RELATED APPLICATIONS INFORMATION This application claims the benefit under §119(e) of U.S. Provisional Application Ser. No. 61/328,927 filed Apr. 28, 2010 and entitled “Nonconforming Anti-Slice Ball,” which is incorporated herein by reference in its 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 golf ball dimple patterns 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. However, with respect to surface characteristics, not all the regions on the surface of a spinning golf ball contribute equally to the generation of the total lift force. As an example, if the surface of the ball has a spherically symmetrical dimple pattern and the ball is hit so that the spin axis passes through the poles, the surface region closest to the golf ball equator (i.e., the great circle orthogonal to the spin axis) is more important in generating lift than are the regions close to the poles. However, 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 are not legal in professional golf, they are very helpful for the recreational golfer in making 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 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 few or no dimples. For this asymmetric golf ball, the measured lift and drag coefficients are strongly influenced by the orientation of the golf ball on the tee before it is struck. 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,
Other golf balls have been constructed of a single or multi-layer core, either solid or wound, that is tightly surrounded by a single or multilayer cover formed from polymeric materials, such as polyurethane, balata rubber, ionomers or a combination. Although some of these golf balls do reduce some hook and slice dispersion, this type of ball construction has the disadvantage of adding cost to the golf ball manufacturing process.
SUMMARY Certain embodiments as disclosed herein provide for a golf ball having a dimple pattern which results in reduced hook and slice dispersion.
In one aspect, a golf ball is designed with 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. In one embodiment, 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 (USGA) 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,
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 dimpleless region may be narrow, like a wide seam, or may be wider, i.e. equivalent to removing two or more rows of dimples next to 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 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 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 so that when the ball is hit with a hook or slice action, the ball tends to rotate about the horizontal spin axis 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. If the ball is tilted 45 degrees to the left it reduces or prevents hook dispersion, but not slice dispersion. 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.
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, 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; and
FIG. 18 is a diagram illustrating a golf ball configured in accordance with another embodiment.
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,
FIGS. 1 to 8 illustrate several embodiments of non-conforming or non-symmetrical balls having different dimple patterns, 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 below 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). Table 1 illustrates the locations of the truncated dimples and each of the different size spherical dimples on one hemisphere of the ball.
TABLE 1
Dimple Pattern Design# = 28-1
Molding cavity internal diameter = 1.692″
Total number of dimples on ball = 410
Dimple # 1 Dimple # 2 Dimple # 3 Dimple # 4
Type spherical Type spherical Type spherical Type truncated
Radius 0.0300 Radius 0.0350 Radius 0.0400 Radius 0.0670
SCD 0.0080 SCD 0.0080 SCD 0.0080 SCD 0.0121
TCD — TCD — TCD — TCD 0.0039
# Phi Theta # Phi Theta # Phi Theta # Phi Theta
1 0 31.89226 1 0 15.8163 1 0 0 1 0 62.0690668
2 90 31.89226 2 17.723349 24.95272 2 45 11.141573 2 0 84.1
3 180 31.89226 3 25.269266 35.26266 3 45 22.380098 3 5.65 73.3833254
4 270 31.89226 4 64.730734 35.26266 4 45 33.669653 4 11.26 84.1
5 72.276651 24.95272 5 135 11.141573 5 13.34 62.0690668
6 90 15.8163 6 135 22.380098 6 16.83 73.3833254
7 107.72335 24.95272 7 135 33.669653 7 22.66 84.1
8 115.26927 35.26266 8 225 11.141573 8 26.32 62.8658456
9 154.73073 35.26266 9 225 22.380098 9 27.98 73.3833254
10 162.27665 24.95272 10 225 33.669653 10 33.82 84.1
11 180 15.8163 11 315 11.141573 11 38.44 61.760315
12 197.72335 24.95272 12 315 22.380098 12 39.02 73.3833254
13 205.26927 35.26266 13 315 33.669653 13 45 84.1
14 244.73073 35.26266 14 50.98 73.3833254
15 252.27665 24.95272 15 51.56 61.760315
16 270 15.8163 16 56.18 84.1
17 287.72335 24.95272 17 62.02 73.3833254
18 295.26927 35.26266 18 63.68 62.8658456
19 334.73073 35.26266 19 67.34 84.1
