Golf ball

A golf ball is provided with evenly and uniformly distributed dimples in a pattern which is governed by repeating polygons such as icosahedral triangles. The dimples are spherical in shape and the aspect ratio of all of the dimples is substantially constant, preferably 0.050. The largest dimples are located just inside the vertexes of the polygons, and the next largest dimples are located at the vertexes so that they are surrounded by the largest sized dimples.

BACKGROUND 
This invention relates to a golf ball, and, more particularly, to a golf 
ball which is provided with a new and unique dimple pattern which provides 
excellent distance and accuracy. 
This invention represents an improvement over the golf ball dimple patterns 
which are described in U.S. Pat. No. 4,560,168 and the golf ball dimple 
patterns which are used on the commercial golf balls sold under the name 
Wilson Staff and TC.sup.2. 
U.S. Pat. No. 4,560,168 describes various icosahedral dimple patterns in 
which the dimples are arranged so that they do not intersect the six great 
circles which bisect the sides of the icosahedral triangles. The dimple 
pattern illustrated in FIGS. 8A and 8B is used on commercial golf balls 
which are sold under the name Ultra. The Ultra golf ball is a two-piece 
golf ball which consists of a solid core and a cover. The Ultra dimple 
pattern includes 432 dimples, and each dimple has the same diameter and 
depth. 
Other figures of U.S. Pat. No. 4,560,168 illustrate using dimples of 
various sizes on the same ball. The aspect ratio of a dimple is determined 
by dividing the depth of the dimple by the diameter of the dimple, and 
column 4, lines 42-45 state that the aspect ratio should be about 0.047 to 
0.060, the optimum being about 0.052. 
The Wilson Staff golf ball is a three-piece golf ball which includes a 
solid core, a layer of elastic windings which are wrapped around the core, 
and a cover. The dimple pattern of the Wilson Staff ball is a 432 dimple 
pattern which is similar to the Ultra pattern except that there are five 
different sized dimples and the dimples are frusto-conical rather than 
spherical. The five dimple diameters are 0.155, 0.150, 0.140, 0.135, and 
0.125 inches. The depths of the dimples are 0.0071, 0.0069, 0.0064, 
0.0062, and 0.0058 inches, respectively. The aspect ratio for each of the 
Wilson Staff dimples is therefore 0.046. 
The Wilson Staff dimples are frusto-conical rather than spherical, i.e., 
the side surface of each dimple is formed by the frustum of a cone or a 
truncated cone rather than by a portion of a sphere. Prior golf balls sold 
under the name Pro Staff also utilized frusto-conical dimples. The bottom 
surface of each Wilson Staff dimple is flat and the depth of the dimple is 
measured to the bottom surface. 
A dimple pattern formed by frusto-conical dimples having different 
diameters and a constant aspect ratio performs satisfactorily when used on 
a three-piece golf ball such as the Wilson Staff ball. However, such a 
dimple pattern does not perform satisfactorily when used on a two-piece 
ball. When the Wilson Staff dimple pattern is used on a two-piece ball 
having the same construction as an Ultra golf ball, the resulting ball is 
significantly shorter than the commercial Ultra ball in both carry and 
total distance (carry plus roll). 
However, when the depth of the dimples increases as the diameter of the 
dimples decreases, a two-piece ball with frusto-conical dimples performs 
well. The Wilson TC.sup.2 golf ball is a two-piece ball with truncated 
cone dimples which utilizes that principle. 
In the golf ball described in U.S. Pat. No. 4,560,168 and in the Wilson 
Staff and TC.sup.2 golf balls, the dimples are arranged so that various 
sized dimples are located throughout the icosahedral pattern. For example, 
in FIGS. 11A and 11B of the patent the largest dimples are located at 
dimple positions 3 and 4. In the Wilson Staff and TC.sup.2 balls the 
largest dimples are located just inside the apexes of the icosahedral 
triangles. 
SUMMARY OF THE INVENTION 
I have found that excellent results can be obtained with a dimple pattern 
which utilizes spherical dimples having different diameters but a constant 
aspect ratio, preferably about 0.050. The largest size dimples are located 
just inside and on the vertices of the polygon on which the dimple pattern 
is based, e.g., a triangle for an icosahedral pattern and a pentagon for a 
dodecahedral pattern.

DESCRIPTION OF SPECIFIC EMBODIMENTS 
FIGS. 1 and 2 represent the dimple pattern of the prior art two-piece Ultra 
golf ball and are essentially reproductions of FIGS. 8A and 8B of U.S. 
