180.1 180.1 1.0L −31.9 53.0 4.75
194 185.0 184.6 12.4R −0.3 4020 5.77 184.7 184.3 12.3R −44.2 49.7 4023 5.76
147 197.9 197.5 11.8R −0.6 3957 5.57 197.1 196.7 11.6R −36.2 53.7 3964 5.53
148 195.7 194.5 21.9R 0.2 3655 5.58 195.9 194.7 22.0R −38.6 53.2 3652 5.59
164 200.5 200.1 11.7R −0.4 3760 5.51 199.8 199.5 11.6R −34.9 53.1 3764 5.48
181 193.3 192.7 14.9R −0.4 3725 5.41 192.8 192.2 14.8R −36.1 52.8 3728 5.39
205 198.6 197.6 20.5R 1.6 6.30 200.1 199.0 20.8R −48.1 47.3 6.40
212 195.9 195.0 18.9R 1.3 3740 6.39 197.1 196.1 19.3R −47.9 47.8 3731 6.46
219 195.9 195.7 9.2R −0.3 3695 6.31 195.7 195.5 9.2R −46.9 48.9 3697 6.29
237 192.8 191.8 19.6R 5.4 3590 6.12 197.8 196.7 20.9R −48.5 49.9 3547 6.43
241 195.1 193.2 27.4R 0.2 3680 6.46 195.3 193.4 27.4R −49.8 48.3 3679 6.47
243 184.6 183.1 23.4R 7.8 6.02 191.1 189.4 25.4R −52.4 47.1 6.48
198 195.3 194.6 16.1R 0.0 3231 6.24 195.3 194.6 16.1R −47.0 50.0 3231 6.24
207 197.7 196.5 21.1R 0.2 6.24 197.9 196.8 21.1R −43.5 48.4 6.25
215 194.8 193.5 22.2R −0.6 3582 6.32 194.3 193.1 22.0R −48.6 50.8 3585 6.29
222 195.7 195.3 12.5R −0.4 3564 6.41 195.3 195.0 12.4R −48.4 49.3 3566 6.39
236 199.5 198.4 20.6R 0.5 3622 6.51 199.9 198.9 20.8R −48.0 48.4 3618 6.54
248 191.2 190.3 18.5R 0.1 3613 6.60 191.3 190.4 18.5R −51.4 50.9 3612 6.61
The non-conforming golf balls described above which have dimple patterns including areas of less dimple volume along at least part of a band around the equator and more dimple volume in the polar regions have a large enough moment of inertia (MOI) difference between the poles horizontal (PH) or maximum orientation and other orientations that the ball has a preferred spin axis extending through the poles of the ball. As described above, this preferred spin axis helps to prevent or reduce the amount of hook or slice dispersion when the ball is hit in a way which would normally produce hooking or slicing in a conventional, symmetrically designed golf ball. This reduction in dispersion is illustrated for the embodiments described above in FIG. 10 and for some of the embodiments in FIG. 12. Although a preferred spin axis may alternatively be established by placing high and low density materials in specific locations within the core or intermediate layers of a golf ball, such construction adds cost and complexity to the golf ball manufacturing process. In contrast, balls having the different dimple patterns described above can be readily manufactured by suitable design of the hemispherical mold cavities, for example as illustrated in FIG. 3 for a 2-9 ball.
Although the illustrated embodiments all have reduced dimple volume in a band around the equator as compared to the dimple volume in the polar regions, other dimple patterns which generate preferred spin axis may be used in alternative embodiments to achieve similar results. For example, the low volume dimples do not have to be located in a continuous band around the ball's equator. The low volume dimples could be interspersed with larger volume dimples about the equator, the band could be wider in some parts of the circumference than others, part of the band could be dimple-less around part or all of the circumference, or there may be no dimples at all around the equatorial region. Another embodiment may comprise a dimple pattern having two or more regions of lower or zero dimple volume on the surface of the ball, with the regions being somewhat co-planar. This also creates a preferred spin axis. In one example, if the two areas of lower volume dimples are placed opposite one another on the ball, then a dumbbell-like weight distribution is created. This results in a ball with a preferred spin axis equal to the orientation of the ball when rotating end-over-end with the “dumbbell” areas.
Although the dimples in the embodiments illustrated in FIGS. 1 to 8 and described above are all circular dimples, it will be understood that there is a wide variety of types and construction of dimples, including non-circular dimples, such as those described in U.S. Pat. No. 6,409,615, hexagonal dimples, dimples formed of a tubular lattice structure, such as those described in U.S. Pat. No. 6,290,615, as well as more conventional dimple types. It will also be understood that any of these types of dimples can be used in conjunction with the embodiments described herein. As such, the term “dimple” as used in this description and the claims that follow is intended to refer to and include any type or shape of dimple or dimple construction, unless otherwise specifically indicated.
As noted above a golf ball's flight trajectory depends on a number of factors, which can be broken down into two major categories: 1) the mechanical interaction between the ball and club and 2) the golf ball's aerodynamic performance.
The ball-club impact (dynamic mechanical interaction) can be thought of as the event that specifies the initial conditions for the aerodynamic flight of the golf ball to follow. Thus it is common when describing the performance of one golf ball versus the other to first describe in detail the specific club used to impact each ball and then to describe the resulting initial conditions of the golf ball flight at the instant the ball leaves the club face, using the terms “vertical launch angle”, “horizontal launch angle”, “initial velocity”, “initial spin”, and “initial spin axis”. Once the ball leaves the face of the club, it is then these initial conditions plus the aerodynamics of the golf ball, its weight, and its size, and the environmental conditions that determine the flight path of the golf ball. The aerodynamics of a golf ball are highly dependent on the ball's dimple pattern and individual dimple characteristics as well as the ball's speed, spin rate, size and mass.
A number of math models have been developed to simulate the trajectory of a golf ball, including those published by T. Mizota, et al in Science and Golf IV Proceedings of the World Scientific Congress of Golf and by A, J. Smits and D. R. Smith in Science and Golf II Proceedings of the World Scientific Congress of Golf These models both calculate the ball's trajectory as a function of the aerodynamic factors and the initial conditions include the ball-club impact factors specified above.
The difference in aerodynamic forces from one commercially available ball to another are relatively small compared to the Polara Ultimate Straight golf ball made by Aero-X Golf, Inc and sold under the Polara Golf Brand, which includes dimple patterns such as those described above in connection with FIGS. 1 to 17. Thus, the Polara Ultimate Straight dimple pattern can have shallow truncated dimples around the equator and on each pole has deep spherical and tiny spherical dimples. When the Polara Ultimate Straight golf ball is flying in its poles-horizontal (PH) orientation, the ball exhibits approximately 30-50% less lift and 10-20% less drag than a normal golf ball similar to the results described above. As a result, the Polara Ultimate Straight dimple pattern and dimple geometry can cause the ball to have a very low trajectory and have a very low maximum height. The low flight will result in the Polara Ultimate Straight ball being airborne for less time than for a ball with the same construction but with a dimple pattern that is typical of a normal symmetrical dimple pattern golf ball. The main reason for this performance is that under typical conditions the Polara Ultimate Straight golf ball usually has considerably lower lift than a normal golf ball. This lower lift property can result in the Polara golf ball not flying as long as a normal golf ball.
FIGS. 29 to 55 illustrate embodiments of a golf ball with a symmetrical dimple pattern that achieves low lift right after impact when the velocity and spin are relatively high and that can be included in the kits described herein in the kits described herein. Any of these balls may be used in place of the asymmetrical balls in the kit with a higher lofted driver as described above, with similar effects. In particular, the embodiments described below achieve relatively low lift even when the spin rate is high, such as that imparted when a golfer slices the golf ball, e.g., 3500 rpm or higher. In the embodiments described below, the lift coefficient after impact can be as low as about 0.18 or less, and even less than 0.15 under such circumstances. In addition, the lift can be significantly lower than conventional golf balls at the end of flight, i.e., when the speed and spin are lower. For example, the lift coefficient can be less than 0.20 when the ball is nearing the end of flight.
Conventional golf balls have been designed for low initial drag and high lift toward the end of flight in order to increase distance. For example, U.S. Pat. No. 6,224,499 to Ogg teaches and claims a lift coefficient greater than 0.18 at a Reynolds number (Re) of 70,000 and a spin of 2000 rpm, and a drag coefficient less than 0.232 at a Re of 180,000 and a spin of 3000 rpm. One of skill in the art will understand that and Re of 70,000 and spin of 2000 rpm are industry standard parameters for describing the end of flight. Similarly, one of skill in the art will understand that a Re of greater than about 160,000, e.g., about 180,000, and a spin of 3000 rpm are industry standard parameters for describing the beginning of flight for a straight shot with only back spin.
The lift (CL) and drag coefficients (CD) vary by golf ball design and are generally a function of the velocity and spin rate of the golf ball. For a spherically symmetrical golf ball the lift and drag coefficients are for the most part independent of the golf ball orientation. The maximum height a golf ball achieves during flight is directly related to the lift force generated by the spinning golf ball while the direction that the golf ball takes, specifically how straight a golf ball flies, is related to several factors, some of which include spin rate and spin axis orientation of the golf ball in relation to the golf ball's direction of flight. Further, the spin rate and spin axis are important in specifying the direction and magnitude of the lift force vector.
The lift force vector is a major factor in controlling the golf ball flight path in the x, y, and z directions. Additionally, the total lift force a golf ball generates during flight depends on several factors, including spin rate, velocity of the ball relative to the surrounding air and the surface characteristics of the golf ball.
For a straight shot, the spin axis is generally parallel to the ground and orthogonal to the direction the ball is traveling and the ball rotates with perfect backspin. In this situation, the spin axis is 0 degrees. But if the ball is not struck perfectly, then the spin axis will be either positive (hook) or negative (slice). When the spin axis is negative, indicating a slice, the spin rate of the ball increases. Similarly, when the spin axis is positive, the spin rate decreases initially but then remains essentially constant with increasing spin axis.
The increased spin imparted when the ball is sliced, increases the lift coefficient (CL). This increases the lift force in a direction that is orthogonal to the spin axis. In other words, when the ball is sliced, the resulting increased spin produces an increased lift force that acts to “pull” the ball to the right. The more negative the spin axis, the greater the portion of the lift force acting to the right, and the greater the slice.
Thus, in order to reduce this slice effect, the ball must be designed to generate a relatively lower lift force at the greater spin rates generated when the ball is sliced.
Referring to FIG. 29, there is shown golf ball 100, which provides a visual description of one embodiment of a dimple pattern that achieves such low initial lift at high spin rates. FIG. 29 is a computer generated picture of dimple pattern 173. As shown in FIG. 29, golf ball 100 has an outer surface 105, which has a plurality of dissimilar dimple types arranged in a cuboctahedron configuration. In the example of FIG. 29, golf ball 100 has larger truncated dimples within square region 110 and smaller spherical dimples within triangular region 115 on the outer surface 105. The example of FIG. 29 and other embodiments are described in more detail below; however, as will be explained, in operation, dimple patterns configured in accordance with the embodiments described herein disturb the airflow in such a way as to provide a golf ball that exhibits low lift at the spin rates commonly seen with a slice shot as described above.
As can be seen, regions 110 and 115 stand out on the surface of ball 100 unlike conventional golf balls. This is because the dimples in each region are configured such that they have high visual contrast. This is achieved for example by including visually contrasting dimples in each area. For example, in one embodiment, flat, truncated dimples are included in region 110 while deeper, round or spherical dimples are included in region 115. Additionally, the radius of the dimples can also be different adding to the contrast.
But this contrast in dimples does not just produce a visually contrasting appearance; it also contributes to each region having a different aerodynamic effect. Thereby, disturbing air flow in such a manner as to produce low lift as described herein.
While conventional golf balls are often designed to achieve maximum distance by having low drag at high speed and high lift at low speed, when conventional golf balls are tested, including those claimed to be “straighter,” it can be seen that these balls had quite significant increases in lift coefficients (CL) at the spin rates normally associated with slice shots. Whereas balls configured in accordance with the embodiments described herein exhibit lower lift coefficients at the higher spin rates and thus do not slice as much.
A ball configured in accordance with the embodiments described herein and referred to as the B2 Prototype, which is a 2-piece Surlyn-covered golf ball with a polybutadiene rubber based core and dimple pattern “273”, and the TopFlite® XL Straight ball were hit with a Golf Labs robot using the same setup conditions so that the initial spin rates were about 3,400-3,500 rpm at a Reynolds Number of about 170,000. The spin rate and Re conditions near the end of the trajectory were about 2,900 to 3,200 rpm at a Reynolds Number of about 80,000. The spin rates and ball trajectories were obtained using a 3-radar unit Trackman™ Net System. FIG. 32 illustrates the full trajectory spin rate versus Reynolds Number for the shots and balls described above.
The B2 prototype ball had dimple pattern design 273, shown in FIG. 31. Dimple pattern design 273 is based on a cuboctahedron layout and has a total of 504 dimples. This is the inverse of pattern 173 since it has larger truncated dimples within triangular regions 115 and smaller spherical dimples within square regions or areas 110 on the outer surface of the ball. A spherical truncated dimple is a dimple which has a spherical side wall and a flat inner end, as seen in the triangular regions of FIG. 4. The dimple patterns 173 and 273, and alternatives, are described in more detail in Tables 5 to 11 of the '028 application.
FIG. 33 illustrates the CL versus Re for the same shots shown in FIG. 32; TopFlite® XL Straight and the B2 prototype golf ball which was configured in accordance with the systems and methods described herein. As can be seen, the B2 ball has a lower CL over the range of Re from about 75,000 to 170,000. Specifically, the CL for the B2 prototype never exceeds 0.27, whereas the CL for the TopFlite® XL Straight gets well above 0.27. Further, at a Re of about 165,000, the CL for the B2 prototype is about 0.16, whereas it is about 0.19 or above for the TopFlite® XL Straight.
FIGS. 32 and 33 together illustrate that the B2 ball with dimple pattern 273 exhibits significantly less lift force at spin rates that are associated with slices. As a result, the B2 prototype will be much straighter, i.e., will exhibit a much lower carry dispersion. For example, a ball configured in accordance with the embodiments described herein can have a CL of less than about 0.22 at a spin rate of 3,200-3,500 rpm and over a range of Re from about 120,000 to 180,000. For example, in certain embodiments, the CL can be less than 0.18 at 3500 rpm for Re values above about 155,000.