20 342.27665 24.95272 20 73.17 73.3833254
21 76.66 62.0690668
22 78.74 84.1
23 84.35 73.3833254
24 90 62.0690668
25 90 84.1
26 95.65 73.3833254
27 101.26 84.1
28 103.34 62.0690668
29 106.83 73.3833254
30 112.66 84.1
31 116.32 62.8658456
32 117.98 73.3833254
33 123.82 84.1
34 128.44 61.760315
35 129.02 73.3833254
36 135 84.1
37 140.98 73.3833254
38 141.56 61.760315
39 146.18 84.1
40 152.02 73.3833254
41 153.68 62.8658456
42 157.34 84.1
43 163.17 73.3833254
44 166.66 62.0690668
45 168.74 84.1
46 174.35 73.3833254
47 180 62.0690668
48 180 84.1
49 185.65 73.3833254
50 191.26 84.1
51 193.34 62.0690668
52 196.83 73.3833254
53 202.66 84.1
54 206.32 62.8658456
55 207.98 73.3833254
56 213.82 84.1
57 218.44 61.760315
58 219.02 73.3833254
59 225 84.1
60 230.98 73.3833254
61 231.56 61.760315
62 236.18 84.1
63 242.02 73.3833254
64 243.68 62.8658456
65 247.34 84.1
66 253.17 73.3833254
67 256.66 62.0690668
68 258.74 84.1
69 264.35 73.3833254
70 270 62.0690668
71 270 84.1
72 275.65 73.3833254
73 281.26 84.1
74 283.34 62.0690668
75 286.83 73.3833254
76 292.66 84.1
77 296.32 62.8658456
78 297.98 73.3833254
79 303.82 84.1
80 308.44 61.760315
81 309.02 73.3833254
82 315 84.1
83 320.98 73.3833254
84 321.56 61.760315
85 326.18 84.1
86 332.02 73.3833254
87 333.68 62.8658456
88 337.34 84.1
89 343.17 73.3833254
90 346.66 62.0690668
91 348.74 84.1
92 354.35 73.3833254
Dimple # 5 Dimple # 6 Dimple # 7
Type spherical Type spherical Type spherical
Radius 0.0670 Radius 0.0725 Radius 0.0750
SCD 0.0121 SCD 0.0121 SCD 0.0121
TCD — TCD — TCD —
# Phi Theta # Phi Theta # Phi Theta
1 12.73 32.21974 1 0 7.87815 1 8.38 51.07352
2 77.27 32.21974 2 0 23.47509 2 23.8 52.408124
3 102.73 32.21974 3 0 40.93451 3 66.2 52.408124
4 167.27 32.21974 4 19.68 42.05 4 81.62 51.07352
5 192.73 32.21974 5 25.81 17.61877 5 98.38 51.07352
6 257.27 32.21974 6 32.87 28.60436 6 113.8 52.408124
7 282.73 32.21974 7 35.9 39.62978 7 156.2 52.408124
8 347.27 32.21974 8 37.5 50.62533 8 171.62 51.07352
9 52.5 50.62533 9 188.38 51.07352
10 54.1 39.62978 10 203.8 52.408124
11 57.13 28.60436 11 246.2 52.408124
12 64.19 17.61877 12 261.62 51.07352
13 70.32 42.05 13 278.38 51.07352
14 90 7.87815 14 293.8 52.408124
15 90 23.47509 15 336.2 52.408124
16 90 40.93451 16 351.62 51.07352
17 109.68 42.05
18 115.81 17.61877
19 122.87 28.60436
20 125.9 39.62978
21 127.5 50.62533
22 142.5 50.62533
23 144.1 39.62978
24 147.13 28.60436
25 154.19 17.61877
26 160.32 42.05
27 180 7.87815
28 180 23.47509
29 180 40.93451
30 199.68 42.05
31 205.81 17.61877
32 212.87 28.60436
33 215.9 39.62978
34 217.5 50.62533
35 232.5 50.62533
36 234.1 39.62978
37 237.13 28.60436
38 244.19 17.61877
39 250.32 42.05
40 270 7.87815
41 270 23.47509
42 270 40.93451
43 289.68 42.05
44 295.81 17.61877
45 302.87 28.60436
46 305.9 39.62978
47 307.5 50.62533
48 322.5 50.62533
49 324.1 39.62978
50 327.13 28.60436
51 334.19 17.61877
52 340.32 42.05
As seen in FIG. 1 and Table 1, 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 below). 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.
Shown in Table 2 are the dimple radius, depth and dimple location information for making an injection molding cavity to produce the dimple pattern 25-1 of FIG. 2.
TABLE 2
Dimple Pattern Design# = 25-1
Molding cavity internal diameter = 1.694″
Total number of dimples on ball = 386
Dimple # 1 Dimple # 2 Dimple # 3 Dimple # 4
Type spherical Type spherical Type truncated Type spherical
Radius 0.0300 Radius 0.0350 Radius 0.0670 Radius 0.0670
SCD 0.0080 SCD 0.0080 SCD 0.0121 SCD 0.0121
TCD — TCD — TCD 0.0039 TCD —
# Phi Theta # Phi Theta # Phi Theta # Phi Theta
1 0 32.02119 1 0 0 1 0 62.32 1 0 7.91
2 90 32.02119 2 0 15.88024 2 0 84.44 2 0 23.57
3 180 32.02119 3 17.72335 25.0536 3 5.65 73.68 3 0 41.1
4 270 32.02119 4 45 11.18662 4 11.26 84.44 4 8.38 51.28
5 45 22.47058 5 13.34 62.32 5 12.73 32.35
6 72.27665 25.0536 6 16.83 73.68 6 19.68 42.22
7 90 15.88024 7 22.66 84.44 7 23.8 52.62
8 107.7233 25.0536 8 26.32 63.12 8 25.81 17.69
9 135 11.18662 9 27.98 73.68 9 32.87 28.72
10 135 22.47058 10 33.82 84.44 10 35.9 39.79
11 162.2767 25.0536 11 38.44 62.01 11 37.5 50.83
12 180 15.88024 12 39.02 73.68 12 52.5 50.83
13 197.7233 25.0536 13 45 84.44 13 54.1 39.79
14 225 11.18662 14 50.98 73.68 14 57.13 28.72
15 225 22.47058 15 51.56 62.01 15 64.19 17.69
16 252.2767 25.0536 16 56.18 84.44 16 66.2 52.62
17 270 15.88024 17 62.02 73.68 17 70.32 42.22
18 287.7233 25.0536 18 63.68 63.12 18 77.27 32.35
19 315 11.18662 19 67.58 84.44 19 81.62 51.28
20 315 22.47058 20 73.17 73.68 20 90 7.91
21 342.2767 25.0536 21 76.66 62.32 21 90 23.57
22 78.84 84.44 22 90 41.1
23 84.35 73.68 23 98.38 51.28
24 90 62.32 24 102.73 32.35
25 90 84.44 25 109.68 42.22
26 95.65 73.68 26 113.8 52.62
27 101.26 84.44 27 115.81 17.69
28 103.34 62.32 28 122.87 28.72
29 106.83 73.68 29 125.9 39.79
30 112.66 84.44 30 127.5 50.83
31 116.32 63.12 31 142.5 50.83
32 117.98 73.68 32 144.1 39.79
