U.S. patent application number 13/097005 was filed with the patent office on 2011-12-01 for nonconforming anti-slice ball.
This patent application is currently assigned to AERO-X GOLF INC.. Invention is credited to David L. Felker, Douglas C. Winfield.
Application Number | 20110294604 13/097005 |
Document ID | / |
Family ID | 44858435 |
Filed Date | 2011-12-01 |
United States Patent
Application |
20110294604 |
Kind Code |
A1 |
Felker; David L. ; et
al. |
December 1, 2011 |
NONCONFORMING ANTI-SLICE BALL
Abstract
A non-conforming golf ball has a plurality of dimples formed on
the outer surface of the ball in a predetermined dimple pattern,
the outer surface comprising one or more first areas which include
a plurality of first dimples which together have a first dimple
volume and at least one second area having a dimple volume less
that the first dimple volume, the first and second areas being
configured to establish a preferred spin axis. The second area may
be a band around the equator which has a lower dimple volume or no
dimples, with the polar regions have a higher volume of dimples,
creating a preferred spin axis through the poles.
Inventors: |
Felker; David L.;
(Escondido, CA) ; Winfield; Douglas C.; (Madison,
AL) |
Assignee: |
AERO-X GOLF INC.
Escondido
CA
|
Family ID: |
44858435 |
Appl. No.: |
13/097005 |
Filed: |
April 28, 2011 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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61328927 |
Apr 28, 2010 |
|
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Current U.S.
Class: |
473/383 |
Current CPC
Class: |
A63B 37/0012 20130101;
A63B 37/0016 20130101; A63B 37/0077 20130101; A63B 37/0006
20130101; B29L 2031/546 20130101; A63B 37/0096 20130101; B29C
33/424 20130101; A63B 37/0017 20130101; A63B 37/009 20130101 |
Class at
Publication: |
473/383 |
International
Class: |
A63B 37/14 20060101
A63B037/14 |
Claims
1. A golf ball having an outer surface, an equator and two poles,
and a plurality of dimples formed on the outer surface of the ball,
the outer surface comprising one or more first areas which include
a plurality of first dimples which together have a first dimple
volume and at least one second area having a dimple volume less
that the first dimple volume, the first and second areas being
configured to establish a preferred spin axis such that the golf
ball exhibits a drag coefficient of less than about 0.27 at a
Reynolds number of about 120,000 and of less than about 0.24 at a
Reynolds number of about 180,000 when the ball is spinning around
its preferred spin axis with a spin rate of about 3,500 rpm or
greater.
2. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is below about
0.26 at a Reynolds number of about 130,000 and a spin rate of about
3,500 rpm.
3. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is below about
0.25 at a Reynolds number of about 140,000 and a spin rate of about
3,500 rpm.
4. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is below about
0.25 at a Reynolds number of about 150,000 and a spin rate of about
3,500 rpm.
5. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is below about
0.24 at a Reynolds number of about 160,000 and a spin rate of about
3,500 rpm.
6. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is below about
0.24 at a Reynolds number of about 170,000 and a spin rate of about
3,500 rpm.
7. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is above about
0.25 at a Reynolds number of about 120,000 and a spin rate of about
3,500 rpm.
8. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is above about
0.24 at a Reynolds number of about 130,000 and a spin rate of about
3,500 rpm.
9. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is above about
0.24 at a Reynolds number of about 140,000 and a spin rate of about
3,500 rpm.
10. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is above about
0.23 at a Reynolds number of about 150,000 and a spin rate of about
3,500 rpm.
11. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is above about
0.22 at a Reynolds number of about 160,000 and a spin rate of about
3,500 rpm.
12. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is above about
0.22 at a Reynolds number of about 170,000 and a spin rate of about
3,500 rpm.
13. The golf ball of claim 1, wherein the drag coefficient when the
golf ball is spinning around its preferred spin axis is above about
0.21 at a Reynolds number of about 180,000 and a spin rate of about
3,500 rpm.
14. The golf ball of claim 1, wherein the first and second areas
define a non-conforming dimple pattern.
15. A golf ball having an outer surface, an equator and two poles,
and a plurality of dimples formed on the outer surface of the ball,
the outer surface comprising one or more first areas which include
a plurality of first dimples which together have a first dimple
volume and at least one second area having a dimple volume less
that the first dimple volume, the first and second areas being
configured to establish a preferred spin axis such that the golf
ball exhibits a drag coefficient of less than about 0.24 over a
range of Reynolds number from about 120,000 to about 180,000 when
the ball is spinning around its preferred spin axis with a spin
rate of about 3,500 rpm or greater.
16. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is below
about 0.26 at a Reynolds number of about 120,000 and a spin rate of
about 3,500 rpm.
17. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is below
about 0.25 at a Reynolds number of about 130,000 and a spin rate of
about 3,500 rpm.
18. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is below
about 0.25 at a Reynolds number of about 140,000 and a spin rate of
about 3,500 rpm.
19. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is below
about 0.24 at a Reynolds number of about 150,000 and a spin rate of
about 3,500 rpm.
20. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is below
about 0.24 at a Reynolds number of about 160,000 and a spin rate of
about 3,500 rpm.
21. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is below
about 0.23 at a Reynolds number of about 170,000 and a spin rate of
about 3,500 rpm.
22. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is below
about 0.22 at a Reynolds number of about 180,000 and a spin rate of
about 3,500 rpm.
23. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is above
about 0.25 at a Reynolds number of about 120,000 and a spin rate of
about 3,500 rpm.
24. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is above
about 0.24 at a Reynolds number of about 130,000 and a spin rate of
about 3,500 rpm.
25. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is above
about 0.24 at a Reynolds number of about 140,000 and a spin rate of
about 3,500 rpm.
26. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is above
about 0.23 at a Reynolds number of about 150,000 and a spin rate of
about 3,500 rpm.
27. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is above
about 012 at a Reynolds number of about 160,000 and a spin rate of
about 3,500 rpm.
28. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is above
about 0.22 at a Reynolds number of about 170,000 and a spin rate of
about 3,500 rpm.
29. The golf ball of claim 15, wherein the drag coefficient when
the golf ball is spinning around its preferred spin axis is above
about 0.21 at a Reynolds number of about 180,000 and a spin rate of
about 3,500 rpm.
30. The golf ball of claim 15, wherein the first and second areas
define a non-conforming dimple pattern.
Description
RELATED APPLICATIONS INFORMATION
[0001] This application claims the benefit under .sctn.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
[0002] 1. Field of the Invention
[0003] The embodiments described herein relate generally to golf
balls and are specifically concerned with golf ball dimple patterns
to create desired flight characteristics.
[0004] 2. Related Art
[0005] 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.
[0006] 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.
[0007] 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.
[0008] 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.
[0009] 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.TM. 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.
[0010] 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
[0011] Certain embodiments as disclosed herein provide for a golf
ball having a dimple pattern which results in reduced hook and
slice dispersion.
[0012] 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 (USDA)
rules.
[0013] 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.
[0014] 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.
[0015] 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.
[0016] 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.
[0017] 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,
[0018] 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".
[0019] 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.
[0020] 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
[0021] 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:
[0022] 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;
[0023] FIG. 2 is a perspective view similar to FIG. 1 illustrating
a second embodiment of a golf ball with a second, different dimple
pattern;
[0024] 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;
[0025] 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;
[0026] 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;
[0027] 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;
[0028] 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;
[0029] FIG. 8 is perspective view similar to FIG. 1 but
illustrating a modified dimple pattern with some rows of dimples
around the equator removed;
[0030] 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;
[0031] 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.TM. ball and the known TopFlite
XL straight ball;
[0032] 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;
[0033] 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;
[0034] FIG. 13 is a side view of the flight paths of FIG. 12,
illustrating the maximum height of each ball;
[0035] 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
[0036] FIG. 18 is a diagram illustrating a golf ball configured in
accordance with another embodiment.
DETAILED DESCRIPTION
[0037] 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.
[0038] 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).
[0039] 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.
[0040] 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.
[0041] 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.
[0042] 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.
[0043] 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-US-00001 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
[0044] 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.
[0045] 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.
[0046] 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.
[0047] 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-US-00002 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
[0048] 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.
[0049] 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.
[0050] 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-US-00003 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
[0051] 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.
[0052] The dimple coordinates for pattern 28-2 are shown in table 4
below.
TABLE-US-00004 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
[0053] FIGS. 4 to 6 illustrate hemispheres of three different balls
30, 40 and 50 with different dimple patterns. The dimple patterns
on balls 30, 40 and 50 are hereinafter referred to as dimple
patterns 25-2, 25-3, and 25-4. Dimple patterns 25-2, 25-3 and 25-4
are related in that they have basically the same design except that
each has a different number of rows of truncated dimples
surrounding the equator. The dimple dimensions and positions for
the balls of FIGS. 4 to 6 are provided below in Tables 5, 6 and 7,
respectively.
[0054] 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.
[0055] 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.
[0056] 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.