Pat. No. 4,560,168. As explained in that patent, the dimples are arranged 
in an icosahedral pattern, and the solid lines in FIGS. 1 and 2 represent 
the sides of icosahedral triangles. The dashed lines are six great circles 
which bisect the sides of the icosahedral triangles. The dimples are 
arranged so that they do not intersect the six great circles. 
All of the dimples in the prior art ball illustrated in FIGS. 1 and 2 have 
a constant diameter of 0.135 inch and a constant depth of 0.007 inch. The 
aspect ratio of the depth divided by the diameter is 0.052. 
FIG. 3 illustrates the method of determining the dimple diameter or chord 
and the depth of a dimple 20 as the terms "diameter" and "depth" are used 
herein. A chord line 21 is drawn tangent to the spherical ball surface 22 
on opposite sides of the dimple. Side wall lines 23 are drawn tangent to 
the dimple walls at the inflection points of the wall, i.e., where the 
curvature of the wall changes sign or where the second derivative of the 
equation for the curve is 0. The intersections of the side wall lines 23 
and the chord line 21 define the edges of the dimple and the chord or 
diameter of the dimple. The depth of the dimple is measured between the 
chord line and the bottom of the dimple at its center. For a dimple in the 
shape of a truncated cone, the inflection point is actually a line segment 
of a discrete length. 
FIGS. 4 and 5 represent the dimple pattern of the prior art three-piece 
Wilson Staff golf ball 25. The dimples 26 are arranged in an icosahedral 
pattern and do not intersect the six great circles which bisect the sides 
of the icosahedral triangles. There are five different sizes of dimples 
represented by the dimples numbered 1 through 5 in FIG. 5, and all dimples 
have the same aspect ratio of 0.046. The diameters and depths of the 
dimples are set forth in Table I. 
TABLE I 
______________________________________ 
Dimple No. 
Diameter (in.) 
Depth (in.) 
Aspect Ratio 
______________________________________ 
1 0.155 0.0071 0.046 
2 0.150 0.0069 0.046 
3 0.140 0.0064 0.046 
4 0.135 0.0062 0.046 
5 0.125 0.0058 0.046 
______________________________________ 
Referring to FIG. 6, the dimples of the Wilson Staff ball are 
frusto-conical or in the shape of a truncated cone. Each dimple has a 
conical side surface 27, and the inclination of the side surface relative 
to the chord line 28 is 13 degrees. Each dimple has a flat bottom surface 
29 which extends parallel to the chord line 28. The depth of the dimple is 
measured from the chord line 28 to the bottom surface 29. The radius of 
the spherical outer surface 30 is about 0.84 inch. 
FIGS. 7 and 8 represent the dimple pattern of the prior art two-piece 
TC.sup.2 golf ball 34. The dimples 35 are arranged in an icosahedral 
pattern and do not intersect the six great circles which bisect the sides 
of the icosahedral triangles. There are five different sizes of dimples 
represented by the dimples numbered 1 through 5 in FIG. 8. The depths of 
the dimples increase as the diameters decrease, and the aspect ratios also 
increase as the diameter decreases. The measurements of the dimples in 
FIGS. 7 and 8 are set forth in Table II. 
TABLE II 
______________________________________ 
Dimple No. 
Diameter (in.) 
Depth (in.) 
Aspect Ratio 
______________________________________ 
1 0.155 0.0050 0.032 
2 0.150 0.0052 0.035 
3 0.140 0.0054 0.039 
4 0.135 0.0056 0.042 
5 0.125 0.0060 0.048 
______________________________________ 
Referring to FIG. 9, the dimples of the Wilson TC.sup.2 ball have the shape 
of truncated cones. The inclination of the conical side surface relative 
to the chord line is 11 degrees. 
The inventive dimple pattern is illustrated in FIGS. 10-13. FIG. 10 shows a 
two-piece golf ball 38 consisting of a solid core 39 and a cover 40. The 
cover has an outer spherical surface 41 and a plurality of recessed 
dimples 42. 
The particular embodiment illustrated in FIGS. 11 and 12 includes 432 
dimples 43 arranged in an icosahedral pattern. The dimples do not 
intersect the six great circles 44 which bisect the sides of the 
icosahedral triangles 45. There are five different sizes of dimples as 
indicated in FIG. 12. 