33 123.82 84.44 33 147.13 28.72
34 128.44 62.01 34 154.19 17.69
35 129.02 73.68 35 156.2 52.62
36 135 84.44 36 160.32 42.22
37 140.98 73.68 37 167.27 32.35
38 141.56 62.01 38 171.62 51.28
39 146.18 84.44 39 180 7.91
40 152.02 73.68 40 180 23.57
41 153.68 63.12 41 180 41.1
42 157.58 84.44 42 188.38 51.28
43 163.17 73.68 43 192.73 32.35
44 166.66 62.32 44 199.68 42.22
45 168.84 84.44 45 203.8 52.62
46 174.35 73.68 46 205.81 17.69
47 180 84.44 47 212.87 28.72
48 180 62.32 48 215.9 39.79
49 185.65 73.68 49 217.5 50.83
50 191.26 84.44 50 232.5 50.83
51 193.34 62.32 51 234.1 39.79
52 196.83 73.68 52 237.13 28.72
53 202.66 84.44 53 244.19 17.69
54 206.32 63.12 54 246.2 52.62
55 207.98 73.68 55 250.32 42.22
56 213.82 84.44 56 257.27 32.35
57 218.44 62.01 57 261.62 51.28
58 219.02 73.68 58 270 7.91
59 225 84.44 59 270 23.57
60 230.98 73.68 60 270 41.1
61 231.56 62.01 61 278.38 51.28
62 236.18 84.44 62 282.73 32.35
63 242.02 73.68 63 289.68 42.22
64 243.68 63.12 64 293.8 52.62
65 247.58 84.44 65 295.81 17.69
66 253.17 73.68 66 302.87 28.72
67 256.66 62.32 67 305.9 39.79
68 258.84 84.44 68 307.5 50.83
69 264.35 73.68 69 322.5 50.83
70 270 62.32 70 324.1 39.79
71 270 84.44 71 327.13 28.72
72 275.65 73.68 72 334.19 17.69
73 281.26 84.44 73 336.2 52.62
74 283.34 62.32 74 340.32 42.22
75 286.83 73.68 75 347.27 32.35
76 292.66 84.44 76 351.62 51.28
77 296.32 63.12
78 297.98 73.68
79 303.82 84.44
80 308.44 62.01
81 309.02 73.68
82 315 84.44
83 320.98 73.68
84 321.56 62.01
85 326.18 84.44
86 332.02 73.68
87 333.68 63.12
88 337.58 84.44
89 343.17 73.68
90 346.66 62.32
91 348.84 84.44
92 354.35 73.68
As indicated in Table 2, 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 below, 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 below, and the spherical dimples are identified as dimple #2 in Table 3. 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 3
Dimple Pattern Design# 2-9
Molding cavity internal diameter = 1.694″
Total number of dimples on ball = 336
Dimple # 1 Dimple # 2
Type truncated Type spherical
Radius 0.0670 Radius 0.0670
SCD 0.0121 SCD 0.0121
TCD 0.0039 TCD —
# Phi Theta # Phi Theta
1 0 62.32 1 0 7.91
2 5.58 84.44 2 0 23.57
3 5.65 73.68 3 0 41.1
4 13.34 62.32 4 8.38 51.28
5 16.83 73.68 5 12.73 32.35
6 16.84 84.44 6 19.68 42.22
7 26.32 63.12 7 23.8 52.62
8 27.98 73.68 8 25.81 17.69
9 28.24 84.44 9 32.87 28.72
10 38.44 62.01 10 35.9 39.79
11 39.02 73.68 11 37.5 50.83
12 39.4 84.44 12 52.5 50.83
13 50.6 84.44 13 54.1 39.79
14 50.98 73.68 14 57.13 28.72
15 51.56 62.01 15 64.19 17.69
16 61.76 84.44 16 66.2 52.62
17 62.02 73.68 17 70.32 42.22
18 63.68 63.12 18 77.27 32.35
19 73.16 84.44 19 81.62 51.28
20 73.17 73.68 20 90 7.91
21 76.66 62.32 21 90 23.57
22 84.35 73.68 22 90 41.1
23 84.42 84.44 23 98.38 51.28
24 90 62.32 24 102.73 32.35
25 95.58 84.44 25 109.68 42.22
26 95.65 73.68 26 113.8 52.62
27 103.34 62.32 27 115.81 17.69
28 106.83 73.68 28 122.87 28.72
29 106.84 84.44 29 125.9 39.79
30 116.32 63.12 30 127.5 50.83
31 117.98 73.68 31 142.5 50.83
32 118.24 84.44 32 144.1 39.79
33 128.44 62.01 33 147.13 28.72
34 129.02 73.68 34 154.19 17.69
35 129.4 84.44 35 156.2 52.62
36 140.6 84.44 36 160.32 42.22
37 140.98 73.68 37 167.27 32.35
38 141.56 62.01 38 171.62 51.28
39 151.76 84.44 39 180 7.91
40 152.02 73.68 40 180 23.57
41 153.68 63.12 41 180 41.1
42 163.16 84.44 42 188.38 51.28
43 163.17 73.68 43 192.73 32.35
44 166.66 62.32 44 199.68 42.22
45 174.35 73.68 45 203.8 52.62
46 174.42 84.44 46 205.81 17.69
47 180 62.32 47 212.87 28.72
48 185.58 84.44 48 215.9 39.79
49 185.65 73.68 49 217.5 50.83
50 193.34 62.32 50 232.5 50.83
51 196.83 73.68 51 234.1 39.79
52 196.84 84.44 52 237.13 28.72
53 206.32 63.12 53 244.19 17.69
54 207.98 73.68 54 246.2 52.62
55 208.24 84.44 55 250.32 42.22
56 218.44 62.01 56 257.27 32.35
57 219.02 73.68 57 261.62 51.28
58 219.4 84.44 58 270 7.91
59 230.6 84.44 59 270 23.57
60 230.98 73.68 60 270 41.1
61 231.56 62.01 61 278.38 51.28
62 241.76 84.44 62 282.73 32.35
63 242.02 73.68 63 289.68 42.22
64 243.68 63.12 64 293.8 52.62
65 253.16 84.44 65 295.81 17.69
66 253.17 73.68 66 302.87 28.72
67 256.66 62.32 67 305.9 39.79
68 264.35 73.68 68 307.5 50.83
69 264.42 84.44 69 322.5 50.83
70 270 62.32 70 324.1 39.79
71 275.58 84.44 71 327.13 28.72
72 275.65 73.68 72 334.19 17.69
73 283.34 62.32 73 336.2 52.62
74 286.83 73.68 74 340.32 42.22
75 286.84 84.44 75 347.27 32.35
76 296.32 63.12 76 351.62 51.28
77 297.98 73.68
78 298.24 84.44
79 308.44 62.01
80 309.02 73.68
81 309.4 84.44
82 320.6 84.44
83 320.98 73.68
84 321.56 62.01
85 331.76 84.44
86 332.02 73.68
87 333.68 63.12
88 343.16 84.44
89 343.17 73.68
90 346.66 62.32
91 354.35 73.68
92 354.42 84.44
Table 4 below 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, 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, as are the dimensions of truncated dimples numbered 4 in Table 4. 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.
