Note: Descriptions are shown in the official language in which they were submitted.
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Title
A GOLF BALL WITH AN AERODYNAMIC SURFACE ON A POLYURETHANE
COVER
Technical Field
The present invention relates to a golf ball with a thermoset polyurethane
cover.
More specifically, the present invention relates to a dimple pattern for a
golf ball with a
thermoset polyurethane cover in which the dimple pattern has different sizes
of
dimples.
Background Art
Golfers realized perhaps as early as the 1800's that golf balls with indented
surfaces flew better than those with smooth surfaces. Hand-hammered gutta-
percha
golf balls could be purchased at least by the 1860's, and golf balls with
brambles
(bumps rather than dents) were in style from the late 1800's to 1908. In 1908,
an
Englishman, William Taylor, received a patent for a golf ball with
indentations
(dimples) that flew better ad more accurately than golf balls with brambles.
A.G.
Spalding & Bros., purchased the U.S. rights to the patent and introduced the
GLORY
ball featuring the TAYLOR dimples. Until the 1970s, the GLORY ball, and most
other
golf balls with dimples had 336 dimples of the same size using the same
pattern, the
ATTI pattern. The ATTI pattern was an octahedron pattern, split into eight
concentric
straight line rows, which was named after the main producer of molds for golf
balls.
The only innovation related to the surface of a golf ball during this sixty
year
period came from Albert Penfold who invented a mesh-pattern golf ball for
Dunlop.
This pattern was invented in 1912 and was accepted until the 1930's.
In the 1970's, dimple pattern innovations appeared from the major golf ball
manufacturers. In 1973, Titleist introduced an icosahedron pattern which
divides the
golf ball into twenty triangular regions. An icosahedron pattern was disclosed
in
British Patent Number 377,354 to John Vernon Pugh, however, this pattern had
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dimples lying on the equator of the golf ball which is typically the parting
line of the
mold for the golf ball. Nevertheless, the icosahedron pattern has become the
dominant
pattern on golf balls today.
In the late 1970s and the 1980's the mathematicians of the major golf ball
manufacturers focused their intention on increasing the dimpled surface area
(the area
covered by dimples) of a golf ball. The dimpled surface for the ATTI pattern
golf balls
was approximately 50%. In the 1970's, the dimpled surface area increased to
greater
than 60% of the surface of a golf ball. Further breakthroughs increased the
dimpled
surface area to over 70%. U.S. Patent Number 4,949,976 to William Gobush
discloses
a golf ball with 78% dimple coverage with up to 422 dimples. The 1990's have
seen
the dimple surface area break into the 80% coverage.
The number of different dimples on a golf ball surface has also increased with
the surface area coverage. The ATTI pattern disclosed a dimple pattern with
only one
size of dimple. The number of different types of dimples increased, with three
different
types of dimples becoming the preferred number of different types of dimples.
U.S.
Patent Number 4,463 to Oka et al., discloses a dimple pattern with four
different types
of dimples on surface where the non-dimpled surface cannot contain an
additional
dimple. United Kingdom patent application number 2157959, to Steven Aoyama,
discloses dimples with five different diameters. Further, William Gobush
invented a
cuboctahedron pattern that has dimples with eleven different diameters. See
500 Year
of Golf Balls, Antique Trade Books, page 189. However, inventing dimple
patterns
with multiple dimples for a golf ball only has value if such a golf ball is
commercialized and available for the typical golfer to play.
Additionally, dimple patterns have been based on the sectional shapes, such as
octahedron, dodecahedron and icosahedron patterns. U.S. Patent 5,201,522
discloses a
golf ball dimple pattern having pentagonal formations with equally number of
dimples
therein. U.S. Patent Number 4,880,241 discloses a golf ball dimple pattern
having a
modified icosahedron pattern wherein small triangular sections lie along the
equator to
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provide a dimple-free equator.
