Golf ball

The golf ball has no three dimples in a row with edges aligned. This pattern produces a golf ball with reduced drag. The preferred golf ball has multiple sizes of dimples.

This invention relates to golf balls and, more particularly, to golf balls 
wherein no three dimples in a row on the surface of the golf ball have 
edges that align. Preferably, multiple sized dimples are used. 
Typically, golf balls are made in a molding process wherein dimples are 
formed in the spherical surface of the golf ball. This molding process is 
done in a conventional manner either by injection molding cover stock 
about a core or by compression molding preformed half shells about a core. 
Generally, the core is either a solid mass of rubber, which gives rise to 
a two piece golf ball or a wound core which gives rise to a three piece 
golf ball. The wound core is made by winding thin elastic thread about a 
center. The center is either a solid mass of rubber or a liquid filled 
sphere which has been frozen temporarily to facilitate winding of the 
thread about the center. One piece golf balls are made from a mass of 
material and are not considered to have a core, either solid or wound. 
The United States Golf Association (USGA) promulgates rules, one of which 
is directed to symmetry of a golf ball. The USGA symmetry requirement 
dictates that a golf ball must be designed and manufactured to perform in 
general as if it were spherically symmetrical. Meeting this task can be 
difficult. 
The present invention provides a golf ball having a spherical surface with 
a plurality of dimples formed therein and no three dimples in a row having 
edges that align. All the dimples can have the same nominal dimple 
diameter; however, in many situations it is preferable that adjacent 
dimples have substantially different nominal dimple diameters. 
Golf balls made in accordance with the present invention are thought to 
have a higher lift to drag ratio than conventionally made balls. The lift 
to drag ratio is the ratio of the lift force on the golf ball to the drag 
force on the golf ball at any one moment during the flight of the golf 
ball through the air. The lift force is the aerodynamic force exerted on 
the golf ball upward and normal to the direction of travel of the golf 
ball during flight. The drag force on the golf ball is the aerodynamic 
force exerted on the golf ball in a direction 180.degree. from the 
direction of flight of the golf ball. It is thought that by having no 
three dimples in a row having edges that align, the lift to drag ratio of 
the golf ball of the present invention is higher than that of conventional 
golf balls which typically have rows of three or more dimples having their 
edges aligned. As a practical matter, a higher lift to drag ratio means 
that the ball can be made to travel farther. 
Preferably, the dimples are formed in the spherical surface of the golf 
ball by having four parting lines which correspond to four great circular 
paths that encircle the golf ball where none of the parting lines 
intersects any of the dimples. The dimples are arranged in two patterns. 
One pattern forms a spherical square while the other pattern forms a 
spherical triangle. The surface of the golf ball is covered with six 
spherical squares and eight spherical triangles, both shapes occupying 
fairly large areas on the surface of the golf ball. It has been found that 
such a pattern is symmetrical and also lends itself to good overall 
surface coverage and minimum land area when multiple sized dimples are 
placed on the surface of the golf ball. 
Preferably, a golf ball is made in accordance with the present invention by 
dividing the surface of the golf ball into six spherical squares and eight 
spherical equilateral triangles. These spherical triangles and spherical 
squares are located by inscribing an octahedron inside the spherical 
surface of a golf ball, projecting the octahedron onto the surface of the 
sphere, locating the midpoint on each edge of the octahedron and then 
connecting each of the midpoints to its nearest neighboring midpoints. The 
geometric form left after connecting the midpoints has six spherical 
squares and eight spherical equilateral triangles. The great circular 
paths follow the edges of the spherical squares and spherical triangles so 
formed. Each one of the four great circular paths passes through six 
midpoints. The four great circular paths correspond to the position of the 
parting lines on the surface of the golf ball. The parting lines are 
coextensive with the four great circular paths. Preferably, the mold 
parting line corresponds to one of the parting lines of the present 
invention, with the other three parting lines being false parting lines. 