The dimple coordinates for pattern 28-2 are shown in table 4 below.
TABLE 4
Dimple Pattern Design# 28-2
Molding cavity internal diameter = 1.692″
Total number of dimples on ball = 410
Dimple # 1 Dimple # 2 Dimple # 3
Type spherical Type spherical Type spherical
Radius 0.0300 Radius 0.0350 Radius 0.0400
SCD 0.0080 SCD 0.0080 SCD 0.0080
TCD — TCD — TCD —
# Phi Theta # Phi Theta # Phi Theta
1 0 31.8922591 1 0 15.816302 1 0 0
2 90 31.8922591 2 17.723349 24.952723 2 45 11.14157
3 180 31.8922591 3 25.269266 35.262662 3 45 22.3801
4 270 31.8922591 4 64.730734 35.262662 4 45 33.66965
5 72.276651 24.952723 5 135 11.14157
6 90 15.816302 6 135 22.3801
7 107.72335 24.952723 7 135 33.66965
8 115.26927 35.262662 8 225 11.14157
9 154.73073 35.262662 9 225 22.3801
10 162.27665 24.952723 10 225 33.66965
11 180 15.816302 11 315 11.14157
12 197.72335 24.952723 12 315 22.3801
13 205.26927 35.262662 13 315 33.66965
14 244.73073 35.262662
15 252.27665 24.952723
16 270 15.816302
17 287.72335 24.952723
18 295.26927 35.262662
19 334.73073 35.262662
20 342.27665 24.952723
Dimple # 5 Dimple # 6 Dimple # 7
Type spherical Type spherical Type spherical
Radius 0.0670 Radius 0.0725 Radius 0.0750
SCD 0.0121 SCD 0.0121 SCD 0.0121
TCD — TCD — TCD —
# Phi Theta # Phi Theta # Phi Theta
1 12.73 32.2197418 1 0 7.8781502 1 8.38 51.07352
2 77.27 32.2197418 2 0 23.475095 2 23.8 52.40812
3 102.73 32.2197418 3 0 40.93451 3 66.2 52.40812
4 167.27 32.2197418 4 19.68 42.05 4 81.62 51.07352
5 192.73 32.2197418 5 25.81 17.618771 5 98.38 51.07352
6 257.27 32.2197418 6 32.87 28.604358 6 113.8 52.40812
7 282.73 32.2197418 7 35.9 39.629784 7 156.2 52.40812
8 347.27 32.2197418 8 37.5 50.625332 8 171.62 51.07352
9 52.5 50.625332 9 188.38 51.07352
10 54.1 39.629784 10 203.8 52.40812
11 57.13 28.604358 11 246.2 52.40812
12 64.19 17.618771 12 261.62 51.07352
13 70.32 42.05 13 278.38 51.07352
14 90 7.8781502 14 293.8 52.40812
15 90 23.475095 15 336.2 52.40812
16 90 40.93451 16 351.62 51.07352
Dimple # 4 Dimple # 4 Dimple # 6
Type truncated Type truncated Type spherical
Radius 0.0670 Radius 0.0670 Radius 0.0725
SCD 0.0121 SCD 0.0121 SCD 0.0121
TCD 0.0039 TCD 0.0039 TCD —
# Phi Theta # Phi Theta # Phi Theta
1 0 62.06907 45 44 106.0691 17 109.68 42.05
2 1 63.06907 46 45 107.0691 18 115.81 17.61877
3 2 64.06907 47 46 108.0691 19 122.87 28.60436
4 3 65.06907 48 47 109.0691 20 125.9 39.62978
5 4 66.06907 49 48 110.0691 21 127.5 50.62533
6 5 67.06907 50 49 111.0691 22 142.5 50.62533
7 6 68.06907 51 50 112.0691 23 144.1 39.62978
8 7 69.06907 52 51 113.0691 24 147.13 28.60436
9 8 70.06907 53 52 114.0691 25 154.19 17.61877
10 9 71.06907 54 53 115.0691 26 160.32 42.05
11 10 72.06907 55 54 116.0691 27 180 7.87815
12 11 73.06907 56 55 117.0691 28 180 23.47509
13 12 74.06907 57 56 118.0691 29 180 40.93451
14 13 75.06907 58 57 119.0691 30 199.68 42.05
15 14 76.06907 59 58 120.0691 31 205.81 17.61877
16 15 77.06907 60 59 121.0691 32 212.87 28.60436
17 16 78.06907 61 60 122.0691 33 215.9 39.62978
18 17 79.06907 62 61 123.0691 34 217.5 50.62533
19 18 80.06907 63 62 124.0691 35 232.5 50.62533
20 19 81.06907 64 63 125.0691 36 234.1 39.62978
21 20 82.06907 65 64 126.0691 37 237.13 28.60436
22 21 83.06907 66 65 127.0691 38 244.19 17.61877
23 22 84.06907 67 66 128.0691 39 250.32 42.05
24 23 85.06907 68 67 129.0691 40 270 7.87815
25 24 86.06907 69 68 130.0691 41 270 23.47509
26 25 87.06907 70 69 131.0691 42 270 40.93451
27 26 88.06907 71 70 132.0691 43 289.68 42.05
28 27 89.06907 72 71 133.0691 44 295.81 17.61877
29 28 90.06907 73 72 134.0691 45 302.87 28.60436
30 29 91.06907 74 73 135.0691 46 305.9 39.62978
31 30 92.06907 75 74 136.0691 47 307.5 50.62533
32 31 93.06907 76 75 137.0691 48 322.5 50.62533
33 32 94.06907 77 76 138.0691 49 324.1 39.62978
34 33 95.06907 78 77 139.0691 50 327.13 28.60436
35 34 96.06907 79 78 140.0691 51 334.19 17.61877
36 35 97.06907 80 79 141.0691 52 340.32 42.05
37 36 98.06907 81 80 142.0691
38 37 99.06907 82 81 143.0691
39 38 100.0691 83 82 144.0691
40 39 101.0691 84 83 145.0691
41 40 102.0691 85 84 146.0691
42 41 103.0691 86 85 147.0691
43 42 104.0691 87 86 148.0691
44 43 105.0691 88 87 149.0691
89 88 150.0691
90 89 151.0691
91 90 152.0691
92 91 153.0691
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 re 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.