This is illustrated in the graphs of FIGS. 47-51, which show the lift coefficient versus Reynolds Number at spin rates of 3,000 rpm, 3,500 rpm, 4,000 rpm, 4,500 rpm and 5,000 rpm, respectively, for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern, and 273 dimple pattern. To obtain the regression data shown in FIGS. 23-28, a Trackman™ Net System™ consisting of 3 radar units was used to track the trajectory of a golf ball that was struck by a Golf Labs robot equipped with various golf clubs. The robot was setup to hit a straight shot with various combinations of initial spin and velocity. A wind gauge was used to measure the wind speed at approximately 20 ft elevation near the robot location. The Trackman™ Net System™ measured trajectory data (x, y, z location vs. time) were then used to calculate the lift coefficients (CL) and drag coefficients (CD) as a function of measured time-dependent quantities including Reynolds Number, Ball Spin Rate, and Dimensionless Spin Parameter. Each golf ball model or design was tested under a range of velocity and spin conditions that included 3,000-5,000 rpm spin rate and 120,000-180,000 Reynolds Number. It will be understood that the Reynolds Number range of 150,000-180,000 covers the initial ball velocities typical for most recreational golfers, who have club head speeds of 85-100 mph. A 5-term multivariable regression model was then created from the data for each ball designed in accordance with the embodiments described herein for the lift and drag coefficients as a function of Reynolds Number (Re) and Dimensionless Spin Parameter (W), i.e., as a function of Re, W, Rê2, Ŵ2, ReW, etc. Typically the predicted CD and CL values within the measured Re and W space (interpolation) were in close agreement with the measured CD and CL values. Correlation coefficients of >96% were typical.
Under typical slice conditions, with spin rates of 3,500 rpm or greater, the 173 and 273 dimple patterns exhibit lower lift coefficients than the other golf balls. Lower lift coefficients translate into lower trajectory for straight shots and less dispersion for slice shots. Balls with dimple patterns 173 and 273 have approximately 10% lower lift coefficients than the other golf balls under Re and spin conditions characteristics of slice shots. Robot tests show the lower lift coefficients result in at least 10% less dispersion for slice shots.
For example, referring again to FIG. 33, it can be seen that while the TopFlite® XL Straight is suppose to be a straighter ball, the data in the graph of FIG. 33 illustrates that the B2 prototype ball should in fact be much straighter based on its lower lift coefficient. The high CL for the TopFlite® XL Straight means that the TopFlite® XL Straight ball will create a larger lift force. When the spin axis is negative, this larger lift force will cause the TopFlite® XL Straight to go farther right increasing the dispersion for the TopFlite® XL Straight. This is illustrated in Table 14:
TABLE 14
Ball Dispersion, ft Distance, yds
TopFlite ® XL Straight 95.4 217.4
Ball 173 78.1 204.4
FIG. 34 shows that for the robot test shots shown in FIG. 32 the B2 ball has a lower CL throughout the flight time as compared to other conventional golf balls, such as the TopFlite® XL Straight. This lower CL throughout the flight of the ball translates in to a lower lift force exerted throughout the flight of the ball and thus a lower dispersion for a slice shot.
As noted above, conventional golf ball design attempts to increase distance, by decreasing drag immediately after impact. FIG. 35 shows the drag coefficient (CD) versus Re for the B2 and TopFlite® XL Straight shots shown in FIG. 5. As can be seen, the CD for the B2 ball is about the same as that for the TopFlite® XL Straight at higher Re. Again, these higher Re numbers would occur near impact. At lower Re, the CD for the B2 ball is significantly less than that of the TopFlite® XL Straight.
In FIG. 36 it can be seen that the CD curve for the B2 ball throughout the flight time actually has a negative inflection in the middle. Thus, the drag for the B2 ball will be less in the middle of the ball's flight as compared to the TopFlite XL Straight. It should also be noted that while the B2 does not carry quite as far as the TopFlite XL Straight, testing reveals that it actually roles farther and therefore the overall distance is comparable under many conditions. This makes sense of course because the lower CL for the B2 ball means that the B2 ball generates less lift and therefore does not fly as high, something that is also verified in testing. Because the B2 ball does not fly as high, it impacts the ground at a shallower angle, which results in increased role.
Returning to FIGS. 29 to 31, the outer surface 105 of golf ball 100 can include dimple patterns of Archimedean solids or Platonic solids by subdividing the outer surface 105 into patterns based on a truncated tetrahedron, truncated cube, truncated octahedron, truncated dodecahedron, truncated icosahedron, icosidodecahedron, rhombicuboctahedron, rhombicosidodecahedron, rhombitruncated cuboctahedron, rhombitruncated icosidodecahedron, snub cube, snub dodecahedron, cube, dodecahedron, icosahedrons, octahedron, tetrahedron, where each has at least two types of subdivided regions (A and B) and each type of region has its own dimple pattern and types of dimples that are different than those in the other type region or regions.
Furthermore, the different regions and dimple patterns within each region are arranged such that the golf ball 100 is spherically symmetrical as defined by the United States Golf Association (“USGA”) Symmetry Rules. It should be appreciated that golf ball 100 may be formed in any conventional manner such as, in one non-limiting example, to include two pieces having an inner core and an outer cover. In other non-limiting examples, the golf ball 100 may be formed of three, four or more pieces.
Tables 19 and 20 below list some examples of possible spherical polyhedron shapes which may be used for golf ball 100, including the cuboctahedron shape illustrated in FIGS. 29 to 31. The size and arrangement of dimples in different regions in the other examples in Tables 14 and 15 can be similar or identical to that of FIGS. 29 to 31.
TABLE 14
13 Archimedean Solids and 5 Platonic solids - relative surface areas for the polygonal patches
% % % % % %
surface surface surface surface surface surface
area area area area area area
for all for all for all Total per per per
Name of # of of the # of of the # of of the number single single single
Archimede Region Region Region Region Region B Region Region Region C Region of A B C
an solid A A shape A's B shape B's C shape C's Regions Region Region Region
truncated 30 triangles 17% 20 Hexagons 30% 12 decagons 53% 62 0.6% 1.5% 4.4%
icosidodeca
-hedron
Rhombicosi 20 triangles 15% 30 squares 51% 12 pentagons 35% 62 0.7% 1.7% 2.9%
dodeca-
hedron
snub 80 triangles 63% 12 Pentagons 37% 92 0.8% 3.1%
dodeca-
hedron
truncated 12 penta- 28% 20 Hexagons 72% 32 2.4% 3.6%
icosahedron gons
truncated 12 squares 19% 8 Hexagons 34% 6 octagons 47% 26 1.6% 4.2% 7.8%
cubocta-
hedron
Rhombicub 8 triangles 16% 18 squares 84% 26 2.0% 4.7%
-octahedron
snub cube 32 triangles 70% 6 squares 30% 38 2.2% 5.0%
Icosado- 20 triangles 30% 12 Pentagons 70% 32 1.5% 5.9%
decahedron
truncated 20 triangles 9% 12 Decagons 91% 32 0.4% 7.6%
dodeca-
hedron
truncated 6 squares 22% 8 Hexagons 78% 14 3.7% 9.7%
octahedron
Cubocta- 8 triangles 37% 6 squares 63% 14 4.6% 10.6%
hedron
truncated 8 triangles 11% 6 Octagons 89% 14 1.3% 14.9%
cube
truncated 4 triangles 14% 4 Hexagons 86% 8 3.6% 21.4%
tetrahedron
TABLE 15
Shape of Surface area
Name of Platonic Solid # of Regions Regions per Region
Tetrahedral Sphere 4 triangle 100% 25%
Octahedral Sphere 8 triangle 100% 13%
Hexahedral Sphere 6 squares 100% 17%
Icosahedral Sphere 20 triangles 100% 5%
Dodecahadral Sphere 12 pentagons 100% 8%
FIG. 30 is a top-view schematic diagram of a golf ball with a cuboctahedron pattern illustrating a golf ball, which may be ball 100 of FIG. 29 or ball 273 of FIG. 31, in the poles-forward-backward (PFB) orientation with the equator 130 (also called seam) oriented in a vertical plane 220 that points to the right/left and up/down, with pole 205 pointing straight forward and orthogonal to equator 130, and pole 210 pointing straight backward, i.e., approximately located at the point of club impact. In this view, the tee upon which the golf ball 100 would be resting would be located in the center of the golf ball 100 directly below the golf ball 100 (which is out of view in this figure). In addition, outer surface 105 of golf ball 100 has two types of regions of dissimilar dimple types arranged in a cuboctahedron configuration. In the cuboctahedral dimple pattern 173, outer surface 105 has larger dimples arranged in a plurality of three square regions 110 while smaller dimples are arranged in the plurality of four triangular regions 115 in the front hemisphere 120 and back hemisphere 125 respectively for a total of six square regions and eight triangular regions arranged on the outer surface 105 of the golf ball 100. In the inverse cuboctahedral dimple pattern 273, outer surface 105 has larger dimples arranged in the eight triangular regions and smaller dimples arranged in the total of six square regions. In either case, the golf ball 100 contains 504 dimples. In golf ball 173, each of the triangular regions and the square regions containing thirty-six dimples. In golf ball 273, each triangular region contains fifteen dimples while each square region contains sixty four dimples. Further, the top hemisphere 120 and the bottom hemisphere 125 of golf ball 100 are identical and are rotated 60 degrees from each other so that on the equator 130 (also called seam) of the golf ball 100, each square region 110 of the front hemisphere 120 borders each triangular region 115 of the back hemisphere 125. Also shown in FIG. 31, the back pole 210 and front pole (not shown) pass through the triangular region 115 on the outer surface 105 of golf ball 100.
Accordingly, a golf ball 100 designed in accordance with the embodiments described herein will have at least two different regions A and B comprising different dimple patterns and types. Depending on the embodiment, each region A and B, and C where applicable, can have a single type of dimple, or multiple types of dimples. For example, region A can have large dimples, while region B has small dimples, or vice versa; region A can have spherical dimples, while region B has truncated dimples, or vice versa; region A can have various sized spherical dimples, while region B has various sized truncated dimples, or vice versa, or some combination or variation of the above. Some specific example embodiments are described in more detail below.
It will be understood that there is a wide variety of types and construction of dimples, including non-circular dimples, such as those described in U.S. Pat. No. 6,409,615, hexagonal dimples, dimples formed of a tubular lattice structure, such as those described in U.S. Pat. No. 6,290,615, as well as more conventional dimple types. It will also be understood that any of these types of dimples can be used in conjunction with the embodiments described herein. As such, the term “dimple” as used in this description and the claims that follow is intended to refer to and include any type of dimple or dimple construction, unless otherwise specifically indicated.
It should also be understood that a golf ball designed in accordance with the embodiments described herein can be configured such that the average volume per dimple in one region, e.g., region A, is greater than the average volume per dimple in another regions, e.g., region B. Also, the unit volume in one region, e.g., region A, can be greater, e.g., 5% greater, 15% greater, etc., than the average unit volume in another region, e.g., region B. The unit volume can be defined as the volume of the dimples in one region divided by the surface area of the region. Also, the regions do not have to be perfect geometric shapes. For example, the triangle areas can incorporate, and therefore extend into, a small number of dimples from the adjacent square region, or vice versa. Thus, an edge of the triangle region can extend out in a tab like fashion into the adjacent square region. This could happen on one or more than one edge of one or more than one region. In this way, the areas can be said to be derived based on certain geometric shapes, i.e., the underlying shape is still a triangle or square, but with some irregularities at the edges. Accordingly, in the specification and claims that follow when a region is said to be, e.g., a triangle region, this should also be understood to cover a region that is of a shape derived from a triangle.
But first, FIG. 37 is a diagram illustrating the relationship between the chord depth of a truncated and a spherical dimple. The golf ball having a preferred diameter of about 1.68 inches contains 504 dimples to form the cuboctahedral pattern, which was shown in FIGS. 29 to 31. As an example of just one type of dimple, FIG. 37 shows truncated dimple 400 compared to a spherical dimple having a generally spherical chord depth of 0.012 inches and a radius of 0.075 inches. The truncated dimple 400 may be formed by cutting a spherical indent with a flat inner end, i.e. corresponding to spherical dimple 400 cut along plane A-A to make the dimple 400 more shallow with a flat inner end, and having a truncated chord depth smaller than the corresponding spherical chord depth of 0.012 inches.
The dimples can be aligned along geodesic lines with six dimples on each edge of the square regions, such as square region 110, and eight dimples on each edge of the triangular region 115. The dimples can be arranged according to the three-dimensional Cartesian coordinate system with the X-Y plane being the equator of the ball and the Z direction passing through the pole of the golf ball 100. The angle Φ is the circumferential angle while the angle θ is the co-latitude with 0 degrees at the pole and 90 degrees at the equator. The dimples in the North hemisphere can be offset by 60 degrees from the South hemisphere with the dimple pattern repeating every 120 degrees. Golf ball 100, in the example of FIG. 29, has a total of nine dimple types, with four of the dimple types in each of the triangular regions and five of the dimple types in each of the square regions. As shown in Table 16 below, the various dimple depths and profiles are given for various implementations of golf ball 100, indicated as prototype codes 173-175. The actual location of each dimple on the surface of the ball for dimple patterns 172-175 is given in Tables 6-9 of the '028 application. Tables 10-11 of the '028 application provide the various dimple depths and profiles for dimple pattern 273 of FIG. 4 and an alternative dimple pattern 2-3, respectively, as well as the location of each dimple on the ball for each of these dimple patterns. Dimple pattern 2-3 is similar to dimple pattern 273 but has dimples of slightly larger chord depth than the ball with dimple pattern 273, as shown in Table 10-11 of the '028 application.