Dimples are distributed over the surface of the golf ball by arranging 
dimples inside each of the six spherical squares and in each of the eight 
spherical equilateral triangles, making sure that none of the dimples 
intersect any of the parting lines and making sure that no three dimples 
in a row have edges that align. Preferably, at least about 50% of the 
surface of the golf ball is covered with dimples. Preferably, each 
spherical square has the same dimple pattern as every other spherical 
square on the surface of the golf ball and each spherical triangle has the 
same dimple pattern as every other spherical triangle on the surface of 
the golf ball. 
The preferred dimple patterns have 440 and 456 dimples. Some manufacturers 
remove a small number of dimples, typically eight, four at each pole, so 
that a trademark and identification number can be affixed to the ball 
(e.g. 432 and 448). However, modern stamping methods allow for affixing 
trademarks and identification numbers without the removal of dimples. 
Thus, the preferred golf ball of the present invention has about 432 to 
440 or about 448 to 456 dimples.

FIGS. 1-7 illustrate the preferred method for arranging dimples on the 
surface of the golf ball in accordance with the present invention. 
FIG. 1 illustrates sphere 10 inside of which octahedron 12 is inscribed. 
The twelve midpoints of each edge of octahedron 12 are numbered 14, 16, 
18, 20, 22, 24, 26, 28, 30, 32, 34 and 36. The edges are identified in 
FIG. 1 by a prime, i.e. 14', 16', 18', 20', 22', 24', 26', 28', 30', 32', 
34' and 36'. By connecting each set of midpoints of each side of each face 
of octahedron 12, an equilateral triangle is created, thus making the 
eight equilateral triangles of the present invention. For example, 
midpoints 16, 18 and 36 are connected to create an equilateral triangle 
having its three vertices identified by the set of three midpoints 
16-18-36. The same has been done for all four faces of the octahedron on 
the right side of FIG. 1. Specifically, the three remaining equilateral 
triangles on the right hand side of FIG. 1 are identified by sets of three 
midpoints: 24-26-36; 26-28-34; and 18-20-34. These sets of midpoints 
identify the vertices of each equilateral triangle. It is clear that by 
connecting the midpoints of edges 14', 16', 20' , 22', 24', 28', 30' and 
32' on the left hand side of FIG. 1, the remaining four equilateral 
triangles are formed. These remaining four equilateral triangles are 
identified by the following sets of three midpoints: 14-16-32; 14-20-30; 
22-24-32; and 22-28-30. 
The four corners of the six squares are also identified as four midpoints 
which correspond to the four corners of the square. Specifically, these 
squares are formed about each one of the six apexes of the octahedron. The 
four corners of each of the six squares correspond to the following six 
sets of four midpoints: 18-36-26-34; 16-18-20-14; 14-32-22-30; 
34-20-30-28; 28-22-24-26; and 36-16-32-24. 
It should be noted that in connecting the midpoints of each edge of the 
octahedron, only the midpoints belonging to one face are interconnected 
and none of the midpoints on one face are connected to midpoints on 
another face, except where there is a common edge. In other words, all 
midpoint connecting lines travel on the surface of the octahedron, not 
through the octahedron. 
Each one of the four great circular paths passes through six midpoints of 
the edges of the octahedron and corresponds to the edges of the 
equilateral triangles and squares which were formed in the manner 
described above. Each great circular path is defined by the following set 
of six midpoints: 24-36-18-20-30-22; 24-26-34-20-14-32; 16-18-34-28-22-32; 
and 16-14-30-28-26-36. 
These paths are clear from FIG. 2 wherein the lines representing the 
octahedron have been deleted and the lines connecting the midpoints 
remain. The midpoints are identified in FIG. 2. The four parting lines 
correspond to the four great circular paths. 
The four great circular paths have a diameter equal to that of sphere 10. 
Dimples are arranged within the geometric figures, equilateral triangles 
and squares, formed between the great circular paths. None of the great 
circular paths intersect the dimples. 
FIGS. 3 and 4 illustrate a preferred dimple pattern of a spherical 
equilateral triangle and a spherical square used for making a golf ball in 
accordance with the present invention having 440 dimples thereon. FIG. 3 
illustrates a preferred spherical equilateral triangle 50 having a dimple 
pattern in accordance with the present invention for making a golf ball 
with 440 dimples. FIG. 4 illustrates a preferred spherical square 52 
having a dimple pattern for a golf ball made in accordance with the 
present invention. Such a pattern produces a preferred 440 dimples. 