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, 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, 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.
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. As illustrated in FIG. 6 and indicated in Table 7 below, 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. 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. As seen in Table 7, 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 below, 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.
TABLE 5
Dimple Pattern Design# = 25-2
Molding cavity internal diameter = 1.694″
Total number of dimples on ball = 336
Dimple # 1 Dimple # 2 Dimple # 3
Type truncated Type spherical Type truncated
Radius 0.0775 Radius 0.0775 Radius 0.0800
SCD 0.0121 SCD 0.0121 SCD 0.0121
TCD 0.0039 TCD — TCD 0.0039
# Phi Theta # Phi Theta # Phi Theta
1 5.579593 73.51994 1 0 23.4884 1 5.591675 85.23955
2 16.75313 73.52028 2 13.0186 32.3247 2 16.84626 85.23955
3 27.91657 73.52668 3 19.9156 42.17697 3 28.29145 85.23955
4 62.08343 73.52668 4 24.008 52.43641 4 39.24409 73.35107
5 73.24687 73.52028 5 26.4186 62.92891 5 39.40674 85.23955
6 84.42041 73.51994 6 63.5814 62.92891 6 50.59326 85.23955
7 95.57959 73.51994 7 65.992 52.43641 7 50.75591 73.35107
8 106.7531 73.52028 8 70.0844 42.17697 8 61.70855 85.23955
9 117.9166 73.52668 9 76.9814 32.3247 9 73.15374 85.23955
10 152.0834 73.52668 10 90 23.4884 10 84.40833 85.23955
11 163.2469 73.52028 11 103.019 32.3247 11 95.59167 85.23955
12 174.4204 73.51994 12 109.916 42.17697 12 106.8463 85.23955
13 185.5796 73.51994 13 114.008 52.43641 13 118.2915 85.23955
14 196.7531 73.52028 14 116.419 62.92891 14 129.2441 73.35107
15 207.9166 73.52668 15 153.581 62.92891 15 129.4067 85.23955
16 242.0834 73.52668 16 155.992 52.43641 16 140.5933 85.23955
17 253.2469 73.52028 17 160.084 42.17697 17 140.7559 73.35107
18 264.4204 73.51994 18 166.981 32.3247 18 151.7085 85.23955
19 275.5796 73.51994 19 180 23.4884 19 163.1537 85.23955
20 286.7531 73.52028 20 193.019 32.3247 20 174.4083 85.23955
21 297.9166 73.52668 21 199.916 42.17697 21 185.5917 85.23955
22 332.0834 73.52668 22 204.008 52.43641 22 196.8463 85.23955
23 343.2469 73.52028 23 206.419 62.92891 23 208.2915 85.23955
24 354.4204 73.51994 24 243.581 62.92891 24 219.2441 73.35107
25 245.992 52.43641 25 219.4067 85.23955
26 250.084 42.17697 26 230.5933 85.23955
27 256.981 32.3247 27 230.7559 73.35107
28 270 23.4884 28 241.7085 85.23955
29 283.019 32.3247 29 253.1537 85.23955
30 289.916 42.17697 30 264.4083 85.23955
31 294.008 52.43641 31 275.5917 85.23955
32 296.419 62.92891 32 286.8463 85.23955
33 333.581 62.92891 33 298.2915 85.23955
34 335.992 52.43641 34 309.2441 73.35107
35 340.084 42.17697 35 309.4067 85.23955
36 346.981 32.3247 36 320.5933 85.23955
37 320.7559 73.35107
38 331.7085 85.23955
39 343.1537 85.23955
40 354.4083 85.23955
Dimple # 4 Dimple # 5
Type truncated Type spherical
Radius 0.0800 Radius 0.0875
SCD 0.0121 SCD 0.0121
TCD 0.0039 TCD —
# Phi Theta # Phi Theta
1 0 7.947466 1 0 40.85302
2 26.63272 17.75117 2 0 62.32899
3 33.30007 28.68155 3 8.422648 51.28898
4 36.11617 39.79409 4 13.60562 62.53208
5 37.72952 50.95749 5 76.39438 62.53208
6 38.62814 62.14951 6 81.57735 51.28898
7 51.37186 62.14951 7 90 40.85302
8 52.27048 50.95749 8 90 62.32899
9 53.88383 39.79409 9 98.42265 51.28898
10 56.69993 28.68155 10 103.6056 62.53208
11 63.36728 17.75117 11 166.3944 62.53208
12 90 7.947466 12 171.5774 51.28898
13 116.6327 17.75117 13 180 40.85302
14 123.3001 28.68155 14 180 62.32899
15 126.1162 39.79409 15 188.4226 51.28898
16 127.7295 50.95749 16 193.6056 62.53208
17 128.6281 62.14951 17 256.3944 62.53208
18 141.3719 62.14951 18 261.5774 51.28898
19 142.2705 50.95749 19 270 40.85302
20 143.8838 39.79409 20 270 62.32899
21 146.6999 28.68155 21 278.4226 51.28898
22 153.3673 17.75117 22 283.6056 62.53208
23 180 7.947466 23 346.3944 62.53208
24 206.6327 17.75117 24 351.5774 51.28898
25 213.3001 28.68155
26 216.1162 39.79409
27 217.7295 50.95749
28 218.6281 62.14951
29 231.3719 62.14951
30 232.2705 50.95749
31 233.8838 39.79409
32 236.6999 28.68155
33 243.3673 17.75117
34 270 7.947466
35 296.6327 17.75117
36 303.3001 28.68155
37 306.1162 39.79409