TABLE 16
Dimple ID# 1 2 3 4 5 6 7 8 9
Ball 175
Type Dimple Region Triangle Triangle Triangle Triangle Square Square Square Square Square
Type Dimple spherical spherical spherical spherical truncated truncated truncated truncated truncated
Dimple Radius, in 0.05 0.0525 0.055 0.0575 0.075 0.0775 0.0825 0.0875 0.095
Spherical Chord 0.008 0.008 0.008 0.008 0.012 0.0122 0.0128 0.0133 0.014
Depth, in
Truncated Chord n/a n/a n/a n/a 0.0035 0.0035 0.0035 0.0035 0.0035
Depth, in
# of dimples in 9 18 6 3 12 8 8 4 4
region
Dimple ID# 1 2 3 4 5 6 7 8 9
Ball 174
Type Dimple Region Triangle Triangle Triangle Triangle Square Square Square Square Square
Type Dimple truncated truncated truncated truncated spherical spherical spherical spherical spherical
Dimple Radius, in 0.05 0.0525 0.055 0.0575 0.075 0.0775 0.0825 0.0875 0.095
Spherical Chord 0.0087 0.0091 0.0094 0.0098 0.008 0.008 0.008 0.008 0.008
Depth, in
Truncated Chord 0.0035 0.0035 0.0035 0.0035 n/a n/a n/a n/a n/a
Depth, in
# of dimples in 9 18 6 3 12 8 8 4 4
region
Dimple ID# 1 2 3 4 5 6 7 8 9
Ball 173
Type Dimple Region Triangle Triangle Triangle Triangle Square Square Square Square Square
Type Dimple spherical spherical spherical spherical truncated truncated truncated truncated truncated
Dimple Radius, in 0.05 0.0525 0.055 0.0575 0.075 0.0775 0.0825 0.0875 0.095
Spherical Chord 0.0075 0.0075 0.0075 0.0075 0.012 0.0122 0.0128 0.0133 0.014
Depth, in
Truncated Chord n/a n/a n/a n/a 0.005 0.005 0.005 0.005 0.005
Depth, in
of dimples in 9 18 6 3 12 8 8 4 4
region
Dimple ID# 1 2 3 4 5 6 7 8 9
Ball 172
Type Dimple Region Triangle Triangle Triangle Triangle Square Square Square Square Square
Type Dimple spherical spherical spherical spherical spherical spherical spherical spherical spherical
Dimple Radius, in 0.05 0.0525 0.055 0.0575 0.075 0.0775 0.0825 0.0875 0.095
Spherical Chord 0.0075 0.0075 0.0075 0.0075 0.005 0.005 0.005 0.005 0.005
Depth, in
Truncated Chord n/a n/a n/a n/a n/a n/a n/a n/a n/a
Depth, in
of dimples in 9 18 6 3 12 8 8 4 4
region
The geometric and dimple patterns 172-175, 273 and 2-3 described above have been shown to reduce dispersion. Moreover, the geometric and dimple patterns can be selected to achieve lower dispersion based on other ball design parameters as well. For example, for the case of a golf ball that is constructed in such a way as to generate relatively low driver spin, a cuboctahedral dimple pattern with the dimple profiles of the 172-175 series golf balls, shown in Table 16, or the 273 and 2-3 series golf balls shown in Tables 10 and 11 of the '028 application, provides for a spherically symmetrical golf ball having less dispersion than other golf balls with similar driver spin rates. This translates into a ball that slices less when struck in such a way that the ball's spin axis corresponds to that of a slice shot. To achieve lower driver spin, a ball can be constructed from e.g., a cover made from an ionomer resin utilizing high-performance ethylene copolymers containing acid groups partially neutralized by using metal salts such as zinc, sodium and others and having a rubber-based core, such as constructed from, for example, a hard Dupont™ Surlyn® covered two-piece ball with a polybutadiene rubber-based core such as the TopFlite XL Straight or a three-piece ball construction with a soft thin cover, e.g., less than about 0.04 inches, with a relatively high flexural modulus mantle layer and with a polybutadiene rubber-based core such as the Titleist ProV1®.
Similarly, when certain dimple pattern and dimple profiles describe above are used on a ball constructed to generate relatively high driver spin, a spherically symmetrical golf ball that has the short iron control of a higher spinning golf ball and when imparted with a relatively high driver spin causes the golf ball to have a trajectory similar to that of a driver shot trajectory for most lower spinning golf balls and yet will have the control around the green more like a higher spinning golf ball is produced. To achieve higher driver spin, a ball can be constructed from e.g., a soft Dupont™ Surlyn® covered two-piece ball with a hard polybutadiene rubber-based core or a relatively hard Dupont™ Surlyn® covered two-piece ball with a plastic core made of 30-100% DuPont™ HPF 2000®, or a three-piece ball construction with a soft thicker cove, e.g., greater than about 0.04 inches, with a relatively stiff mantle layer and with a polybutadiene rubber-based core.
It should be appreciated that the dimple patterns and dimple profiles used for 172-175, 273, and 2-3 series golf balls causes these golf balls to generate a lower lift force under various conditions of flight, and reduces the slice dispersion.
Golf balls dimple patterns 172-175 were subjected to several tests under industry standard laboratory conditions to demonstrate the better performance that the dimple configurations described herein obtain over competing golf balls. In these tests, the flight characteristics and distance performance for golf balls with the 173-175 dimple patterns were conducted and compared with a Titleist Pro V1® made by Acushnet. Also, each of the golf balls with the 172-175 patterns were tested in the Poles-Forward-Backward (PFB) and Pole Horizontal (PH) orientations. The Pro V1® being a USGA conforming ball and thus known to be spherically symmetrical was tested in no particular orientation (random orientation). Golf balls with the 172-175 patterns were all made from basically the same materials and had a standard polybutadiene-based rubber core having 90-105 compression with 45-55 Shore D hardness. The cover was a Surlyn™ blend (38% 9150, 38% 8150, 24% 6320) with a 58-62 Shore D hardness, with an overall ball compression of approximately 110-115.
The tests were conducted with a “Golf Laboratories” robot and hit with the same Taylor Made® driver at varying club head speeds. The Taylor Made® driver had a 10.5° r7 425 club head with a lie angle of 54 degrees and a REAX 65 ‘R’ shaft. The golf balls were hit in a random-block order, approximately 18-20 shots for each type ball-orientation combination. Further, the balls were tested under conditions to simulate a 20-25 degree slice, e.g., a negative spin axis of 20-25 degrees.
The testing revealed that the 172-175 dimple patterns produced a ball speed of about 125 miles per hour, while the Pro V1® produced a ball speed of between 127 and 128 miles per hour.
The data for each ball with patterns 172-175 also indicates that velocity is independent of orientation of the golf balls on the tee.
The testing also indicated that the 172-175 patterns had a total spin of between 4200 rpm and 4400 rpm, whereas the Pro V1® had a total spin of about 4000 rpm. Thus, the core/cover combination used for balls with the 172-175 patterns produced a slower velocity and higher spinning ball.
Keeping everything else constant, an increase in a ball's spin rate causes an increase in its lift. Increased lift caused by higher spin would be expected to translate into higher trajectory and greater dispersion than would be expected, e.g., at 200-500 rpm less total spin; however, the testing indicates that the 172-175 patterns have lower maximum trajectory heights than expected. Specifically, the testing revealed that the 172-175 series of balls achieve a max height of about 21 yards, while the Pro V1® is closer to 25 yards.
The data for each of golf balls with the 172-175 patterns indicated that total spin and max height was independent of orientation, which further indicates that the 172-175 series golf balls were spherically symmetrical.
Despite the higher spin rate of a golf ball with, e.g., pattern 173, it had a significantly lower maximum trajectory height (max height) than the Pro V1®. Of course, higher velocity will result in a higher ball flight. Thus, one would expect the Pro V1® to achieve a higher max height, since it had a higher velocity. If a core/cover combination had been used for the 172-175 series of golf balls that produced velocities in the range of that achieved by the Pro V1®, then one would expect a higher max height. But the fact that the max height was so low for the 172-175 series of golf balls despite the higher total spin suggests that the 172-175 Vballs would still not achieve as high a max height as the Pro V1® even if the initial velocities for the 172-175 series of golf balls were 2-3 mph higher.
FIG. 38 is a graph of the maximum trajectory height (Max Height) versus initial total spin rate for all of the 172-175 series golf balls and the Pro V1®. These balls were when hit with Golf Labs robot using a 10.5 degree Taylor Made r7 425 driver with a club head speed of approximately 90 mph imparting an approximately 20 degree spin axis slice. As can be seen, the 172-175 series of golf balls had max heights of between 18-24 yards over a range of initial total spin rates of between about 3700 rpm and 4100 rpm, while the Pro V1® had a max height of between about 23.5 and 26 yards over the same range.
The maximum trajectory height data correlates directly with the CL produced by each golf ball. These results indicate that the Pro V1® golf ball generated more lift than any of the 172-175 series balls. Further, some of balls with the 172-175 patterns climb more slowly to the maximum trajectory height during flight, indicating they have a slightly lower lift exerted over a longer time period. In operation, a golf ball with the 173 pattern exhibits lower maximum trajectory height than the leading comparison golf balls for the same spin, as the dimple profile of the dimples in the square and triangular regions of the cuboctahedral pattern on the surface of the golf ball cause the air layer to be manipulated differently during flight of the golf ball.
Despite having higher spin rates, the 172-175 series golf balls have Carry Dispersions that are on average less than that of the Pro V1® golf ball. The data in FIGS. 12-16 clearly shows that the 172-175 series golf balls have Carry Dispersions that are on average less than that of the Pro V1® golf ball. It should be noted that the 172-175 series of balls are spherically symmetrical and conform to the USGA Rules of Golf.
FIG. 39 is a graph illustrating the carry dispersion for the balls tested and shown in FIG. 38. As can be seen, the average carry dispersion for the 172-175 balls is between 50-60 ft, whereas it is over 60 feet for the Pro V1®.
FIGS. 39-43 are graphs of the Carry Dispersion versus Total Spin rate for the 172-175 golf balls versus the Pro V1®. The graphs illustrate that for each of the balls with the 172-175 patterns and for a given spin rate, the balls with the 172-175 patterns have a lower Carry Dispersion than the Pro V1®. For example, for a given spin rate, a ball with the 173 pattern appears to have 10-12 ft lower carry dispersion than the Pro V1® golf ball. In fact, a 173 golf ball had the lowest dispersion performance on average of the 172-175 series of golf balls.
The overall performance of the 173 golf ball as compared to the Pro V1® golf ball is illustrated in FIGS. 44 and 45. The data in these figures shows that the 173 golf ball has lower lift than the Pro V1® golf ball over the same range of Dimensionless Spin Parameter (DSP) and Reynolds Numbers.
FIG. 44 is a graph of the wind tunnel testing results showing of the Lift Coefficient (CL) versus DSP for the 173 golf ball against different Reynolds Numbers. The DSP values are in the range of 0.0 to 0.4. The wind tunnel testing was performed using a spindle of 1/16th inch in diameter.
FIG. 45 is a graph of the wind tunnel test results showing the CL versus DSP for the Pro V1 golf ball against different Reynolds Numbers.
In operation and as illustrated in FIGS. 44 and 45, for a DSP of 0.20 and a Re of greater than about 60,000, the CL for the 173 golf ball is approximately 0.19-0.21, whereas for the Pro V1® golf ball under the same DSP and Re conditions, the CL is about 0.25-0.27. On a percentage basis, the 173 golf ball is generating about 20-25% less lift than the Pro V1® golf ball. Also, as the Reynolds Number drops down to the 60,000 range, the difference in CL is pronounced—the Pro V1® golf ball lift remains positive while the 173 golf ball becomes negative. Over the entire range of DSP and Reynolds Numbers, the 173 golf ball has a lower lift coefficient at a given DSP and Reynolds pair than does the Pro V1® golf ball. Furthermore, the DSP for the 173 golf ball has to rise from 0.2 to more than 0.3 before CL is equal to that of CL for the Pro V1® golf ball. Therefore, the 173 golf ball performs better than the Pro V1® golf ball in terms of lift-induced dispersion (non-zero spin axis).
Therefore, it should be appreciated that the cuboctahedron dimple pattern on the 173 golf ball with large truncated dimples in the square sections and small spherical dimples in the triangular sections exhibits low lift for normal driver spin and velocity conditions. The lower lift of the 173 golf ball translates directly into lower dispersion and, thus, more accuracy for slice shots.
“Premium category” golf balls like the Pro V1® golf ball often use a three-piece construction to reduce the spin rate for driver shots so that the ball has a longer distance yet still has good spin from the short irons. The 173 dimple pattern can cause the golf ball to exhibit relatively low lift even at relatively high spin conditions. Using the low-lift dimple pattern of the 173 golf ball on a higher spinning two-piece ball results in a two-piece ball that performs nearly as well on short iron shots as the “premium category” golf balls currently being used.
The 173 golf ball's better distance-spin performance has important implications for ball design in that a ball with a higher spin off the driver will not sacrifice as much distance loss using a low-lift dimple pattern like that of the 173 golf ball. Thus the 173 dimple pattern or ones with similar low-lift can be used on higher spinning and less expensive two-piece golf balls that have higher spin off a PW but also have higher spin off a driver. A two-piece golf ball construction in general uses less expensive materials, is less expensive, and easier to manufacture. The same idea of using the 173 dimple pattern on a higher spinning golf ball can also be applied to a higher spinning one-piece golf ball.
Golf balls like the MC Lady and MaxFli Noodle use a soft core (approximately 50-70 PGA compression) and a soft cover (approximately 48-60 Shore D) to achieve a golf ball with fairly good driver distance and reasonable spin off the short irons. Placing a low-lift dimple pattern on these balls allows the core hardness to be raised while still keeping the cover hardness relatively low. A ball with this design has increased velocity, increased driver spin rate, and is easier to manufacture; the low-lift dimple pattern lessens several of the negative effects of the higher spin rate.
The 172-175 dimple patterns provide the advantage of a higher spin two-piece construction ball as well as being spherically symmetrical. Accordingly, the 172-175 series of golf balls perform essentially the same regardless of orientation.
In an alternate embodiment, a non-Conforming Distance Ball having a thermoplastic core and using the low-lift dimple pattern, e.g., the 173 pattern, can be provided. In this alternate embodiment golf ball, a core, e.g., made with DuPont™ Surlyn® HPF 2000 is used in a two- or multi-piece golf ball. The HPF 2000 gives a core with a very high COR and this directly translates into a very fast initial ball velocity—higher than allowed by the USGA regulations.
In yet another embodiment, as shown in FIG. 46, golf ball 600 is provided having a spherically symmetrical low-lift pattern that has two types of regions with distinctly different dimples. As one non-limiting example of the dimple pattern used for golf ball 600, the surface of golf ball 600 is arranged in an octahedron pattern having eight symmetrical triangular shaped regions 602, which contain substantially the same types of dimples. The eight regions 602 are created by encircling golf ball 600 with three orthogonal great circles 604, 606 and 608 and the eight regions 602 are bordered by the intersecting great circles 604, 606 and 608. If dimples were placed on each side of the orthogonal great circles 604, 606 and 608, these “great circle dimples” would then define one type of dimple region two dimples wide and the other type region would be defined by the areas between the great circle dimples. Therefore, the dimple pattern in the octahedron design would have two distinct dimple areas created by placing one type of dimple in the great circle regions 604, 606 and 608 and a second type dimple in the eight regions 602 defined by the area between the great circles 604, 606 and 608.
As can be seen in FIG. 46, the dimples in the region defined by circles 604, 606, and 608 can be truncated dimples, while the dimples in the triangular regions 602 can be spherical dimples. In other embodiments, the dimple type can be reversed. Further, the radius of the dimples in the two regions can be substantially similar or can vary relative to each other.