[0057] 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-US-00005 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-US-00006 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-US-00007 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
[0058] 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.
[0059] 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.
[0060] 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.
[0061] The dimple parameters and coordinates for making one
hemisphere of the 28-3 ball are listed below in Table 8.
TABLE-US-00008 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
[0062] 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''.
[0063] 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.
[0064] 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.
[0065] 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 d.sub.2 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 d.sub.1, which is smaller
than the spherical chord depth d.sub.2. The volume of cover
material removed above the edges of the dimple is represented by
volume V3 above the dotted line, with a depth d.sub.3. In FIG. 9,
[0066] V1=volume of truncated dimple, [0067] V1+V2=volume of
spherical dimple, [0068] V1+V2+V3=volume of cover removed to create
spherical dimple, and [0069] V1+V3=volume of cover removed to
create truncated dimple.
[0070] 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.
[0071] 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 28-3). In one embodiment,
balls having these patterns were drawn in SolidWorks.RTM. and their
MOI's were calculated along with the known Polara.TM. golf ball
referenced above as a standard. SolidWorks.RTM. was used to
calculate the MOI's based on each ball having a uniform solid
density of 0.036413 lbs/in 3. The other physical size and weight
parameters for each ball are given in Table 9 below.
TABLE-US-00009 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-US-00010 TABLE 10 % MOI delta Px, lbs .times. Py, lbs .times.
Pz, lbs .times. 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%
[0072] With the Polara.TM. 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.
[0073] 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-US-00011 TABLE 11 % MOI difference between Avg C-DISP, Avg
C-DIST, Avg T-DISP, Avg T-DIST, Ball Orientation orientations ft
yds ft yds 28-2 PH 0.488% 9.6 180.6 7.3 201.0 28-1 PH 0.487% -2.6
174.8 -7.6 200.5 TopFLite XL random 0.000% 66.5 189.3 80.6 200.4
Straight 25-1 PH 0.341% 7.4 184.7 9.6 207.5 28-3 PH 0.334% 16.3
191.8 23.5 211.8 Polara PFB 0.271% 29.7 196.6 38.0 214.6 2-9 PH
0.258% 12.8 192.2 10.5 214.5 25-4 PH 0.074% 56.0 185.4 71.0 197.3
25-2 PH 0.062% 52.8 187.0 68.1 199.9 25-3 PH 0.033% 63.4 188.0 75.1
197.9
[0074] 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.
[0075] 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.
[0076] 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.
[0077] 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.
[0078] 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.
[0079] 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).
[0080] 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.
[0081] 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:
TABLE-US-00012 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
[0082] 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-US-00013 TABLE 12 Rows of truncated around the equator % MOI
Design # (per hemisphere) Delta 25-2 2 0.062% 25-3 4 0.033% 25-4 3
0.074%
[0083] FIG. 11 shows the average Carry and Total Distance versus
the MOI difference between the Minimum and Maximum orientations for
each dimple design.
[0084] 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-US-00014 TABLE 13 Results from 4-15-10 slice test Average
Values for TrackMan Data Carry Carry Total Total Ball Dispersion,
Distance, Dispersion, Distance, Name Orientation ft yds ft yds
Roll, 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
[0085] 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.RTM. 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.RTM. 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.TM.
blend (50% 9150, 50% 8150) cover. The cover was approximately 0.06
inches thick.
[0086] The tests were conducted with a "Golf Laboratories" robot
and hit with the same Taylor Made.RTM. driver at varying club head
speeds. The Taylor Made.RTM. driver had a 10.5.degree. 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.
[0087] 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.RTM. 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
[0088] 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.RTM. XL Straight, Polara 2p and Titleist Pro
V1.RTM.. The curves in each graph were generated from the
regression analysis of multiple straight shots for each ball design
in a specific orientation.
[0089] 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:
CL.sub.Regression=a.sub.1*Re+a.sub.2*W+a.sub.3*Re 2+a.sub.4*W
2+a.sub.5*ReW+a.sub.6
CD.sub.Regression=b.sub.1*Re+b.sub.2*W+b.sub.3*Re 2+b.sub.4*W
2+b.sub.5*ReW+b.sub.6
Where a.sub.i with i=1-6 are regression coefficients for Lift
Coefficient and
[0090] b.sub.i with i=1-6 are regression coefficients for Drag
Coefficient
[0091] 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.
[0092] 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-US-00015 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-US-00016 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
[0093] 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.
[0094] 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.
[0095] 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-US-00017 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-US-00018 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-US-00019 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
[0096] 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.
[0097] 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.
[0098] 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.
[0099] 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.
* * * * *