38 307.7295 50.95749
39 308.6281 62.14951
40 321.3719 62.14951
41 322.2705 50.95749
42 323.8838 39.79409
43 326.6999 28.68155
44 333.3673 17.75117
TABLE 6
Dimple Pattern Design# = 25-3
Molding cavity internal diameter = 1.694″
Total number of dimples on ball = 336
Dimple # 1 Dimple # 2 Dimple # 3 Dimple # 4 Dimple # 5
Type spherical Type truncated Type spherical Type truncated Type truncated
Radius 0.0775 Radius 0.0800 Radius 0.0800 Radius 0.0775 Radius 0.0875
SCD 0.0121 SCD 0.0121 SCD 0.0121 SCD 0.0121 SCD 0.0121
TCD — TCD 0.0039 TCD — TCD 0.0039 TCD 0.0039
# Phi Theta # Phi Theta # Phi Theta # Phi Theta # Phi Theta
1 0 23.4884 1 5.591675 85.23955 1 0 7.947466 1 5.579593 73.51994 1 0 62.32899
2 13.0186 32.3247 2 16.84626 85.23955 2 26.63272 17.75117 2 16.75313 73.52028 2 8.42265 51.28898
3 19.9156 42.17697 3 28.29145 85.23955 3 33.30007 28.68155 3 24.00802 52.43641 3 13.6056 62.53208
4 70.0844 42.17697 4 37.72952 50.95749 4 36.11617 39.79409 4 26.41855 62.92891 4 76.3944 62.53208
5 76.9814 32.3247 5 38.62814 62.14951 5 53.88383 39.79409 5 27.91657 73.52668 5 81.5774 51.28898
6 90 23.4884 6 39.24409 73.35107 6 56.69993 28.68155 6 62.08343 73.52668 6 90 62.32899
7 103.019 32.3247 7 39.40674 85.23955 7 63.36728 17.75117 7 63.58145 62.92891 7 98.4226 51.28898
8 109.916 42.17697 8 50.59326 85.23955 8 90 7.947466 8 65.99198 52.43641 8 103.606 62.53208
9 160.084 42.17697 9 50.75591 73.35107 9 116.6327 17.75117 9 73.24687 73.52028 9 166.394 62.53208
10 166.981 32.3247 10 51.37186 62.14951 10 123.3001 28.68155 10 84.42041 73.51994 10 171.577 51.28898
11 180 23.4884 11 52.27048 50.95749 11 126.1162 39.79409 11 95.57959 73.51994 11 180 62.32899
12 193.019 32.3247 12 61.70855 85.23955 12 143.8838 39.79409 12 106.7531 73.52028 12 188.423 51.28898
13 199.916 42.17697 13 73.15374 85.23955 13 146.6999 28.68155 13 114.008 52.43641 13 193.606 62.53208
14 250.084 42.17697 14 84.40833 85.23955 14 153.3673 17.75117 14 116.4186 62.92891 14 256.394 62.53208
15 256.981 32.3247 15 95.59167 85.23955 15 180 7.947466 15 117.9166 73.52668 15 261.577 51.28898
16 270 23.4884 16 106.8463 85.23955 16 206.6327 17.75117 16 152.0834 73.52668 16 270 62.32899
17 283.019 32.3247 17 118.2915 85.23955 17 213.3001 28.68155 17 153.5814 62.92891 17 278.423 51.28898
18 289.916 42.17697 18 127.7295 50.95749 18 216.1162 39.79409 18 155.992 52.43641 18 283.606 62.53208
19 340.084 42.17697 19 128.6281 62.14951 19 233.8838 39.79409 19 163.2469 73.52028 19 346.394 62.53208
20 346.981 32.3247 20 129.2441 73.35107 20 236.6999 28.68155 20 174.4204 73.51994 20 351.577 51.28898
21 129.4067 85.23955 21 243.3673 17.75117 21 185.5796 73.51994 21 0 40.85302
22 140.5933 85.23955 22 270 7.947466 22 196.7531 73.52028 22 90 40.85302
23 140.7559 73.35107 23 296.6327 17.75117 23 204.008 52.43641 23 180 40.85302
24 141.3719 62.14951 24 303.3001 28.68155 24 206.4186 62.92891 24 270 40.85302
25 142.2705 50.95749 25 306.1162 39.79409 25 207.9166 73.52668
26 151.7085 85.23955 26 323.8838 39.79409 26 242.0834 73.52668
27 163.1537 85.23955 27 326.6999 28.68155 27 243.5814 62.92891
28 174.4083 85.23955 28 333.3673 17.75117 28 245.992 52.43641
29 185.5917 85.23955 29 253.2469 73.52028
30 196.8463 85.23955 30 264.4204 73.51994
31 208.2915 85.23955 31 275.5796 73.51994
32 217.7295 50.95749 32 286.7531 73.52028
33 218.6281 62.14951 33 294.008 52.43641
34 219.2441 73.35107 34 296.4186 62.92891
35 219.4067 85.23955 35 297.9166 73.52668
36 230.5933 85.23955 36 332.0834 73.52668
37 230.7559 73.35107 37 333.5814 62.92891
38 231.3719 62.14951 38 335.992 52.43641
39 232.2705 50.95749 39 343.2469 73.52028
40 241.7085 85.23955 40 354.4204 73.51994
41 253.1537 85.23955
42 264.4083 85.23955
43 275.5917 85.23955
44 286.8463 85.23955
45 298.2915 85.23955
46 307.7295 50.95749
47 308.6281 62.14951
48 309.2441 73.35107
49 309.4067 85.23955
50 320.5933 85.23955
51 320.7559 73.35107
52 321.3719 62.14951
53 322.2705 50.95749
54 331.7085 85.23955
55 343.1537 85.23955
56 354.4083 85.23955
TABLE 7
Dimple Pattern Design# = 25-4
Molding cavity internal diameter = 1.694″
Total number of dimples on ball = 336
Dimple # 1 Dimple # 2 Dimple # 3 Dimple # 4
Type truncated Type spherical Type truncated Type spherical