FIGS. 52 and 53 are graphs which were generated for balls 273 and 2-3 in a similar manner to the graphs illustrated in FIGS. 47 to 51 for some known balls and the 173 and 273 balls. FIGS. 52 and 53 show the lift coefficient versus Reynolds Number at initial spin rates of 4,000 rpm and 4,500 rpm, respectively, for the 273 and 2-3 dimple pattern. FIGS. 54 and 55 are graphs illustrating the drag coefficient versus Reynolds number at initial spin rates of 4000 rpm and 4500 rpm, respectively, for the 273 and 2-3 dimple pattern. FIGS. 52 to 55 compare the lift and drag performance of the 273 and 2-3 dimple patterns over a range of 120,000 to 140,000 Re and for 4000 and 4500 rpm. This illustrates that balls with dimple pattern 2-3 perform better than balls with dimple pattern 273. Balls with dimple pattern 2-3 were found to have the lowest lift and drag of all the ball designs which were tested.
FIGS. 57 to 86 illustrate a number of different embodiments of a golf ball designed to have a MOI differential designed such that, when properly aligned before taking a golf shot, the ball resists hooking or slicing and that can be included in the kits described herein. FIGS. 25 to 29 illustrate some alternative dimple patterns which may be applied to the outer surface of the golf balls of FIGS. 1A to 24.
In other embodiments, the ball may have non-spherical aspects of various combinations of the core and cover parts which have different specific gravities. The different shaped ball parts combined with the different specific gravities of the materials for different ball parts is what causes the MOI differential between spin axes. The golf ball is spherical, but the inner layers are not necessarily completely spherical or symmetrical layers or parts.
In the embodiments illustrated in FIGS. 57A to 72, the core of the golf ball is composed of a mantle layer (outer core) and an inner core, while in the embodiment of FIGS. 73 to 86, a one-piece core is shown. In reality, the core may be made of one material in one piece or multiple materials and/or multiple layers or pieces. In the following discussion, whenever the core is referred to in general, it can be a one piece or multi-piece core even though it is referred to only as a core. The mantle layer in some embodiments is a core layer directly below the cover. There may be one or more mantle layers and one or more cover layers.
In the embodiments of FIGS. 57 to 86, the core is not completely spherical. It has regions that are larger or smaller in radius. The core can have high or low regions, areas where material is added or removed, or may be of many other completely or partially non-spherical shapes, just a few of which are described here. The cover is placed over the core, thus it has thicker or thinner regions that corresponding to the topography of the core. In other words, an inner surface of the cover which opposes the at least partially non-spherical surface of the core is of complementary at least partially non-spherical shape, resulting in thicker and thinner regions if the outer surface of the cover is substantially spherical. The cover may be a single layer or may comprise two, three or more cover layers over the core, so that the outer cover is spherical and uniform in thickness and the layer or layers below, which would be called the inner cover layer or layers (these also might be considered “mantle layers”), would not all be of uniform thickness. A multiple layer cover with different types of materials such as Surlyn, polyurethane or other materials used for golf ball covers and mantle layers could also be envisioned, each with different specific gravities, colors, and physical properties. However, the major point is that somewhere in the construction of the ball is at least one layer or ball part that is not uniform in thickness or not uniform in radius and because of this design element and the proper selection of specific gravity for the different ball components, the ball has a different moment of inertia when rotating about at least one of the principle axes (by “principle axes” is meant the 3 orthogonal axes of a ball usually defined by x, y and z). The axes are usually defined as two being perpendicular to each other and residing in equatorial plane, and the third being perpendicular to the equatorial plane and going through the poles. In some embodiments, the MOI of the ball as measured about each of the orthogonal axes can each be a different value or the MOI can be substantially the same for two axes and different for the third.
In each embodiment, at least two components of the ball have different specific gravities. One is denser than the other. The cover can be more or less dense than the core. The mantle layer can be more of less dense than the cover, the mantle layer can be more or less dense than the core, two mantle layers can differ in density, two cover layers can differ in density, etc. In any case, the ball will have a MOI differential depending upon the shape of the core, cover and mantle layers and the density differences among them. A spherical inner core or uniform thickness cover or uniform thickness mantle layer can be higher or lower specific gravity compared to any of the other mantle, cover or core layers.
As illustrated in FIGS. 57A, 57B and 58, a first embodiment of a golf ball 10 constructed to resist hooking and slicing has a two part core comprising an inner core 20 covered by an outer core or mantle layer 22, and an outer cover 24. FIGS. 57A and 57B illustrate two perpendicular cross sectional views of the ball. In the first embodiment, the mantle layer 22 of the core is partially non-spherical and has diametrically opposite flattened areas or spots 25 on opposite sides of the ball in the same region that the known Polara ball has deep polar dimples. This means that the ball has a higher moment of inertia when rotating in the PH orientation than in other orientations or spin axes. Different parts of the ball may also be of different materials having different specific gravities, as explained in more detail below. The two removed areas or flattened areas 25 are exactly the same size and shape. They are 180 degrees opposite from each other. This core shape causes the cover to have a complementary inner surface shape with two circular regions 26 that are opposite each other and oppose the flattened areas 25, and are thicker than the rest of the cover. In alternative embodiments, the core may be a single piece or may have more than two parts.
FIG. 58 illustrates the core of design “A1” (FIGS. 1A and 1B) showing the outer core (mantle) 22 over the inner core 20, with the cover layer 24 removed. The inner core in this case has a radius of 0.74 inches, and the outer core has a radius ranging from 0.76 to 0.79 inches. This design has two regions where a disk shaped element has been removed from the core and the two regions are 180 degrees opposite of each other. The radius at the center of each of these areas is 0.76 inches and rises to 0.79 inches at the edges of the disks (the diagram may not have the exact correct aspect ratio and it may appear that the core is not spherical, however, the inner core for this example and the examples of FIGS. 57A to 60 and 63 to 68 are meant to be spherical). The height of the disk removed from each pole is at most 0.03 inches. This same basic design idea could be used with larger or smaller cores ranging from less than 1 inch in diameter to something approaching less than 0.015 inches than the outside diameter of the ball. The thickness of the cover of the ball and the outside diameter of the ball limit the maximum diameter of the core, but the size of the disk removed from each end could vary from as little as 0.001 inch radius up to almost the entire radius of the core (at which point the core would become a thin disk shaped object). In all of these cases the MOI differential would be smallest to largest going from the least amount of material removed from the core to the disk shaped material with enough thickness and specific gravity difference between the other layers as to maximize the overall MOI differential of the ball.
This embodiment and all other ball construction embodiments described below in connection with FIGS. 59 to 86 can be combined with surface features or dimples forming a symmetrical pattern or can be combined with an asymmetrical pattern such as that of the original Polara golf ball (deep dimples around the equator and shallow dimples on the poles) or the asymmetrical dimple pattern of the new Polara Ultimate Straight golf balls that have deeper dimples on the poles and shallow dimples around the ball's equator, or the dimple patterns of any of the non-confirming balls described in co-pending application Ser. No. 13/097,013 filed on Aug. 28, 2011, the contents of which are incorporated herein by reference. An asymmetrical dimple or surface feature pattern is one which is non-conforming or not spherically symmetrical as defined by the United States Golf Association (USGA) rules.
In the case of the Polara Ultimate Straight dimple pattern combined with design “A1”, if the flat spot on the core was centered with the pole of the dimple pattern (the deep dimpled region), and the density of the materials for the core and cover mantle layer we chosen so that core was higher specific gravity than the cover, then the MOI differentials caused by the ball construction and dimple pattern would reinforce each other and create a larger MOI differential than when just the Polara dimple pattern was used on a symmetrical ball construction or when a symmetrical dimple pattern was combined with the ball construction of FIGS. 57A to 58, such as the symmetrical dimple patterns described in co-pending application Ser. No. 12/765,762 filed on Apr. 22, 2010, the contents of which are incorporated herein by reference, or other symmetrical dimple patterns.
Another example similar to the ball 10 of FIG. 57A to 58 but not shown in the drawings, would be a core with 3, 4, 5 or more regions removed from the core and all the regions symmetrically positioned about the core so that they were in the same plane and were equally spaced from each other so as to create a ball that has the center of gravity in the physical center of the core. The regions could be the same size and shape as each other, or they could be different sizes and shapes. In this example the regions removed from the core have a flat base, but in other instances they could have a non-flat base, such as a spherical or elliptically shaped based, for example they may be more scooped out of the core as opposed to sliced off of the core. Alternatively, the shapes could be indented regions with high or low spots within each region, or the core regions could be any combination of any of these suggested shapes. The idea is simply to remove portions of the core to allow for the establishment of an asymmetry that establishes an MOI differential that helps prevent part or most of a hook or slice. The removed regions of the core could also exist in more than one plane as long as they still established a net asymmetry in the core weight distribution and the center of gravity was still in the center of the ball.
FIGS. 59 to 60 illustrate a modified ball 30 (design “B1”) which is similar to ball 10, and like reference numbers are used for the various parts of ball 30. However, in this alternative, rather than providing diametrically opposite flat regions on the core or mantle, mantle 32 has an annular band 34 removed from around the entire core, and the cover 35 has an opposing surface of complementary shape with a thicker band 36 of material surrounding band 34. In this design, the center of gravity of the core has not moved and is still in the center of the core. If the ball is to roll normally, it is important that the center of gravity for all of these designs be close to the center of the golf ball, as determined from the intersection point of the 3 orthogonal axes of the ball. In this embodiment, the dimple pattern on the outer cover may correspond to the Polara dimple pattern having deep dimples around the equator, or other symmetrical or asymmetrical dimple patterns. In this embodiment, the high MOI orientation is the POP orientation.
FIG. 60 illustrates the core of the ball 30 of FIGS. 59A and 59B (Design “B1”), with the outer layer removed, showing the outer core (mantle) 32 over the inner core 20. The inner core in this case has a radius of 0.74 inches, and the outer core has a radius ranging from 0.76 to 0.79 inches. The 0.74 radius occurs at the center of area where material has been removed in a band shape around the core. At the edges of the band the core radius is equal to the radius everywhere outside the band. One of more parallel or non-coplanar bands could also be used to create a MOI differential. The bands could be wider or more narrow and thicker or thinner than shown in this example. Obviously the wider the band, the smaller the underlying core radius would have to be in order to maintain the core as a perfectly spherical unit, not intersecting with the band on the outer core (mantle layer). In other embodiments, the outer cones may have flat portions at the poles as well as one or more flattened bands extending around the ball.
FIG. 61 illustrates a modification of the ball 30 of FIG. 59A to 60. In the ball 40 of FIG. 61, a golf ball core is illustrated in which the underlying inner core 44 also has a banded region 42 corresponding to banded region 45 in the mantle layer 46. The bands in the two core layers could be the same or different widths. The dimension of the bands could range in size and thicknesses on the order of 0.001 wide (in which case they would create very little MOI differential) to the modified embodiment of a ball 50 illustrated in FIG. 62 where the core 60 has core layers 61, 62 which are disk shaped pieces having part spherical ends 64 (in which case they create a large MOI differential for the ball). A cover layer 52 having a spherical outer surface surrounds core 60, and thus has thinner regions 53 around part spherical ends 64 and significantly thicker regions 58 around the bands or opposite faces 56 of the disk shaped core pieces.
FIG. 63 illustrates another embodiment of a golf ball 65 (design “C1”) which has an ellipsoid type core to establish the asymmetry necessary for creating the differential MOI. A number of designs are also possible where multiple ellipsoid shaped core shapes are combined to form a core that still has a MOI differential and the center of gravity of the core is still in the center of the core. In the embodiment of FIG. 63, the inner core 66 is spherical, while the outer core layer or mantel 67 is of ellipsoidal shape, having thicker regions 68 and thinner regions 69, with the outer cover 70 having an opposing inner surface of complementary elliptical shape, so that the cover is thinner adjacent the thicker regions of the mantel 67. Any combination and any number of each of the designs of FIGS. 57A to 62 can be combined to give further examples that would produce a ball with a differential MOI and would still have the center of gravity of the ball in the center of the ball (thus it would roll without wobbling).
FIG. 64 illustrates one example of possible dimensions for an ellipsoid like core of a ball similar to that of FIG. 63 (Design “C1”) showing the outer layer removed to expose the outer core (mantle) 67 over the inner core 66. The inner core in this case has a radius of 0.74 inches, and the outer core has a radius ranging from 0.74 to 0.79 inches. This core is ellipsoid shaped. At its point of greatest width, the ellipsoid has a radius a of 0.79 inches and at its narrowest point it has a radius to of 0.74 inches.
FIGS. 65 and 66 illustrates another embodiment of a golf ball 75 (design “D1”) which has a two piece core with an inner core 20 and an outer core layer or mantle 76 that encircles the core 20 and has a raised band 78 around the outer surface. The cover 80 has an outer spherical surface with any selected dimple pattern, as in the previous embodiments, and an inner surface with an indented channel into which band 78 extends, with a thinner area 82 around raised band 78. Band 78 has a rounded, convex outer end with the opposing recess in cover 80 having a concave inner end.
FIG. 66 illustrates one example of the two layer core of ball 41 (Design “D1”) of FIG. 65 with the outer cover removed, showing the outer surface of mantle layer 76 over the inner core 20. The inner core in this case has a radius of 0.74 inches, and the outer core has a radius ranging from 0.79 to 0.82 inches. The 0.82 radius occurs on the portion of the core that is essentially a band 78 of material surrounding the core. The height of the band 78 is around 0.03 inches. The other portion 83 of the outer core has a radius of 0.79 inches uniformly surrounding the rest of the core.
FIG. 67 illustrates another embodiment of a golf ball 85 (design “E1”) that is essentially a combination of Design “D1” and Design “A1”, having both a raised band 78 on mantle 86 at the equator, as in the embodiment of FIGS. 65 and 66 (Design “D1”) and opposite flattened areas 25 in the opposite polar regions, as in the embodiment of FIGS. 57A to 58 (Design “A1”). In this embodiment, the mantle is thicker in the equatorial region than in the polar region. The outer cover 87 has a complementary inner surface shape and an outer spherical surface, resulting in corresponding thicker areas 88 at the polar region and thinner areas 89 in the equatorial region.
FIG. 68 illustrates one example of the two layer core of ball 85 (Design “E1”) of FIG. 11 with the outer cover removed, showing the outer core (mantle) 87 over the inner core 20. The inner core 20 in this example has a radius of 0.74 inches, and the outer core has a radius ranging from 0.79 to 0.82 inches. The 0.82 radius occurs on the portion of the core that is essentially a band 78 of material surrounding the core. The other portion of the outer core has a radius of 0.79 inches except on the two opposite sides where the core has two disk shaped portions removed in the same fashion as Design “A1”, producing flattened areas 25. As with Design “A1”, the radius at the center of each of these disk areas is 0.76 inches and rises to 0.79 inches at the edges of the disks.