The two sets of preferred dimensions for the respectively labeled dimples 
in FIGS. 3 and are given below in Tables I and II: 
TABLE I 
______________________________________ 
(FIG. 3 and 4) 
Type Diameter (inches) 
Depth (inches) 
______________________________________ 
A 0.090 0.0071 
B 0.095 0.0075 
C 0.100 0.0079 
D 0.105 0.0083 
E 0.115 0.0091 
F 0.125 0.0099 
G 0.130 0.0102 
H 0.140 0.0110 
I 0.145 0.0114 
J 0.150 0.0118 
K 0.160 0.0126 
L 0.170 0.0134 
______________________________________ 
TABLE II 
______________________________________ 
(FIG. 3 and 4) 
Type Diameter (inches) 
Depth (inches) 
______________________________________ 
A 0.090 0.0079 
B 0.095 0.0083 
C 0.100 0.0088 
D 0.105 0.0092 
E 0.115 0.0101 
F 0.125 0.0110 
G 0.130 0.0114 
H 0.140 0.0123 
I 0.145 0.0127 
J 0.150 0.0131 
K 0.160 0.0140 
L 0.170 0.0149 
______________________________________ 
FIGS. 5 and 6 illustrate a preferred dimple pattern of a spherical 
equilateral triangle and a spherical square used to make a golf ball in 
accordance with the present invention having 456 dimples. FIG. 5 
illustrates a preferred spherical equilateral triangle 54 having a dimple 
pattern for a golf ball made in accordance with the present invention such 
that a golf ball with a preferred 456 dimples is produced. FIG. 6 
illustrates a preferred spherical square 56 having a dimple pattern for a 
golf ball made in accordance with the present invention such that a golf 
ball with a preferred 456 dimples is produced. 
The preferred dimensions for the respectively labeled dimples in FIGS. 5 
and 6 are given below in Table III: 
TABLE III 
______________________________________ 
(FIGS. 5 and 6) 
Type Diameter (inches) 
Depth (inches) 
______________________________________ 
M 0.085 0.0067 
N 0.100 0.0079 
O 0.115 0.0091 
P 0.120 0.0095 
Q 0.125 0.0099 
R 0.130 0.0102 
S 0.135 0.0106 
T 0.140 0.0110 
U 0.150 0.0118 
V 0.160 0.0126 
______________________________________ 
FIG. 7 is a projected view of golf ball 60 made in accordance with the 
present invention and having 440 dimples thereon. The great circular paths 
have been numbered 62, 64, 66 and 68. 
FIG. 8 is a projected view of golf ball 70 made in accordance with the 
present invention and having 456 dimples thereon. The great circular paths 
have been numbered 72, 74, 76 and 78. 
To illustrate dimples with edges aligned and edges not aligned, FIGS. 9-12 
are presented herein. FIG. 9 illustrates three dimples in a row having 
edges that are aligned. FIGS. 10-12 illustrate three dimples in a row with 
edges not aligned. In FIG. 10 the dimples alternate nominal dimple 
diameter. In FIG. 11, the dimples are staggered and in FIG. 12 the dimples 
not only have different nominal dimple diameters but also are staggered. 
To determine if any three dimples are considered to be "in a row", the 
following steps are taken as illustrated in FIG. 13: 
(1) The great circle arc segment AB is created between the centers of the 
first dimple A and the second dimple B. 
(2) The great circle arc segment BC is created between the centers of the 
second dimple B and the third dimple C. 
(3) Dimples A, B, and C are considered to be "in a row" if and only if: 
(a) the angle between AB and BC at the center of dimple B is greater than 
or equal to 90.degree.; and 
(b) neither AB nor BC intersect any dimple other than A, B or C. 
In this case, the dimples A, B, and C of FIG. 13 are "in a row". 
To determine if any three dimples in a row have "edges that align", the 
following steps are taken as illustrated in FIG. 14: 
(1) The great circle arc segment AC is created between the centers of the 
first and third dimples of the row, A and C respectively. 