Radius 0.0775 Radius 0.0775 Radius 0.0800 Radius 0.0800
SCD 0.0121 SCD 0.0121 SCD 0.0121 SCD 0.0121
TCD 0.0039 TCD — TCD 0.0039 TCD —
# Phi Theta # Phi Theta # Phi Theta # Phi Theta
1 5.579593 73.5199369 1 0 23.4884 1 5.591675 85.2395467 1 0 7.947466
2 16.75313 73.5202824 2 13.0186 32.3247 2 16.84626 85.2395467 2 26.63272 17.75117
3 26.41855 62.9289055 3 19.9156 42.17697 3 28.29145 85.2395467 3 33.30007 28.68155
4 27.91657 73.5266783 4 24.008 52.43641 4 38.62814 62.1495131 4 36.11617 39.79409
5 62.08343 73.5266783 5 65.992 52.43641 5 39.24409 73.3510713 5 37.72952 50.95749
6 63.58145 62.9289055 6 70.0844 42.17697 6 39.40674 85.2395467 6 52.27048 50.95749
7 73.24687 73.5202824 7 76.9814 32.3247 7 50.59326 85.2395467 7 53.88383 39.79409
8 84.42041 73.5199369 8 90 23.4884 8 50.75591 73.3510713 8 56.69993 28.68155
9 95.57959 73.5199369 9 103.019 32.3247 9 51.37186 62.1495131 9 63.36728 17.75117
10 106.7531 73.5202824 10 109.916 42.17697 10 61.70855 85.2395467 10 90 7.947466
11 116.4186 62.9289055 11 114.008 52.43641 11 73.15374 85.2395467 11 116.6327 17.75117
12 117.9166 73.5266783 12 155.992 52.43641 12 84.40833 85.2395467 12 123.3001 28.68155
13 152.0834 73.5266783 13 160.084 42.17697 13 95.59167 85.2395467 13 126.1162 39.79409
14 153.5814 62.9289055 14 166.981 32.3247 14 106.8463 85.2395467 14 127.7295 50.95749
15 163.2469 73.5202824 15 180 23.4884 15 118.2915 85.2395467 15 142.2705 50.95749
16 174.4204 73.5199369 16 193.019 32.3247 16 128.6281 62.1495131 16 143.8838 39.79409
17 185.5796 73.5199369 17 199.916 42.17697 17 129.2441 73.3510713 17 146.6999 28.68155
18 196.7531 73.5202824 18 204.008 52.43641 18 129.4067 85.2395467 18 153.3673 17.75117
19 206.4186 62.9289055 19 245.992 52.43641 19 140.5933 85.2395467 19 180 7.947466
20 207.9166 73.5266783 20 250.084 42.17697 20 140.7559 73.3510713 20 206.6327 17.75117
21 242.0834 73.5266783 21 256.981 32.3247 21 141.3719 62.1495131 21 213.3001 28.68155
22 243.5814 62.9289055 22 270 23.4884 22 151.7085 85.2395467 22 216.1162 39.79409
23 253.2469 73.5202824 23 283.019 32.3247 23 163.1537 85.2395467 23 217.7295 50.95749
24 264.4204 73.5199369 24 289.916 42.17697 24 174.4083 85.2395467 24 232.2705 50.95749
25 275.5796 73.5199369 25 294.008 52.43641 25 185.5917 85.2395467 25 233.8838 39.79409
26 286.7531 73.5202824 26 335.992 52.43641 26 196.8463 85.2395467 26 236.6999 28.68155
27 296.4186 62.9289055 27 340.084 42.17697 27 208.2915 85.2395467 27 243.3673 17.75117
28 297.9166 73.5266783 28 346.981 32.3247 28 218.6281 62.1495131 28 270 7.947466
29 332.0834 73.5266783 29 219.2441 73.3510713 29 296.6327 17.75117
30 333.5814 62.9289055 30 219.4067 85.2395467 30 303.3001 28.68155
31 343.2469 73.5202824 31 230.5933 85.2395467 31 306.1162 39.79409
32 354.4204 73.5199369 32 230.7559 73.3510713 32 307.7295 50.95749
33 231.3719 62.1495131 33 322.2705 50.95749
34 241.7085 85.2395467 34 323.8838 39.79409
35 253.1537 85.2395467 35 326.6999 28.68155
36 264.4083 85.2395467 36 333.3673 17.75117
37 275.5917 85.2395467
38 286.8463 85.2395467
39 298.2915 85.2395467
40 308.6281 62.1495131
41 309.2441 73.3510713
42 309.4067 85.2395467
43 320.5933 85.2395467
44 320.7559 73.3510713
45 321.3719 62.1495131
46 331.7085 85.2395467
47 343.1537 85.2395467
48 354.4083 85.2395467
Dimple # 5 Dimple # 6
Type truncated Type spherical
Radius 0.0875 Radius 0.0875
SCD 0.0121 SCD 0.0121
TCD 0.0039 TCD —
# Phi Theta # Phi Theta
1 0 62.3289928 1 0 40.85302
2 13.60562 62.5320764 2 8.42265 51.28898
3 76.39438 62.5320764 3 81.5774 51.28898
4 90 62.3289928 4 90 40.85302
5 103.6056 62.5320764 5 98.4226 51.28898
6 166.3944 62.5320764 6 171.577 51.28898
7 180 62.3289928 7 180 40.85302
8 193.6056 62.5320764 8 188.423 51.28898
9 256.3944 62.5320764 9 261.577 51.28898
10 270 62.3289928 10 270 40.85302
11 283.6056 62.5320764 11 278.423 51.28898
12 346.3944 62.5320764 12 351.577 51.28898
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 means 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 indicates the dimple parameters and coordinates for golf ball 60. As illustrated in Table 8, 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 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 listed below in Table 8.