In the above embodiments, the mantle density or specific gravity may be greater than the cover layer density, but that does not have to be the case in all embodiments. The cover density may also be higher than the mantle density in the above embodiments, and this structure still results in a MOI differential. As long as there is a difference in the core and mantle densities in any of designs A1 to E1 of FIGS. 57A to 68, the balls display an MOI differential. Other examples of balls that would exhibit a desired MOI differential are described below, and include balls with two or more raised bands encircling the core, with the bands being parallel or not coplanar but still the resulting ball would have a center of gravity that corresponded closely or exactly to the center of the ball. The multiple variations of “D1” and “E1” designs could also be combined with one or more of the “A1”, “B1” or “C1” designs as well as symmetrical or asymmetrical dimple patterns so as to produce a ball with a desirable MOI differential.
One consideration when having more than one band or recess in a core, mantle or cover is that the shape would be easier to injection mold and then remove from the mold if there were no undercut portions of the shape such that when the part was removed from the mold that it was caught on a protruding part of the mold that was closer to the parting line of the mold. The dimensions for some specific examples of Designs “A1” through “E1” are provided below. There could be many other examples, with an almost infinite combination of dimensions and the examples discussed above are just a few simple designs selected for illustration of the invention and some of its various aspects.
Table 17 below shows the dimensions of a 1.68″ outer diameter golf ball of embodiments A1 through E1 (labeled A1, B1 . . . . E1, respectively. In Table 1 the outer core is referred to as the “mantle”. The numbers in Table 1 are expressed in “inches”. For these particular examples, the width of the raised band for the mantle in ball designs D1 and E1 is 0.50 inches and the width of the flat area for the mantle on ball design B1 is 0.50 inches.
TABLE 17
spherical cover and cover and
cover cover mantle mantle mantle mantle inner mantle total mantle total
thickness thickness radius at radius at cover's thickness thickness core's thickness at thickness at
Ball in thinnest in thickest thinnest thickest cuter in thinnest in thick outer thinnest point thickest point
Design area area location location radius area area radius of cover of cover
Al 0.050 0.080 0.760 0.790 0.84 0.020 0.050 0.74 0.100 0.100
B1 0.050 0.080 0.760 0.790 0.84 0.020 0.050 0.74 0.100 0.100
C1 0.050 0.080 0.760 0.790 0.84 0.020 0.050 0.74 0.100 0.100
D1 0.020 0.050 0.790 0.820 0.84 0.050 0.080 0.74 0.100 0.100
E1 0.020 0.080 0.760 0.820 0.84 0.02 0.08 0.74 0.100 0.100
Tables 18 and 19 below provide the differential MOI data between the x, y and z spin axes for a combination of different specific gravity materials used with designs A1-E1. Any combination of specific gravities of materials could be used and this would in turn change the resulting MOI differential for the ball. It may be higher or lower than what is shown below.
TABLE 18
MOI Differential results for a ball without dimples.
Density,
g/cm{circumflex over ( )}3 Mass, g Volume, cm{circumflex over ( )}3 Ix, g cm{circumflex over ( )}2 Iy, g cm{circumflex over ( )}2 Iz, g cm{circumflex over ( )}2 Ix vs Iz
A-1
core 1.150 31.988 27.815 45.2036626 45.2036626 45.2036626 0.000%
mantle 1.200 7.147 5.956 17.9032281 17.9032323 18.2307139 -1.813%
cover 1.000 6.913 6.913 19.8552703 19.8552597 19.5823628 1.384%
sum 46.048 40.684 82.9621610 82.9621546 83.0167393 -0.06577%
B-1
core 1.150 31.988 27.815 45.2036626 45.2036626 45.2036626 0.000%
mantle 1.200 6.407 5.340 16.6013852 16.6013852 15.0624696 9.720%
cover 1.000 7.529 7.529 20.9401340 20.9401372 22.2225662 -5.942%
sum 45.925 40.684 82.7451819 82.7451851 82.4886984 0.31045%
C-1
core 1.150 31.988 27.815 45.2036626 45.2036626 45.2036626 0.000%
mantle 1.200 4.207 3.506 11.1097041 11.1097041 8.8554597 22.582%
cover 1.000 9.363 9.363 25.5165339 25.4934977 27.3950744 -7.101%
sum 45.558 40.684 81.8299006 81.8068645 81.4541968 0.46018%
D-1
core 1.150 31.988 27.815 45.2036626 45.2036626 45.2036626 0.000%
mantle 1.200 8.725 7.271 21.4594972 21.4594993 24.2785243 -12.327%
cover 1.000 5.598 5.598 16.8917074 16.8917074 14.5425197 14.947%
sum 46.311 40.684 83.5548672 83.5548693 84.0247067 -0.56074%
E -1
core 1.150 31.988 27.815 45.2036626 45.2036626 45.2036626 0.000%
mantle 1.200 8.639 7.199 21.1233135 21.1233135 24.2698234 -13.863%
cover 1.000 5.670 5.670 17.1718622 17.3621632 14.5497712 16.532%
sum 46.296 40.684 83.4988384 83.6891394 84.0232572 -0.62609%
TABLE 19
MOI Differential results for a ball with dimples.
MOI Calcs w/ accounting for dimple volumes
weight of dimples in cover
material weight Volume 0.4 grams
specific w/o weight with without Volume with
gravity, g/cc dimples, g dimples, g dimples, cm{circumflex over ( )}3 Dimples, cm{circumflex over ( )}3 Ix, g cm{circumflex over ( )}2 Iy, g cm{circumflex over ( )}2 Iz, g cm{circumflex over ( )}2 Ix vs Iz
A-1
core 1.150 31.99 31.99 27.82 27.82 45.20366 45.20366 45.20366 0.0000%
mantle 1.200 7.15 7.15 5.96 5.96 17.90323 17.90323 18.23071 -1.8126%
cover 1.000 6.91 6.51 6.91 6.51 18.70648 18.70647 18.44937 1.3840%
ball 46.05 45.65 40.68 40.28 81.81338 81.81337 81.88374 -0.0860%
B-1
core 1.150 31.99 31.99 27.82 27.82 45.20366 45.20366 45.20366 0.0000%
mantle 1.200 6.41 6.41 5.34 5.34 16.60139 16.60139 15.06247 9.7203%
cover 1.000 7.53 7.13 7.53 7.13 19.82770 19.82770 21.04200 -5.9423%
ball 45.92 45.52 40.68 40.28 81.63275 81.63275 81.30814 0.3984%
C-1
core 1.150 31.99 31.99 27.82 27.82 45.20366 45.20366 45.20366 0.0000%
mantle 1.200 4.21 4.21 3.51 3.51 11.10970 11.10970 8.85546 22.5818%
cover 1.000 9.36 8.96 9.36 8.96 24.42646 24.40441 26.22475 -7.1007%
ball 45.56 45.16 40.68 40.28 80.73982 80.71777 80.28387 0.5663%
D-1
core 1.000 27.82 27.82 27.82 27.82 39.30753 39.30753 39.30753 0.0000%
mantle 1.600 11.63 11.63 7.27 7.27 28.61266 28.61267 32.37137 -12.3268%
cover 1.000 5.60 5.20 5.60 5.20 15.68471 15.68471 13.50338 14.9467%
ball 45.05 44.65 40.68 40.28 83.60491 83.60491 85.18228 -1.8691%
E-1
core 1.040 28.93 28.93 27.82 27.82 40.87983 40.87983 40.87983 0.0000%
mantle 1.600 11.53 11.53 7.21 7.21 28.16442 28.16442 32.35976 -13.8634%
cover 1.000 5.67 5.27 5.67 5.27 15.96049 16.13736 13.52337 16.5319%
ball 46.13 45.73 40.69 40.29 85.00474 85.18162 86.76297 -2.0472%
Tables 18 and 19 above provide the MOI Differential for Designs A1-E1. The MOI for rotation about the x and y axes are the same, but the MOI for rotation about the z axis is different. The actual MOI differential for the entire ball design is given in the far right column of the last row for each ball design. The far right column is labeled “Ix vs Iz”. This is the MOI Differential defined as the MOI percent difference between the ball rotating around the X-axis versus rotating around the Z-axis. Whether the value is positive or negative does not matter, this is just a matter of which axis MOI value was subtracted from the other. What matters is the absolute value of the “Ix vs Iz” value. For example, E-1 design has almost 10× the Moment of Inertia Differential (MOI differential) as A-1 design. The formula for calculating the MOI differential is as follows:
Moment of Inertia Differential=(MOI X-axis−MOI Z-axis)/((MOI X-axis+MOI Z-Axis)/2).
FIGS. 69 and 70 illustrate another embodiment of a golf ball 90 (design 1B) which has a spherical inner core 20 as in some of the previous embodiments, an outer core or mantle 92 which has two raised bands 94 encircling the core and crossing over in an X pattern at a non-perpendicular angle, and an outer cover layer 95 over the mantle layer 92 having a complementary inner surface shape with cross over channels. FIG. 70 illustrates the core with the cover layer removed. In this embodiment, the bands cross over at an angle θ of around 30 to 40 degrees, but other cross over angles may be used in other embodiments.
FIG. 71 illustrates a modified core 96 (design 1A) which may be used in place of the core of FIG. 13 and is a variation of the core of FIGS. 69 and 70 combined with the core design of FIG. 57A to 58, where flattened areas 25 are provided on the mantle layer at the poles. The core is otherwise identical to that of FIGS. 69 and 70 and like reference numbers are used as appropriate.
FIG. 72 illustrates another modified core 98 (design 1C) which is similar to that of FIG. 70 with flattened areas 25 at the poles, but in this case the two bands 99 cross over at a larger angle of around 90 degrees. The bands may alternatively be designed as in FIG. 70.
FIGS. 73 and 74 illustrate another embodiment of a golf ball 100 (design 2A) which has a core 102 which has two indented channels or grooves 104 where core material is removed and which cross over in an X pattern in a similar manner to the raised bands of FIGS. 69 and 70. An outer cover layer 105 with a spherical outer surface extends over mantle 102, and has portions 106 extending into the grooves or channels on the outer surface of the mantle. FIG. 74 illustrates core 102 with the outer cover removed. The cross over angle may be similar to that of FIGS. 57 and 60 or may be larger as in FIG. 72. FIG. 73 is a modified version of design 2A in that it shows the case of the channels in the core have sloped sides, as opposed to FIG. 74 where the sides of the channel are perpendicular to the base of the channel. The design 58A data in Tables 24-32 is for the case of the channels having perpendicular sides.
FIG. 75 illustrates a modified core 110 (design 2B) which may be used in place of the core of FIGS. 73 and 74. In this case the core of FIGS. 73 and 74 is combined with the core design of FIG. 57A to 58, with flattened areas 25 at the opposite polar regions of the ball.
In the embodiments of FIGS. 73 to 75, the radius of core 102 is 0.740 inches. Although the core is one piece in the illustrated embodiment, it may comprise an inner core and mantle as in the previous embodiments, with the grooves or channels on the outer surface of the mantle layer.
In all of the embodiments of FIGS. 74 to 75, the center of gravity or cg is still in the center of the ball.
FIGS. 76 and 77 illustrate another embodiment of a golf ball 115 (design 4A) which has a core 116 and a cover 118. FIG. 76 illustrates the core 116 with the cover removed. As seen in FIGS. 76 and 77, the outer surface of core 116 has two parallel channels or recesses 122 extending in circular paths around the outside of core 116. As illustrated in FIG. 77, cover material 124 extends into each recess to form thickened regions of the cover. In other embodiments, the channels 122 may be non-parallel and extend at a slight angle to one another, or may be non-straight (wavy). In one example of ball 115, the core radius was 0.820, the separation between channels 122 was 0.50 inches, and the depth and width of each channel were both around 0.10 inches.
FIG. 78 illustrates a modified core 125 (design 4D) which may replace core 116 of FIGS. 76 and 77. Core 125 combines the flattened core end areas 25 of the first embodiment (Design A) with the parallel channels 122 encircling the core in design 4A, and the core and channels in FIG. 78 are of similar dimensions to those of FIGS. 76 and 77.
FIGS. 79 and 80 illustrate another embodiment of a golf ball 130 (design 4C) which has a core 135 and cover 134, with FIG. 79 illustrating the core with the cover removed. As best seen in FIG. 79, the outer surface 132 of core 135 has a first pair of parallel channels or recesses 136 positioned as in the embodiment of FIGS. 76 and 77, and a second pair of parallel channels or recesses 138 extending perpendicular to recesses 136 and crossing over the recesses 136. As in design 4A and 4D, cover material 139 extends into all of the channels 136, 138. In the embodiments of FIGS. 70 to 80, the raised bands or grooves can also be made thinner or less deep or less high or have tapered, non-perpendicular side walls. These modifications may make parts of the ball easier to injection or compression mold and then remove from the mold. The grooves do not have to be molded into the structure, they can also be cut out as a post-molding step. The raised bands could also be cut out in a post-molding step if the mantle or core is molded at a larger diameter to accommodate the height of the bands. The cover or adjacent outer layer can then be injection molded around the mantle or core.
FIG. 86 illustrates an embodiment of a modified core (or mantle layer) 170 which has wider raised bands 174. In this core, the raised bands 174 are designed to provide an MOI differential between different axes, yet be easily removed from a mold. The core of FIG. 86 has a spherical radius (areas without bands) of 0.785 inches, and the distance from the center of the ball to a flattened area is around 0.765 inches (i.e. a thickness of about 0.020 inches of material is removed to form the flattened areas 25). The width of the top portion of the wide band is 0.122 inches, and the total width of the band including the opposite tapered sides 175 of the band is around 0.40 inches. The thickness of the band at the thickest point is 0.035 inches, and the distance from the center of the ball is around 0.820 inches at the thickest point. The width of the top portion of the band and maximum thickness is the same for the bands shown on the mantles in FIGS. 13-16. However, in the case of FIGS. 13-16, the widest part of the band is only 0.20 inches, as compared to 0.40 inches in this embodiment. The opposite sides 175 of the band in FIG. 86 are wider than in the embodiments of FIGS. 70 to 80 and tapered at a shallow angle, to make the core easier to demold. The total width of each band is around 0.04 inches. Any of the bands of FIGS. 69 to 80 may have bands or grooves of shape and dimensions similar to bands 174 of FIG. 86.