(2) The great circle arc T.sub.1 is created tangent to dimples A and C and 
not intersecting AC. 
(3) The great circle arc T.sub.2 is created tangent to dimples A and C and 
not intersecting AC. 
(4) Dimples A, B, and C are considered to have "edges that align" if and 
only if: 
(a) the center of dimple B is on the same side of T.sub.1 as the centers of 
dimples A and C, and dimple B is tangent to T.sub.1 ; or 
(b) the center of dimple B is on the same side of T.sub.2 as the centers of 
dimples A and C, and dimple B is tangent to T.sub.2. 
In this case the dimples A, B and C of FIG. 14 do not have "edges that 
align." 
These and other aspects of the present invention will be more fully 
appreciated with reference to the following example: 
EXAMPLE 1 
A flight test was performed using golf balls having surlyn covers and wound 
cores. Golf balls having patterns made in accordance with FIG. 7 and FIG. 
8 and dimple dimensions in accordance with Tables I and III, respectively, 
were tested against a commercial ball having 384 dimples thereon sold 
under the trade name Titleist 384 DT by Acushnet Company. The results are 
illustrated below in Table IV: 
TABLE IV 
______________________________________ 
Distance (yds) 
FIG. 7 FIG. 8 
Club 440 dimples 
456 dimples 
______________________________________ 
Low Driver +7.3 +4.8 
(11.degree. loft angle) 
Medium Driver +2.3 +2.5 
(13.degree. loft angle) 
High Driver -1.2 -0.6 
(15.degree. loft angle) 
#5 Iron -2.5 -1.6 
(26.degree. loft angle) 
______________________________________ 
Table IV gives the results relative to the 384 ball, e.g. "+7.3 yds" means 
that when hit with a low driver at a loft angle of 11.degree., the ball of 
FIG. 7 went 7.3 yards farther than the conventional 384 dimpled ball. 
Measurements were made with a dual pendulum driving machine using four 
different club heads. The loft angle is the angle made by the face of the 
club head with the vertical at the point of impact with the ball. 
The balls of FIG. 7 (440 dimples) and FIG. 8 (456 dimples) also flew higher 
than the conventional 384 dimpled ball, indicating that the lift to drag 
ratio of the balls made in accordance with the present invention was 
higher than that of the 384 dimpled ball. 
By making no three dimples in a row having aligned edges, the aerodynamic 
drag of the golf ball is thought to be reduced. When adjacent dimple edges 
are aligned, the vortices formed due to air current over the golf ball 
surface are thought to become cumulative or to "stack up"" thereby 
increasing the drag on the golf ball. By staggering the dimple edges, drag 
should decrease. 
Preferably, to enable the balls made in accordance with the present 
invention to travel farther, a two piece construction, i.e. a solid core 
with one piece cover, is employed and the construct is such that the ball 
has a low spin rate in flight. 
It has also been found that decreased land area and therefore increased 
dimple coverage of the golf ball surface can be obtained with the present 
invention. 
A great circular path has the same diameter as that of the golf ball or 
sphere. 
For any number appearing in the claims which is not modified by the term 
"about", it will be understood that the term "about" modifies such number. 
A dimple, as used in the specification and claims and as used in the golf 
industry, is a standard term well known to those of skill in the art. 
When referring to a dimple diameter, the term "diameter" as used herein 
means the diameter of a circle defined by the edges of the dimple. When 
the edges of a dimple are non-circular, the diameter means the diameter of 
a circle which has the same area as the area defined by the edges of the 
dimples. When the term "depth" is used herein, it is defined as the 
distance from the continuation of the periphery line of the surface of the 
golf ball to the deepest part of a dimple which is a section of a sphere. 
When the dimple is not a section of a sphere, the depth in accordance with 
the present invention is computed by taking a cross-section of the dimple 
at its widest point. The area of the cross-section is computed and then a 
section of a circle of equal area is substituted for the cross-section. 
The depth is the distance from the continuation of the periphery line to 
the deepest part of the section of the circle. 
It will be understood that the claims are intended to cover all changes and 
modifications of the preferred embodiment of the invention herein chosen 
for the purpose of illustration which do not constitute a departure from 
the spirit and scope of the invention.