TABLE 8
Dimple Pattern Design# 28-3
Molding cavity internal diameter = 1.692″
Total number of dimples on ball = 354
Dimple # 1 Dimple # 2 Dimple # 3
Type spherical Type spherical Type spherical
Radius 0.0475 Radius 0.0750 Radius 0.0775
SCD 0.0080 SCD 0.0080 SCD 0.0080
TCD — TCD — TCD —
# Phi Theta # Phi Theta # Phi Theta
1 0 0 1 12.927785 31.884481 1 0 23.102459
2 0 6.6748046 2 77.072215 31.884481 2 27.477912 18.124586
3 0 13.353545 3 102.92779 31.884481 3 62.522088 18.124586
4 45 9.4610963 4 167.07221 31.884481 4 90 23.102459
5 90 6.6748046 5 192.92779 31.884481 5 117.47791 18.124586
6 90 13.353545 6 257.07221 31.884481 6 152.52209 18.124586
7 135 9.4610963 7 282.92779 31.884481 7 180 23.102459
8 180 6.6748046 8 347.07221 31.884481 8 207.47791 18.124586
9 180 13.353545 9 242.52209 18.124586
10 225 9.4610963 10 270 23.102459
11 270 6.6748046 11 297.47791 18.124586
12 270 13.353545 12 332.52209 18.124586
13 315 9.4610963
Dimple # 5 Dimple # 6
Type spherical Type spherical
Radius 0.0800 Radius 0.0825
SCD 0.0080 SCD 0.0080
TCD — TCD —
# Phi Theta # Phi Theta
1 23.959474 52.85795 1 19.446897 42.09101
2 33.420036 28.804503 2 70.553103 42.09101
3 36.311426 39.777883 3 109.4469 42.09101
4 37.838691 50.813627 4 160.5531 42.09101
5 52.161309 50.813627 5 199.4469 42.09101
6 53.688574 39.777883 6 250.5531 42.09101
7 56.579964 28.804503 7 289.4469 42.09101
8 66.040526 52.85795 8 340.5531 42.09101
9 113.95947 52.85795 9 0 40.242952
10 123.42004 28.804503 10 90 40.242952
11 126.31143 39.777883 11 180 40.242952
12 127.83869 50.813627 12 270 40.242952
13 142.16131 50.813627 13 8.3680473 51.180102
14 143.68857 39.777883 14 81.631953 51.180102
15 146.57996 28.804503 15 98.368047 51.180102
16 156.04053 52.85795 16 171.63195 51.180102
17 203.95947 52.85795 17 188.36805 51.180102
18 213.42004 28.804503 18 261.63195 51.180102
19 216.31143 39.777883 19 278.36805 51.180102
20 217.83869 50.813627 20 351.63195 51.180102
21 232.16131 50.813627
22 233.68857 39.777883
23 236.57996 28.804503
24 246.04053 52.85795
25 293.95947 52.85795
26 303.42004 28.804503
27 306.31143 39.777883
28 307.83869 50.813627
29 322.16131 50.813627
30 323.68857 39.777883
31 326.57996 28.804503
32 336.04053 52.85795
Dimple # 4
Type truncated
Radius 0.0670
SCD 0.0121
TCD 0.0039
# Phi Theta
1 0 62.0690668
2 0 83.5
3 5.65 73.3833254
4 11.26 83.5
5 13.34 62.0690668
6 16.83 73.3833254
7 22.66 83.5
8 26.32 62.8658456
9 27.98 73.3833254
10 33.82 83.5
11 38.44 61.760315
12 39.02 73.3833254
13 45 83.5
14 50.98 73.3833254
15 51.56 61.760315
16 56.18 83.5
17 62.02 73.3833254
18 63.68 62.8658456
19 67.34 83.5
20 73.17 73.3833254
21 76.66 62.0690668
22 78.74 83.5
23 84.35 73.3833254
24 90 62.0690668
25 90 83.5
26 95.65 73.3833254
27 101.26 83.5
28 103.34 62.0690668
29 106.83 73.3833254
30 112.66 83.5
31 116.32 62.8658456
32 117.98 73.3833254
33 123.82 83.5
34 128.44 61.760315
35 129.02 73.3833254
36 135 83.5
37 140.98 73.3833254
38 141.56 61.760315
39 146.18 83.5
40 152.02 73.3833254
41 153.68 62.8658456
42 157.34 83.5
43 163.17 73.3833254
44 166.66 62.0690668
45 168.74 83.5
46 174.35 73.3833254
47 180 62.0690668
48 180 83.5
49 185.65 73.3833254
50 191.26 83.5
51 193.34 62.0690668
52 196.83 73.3833254
53 202.66 83.5
54 206.32 62.86585
55 207.98 73.38333
56 213.82 83.5
57 218.44 61.76032
58 219.02 73.38333
59 225 83.5
60 230.98 73.38333
61 231.56 61.76032
62 236.18 83.5
63 242.02 73.38333
64 243.68 62.86585
65 247.34 83.5
66 253.17 73.38333
67 256.66 62.06907
68 258.74 83.5
69 264.35 73.38333
70 270 62.06907
71 270 83.5
72 275.65 73.38333
73 281.26 83.5
74 283.34 62.06907
75 286.83 73.38333
76 292.66 83.5
77 296.32 62.86585
78 297.98 73.38333
79 303.82 83.5
80 308.44 61.76032
81 309.02 73.38333
82 315 83.5
83 320.98 73.38333
84 321.56 61.76032
85 326.18 83.5
86 332.02 73.38333
87 333.68 62.86585
88 337.34 83.5
89 343.17 73.38333
90 346.66 62.06907
91 348.74 83.5
92 354.35 73.38333
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 dimpleless region or land area about the equator. The dimpleless 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 (i.e. balls 2-9, 25-1 to 25-4, and 28-1 to 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 9 below.
TABLE 9
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 9. Table 10 shows the MOI calculations.
TABLE 10
% MOI
delta
Px, lbs × Py, lbs × Pz, lbs × MOI Delta = % (Pmax − relative to
Ball inch{circumflex over ( )}2 inch{circumflex over ( )}2 inch{circumflex over ( )}2 Pmax Pmin Pmax − Pmin 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 10. 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 10. Generally a golf ball weighs about 45.5-45.9 g. Comparing the MOI values of all of the balls in Table 10 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 11 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 11 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 11
% MOI Avg Avg Avg Avg
difference C- C- T- T-
Orien- between DISP, DIST, DISP, DIST,
Ball tation 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
As illustrated in Table 11, 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 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:
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 12 below.
TABLE 12
Rows of truncated
Design around the equator % MOI
# (per hemisphere) 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 13 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 13
Results from 4-15-10 slice test
Average Values for TrackMan Data
Carry Total Total
Carry Dis- Disper- Dis-
Ball Dispersion, tance, sion, tance, Roll,
Name Orientation 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 14A and 14B 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 14A and 14B. 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 14A
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 14B
Drag Coefficient regression equation coeficient
Ball Design# Orientation b4 b3 b5 b2 b1 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 150,000 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 15-17 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 15
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 16
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] [deg] [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 17
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 dimpleless 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.
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.