The density, mass, volume and MOI values for a ball made with the wide X-band mantle or outer core layer 170 of FIG. 30 and corresponding cover and solid core (similar to the cover and core in FIG. 69) are given in Table F1 below:
TABLE F1
MOI calculations for ball with core of FIG. 30
Wide Density, Volume,
X-Band g/cm{circumflex over ( )}3 Mass, g cm{circumflex over ( )}3 Ix, g cm{circumflex over ( )}2 Iy, g cm{circumflex over ( )}2 Iz, g cm{circumflex over ( )}2 Ix vs Iz
core 1.150 31.988 27.815 45.2036626 45.2036626 45.2036626 0.000%
mantle 1.200 7.989 6.657 19.6718063 19.5247132 21.9639651 -11.011%
cover 1.000 6.212 6.212 18.3814513 18.5040295 16.4713198 10.961%
sum 46.188 40.684 83.2569203 83.2324053 83.6389475 -0.45780%
In the embodiments of FIGS. 76 to 80, the golf ball is formed from two pieces, specifically core and a cover layer. However, the core may alternatively be two parts or pieces, comprising an inner core and mantle layer, with the grooves or channels in the outer surface of the mantle layer, or the cover layer 118 or 134 may instead be a mantle layer, with a cover layer of uniform thickness surrounding layer 118 or 134.
In the above embodiments, at least one inner layer or part of the ball is non-spherical and is asymmetrical in such a way that the MOI measured in three orthogonal axes is different for at least one of the axes. The non-spherical part in many of the above embodiments is described as an outer core layer or mantle, but could also be an inner cover layer of a two part cover. The design is such that at least one layer of the cover or core is non-uniform in thickness and non-uniform in radius. In one embodiment, the diameter of the entire core (including the inner core and any outer core layer) may be greater than 1.61 inches. At least one core or cover layer has a higher specific gravity than other layers. In one embodiment, the difference in the MOI of any two axes is less than about 3 gm cm2.
As noted above, various types of symmetric or asymmetric dimple patterns may be provided on the outer cover of the golf balls described above. Golf balls with asymmetric dimple patterns are described in described in co-pending patent application Ser. No. 13/097,013 of the same Applicant filed on Aug. 28, 2011, the entire contents of which are incorporated herein by reference. Any of the dimple patterns described in that application may be combined with any of the golf balls described above with different MOI on at least two of the three perpendicular spin axes or principal axes. Two examples of dimple patterns described in application Ser. No. 13/097,013 are illustrated in FIGS. 81 and 82, with FIG. 81 illustrating a golf ball 140 with a dimple pattern which is the same as the 28-1 ball as described in application Ser. No. 13/097,013 and FIG. 82 illustrating a golf ball 140 with a dimple pattern which is the same as the a 25-1 ball as described in application Ser. No. 13/097,013. These dimple patterns (dimple positions, sizes, locations) are described in detail in application Ser. No. 13/097,013 referenced above, and are therefore not described in detail herein. Instead, reference is made to the description in application Ser. No. 13/097,013 for details of these dimple patterns. These dimple patterns or any other asymmetrical dimple patterns, such as dimple patterns 25-2, 25-3, 25-4, 28-2 and 28-3 described in application Ser. No. 13/097,013 referenced above, may be combined with the golf balls having different MOI on at least two axes to produce more variation in MOI.
Alternatively, the differential may result only from the asymmetry of the dimple pattern, as described application Ser. No. 13/097,013 referenced above. The MOI variations in several such balls are provided in Table 20 below.
TABLE 20
% MOI delta
Ix, lbs X Iy, lbs X Iz, lbs X MOI Delta = % (Imax - relative to
Ball inch{circumflex over ( )}2 inch{circumflex over ( )}2 inch{circumflex over ( )}2 Imax Imin Imax - Imin Imin)/Imax Polara
Polara 0.025848 0.025917 0.025919 0.025919 0.025848 0.0000703 0.271% 0.0%
2-9 0.025740 0.025741 0.025806 0.025806 0.025740 0.0000665 0.258% -5.0%
25-1 0.025712 0.025713 0.025800 0.025800 0.025712 0.0000880 0.341% 25.7%
25-2 0.02556791 0.02557031 0.02558386 0.0255839 0.0255679 1.595E−05 0.062% -77.0%
25-3 0.0255822 0.02558822 0.02559062 0.0255906 0.0255822 8.42E−06 0.033% -87.9%
25-4 0.02557818 0.02558058 0.02559721 0.0255972 0.0255782 1.903E−05 0.074% -72.6%
28-1 0.025638 0.025640 0.025764 0.025764 0.025638 0.0001254 0.487% 79.5%
28-2 0.025638 0.025640 0.025764 0.025764 0.025638 0.0001258 0.488% 80.0%
28-3 0.02568461 0.02568647 0.02577059 0.0257706 0.0256846 8.598E−05 0.334% 23.0%
With the original Polara™ golf ball dimple pattern (deep spherical dimples around the equator and shallow truncated dimples on the poles) as a standard, the MOI differences between each orientation of balls with different asymmetric dimple patterns are compared to the original Polara golf ball in addition to being compared to each other. In Table 20, the largest difference between any two orientations is called the “MOI Delta”. In this case the MOI Delta and the previously defined MOI Differentials are different quantities because they are calculated differently. However, they both define a difference in MOI between one rotational axis and the other. And it is this difference, no matter how it is defined, which is important to understand in order to make balls which will perform straighter when hit with a slice or hook type golf swing. In Table 20, the two columns to the right quantify the MOI Delta in terms of the maximum % difference in MOI between two orientations and the MOI Delta relative to the MOI Delta for the original Polara ball. Because the density value used to calculate the mass and MOI (using the solid works CAD program) was lower than the average density of a golf ball, the predicted weight and MOI for each ball are relative to each other, but not exactly the same as the actual MOI values of the golf balls that were made, robot tested and shown in Table 20. Generally a golf ball weighs about 45.5-45.9 g. Comparing the MOI values of all of the balls in Table 20 is quite instructive, in that it predicts the relative order of MOI difference between the different designs.
Design 25-1 of FIG. 82 is very similar to the dimple pattern on the new Polara Ultimate Straight golf balls and has three rows of shallow dimples around the ball's equator and deep spherical dimples (larger dimples) as well as smaller dimples at the polar region. The main difference between dimple patterns 28-1 of FIG. 81 and pattern 25-1 of FIG. 82 is that the 28-1 pattern has more weight removed from the polar regions than pattern 25-1, because the small dimples between the larger, deep dimples are larger in number and volume in dimple pattern 28-1. Dimple patterns 25-2, 25-3 and 25-4 as described in U.S. patent application Ser. No. 13/097,013 referenced above also have truncated dimples around the equatorial region but of larger diameter than those of patterns 25-1 and 28-1, so that more weight is removed around the equator, resulting in a smaller MOI difference between the PH and POP orientations. Dimple pattern 28-2 is nearly identical to 28-1 except that the seam that separates one hemisphere of the ball from the other is wider in pattern 28-2. Dimple pattern 28-3 has similar row of truncated dimples at the equatorial region but has a different dimple arrangement in the polar region, with small spherical dimples arranged together in an area around each pole, and larger, deep spherical dimples between the area of smaller dimples and the equatorial region. Any of these dimple patterns may be used on the outer surface of any of the balls in the preceding embodiments.
Table 21 shows that a ball's MOI Delta does strongly influence the balls dispersion control. In general as the relative MOI Delta of each ball increases, for a slice shot the dispersion distance decreases. Balls 28-3, 25-1, 28-1 and 28-2 all have higher MOI deltas relative to the Polara, and they all have better dispersion control than the Polara. This is shown in Table 5 below.
TABLE 21
% MOI
difference Avg Avg Avg Avg
between C-DISP, C-DIST, T-DISP, T-DIST,
Ball Orientation orientations ft yds ft yds
28-2 PH 0.488% 9.6 180.6 7.3 201.0
28-1 PH 0.487% -2.6 174.8 -7.6 200.5
TopFLite random 0.000% 66.5 189.3 80.6 200.4
XL
Straight
25-1 PH 0.341% 7.4 184.7 9.6 207.5
28-3 PH 0.334% 16.3 191.8 23.5 211.8
Polara PFB 0.271% 29.7 196.6 38.0 214.6
2-9 PH 0.258% 12.8 192.2 10.5 214.5
25-4 PH 0.074% 56.0 185.4 71.0 197.3
25-2 PH 0.062% 52.8 187.0 68.1 199.9
25-3 PH 0.033% 63.4 188.0 75.1 197.9
Golf balls of the embodiments with asymmetrical dimple patterns described above exhibit lower aerodynamic lift properties in one orientation than in another. If these dimple patterns are provided on balls with core and cover layers constructed as described above in connection with the embodiments of FIGS. 57A to 80, the lower lift properties of dimple patterns like those above act to reinforce the slice and hook correcting MOI differential properties of the ball construction and thus help reduce the slice or hook even further as the ball is flying through the air. A symmetrical low-lift dimple pattern can also be added to the ball constructions of FIGS. 57A to 80 with differential MOI so that the lift characteristic helps the ball reduce hook and slice dispersion in the high MOI or any other orientation. With the asymmetrical dimple designs described above, such as those of FIGS. 81 and 82 for example, the ball is aligned so the horizontal axis is pointed at the golfer (PH=poles horizontal orientation) and as long as this horizontal axis does not represent the lowest of the MOI differential axis values (ideally the horizontal axis represents the highest MOI differential axis configuration) the ball will exhibit slice and hook correcting behavior. In this configuration the horizontal axis is also parallel to the ground and is orthogonal to the intended direction of travel. The horizontal axis in this configuration would also be essentially aligned perpendicular to the plane of the club face and is aligned horizontally pointing towards the golfer.
Any combination of symmetrical or asymmetrical dimple patterns, such as the dimple patterns of FIGS. 81 and 82 or any other dimple patterns described in U.S. patent application Ser. No. 13/097,013 referenced above, can also be combined with these designs or combination of designs. The dimple patterns could also be combined so that the MOI differentials caused by the ball construction, dimple patterns and specific gravities of layers all work together to give the maximum MOI differential or they could be oriented so that they did not maximize the ball's MOI differential but instead lowered the MOI differential of the ball because the maximum MOI axis of each part did not correspond to the same location.
FIG. 83 illustrates a ball 140 according to another embodiment which has a different, crossing dimple pattern. This ball has two bands 142 of smaller dimples 144 which cross over one another in a similar manner to the cross over channels on the core of the ball of FIG. 84. The remainder of the ball surface has larger dimples 145 of varying sizes. The smaller dimples 144 may also be of different sizes.
FIG. 84 illustrates another ball 150 with a modified cross over dimple pattern similar to that of ball 140 but with the dimples in the cross over bands 151 including some truncated spherical dimples 152 and sets of four smaller dimples 154 at spaced locations in each band. Dimples 155 in the areas outside bands 151 are of varying sizes but the majority are larger than the dimples in bands 151.
FIG. 85 illustrates another embodiment of a golf ball 160 with a cross over dimple pattern similar to FIG. 83, but with two cross over bands 162 of spherical truncated dimples 164 and an open area 165 of no dimples at each cross over point. The remainder of the dimples in areas outside the cross-over bands 162 are spherical dimples 166 in a range of different sizes. This dimple pattern is referred to as dimple pattern 95-3 in the following description. The spherical truncated dimples are formed as described in co-pending patent application Ser. No. 13/097,013 referenced above, the contents of which are incorporated herein by reference (see FIG. 9 of application Ser. No. 13/097,013 and corresponding description).
The dimple co-ordinates for one embodiment of dimple pattern 95-3 of FIG. 29 are shown in Table 22 below.
TABLE 22
Design parameters for dimple pattern 95-3.