Although there are hundreds of published patents related to golf ball
dimple patterns, there still remains a need to improve upon current dimple
patterns,
particularly for golf balls with thermoset polyurethane covers. Golf balls
with
thermoset polyurethane covers such as the Maxfli REVOLUTION, the Maxfli HT,
the
Titleist PROFESSIONAL, the Titleist TOUR PRESTIGE, and the Slazenger RAM 420
all need to compensate for the inherent properties of the polyurethane
material which
include the increased spin, the higher drag levels, and manufacturing
difficulties. There
is still a need for a dimple pattern designed to maximize the aerodynamics of
a golf ball
with a thermoset polyurethane cover.
Brief Disclosure of the Invention
The present invention provides a novel dimple pattern that reduces high speed
drag on a golf ball while increasing its low speed lift thereby providing a
golf ball that
travels greater distances. The present invention is able to accomplish this by
providing
multiples sets of dimples arranged in a pattern that covers as much as eighty-
six percent
of the surface of the golf ball.
One aspect of the present invention is a dimple pattern on a golf ball having
a
thermoset cover with a surface coated with at least a base coat. The preferred
thermoset
is polyurethane, however, those skilled in the art will recognize that other
thermoset
materials may be employed in practicing the present invention. The golf ball
includes a
plurality of different sets of dimples disposed on the surface. Each of the
different sets
of dimples has a different diameter than any other set of dimples. The depth
of each of
the dimples of the plurality of different sets of dimples is limited to 0.0060
inches from
the chord of each dimple. The depth of each of the dimples of the plurality of
different
sets of dimples may be between 0.0045 and 0.0060 inches from the chord. Each
of the
dimples of the plurality of different sets of dimples has an entry angle, and
the entry
angle of each dimple may be between 14 and 16 degrees. Each of the dimples of
the
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plurality of different sets of dimples has an edge radius, and the edge radius
of each
dimple may be between 0.020 and 0.050 inches.
Another aspect of the present invention is a dimple pattern on a golf ball
with a
thermoset polyurethane cover that provides greater low speed lift and lower
high speed
drag. The golf ball includes a plurality of different sets of dimples disposed
on the
surface of the coated thermoset polyurethane cover. Each of the different sets
of
dimples having a different diameter than any other set of dimples. The
plurality of
different sets of dimples cover at least eighty-three percent of the surface
of the golf
ball. The golf ball has a lift coefficient greater than 0.20 at a Reynolds
number of
70,000 and 2000 rpm, and a drag coefficient less than 0.232 at a Reynolds
number of
180,000 and 3000 rpm.
Brief Description of the Drawings
FIG. 1 is an equatorial view of a preferred embodiment of a golf ball of the
present invention.
FIG. lA is the view of FIG. 1 illustrating the rows of dimples.
FIG. 1B is the view of FIG. 1 illustrating the transition region of dimples.
FIG. 2 is a polar view of the golf ball of FIG. 1.
FIG. 2A is the view of FIG. 2 illustrating the cascading pentagons of dimples.
FIG. 2B is the view of FIG. 2 illustrating the single encompassing pentagon of
dimples.
FIG. 3 is a polar view of the golf ball of FIG. 1 illustrating the star
configuration.
FIG. 4 is an enlarged cross-sectional view of a dimple of a first set of
dimples of
the golf ball of the present invention.
FIG. 4A is an isolated cross-sectional view to illustrate the definition of
the
entry radius.
FIG. 5 is an enlarged cross-sectional view of a dimple of a second set of
dimples
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of the golf ball of the present invention.
FIG. 6 is an enlarged cross-sectional view of a dimple of a third set of
dimples
of the golf ball of the present invention.
FIG. 7 is an enlarged cross-sectional view of a dimple of a fourth set of
dimples
5 of the golf ball of the present invention.
FIG. 8 is an enlarged cross-sectional view of a dimple of a fifth set of
dimples
of the golf ball of the present invention.
FIG. 9 is an enlarged cross-sectional view of a dimple of a sixth set of
dimples
of the golf ball of the present invention.
FIG. 10 is an enlarged cross-sectional view of a dimple of a seventh set of
dimples of the golf ball of the present invention.
FIG. 11 is a polar view of an alternative embodiment of the golf ball of the
present invention.
FIG. 12 is an equatorial view of yet another alternative embodiment of a golf
ball of the present invention.
FIG. 13 is a graph of the lift coefficient versus Reynolds number.
FIG. 14 is graph of the drag coefficient versus Reynolds number.