The diameters of the dimples in FIG. 12 are the same as for the Wilson 
Staff and Wilson TC.sup.2 prior art balls. However, unlike the two-piece 
Wilson TC.sup.2 ball, the depths of the dimples in FIGS. 10-13 increase as 
the diameters increase. Unlike the three-piece Wilson Staff ball, which 
has an aspect ratio of 0.046, the aspect ratio of the inventive ball is 
constant at 0.050. Each dimple is in the shape of a sphere as illustrated 
in FIG. 13 rather than a truncated cone as in the Wilson Staff and 
TC.sup.2 balls. The depth of each dimple is measured from the chord line 
46 to the bottom of the dimple. The measurements of the dimples in FIGS. 
10-13 are set forth in Table III. 
TABLE III 
______________________________________ 
Dimple No. 
Diameter (in.) 
Depth (in.) 
Aspect Ratio 
______________________________________ 
1 0.155 0.0078 0.050 
2 0.150 0.0075 0.050 
3 0.140 0.0070 0.050 
4 0.135 0.0068 0.050 
5 0.125 0.0063 0.050 
______________________________________ 
Referring to FIGS. 11 and 12, the largest sized dimples are at dimple 
positions 1 and 2. The largest dimples are located at dimple position No. 
1, which lies just inside the included angle formed by each apex of the 
icosahedral triangle and is tangent or almost tangent to the sides of the 
icosahedral triangle. The next largest dimple is at position No. 2 at each 
of the apexes of the icosahedral triangle. All of the other dimples are 
smaller. 
Referring to FIG. 11, the six great circles define 12 pentagons and 20 
small triangles, forming what is sometimes called an icosadodecahedron 
pattern. The apexes of five icosahedral triangles meet at the center of 
each pentagon. Dimple position No. 2 is in the center of each pentagon, 
and each No. 2 dimple is surrounded by five No. 1 dimples. 
The prior art Staff and TC.sup.2 balls illustrated in FIGS. 4 and 5 and 7 
and 8 have the same arrangement of dimples as that illustrated in FIGS. 11 
and 12. However, dimples of the Staff and TC.sup.2 balls were truncated 
cones rather than portions of spheres, and the dimples did not have a 
constant aspect ratio of 0.050. 
FIGS. 14-20 illustrate the dimple patterns of four sample golf balls which 
were made in order to find the optimum dimple pattern. The dimple pattern 
of FIGS. 14 and 15 has four different sized dimples with a constant aspect 
ratio of 0.052. The largest dimples are located in dimple position Nos. 2, 
4, and 5. 
The dimple pattern of FIGS. 16 and 17 has six different sized dimples with 
a constant aspect ratio of 0.052. The biggest dimples are located in 
dimple position No. 2. 
The dimple pattern of FIGS. 18 and 19 has three different sized dimples 
with a constant aspect ratio of 0.052. The biggest dimples are located in 
dimple position Nos. 2, 4, and 5. 
The dimple pattern of FIGS. 20 and 21 has six different sized dimples with 
a constant aspect ratio of 0.052. The biggest dimples were located in 
dimple position Nos. 2 and 7. 
The performance of the dimple pattern illustrated in FIGS. 10-13 was 
demonstrated by comparative tests referred to in Tables IV and V in which 
the Ultra commercial golf ball was used as the control. All of the balls 
were two-piece balls which had 432 spherical dimples. Sample Nos. 1 and 6 
were injection molded, and Sample Nos. 1A and 2-5 were compression molded. 
Sample No. 1 was the Ultra prior art golf ball in which the chord and depth 
was the same for all dimples. Sample No. 1A used the same dimple pattern 
but was compression molded. Sample No. 2 used the dimple pattern 
illustrated in FIGS. 14 and 15. Sample No. 3 used the dimple pattern 
illustrated in FIGS. 16 and 17. Sample No. 4 used the dimple pattern 
illustrated in FIGS. 18 and 19. Sample No. 5 used the dimple pattern 
illustrated in FIGS. 20 and 21. Sample No. 6 used the dimple pattern 
illustrated in FIGS. 10-13. Table IV includes the dimple information for 
the samples. 
TABLE IV 
______________________________________ 
Chord Depth Aspect Dimple 
Sample (in.) (in.) Ratio Shape 
______________________________________ 
No. 1 0.135 0.0070 0.052 Spherical 
(Ultra) 
No. 1A 0.135 0.0070 0.052 Spherical 
No. 2 0.170 0.0088 0.052 Spherical 
0.125 0.0065 
0.110 0.0057 
0.100 0.0052 
No. 3 0.160 0.0083 0.052 Spherical 
0.150 0.0078 
0.140 0.0073 
0.135 0.0070 
0.110 0.0057 
0.120 0.0062 
No. 4 0.170 0.0088 0.052 Spherical 
0.120 0.0062 
0.100 0.0052 
No. 5 0.170 0.0088 0.052 Spherical 
0.160 0.0083 
0.140 0.0073 
0.130 0.0068 
0.120 0.0062 
0.100 0.0052 
No. 6 0.155 0.0078 0.050 Spherical 
0.150 0.0075 
0.140 0.0070 
0.135 0.0068 
0.125 0.0063 
______________________________________ 
Sample No. 1 was used as a control for Sample No. 6. Both balls were 
injection molded. Sample No. 1A was used as a control for Sample Nos. 2-5. 