Dimple Location Coordinates Dimple Dimple Dimple
Phi Theta Radius, in depth, in shape
21.8270 84.6792 0.0750 0.0080 spherical
32.3147 84.6792 0.0750 0.0080 spherical
42.7978 84.6792 0.0750 0.0080 spherical
137.2022 84.6792 0.0750 0.0080 spherical
147.6853 84.6792 0.0750 0.0080 spherical
158.1730 84.6792 0.0750 0.0080 spherical
201.8270 84.6792 0.0750 0.0080 spherical
212.3147 84.6792 0.0750 0.0080 spherical
222.7978 84.6792 0.0750 0.0080 spherical
317.2022 84.6792 0.0750 0.0080 spherical
327.6853 84.6792 0.0750 0.0080 spherical
338.1730 84.6792 0.0750 0.0080 spherical
11.1741 84.5082 0.0775 0.0085 spherical
168.8259 84.5082 0.0775 0.0085 spherical
191.1741 84.5082 0.0775 0.0085 spherical
348.8259 84.5082 0.0775 0.0085 spherical
0.0000 84.1660 0.0825 0.0085 spherical
180.0000 84.1660 0.0825 0.0085 spherical
18.8528 74.3007 0.0800 0.0080 spherical
161.1472 74.3007 0.0800 0.0080 spherical
198.8528 74.3007 0.0800 0.0080 spherical
341.1472 74.3007 0.0800 0.0080 spherical
42.1883 74.0879 0.0775 0.0080 spherical
137.8117 74.0879 0.0775 0.0080 spherical
222.1883 74.0879 0.0775 0.0080 spherical
317.8117 74.0879 0.0775 0.0080 spherical
30.4890 74.0478 0.0800 0.0080 spherical
149.5110 74.0478 0.0800 0.0080 spherical
210.4890 74.0478 0.0800 0.0080 spherical
329.5110 74.0478 0.0800 0.0080 spherical
6.5803 73.7747 0.0900 0.0085 spherical
173.4197 73.7747 0.0900 0.0085 spherical
186.5803 73.7747 0.0900 0.0085 spherical
353.4197 73.7747 0.0900 0.0085 spherical
14.2046 63.3087 0.0900 0.0080 spherical
165.7954 63.3087 0.0900 0.0080 spherical
194.2046 63.3087 0.0900 0.0080 spherical
345.7954 63.3087 0.0900 0.0080 spherical
40.4957 63.0753 0.0825 0.0080 spherical
139.5043 63.0753 0.0825 0.0080 spherical
220.4957 63.0753 0.0825 0.0080 spherical
319.5043 63.0753 0.0825 0.0080 spherical
27.6319 63.0681 0.0825 0.0080 spherical
152.3681 63.0681 0.0825 0.0080 spherical
207.6319 63.0681 0.0825 0.0080 spherical
332.3681 63.0681 0.0825 0.0080 spherical
0.0000 62.6719 0.0925 0.0085 spherical
180.0000 62.6719 0.0925 0.0085 spherical
37.7785 52.1889 0.0775 0.0080 spherical
142.2215 52.1889 0.0775 0.0080 spherical
217.7785 52.1889 0.0775 0.0080 spherical
322.2215 52.1889 0.0775 0.0080 spherical
23.4384 51.9772 0.0850 0.0080 spherical
156.5616 51.9772 0.0850 0.0080 spherical
203.4384 51.9772 0.0850 0.0080 spherical
336.5616 51.9772 0.0850 0.0080 spherical
7.9879 51.9242 0.0900 0.0080 spherical
172.0121 51.9242 0.0900 0.0080 spherical
187.9879 51.9242 0.0900 0.0080 spherical
352.0121 51.9242 0.0900 0.0080 spherical
16.7776 41.7657 0.0775 0.0080 spherical
163.2224 41.7657 0.0775 0.0080 spherical
196.7776 41.7657 0.0775 0.0080 spherical
343.2224 41.7657 0.0775 0.0080 spherical
33.2575 41.7337 0.0800 0.0080 spherical
146.7425 41.7337 0.0800 0.0080 spherical
213.2575 41.7337 0.0800 0.0080 spherical
326.7425 41.7337 0.0800 0.0080 spherical
0.0000 41.4315 0.0825 0.0080 spherical
180.0000 41.4315 0.0825 0.0080 spherical
9.5096 32.4648 0.0700 0.0080 spherical
170.4904 32.4648 0.0700 0.0080 spherical
189.5096 32.4648 0.0700 0.0080 spherical
350.4904 32.4648 0.0700 0.0080 spherical
27.9004 31.5681 0.0700 0.0080 spherical
152.0996 31.5681 0.0700 0.0080 spherical
207.9004 31.5681 0.0700 0.0080 spherical
332.0996 31.5681 0.0700 0.0080 spherical
0.0000 24.5882 0.0600 0.0080 spherical
180.0000 24.5882 0.0600 0.0080 spherical
19.4033 23.0874 0.0525 0.0080 spherical
160.5967 23.0874 0.0525 0.0080 spherical
199.4033 23.0874 0.0525 0.0080 spherical
340.5967 23.0874 0.0525 0.0080 spherical
0.0000 16.8793 0.0500 0.0080 spherical
180.0000 16.8793 0.0500 0.0080 spherical
75.8147 74.9004 0.0500 0.0050 spherical
104.1853 74.9004 0.0500 0.0050 spherical
255.8147 74.9004 0.0500 0.0050 spherical
284.1853 74.9004 0.0500 0.0050 spherical
84.0292 38.1323 0.0525 0.0050 spherical
90.0000 53.9939 0.0525 0.0050 spherical
95.9708 38.1323 0.0525 0.0050 spherical
264.0292 38.1323 0.0525 0.0050 spherical
270.0000 53.9939 0.0525 0.0050 spherical
275.9708 38.1323 0.0525 0.0050 spherical
90.0000 30.2529 0.0550 0.0050 spherical
270.0000 30.2529 0.0550 0.0050 spherical
78.1543 66.8061 0.0700 0.0050 spherical
101.8457 66.8061 0.0700 0.0050 spherical
258.1543 66.8061 0.0700 0.0050 spherical
281.8457 66.8061 0.0700 0.0050 spherical
79.8109 56.9863 0.0725 0.0050 spherical
84.6928 74.7269 0.0725 0.0050 spherical
95.3072 74.7269 0.0725 0.0050 spherical
100.1891 56.9863 0.0725 0.0050 spherical
259.8109 56.9863 0.0725 0.0050 spherical
264.6928 74.7269 0.0725 0.0050 spherical
275.3072 74.7269 0.0725 0.0050 spherical
280.1891 56.9863 0.0725 0.0050 spherical
82.8467 46.9968 0.0750 0.0050 spherical
97.1533 46.9968 0.0750 0.0050 spherical
262.8467 46.9968 0.0750 0.0050 spherical
277.1533 46.9968 0.0750 0.0050 spherical
90.0000 84.1660 0.0825 0.0050 spherical
270.0000 84.1660 0.0825 0.0050 spherical
78.3009 83.9948 0.0850 0.0050 spherical
101.6991 83.9948 0.0850 0.0050 spherical
258.3009 83.9948 0.0850 0.0050 spherical
281.6991 83.9948 0.0850 0.0050 spherical
90.0000 64.0023 0.0900 0.0050 spherical
270.0000 64.0023 0.0900 0.0050 spherical
0.0000 9.0005 0.0525 0.0039 truncated
30.0000 15.5797 0.0525 0.0039 truncated
40.1871 23.7627 0.0525 0.0039 truncated
45.3421 32.3801 0.0525 0.0039 truncated
48.2621 41.1300 0.0525 0.0039 truncated
49.9941 49.9212 0.0525 0.0039 truncated
50.9686 58.7736 0.0525 0.0039 truncated
51.5123 67.7222 0.0525 0.0039 truncated
51.9298 76.6289 0.0525 0.0039 truncated
52.3885 85.5337 0.0525 0.0039 truncated
60.0000 17.9044 0.0525 0.0039 truncated
60.0000 27.2199 0.0525 0.0039 truncated
60.0000 36.1155 0.0525 0.0039 truncated
60.0000 45.0000 0.0525 0.0039 truncated
60.0000 54.0000 0.0525 0.0039 truncated
60.0000 63.0000 0.0525 0.0039 truncated
60.0000 72.0000 0.0525 0.0039 truncated
60.0000 81.0000 0.0525 0.0039 truncated
67.8935 76.6701 0.0525 0.0039 truncated
68.1082 85.5337 0.0525 0.0039 truncated
68.1818 67.7570 0.0525 0.0039 truncated
68.9243 58.8870 0.0525 0.0039 truncated
70.2769 49.9570 0.0525 0.0039 truncated
71.9425 41.1058 0.0525 0.0039 truncated
74.5088 32.2228 0.0525 0.0039 truncated
78.9041 23.7143 0.0525 0.0039 truncated
90.0000 15.5797 0.0525 0.0039 truncated
101.0959 23.7143 0.0525 0.0039 truncated
105.4912 32.2228 0.0525 0.0039 truncated
108.0575 41.1058 0.0525 0.0039 truncated
109.7231 49.9570 0.0525 0.0039 truncated
111.0757 58.8870 0.0525 0.0039 truncated
111.8182 67.7570 0.0525 0.0039 truncated
111.8918 85.5337 0.0525 0.0039 truncated
112.1065 76.6701 0.0525 0.0039 truncated
120.0000 17.9044 0.0525 0.0039 truncated
120.0000 27.2199 0.0525 0.0039 truncated
120.0000 36.1155 0.0525 0.0039 truncated
120.0000 45.0000 0.0525 0.0039 truncated
120.0000 54.0000 0.0525 0.0039 truncated
120.0000 63.0000 0.0525 0.0039 truncated
120.0000 72.0000 0.0525 0.0039 truncated
120.0000 81.0000 0.0525 0.0039 truncated
127.6115 85.5337 0.0525 0.0039 truncated
128.0702 76.6289 0.0525 0.0039 truncated
128.4877 67.7222 0.0525 0.0039 truncated
129.0314 58.7736 0.0525 0.0039 truncated
130.0059 49.9212 0.0525 0.0039 truncated
131.7379 41.1300 0.0525 0.0039 truncated
134.6579 32.3801 0.0525 0.0039 truncated
139.8129 23.7627 0.0525 0.0039 truncated
150.0000 15.5797 0.0525 0.0039 truncated
180.0000 9.0005 0.0525 0.0039 truncated
210.0000 15.5797 0.0525 0.0039 truncated
220.1871 23.7627 0.0525 0.0039 truncated
225.3421 32.3801 0.0525 0.0039 truncated
228.2621 41.1300 0.0525 0.0039 truncated
229.9941 49.9212 0.0525 0.0039 truncated
230.9686 58.7736 0.0525 0.0039 truncated
231.5123 67.7222 0.0525 0.0039 truncated
231.9298 76.6289 0.0525 0.0039 truncated
232.3885 85.5337 0.0525 0.0039 truncated
240.0000 17.9044 0.0525 0.0039 truncated
240.0000 27.2199 0.0525 0.0039 truncated
240.0000 36.1155 0.0525 0.0039 truncated
240.0000 45.0000 0.0525 0.0039 truncated
240.0000 54.0000 0.0525 0.0039 truncated
240.0000 63.0000 0.0525 0.0039 truncated
240.0000 72.0000 0.0525 0.0039 truncated
240.0000 81.0000 0.0525 0.0039 truncated
247.8935 76.6701 0.0525 0.0039 truncated
248.1082 85.5337 0.0525 0.0039 truncated
248.1818 67.7570 0.0525 0.0039 truncated
248.9243 58.8870 0.0525 0.0039 truncated
250.2769 49.9570 0.0525 0.0039 truncated
251.9425 41.1058 0.0525 0.0039 truncated
254.5088 32.2228 0.0525 0.0039 truncated
258.9041 23.7143 0.0525 0.0039 truncated
270.0000 15.5797 0.0525 0.0039 truncated
281.0959 23.7143 0.0525 0.0039 truncated
285.4912 32.2228 0.0525 0.0039 truncated
288.0575 41.1058 0.0525 0.0039 truncated
289.7231 49.9570 0.0525 0.0039 truncated
291.0757 58.8870 0.0525 0.0039 truncated
291.8182 67.7570 0.0525 0.0039 truncated
291.8918 85.5337 0.0525 0.0039 truncated
292.1065 76.6701 0.0525 0.0039 truncated
300.0000 17.9044 0.0525 0.0039 truncated
300.0000 27.2199 0.0525 0.0039 truncated
300.0000 36.1155 0.0525 0.0039 truncated
300.0000 45.0000 0.0525 0.0039 truncated
300.0000 54.0000 0.0525 0.0039 truncated
300.0000 63.0000 0.0525 0.0039 truncated
300.0000 72.0000 0.0525 0.0039 truncated
300.0000 81.0000 0.0525 0.0039 truncated
307.6115 85.5337 0.0525 0.0039 truncated
308.0702 76.6289 0.0525 0.0039 truncated
308.4877 67.7222 0.0525 0.0039 truncated
309.0314 58.7736 0.0525 0.0039 truncated
310.0059 49.9212 0.0525 0.0039 truncated
311.7379 41.1300 0.0525 0.0039 truncated
314.6579 32.3801 0.0525 0.0039 truncated
319.8129 23.7627 0.0525 0.0039 truncated
330.0000 15.5797 0.0525 0.0039 truncated
The balls of FIGS. 83 to 85 may be one piece or multiple piece balls, and have crossing patterns that are asymmetrical about all three axes. Where a cross over dimple pattern is combined with a ball having cross over bands and mating recesses in opposing layers, the cross over points in the dimple pattern and underlying layers may be aligned to enhance the asymmetrical effect. Table 23 below compares the MOI about each spin axis for a one piece ball with dimple pattern 25-1 of FIG. 26, dimple pattern 28-1 of FIG. 81, and the cross over dimple pattern of FIG. 84. Note the ball with the crossing dimple pattern is asymmetrical about all 3 axes as compared to the 25-1 and 28-1 balls which are asymmetrical about only 2 axes. The two orthogonal axes going through the equator have essentially the same MOI values for designs 25-1 and 28-1—this is why the Ix vs Iy differs by only 0.006% and 0.007%, respectively. In contrast, the Ix and Iy MOI differentials for the Crossing Pattern design differ by more than 12 times as much, 0.082%. This means that the crossing pattern's asymmetrical design has 3 different principle moments of inertia, whereas designs 25-1 and 28-1 only have 2 principle moments of inertia.
TABLE 23
Comparison of 25-1, 28-1 and Crossing Pattern designs
Density Volume
Design g/cm{circumflex over ( )}3 Mass, g cm{circumflex over ( )}3 Ix, g cm{circumflex over ( )}2 Iy, g cm{circumflex over ( )}2 Iz, g cm{circumflex over ( )}2 Ix vs Iz Ix vs Iy Iy vs Iz
25-1, 1-piece 1.00 40.219 40.219 72.596764 72.601333 72.831183 -0.322% -0.006% -0.316%
ball
28-1, 1-piece 1.00 40.156 40.156 72.368261 72.373179 72.724804 -0.491% -0.007% -0.485%
ball
Crossing Pattern, 1.00 40.161 40.161 72.374305 72.433659 72.697310 -0.445% -0.082% -0.363%
1-piece ball
Any of the balls of FIGS. 57 to 80 may have one piece, two piece or multiple piece cores, one layer covers or multiple layer covers, and may have various different dimple patterns, including those of FIGS. 81 to 86.
Tables 24, 25 and 26 contain the density, volume and mass information for each of the individual layers and the complete balls for all of the ball designs of FIGS. 69 to 80 in combination with the dimple patterns 28-1 of FIG. 81 (Table 8), dimple pattern 25-1 of FIG. 26 (Table 25) and dimple pattern 95-3 of FIG. 83 (Table 10). In designs 2A, 2B, 4A, 4B and 4C the width and depth of the channels were 0.10 inches. The angle between the bands in designs 1A and 1B was 30 degrees and in design 1C the angle was 90 degrees. The angle between the channels in designs 2A and 2B was 30 degrees. The distance between the channels in designs 4A and 4D was 0.50 inches.