Best Models) For Carrying Out The Invention
As shown in FIGS. 1-3, a golf ball is generally designated 20. The golf
ball may be a one-piece, two-piece, a three piece, or the like golf ball.
Further, the
three-piece golf ball may have a wound layer, or a solid boundary layer. The
cover 21
of the golf ball 20 may be any suitable material. A preferred cover 21 is
composed of a
thermoset polyurethane material. However, those skilled in the pertinent art
will
recognize that other cover materials may be utilized without departing from
the scope
and spirit of the present invention. The golf ball 20 may have a finish of a
basecoat
and/or top coat.
The golf ball 20 has a surface 22. The golf ball 20 also has an equator 24
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dividing the golf ball 20 into a first hemisphere 26 and a second hemisphere
28. A first
pole 30 is located ninety degrees along a longitudinal arc from the equator 24
in the
first hemisphere 26. A second pole 32 is located ninety degrees along a
longitudinal arc
from the equator 24 in the second hemisphere 28.
On the surface 22, in both hemispheres 26 and 28, are 382 dimples partitioned
into seven different sets of dimples. A first set of dimples 34 are the most
numerous
dimples consisting of two-hundred twenty dimples in the preferred embodiment.
A
second set of dimples 36 are the next most numerous dimples consisting of one-
hundred dimples. A third set of dimples 38 and a fourth set of dimples 40 are
the next
most numerous with each set 38 and 40 consisting of twenty dimples in the
preferred
embodiment. A fifth set of dimples 42 and a sixth set of dimples 44 are the
next most
numerous with each set 42 and 44 consisting of ten dimples in the preferred
embodiment. The seventh set of dimples 46 consist of only two dimples. In a
preferred
embodiment, the 382 dimples account for 86% of the surface 22 of the golf
ball.
The two dimples of the seventh set of dimples 46 are each disposed on
respective
poles 30 and 32. Each of the fifth set of dimples 42 is adjacent one of the
seventh set of
dimples 46. The five dimples of the fifth set of dimples 42 that are disposed
within the
first hemisphere 26 are each an equal distance from the equator 24 and the
first pole 30.
The five dimples of the fifth set of dimples 42 that are disposed within the
second
hemisphere 28 are each an equal distance from the equator 24 and the second
pole 32.
These polar dimples 42 and 46 account for approximately 2% of the surface 22
of the
golf ball 20.
A cross-section of a dimple of the fifth set of dimples 42 is shown in FIG. 8.
The radius RS of the dimple 42 is approximately 0.0720 inches, the chord depth
CS is
approximately 0.0054 inches, the entry angle 05 is approximately 15.7 degrees,
and the
edge radius ERS is approximately 0.0336 inches. A cross-section of a dimple of
the
seventh set of dimples 46 is shown in FIG.10. The radius R~ of the dimple 46
is
approximately 0.0510 inches, the chord depth C~ is approximately 0.0049
inches, the
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entry angle 0, is approximately 13.4 degrees, and the edge radius ER, is
approximately
0.0336 inches.
The ten dimples of the sixth set of dimples 44 account for approximately 3% of
the surface 22 of the golf ball 20. The five dimples of the sixth set of
dimples 44 that
are disposed within the first hemisphere 26 are each an equal distance from
the equator
24 and the first pole 30. The five dimples of the sixth set of dimples 44 that
are
disposed within the second hemisphere 28 are each an equal distance from the
equator
24 and the second pole 32. Also, each of the sixth set of dimples 44 is
adjacent to three
different sets of dimples 34, 36 and 40.
A cross-section of a dimple of the sixth set of dimples 44 is shown in FIG.9.
The
radius R6 of the dimple 44 is approximately 0.0930 inches, the chord depth C6
is
approximately 0.0051 inches, the entry angle O6 is approximately 15.2 degrees,
and the
edge radius ER6 is approximately 0.0333 inches. The extraordinarily large
diameter of
each of the sixth set of dimples 44 allows for the extraordinary surface
coverage of the
dimple pattern of the present invention. This is contrary to conventional
thinking that
teaches that dimples with smaller diameters would provide for greater surface
coverage.