These balls were compression molded. Table V compares the average carry 
distance and total distance in yards for Sample Nos. 2-6. The number shown 
in the table is the difference in yards between that ball's distance and 
that of its control. Thirty balls of each sample were hit with a 
True-Temper golf machine using a metal driver and a club head speed of 150 
feet per second. Only the balls which landed in the fairway were measured. 
TABLE V 
______________________________________ 
Sample No. 2 No. 3 No. 4 No. 5 No. 6 
______________________________________ 
Carry Avg. 
0.2 -0.8 -1.8 -2.6 2.0 
Diff. from 
Control 
Total Avg. 
-4.6 -3.3 -4.2 -5.1 5.2 
Diff. from 
Control 
______________________________________ 
Table V indicates that the only sample which was longer in total distance 
than its control was Sample No. 6, which was formed in accordance with the 
invention. The primary difference between Sample No. 6 and Sample Nos. 2-5 
was the location of the largest sized dimples. Referring to FIGS. 11 and 
12, in Sample No. 6 the largest sized dimples were in dimple position No. 
1, which was in each of the corners or vertexes of the icosahedral 
triangles. The next largest sized dimple was in dimple position No. 2, 
which was at each of the vertexes of the icosahedral triangles and which 
was surrounded by No. 1 dimples. The dimples in dimple position No. 2 were 
just slightly smaller than the dimples in dimple position No. 1, and all 
of the other dimples were smaller than dimple Nos. 1 and 2. 
Comparing FIG. 11 with FIGS. 14, 16, 18, and 20, the dimple patterns in 
FIGS. 14, 16, and 18 also have a dimple located at the vertex of five 
adjacent icosahedral triangles which are surrounded by five larger 
dimples. However, FIGS. 14, 16, and 18 are different from FIG. 13 in at 
least one of several ways: either the five surrounding dimples are not the 
largest sized dimples, other dimples are at least as large, the center or 
surrounded dimple is not the next largest sized dimple, etc. In FIG. 20, 
the center dimple is surrounded by dimples that are not the largest-sized 
dimples. 
Referring again to FIGS. 11 and 12, the largest sized dimples, dimples no. 
1, form a cluster of five dimples which surround the next largest sized 
dimple, dimple No. 2. The chord or diameter of dimple No. 2 is 96.8% of 
the chord or diameter of dimple No. 1. The chord or diameter of dimple No. 
3 is 90.3% of the diameter of dimple No. 1, the diameter of dimple No. 4 
is 87.1% of the diameter of dimple No. 1, and the diameter of dimple No. 5 
is 80.6% of the diameter of dimple No. 1. 
The dimple pattern of Sample No. 6 also differs from the dimple patterns of 
Samples Nos. 1-5 by having a constant aspect ratio of 0.050 rather than 
0.052. 
Comparing FIGS. 11 and 12 with the dimple patterns of the prior art Wilson 
Staff and TC.sup.2 golf balls illustrated in FIGS. 4 and 5 and 7 and 8, 
the dimple patterns of the prior art Staff and TC.sup.2 balls also have a 
cluster of the five largest dimples, dimple No. 1, surrounding the next 
largest sized dimple, dimple No. 2, and the dimples have the same diameter 
as the dimples of the inventive pattern. However, the aspect ratio of the 
Wilson Staff dimples was 0.046. The aspect ratios of the TC.sup.2 dimples 
varied, the aspect ratio increasing as the diameter of the dimples 
decreased. Also, the Staff and TC.sup.2 dimples were truncated cones 
rather than portions of spheres. 
All dimple dimensions referred to herein refer to the mold dimensions or, 
equivalently, to an unfinished ball as it comes out of the mold rather 
than to a painted or otherwise finished ball. The balls are finished in 
the conventional manner. 
While in the foregoing specification a detailed description of a specific 
embodiment of the invention was set forth for the purpose of illustration, 
it will be understood that many of the details herein given may be varied 
considerably by those skilled in the art without departing from the spirit 
and scope of the invention.