TABLE 24
Dimples Cover Mantle Core Ball
Ball Design w/ Density. volume, Density, volume, Density. volume, Density. volume, mass, volume,
Dimple Design g/cc cc g/cc cc g/cc cc g/cc cc g cc
4D w/ 28-1 1.295 0.5347 1.295 4.1838 1.120 36.5006 45.61 40.15
4C w/ 28-1 1.260 0.5347 1.260 5.1574 1.120 35.5270 45.61 40.15
4A w/ 28-1 1.300 0.5347 1.300 4.0509 1.120 36.6335 45.60 40.15
2B w/ 28-1 1.300 0.5347 1.300 4.0666 1.120 36.6177 45.60 40.15
2A w/ 28-1 1.300 0.5347 1.300 3.9337 1.120 36.7506 45.58 40.15
1A w/ 28-1 1.000 0.5347 1.000 6.6250 1.200 6.2439 1.150 27.8154 45.57 40.15
1B w/ 28-1 1.000 0.5347 1.000 6.5930 1.200 6.2760 1.150 27.8154 45.58 40.15
1C w/ 28-1 1.000 0.5347 1.000 6.6157 1.200 6.2533 1.150 27.8154 45.57 40.15
TABLE 25
Dimples Cover Mantle Core Ball
Ball Design w/ Density. volume, Density, volume, Density. volume, Density. volume, mass volume,
Dimple Design g/cc cc g/cc cc g/cc cc g/cc cc (grams) cc
4D w/ 25-1 1.295 0.4717 1.295 4.1838 1.120 36.5006 45.61 40.21
4C w/ 25-1 1.260 0.4717 1.260 5.1574 1.120 35.5270 45.61 40.21
4A w/ 25-1 1.300 0.4717 1.300 4.0509 1.120 36.6335 45.60 40.21
2B w/ 25-1 1.300 0.4717 1.300 4.0666 1.120 36.6177 45.60 40.21
2A w/ 25-1 1.300 0.4717 1.300 3.9337 1.120 36.7506 45.58 40.21
1A w/ 25-1 1.000 0.4717 1.000 6.6250 1.200 6.2439 1.150 27.8154 45.57 40.21
1B w/ 25-1 1.000 0.4717 1.000 6.5930 1.200 6.2760 1.150 27.8154 45.58 40.21
1C w/ 25-1 1.000 0.4717 1.000 6.6157 1.200 6.2533 1.150 27.8154 45.57 40.21
TABLE 26
Dimples Cover Mantle Core Ball
Ball Design w/ Density. volume, Density. volume, Density. volume, Density. volume, mass
Dimple Design g/cc cc g/cc cc g/cc cc g/cc cc (grams) volume, cc
4D w/ 95-3 1.295 0.5076 1.295 4.1838 1.120 36.5006 45.64 40.18
4C w/ 95-3 1.260 0.5076 1.260 5.1574 1.120 35.5270 45.65 40.18
4A w/ 95-3 1.300 0.5076 1.300 4.0509 1.120 36.6335 45.64 40.18
2B w/ 95-3 1.300 0.5076 1.300 4.0666 1.120 36.6177 45.64 40.18
2A w/ 95-3 1.300 0.5076 1.300 3.9337 1.120 36.7506 45.61 40.18
1A w/ 95-3 1.000 0.5076 1.000 6.6250 1.200 6.2439 1.150 27.8154 45.60 40.18
1B w/ 95-3 1.000 0.5076 1.000 6.5930 1.200 6.2760 1.150 27.8154 45.60 40.18
1C w/ 95-3 1.000 0.5076 1.000 6.6157 1.200 6.2533 1.150 27.8154 45.60 40.18
Tables 27, 28 and 29 contain the moment of inertia values for each of the principle axes of rotation for all of the individual layers of each ball design in FIGS. 69 to 80 in combination with dimple pattern 28-1 (Table 27), 25-1 (Table 28) and 95-3 (Table 29). The units for the moment of inertia values in Tables 27-29 are lb incĥ2. These dimple patterns are configured such that a MOI differential between any two of the three orthogonal axes is created in the cover layer. The MOI differential in the cover layer and the MOI in the remainder of the ball are each less than the MOI differential of the entire ball, as seen in the tables below. In some embodiments, the sum of the MOI differentials of the individual parts is less than the MOI differential of the entire ball between at least two of the three orthogonal axes.
TABLE 27
Ball Design
w/ Dimple
Design Ix Iy Iz
Dimples
4D w/ 28-1 0.000763 0.000605 0.000763
4C w/ 28-1 0.000743 0.000588 0.000743
4A w/ 28-1 0.000766 0.000607 0.000766
2B w/ 28-1 0.000766 0.000607 0.000766
2A w/ 28-1 0.000766 0.000607 0.000766
1A w/ 28-1 0.000589 0.000467 0.000589
1B w/ 28-1 0.000589 0.000467 0.000589
1C w/ 28-1 0.000589 0.000467 0.000589
Cover
4D w/ 28-1 0.005173 0.005173 0.005540
4C w/ 28-1 0.006405 0.005923 0.006405
4A w/ 28-1 0.004949 0.004949 0.005553
2B w/ 28-1 0.005126 0.005047 0.005565
2A w/ 28-1 0.004883 0.004803 0.005557
1A w/ 28-1 0.006589 0.006650 0.006131
1B w/ 28-1 0.006547 0.006608 0.006131
1C w/ 28-1 0.006368 0.006650 0.006326
Mantle
4D w/ 28-1
4C w/ 28-1
4A w/ 28-1
2B w/ 28-1
2A w/ 28-1
1A w/ 28-1 0.006340 0.006266 0.006889
1B w/ 28-1 0.006391 0.006317 0.006890
1C w/ 28-1 0.006605 0.006267 0.006655
Core
4D w/ 28-1 0.023854 0.023854 0.023537
4C w/ 28-1 0.022634 0.023062 0.022634
4A w/ 28-1 0.024063 0.024063 0.023544
2B w/ 28-1 0.023911 0.023980 0.023533
2A w/ 28-1 0.024121 0.024190 0.023540
1A w/ 28-1 0.015433 0.015433 0.015433
1B w/ 28-1 0.015433 0.015433 0.015433
1C w/ 28-1 0.015433 0.015433 0.015433
TABLE 28
Ball Design
w/ Dimple
Design Ix Iy Iz
Dimples
4D w/ 25-1 0.000662 0.000558 0.000662
4C w/ 25-1 0.000644 0.000542 0.000644
4A w/ 25-1 0.000664 0.000560 0.000664
2B w/ 25-1 0.000664 0.000560 0.000664
2A w/ 25-1 0.000664 0.000560 0.000664
1A w/ 25-1 0.000511 0.000431 0.000511
1B w/ 25-1 0.000511 0.000431 0.000511
1C w/ 25-1 0.000511 0.000431 0.000511
Cover
4D w/ 25-1 0.005173 0.005173 0.005540
4C w/ 25-1 0.006405 0.005923 0.006405
4A w/ 25-1 0.004949 0.004949 0.005553
2B w/ 25-1 0.005126 0.005047 0.005565
2A w/ 25-1 0.004883 0.004803 0.005557
1A w/ 25-1 0.006589 0.006650 0.006131
1B w/ 25-1 0.006547 0.006608 0.006131
1C w/ 25-1 0.006368 0.006650 0.006326
Mantle
4D w/ 25-1
4C w/ 25-1
4A w/ 25-1
2B w/ 25-1
2A w/ 25-1
1A w/ 25-1 0.006340 0.006266 0.006889
1B w/ 25-1 0.006391 0.006317 0.006890
1C w/ 25-1 0.006605 0.006267 0.006655
Core
4D w/ 25-1 0.023854 0.023854 0.023537
4C w/ 25-1 0.022634 0.023062 0.022634
4A w/ 25-1 0.024063 0.024063 0.023544
2B w/ 25-1 0.023911 0.023980 0.023533
2A w/ 25-1 0.024121 0.024190 0.023540
1A w/ 25-1 0.015433 0.015433 0.015433
1B w/ 25-1 0.015433 0.015433 0.015433
1C w/ 25-1 0.015433 0.015433 0.015433
TABLE 29
Ball Design
w/ Dimple
Design Ix Iy Iz
Dimples
4D w/ 95-3 0.000593 0.000711 0.000722
4C w/ 95-3 0.000577 0.000692 0.000703
4A w/ 95-3 0.000595 0.000714 0.000725
2B w/ 95-3 0.000595 0.000714 0.000725
2A w/ 95-3 0.000595 0.000714 0.000725
1A w/ 95-3 0.000458 0.000549 0.000558
1B w/ 95-3 0.000458 0.000549 0.000558
1C w/ 95-3 0.000458 0.000549 0.000558
Cover
4D w/ 95-3 0.005173 0.005173 0.005540
4C w/ 95-3 0.006405 0.005923 0.006405
4A w/ 95-3 0.004949 0.004949 0.005553
2B w/ 95-3 0.005126 0.005047 0.005565
2A w/ 95-3 0.004883 0.004803 0.005557
1A w/ 95-3 0.006589 0.006650 0.006131
1B w/ 95-3 0.006547 0.006608 0.006131
1C w/ 95-3 0.006368 0.006650 0.006326
Mantle
4D w/ 95-3
4C w/ 95-3
4A w/ 95-3
2B w/ 95-3
2A w/ 95-3
1A w/ 95-3 0.006340 0.006266 0.006889
1B w/ 95-3 0.006391 0.006317 0.006890
1C w/ 95-3 0.006605 0.006267 0.006655
Core
4D w/ 95-3 0.023854 0.023854 0.023537
4C w/ 95-3 0.022634 0.023062 0.022634
4A w/ 95-3 0.024063 0.024063 0.023544
2B w/ 95-3 0.023911 0.023980 0.023533
2A w/ 95-3 0.024121 0.024190 0.023540
1A w/ 95-3 0.015433 0.015433 0.015433
1B w/ 95-3 0.015433 0.015433 0.015433
1C w/ 95-3 0.015433 0.015433 0.015433
Tables 30, 31 and 32 contain the ball mass, ball volume, ball moment of inertia values for each of the principle axes of rotation and the MOI Differential for each of the complete ball designs of FIGS. 69 to 80 in combination with dimple patterns 28-1 (Table 30), dimple pattern 25-1 (Table 31) and dimple pattern 95-3 (Table 32). The moment of inertia is expressed as “lb incĥ2” units in Tables 30-32. The tables below show that the MOI differential is generally highest for the balls with dimple pattern 28-1 and 95-3, and with ball constructions 2A and 4A.
TABLE 30
Ball
Ball
Design
w/
Dimple mass, volume, MOI
Design g cc Ix′ Iy′ Iz′ Differential
4D w/ 45.61 40.15 0.028263 0.028263 0.028471 0.734%
28-1
4C w/ 45.61 40.15 0.028297 0.028397 0.028297 0.356%
28-1
4A w/ 45.60 40.15 0.028247 0.028247 0.028489 0.856%
28-1
2B w/ 45.60 40.15 0.028271 0.028260 0.028491 0.814%
28-1
2A w/ 45.58 40.15 0.028237 0.028226 0.028490 0.930%
28-1
1A w/ 45.57 40.15 0.027773 0.027760 0.027987 0.812%
28-1
1B w/ 45.58 40.15 0.027781 0.027769 0.027987 0.782%
28-1
1C w/ 45.57 40.15 0.027817 0.027760 0.027948 0.672%
28-1
TABLE 31
Ball
Ball
Design
w/ vol-
Dimple mass ume, MOI
Design (grams) cc Ix′ Iy′ Iz′ Differential
4D w/ 45.61 40.21 0.028365 0.028365 0.028519 0.541%
25-1
4C w/ 45.61 40.21 0.028395 0.028443 0.028395 0.169%
25-1
4A w/ 45.60 40.21 0.028348 0.028348 0.028537 0.662%
25-1
2B w/ 45.60 40.21 0.028373 0.028362 0.028538 0.620%
25-1
2A w/ 45.58 40.21 0.028339 0.028328 0.028537 0.735%
25-1
1A w/ 45.57 40.21 0.027851 0.027839 0.028023 0.661%
25-1
1B w/ 45.58 40.21 0.027859 0.027847 0.028023 0.630%
25-1
1C w/ 45.57 40.21 0.027895 0.027839 0.027984 0.521%
25-1
TABLE 32
Ball
Ball
Design
w/ vol-
Dimple mass ume, MOI
Design (grams) cc Ix′ Iy′ Iz′ Differential
4D w/ 45.64 40.18 0.028304 0.028315 0.028483 0.630%
95-3
4C w/ 45.65 40.18 0.028347 0.028283 0.028462 0.632%
95-3
4A w/ 45.64 40.18 0.028288 0.028299 0.028501 0.751%
95-3
2B w/ 45.64 40.18 0.028323 0.028301 0.028503 0.710%
95-3
2A w/ 45.61 40.18 0.028289 0.028267 0.028502 0.825%
95-3
1A w/ 45.60 40.18 0.027813 0.027792 0.027996 0.731%
95-3
1B w/ 45.60 40.18 0.027821 0.027801 0.027996 0.700%
95-3
1C w/ 45.60 40.18 0.027857 0.027792 0.027957 0.590%
95-3
If a ball is designed with an internal construction providing a preferred spin axis due to differential MOI between the spin axes, the dimple pattern can be designed to have the lowest lift or lift coefficient (CL) and drag or drag coefficient (CD) when the ball is spinning about the preferred spin axis, i.e. the spin axis corresponding to the highest MOI. This decouples the dimple pattern from the mechanism for creating a preferred spin axis. The differential MOI may be achieved by different specific gravity layers in the ball or by different non-spherical geometry in at least one layer, or both, as described in the above embodiments.
FIGS. 57A to 85 provide various examples of possible constructions of the pieces of a multi-piece golf ball designed to provide a preferred spin axis, combined with various patterns of outer surface features or dimples to create an MOI differential between two or all three of the spin axes. There are other possible configurations. In alternative embodiments, a ball may have a core with one or more recessed regions which the mantle does not extend into, a core may be positioned non-centrally with respect to the outer surface of the ball, a channel or band may be intermittent rather than extending continuously about the ball, or a ball layer may have projections which do not extend radially. Dimple patterns may be designed to augment the MOI differential. In the above embodiments and variations thereof, the spin axis with the highest MOI is the preferred spin axis and most importantly a golf ball with a MOI differential and preferred spin axis resists tilting of the ball's spin axis when it is hit with a slice or hook type golf club swing. The ball's resistance to tilting of the spin axis means the ball resists hooking and slicing (left or right dispersion from the intended direction of flight).
The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles described herein can be applied to other embodiments without departing from the spirit or scope of the invention. Thus, it is to be understood that the description and drawings presented herein represent a presently preferred embodiment of the invention and are therefore representative of the subject matter which is broadly contemplated by the present invention. It is further understood that the scope of the present invention fully encompasses other embodiments that may become obvious to those skilled in the art and that the scope of the present invention is accordingly limited by nothing other than the appended claims.
In order to obtain a low L/D (lift/drag) ratio, high drag and low lift dimples may be employed. Balls with L/D ratios similar or less than the values measured for ProVI and other standard golf balls may be used in the kit described above, as well as any of the non-conforming or conforming golf balls described above in connection with FIGS. 1 to 55.
In other kit examples, golf balls are selected for the kit which have a L/D ratio of less than about 0.75, and preferably less than about 0.70, at a spin rate of 3,000 rpm and at a Reynolds number of about 160,000.
The above embodiments describe various examples of a kit combining a higher lofted driver with a golf ball which has a lower flight trajectory, which may result from lower lift due to predetermined dimple patterns, as described above in connection with FIGS. 1 to 55, or which may result from using golf balls with higher drag, higher weight, or smaller size. In the kits described above, the increased spin resulting from the higher lofted club provides extra lift and a higher launch angle to a relatively low lift golf ball, resulting in the ball climbing higher and traveling much further than expected.
It should be understood that the term “dimples” is meant to include any and all of the surface modifications that are applied to the exterior of the golf ball in order to modify the flight characteristics of the golf ball.
The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles described herein can be applied to other embodiments without departing from the spirit or scope of the invention. Thus, it is to be understood that the description and drawings presented herein represent a presently preferred embodiment of the invention and are therefore representative of the subject matter which is broadly contemplated by the present invention. It is further understood that the scope of the present invention fully encompasses other embodiments that may become obvious to those skilled in the art and that the scope of the present invention is accordingly limited by nothing other than the appended claims.