All of the fourth set of dimples 40 are adjacent to at least one of the sixth
set of
dimples 44. The twenty dimples of the fourth set of dimples 40 cover
approximately
2.7% of the surface 22 of the golf ball 20. The ten dimples of the fourth set
of dimples
40 that are disposed within the first hemisphere 26 are each an equal distance
from the
equator 24 and the first pole 30. The ten dimples of the fourth set of dimples
40 that
are disposed within the second hemisphere 28 are each an equal distance from
the
equator 24 and the second pole 32. Also, each of the fourth set of dimples 40
is
adjacent to three different sets of dimples 36, 38 and 44.
A cross-section of a dimple of the fourth set of dimples 40 is shown in FIG.
7.
The radius R4 of the dimple 40 is approximately 0.062 inches, the chord depth
C4 is
approximately 0.0052 inches, the entry angle 04 is approximately 15.2 degrees,
and the
edge radius ER4 is approximately 0.0358 inches.
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All of the third set of dimples 38 are adjacent to at least one of the sixth
set of
dimples 44. The twenty dimples of the third set of dimples 38 cover
approximately
3.8% of the surface 22 of the golf ball 20. The ten dimples of the third set
of dimples 38
that are disposed within the first hemisphere 26 are each an equal distance
from the
equator 24 and the first pole 30. The ten dimples of the third set of dimples
38 that are
disposed within the second hemisphere 28 are each an equal distance from the
equator
24 and the second pole 32. Also, each of the fourth set of dimples 38 is
adjacent to
three different sets of dimples 34, 36 and 40.
A cross-section of a dimple of the third set of dimples 38 is shown in FIG. 6.
The
radius R3 of the dimple 38 is approximately 0.074 inches, the chord depth C3
is
approximately 0.0053 inches, the entry angle 03 is approximately 15.3 degrees,
and the
edge radius ER3 is approximately 0.0344 inches.
The two-hundred twenty dimples of the first set of dimples 34 are the most
influential of the different sets of dimples 34-46 due to their number, size
and
placement on the surface 22 of the golf ball 20. The two-hundred twenty
dimples of the
first set of dimples 34 cover approximately 53% of the surface 22 of the golf
ball 20.
The one-hundred ten dimples of the first set of dimples 34 that are disposed
within the
first hemisphere 26 are disposed in either a first row 80 and a second row 82
above the
equator 24, or a pseudo-star configuration 84 about the first pole 30 that is
best
illustrated in FIG. 3. Similarly, the one-hundred ten dimples of the first set
of dimples
34 that are disposed within the second hemisphere 28 are disposed in either a
first row
90 and a second row 92 below the equator 24, or a pseudo-star configuration
94, not
shown, about the second pole 32, not shown.
A cross-section of a dimple of the first set of dimples 34 is shown in FIG. 4.
The
radius R, of the dimple 34 is approximately 0.0834 inches, the chord depth C,
is
approximately 0.0053 inches, the entry angle 0, is approximately 15.3 degrees,
and the
edge radius ER, is approximately 0.0344 inches. Unlike the use of the term
"entry
radius" or "edge radius" in the prior art, the edge radius as defined herein
is a value
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utilized in conjunction with the entry angle to delimit the concave and convex
segments
of the dimple contour. The first and second derivatives of the two Bezier
curves are
forced to be equal at this point defined by the edge radius and the entry
angle, as shown
in FIG. 4A. The one-hundred dimples of the second set of dimples 36 are the
next
most influential of the different sets of dimples 34-46 due to their number,
size and
placement on the surface 22 of the golf ball 20. The one-hundred dimples of
the second
set of dimples 36 cover approximately 22% of the surface 22 of the golf ball
20. Thus,
together the first set of dimples 34 and the second set of dimples 36 cover
over
approximately 75% of the surface 22 of the golf ball 20. The fifty dimples of
the
second set of dimples 36 that are disposed within the first hemisphere 26 are
disposed
in either a third row 86 above the equator, a second pentagon 102 about the
first pole
30, or along a transition latitudinal region 70. Similarly, the fifty dimples
of the second
set of dimples 36 that are disposed within the second hemisphere 28 are
disposed in
either a third row 96 below the equator 24, a second pentagon 102a, not shown,
about
the second pole 32, or along a transition latitudinal region 72. A cross-
section of a
dimple of the second set of dimples 36 is shown in FIG. 5. The radius RZ of
the dimple
36 is approximately 0.079 inches, the chord depth CZ is approximately 0.0053
inches,
the entry angle Oz is approximately 15.1 degrees, and the edge radius ERz is
approximately 0.0315 inches.
As best illustrated in FIG. lA, each hemisphere 26 and 28 begins with three
rows
from the equator 24. The first and second rows 80 and 82 of the first
hemisphere 26
and the first and second rows 90 and 92 of the second hemisphere 28 are
composed of
the first set of dimples 34. The third row 86 of the first hemisphere 26 and
the third row
96 of the second hemisphere 28 are composed of the second set of dimples 36.
This
pattern of rows is utilized to achieve greater surface coverage of dimples on
the golf
ball 20. However, as mentioned previously, conventional teaching would dictate
that
additional rows of smaller diameter dimples should be utilized to achieve
greater
surface area coverage. However, the dimple pattern of the present invention
transitions
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from rows of equal dimples into a pentagonal region 98. The pentagonal region
98 is
best seen in FIG. 2A. A similar pentagonal region 98a, not shown, is disposed
about
the second pole 32. The pentagonal region 98 has five pentagons 100, 102, 104,
106
and 108 expanding from the first pole 30. Similar pentagons 100a, 102a, 104a,
106a
5 and 108a expand from the second pole 32. The first pentagon 100 consists of
the fifth
set of dimples 42. The second pentagon 102 consists of the second set of
dimples 36.
The third pentagon 104 consists of the first set of dimples 34. The fourth
pentagon 106
also consists of the first set of dimples 34. The fifth pentagon 108 consists
of the first
set of dimples 34 and the sixth set of dimples 44. However, the greater fifth
pentagon
10 108' would include the fifth pentagon 108 and all dimples disposed between
the third
row 86 and the fifth pentagon 108. The pentagonal region 98 allows for the
greater
surface area of the dimple pattern of the present invention.
FIG. 2B illustrates five triangles 130-138 that compose the pentagonal region
98.
Dashed line 140 illustrates the extent of the greater pentagonal region 98'
which
overlaps with the transition latitudinal region 70.
As best illustrated in FIG. 1B, all of the dimples of the third set of dimples
38, the
fourth set of dimples 40 and the sixth set of dimples 44 are disposed within
the
transition latitudinal regions 70 and 72. The transition latitudinal regions
70 and 72
transition the dimple pattern of the present invention from the rows 80, 82,
86, 90, 92
and96 to the pentagonal regions 98 and 98a. Each of the transition latitudinal
regions 70
and 72 cover a circumferencial area between 40 to 60 longitudinal degrees from
the
equator 24 in their respective hemispheres 26 and 28. The first transition
latitudinal
region 70 has a polar boundary 120 at approximately 60 longitudinal degrees
from the
equator 24, and an equatorial boundary 122 at approximately 40 longitudinal
degrees
from the equator 24. Similarly, the second transition latitudinal region 72
has a polar
boundary 120a at approximately 60 longitudinal degrees from the equator 24,
and an
equatorial boundary 122a at approximately 40 longitudinal degrees from the
equator
24.
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Alternative embodiments of the dimple pattern of the present invention are
illustrated in FIGS. 11 and 12. The dimple pattern on the golf ball 20a of
FIG. 11 only
has five different sets of dimples 34, 36, 40, 42 and 44. The dimple pattern
on the golf
ball 20b of FIG. 12 only has six different sets of dimples 34, 36, 38, 40, 42
and 44.
Both of the dimple patterns of the golf balls 20a and 20b have had the seventh
set of
dimples 46 that are disposed at the poles 30 and 32 removed, and the dimple
patter of
the golf ball 20a has had all of the dimples of the third set of dimples 38
substituted
with dimples from the fifth set of dimples 42.
The force acting on a golf ball in flight is calculated by the following
trajectory
equation:
F=FL + FD + G (A)
wherein F is the force acting on the golf ball; FL is the lift; FD is the
drag; and G is
gravity. The lift and the drag in equation A are calculated by the following
equations:
FL = O.SCLApv2 (B)
FD = O. SCDApv2 (C)
wherein CL is the lift coefficient; CD is the drag coefficient; A is the
maximum cross-
sectional area of the golf ball; p is the density of the air; and v is the
golf ball airspeed.
The drag coefficient, CD, and the lift coefficient, CL, may be calculated
using the
following equations:
CD = 2FD /Apv2 (D)
CL = 2FL IAP~'2
The Reynolds number R is a dimensionless parameter that quantifies the ratio
of
inertial to viscous forces acting on an object moving in a fluid. Turbulent
flow for a
dimpled golf ball occurs when R is greater than 40000. If R is less than
40000, the flow
may be laminar. The turbulent flow of air about a dimpled golf ball in flight
allows it
to travel farther than a smooth golf ball.
The Reynolds number R is calculated from the following equation:
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R = vD~,u (F)
wherein v is the average velocity of the golf ball; D is the diameter of the
golf ball
(usually 1.68 inches); p is the density of air (0.00238 slugs/ft3 at standard
atmospheric
conditions); and ~.c is the absolute viscosity of air (3.74 x 10-' lb*sec/ft2
at standard
atmospheric conditions). A Reynolds number, R, of 180,000 for a golf ball
having a
USGA approved diameter of 1.68 inches, at standard atmospheric conditions,
approximately corresponds to a golf ball hit from the tee at 200 ft/s or 136
mph, which
is the point in time during the flight of a golf ball when the golf ball
attains its highest
speed. A Reynolds number, R, of 70,000 for a golf ball having a USGA approved
diameter of 1.68 inches, at standard atmospheric conditions, approximately
corresponds
to a golf ball at its apex in its flight, 78 ft/s or 53 mph, which is the
point in time during
the flight of the golf ball when the travels at its slowest speed. Gravity
will increase
the speed of a golf ball after its reaches its apex.
FIG. 13 illustrates the lift coefficient of a golf ball 20 with the dimple
pattern of
the present invention thereon as compared to the Titlelist PROFESSIONAL, the
Titlelist TOUR PRESTIGE, the Maxfli REVOLUTION and the Maxfli HT
URETHANE. FIG. 14 illustrates the drag coefficient of a golf ball 20 with the
dimple
pattern of the present invention thereon as compared to the Titlelist
PROFESSIONAL,
the Titlelist TOUR PRESTIGE, the Maxfli REVOLUTION and the Maxfli HT
URETHANE.
All of the golf balls for the comparison test, including the golf ball 20 with
the
dimple pattern of the present invention, have a thermoset polyurethane cover.
The golf
ball 20 with the dimple pattern of the present invention was constructed as
set forth in
U.S. Patent Number 6,117,024, filed on July 27, 1999, for a Golf Ball With A
Polyurethane Cover which pertinent parts are hereby incorporated by reference.
The
aerodynamics of the dimple pattern of the present invention provides a greater
lift with
a reduced drag thereby translating into a golf ball 20 that travels a greater
distance than
golf balls of similar constructions.
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As compared to other golf balls having polyurethane covers, the golf ball 20
of
the present invention is the only one that combines a lower drag coefficient
at high
speeds, and a greater lift coefficient at low speeds. Specifically, as shown
in FIGS. 13
and 14, none of the other golf balls have a lift coefficient, CL, greater than
0.18 at a
Reynolds number of 70,000, and a drag coefficient CD less than 0.23 at a
Reynolds
number of 180,000. For example, while the Titliest PROFESSIONAL has a CL
greater
than 0.18 at a Reynolds number of 70,000, its CD is greater than 0.23 at a
Reynolds
number of 180,000. Also, while the Maxfli REVOLUTION has a drag coefficient CD
greater than 0.23 at a Reynolds number of 180,000, its CL is less than 0.18 at
a
Reynolds number of 70,000.
In this regard, the Rules of Golf, approved by the United States Golf
Association
("USGA") and The Royal and Ancient Golf Club of Saint Andrews, limits the
initial
velocity of a golf ball to 250 feet (76.2m) per second (a two percent maximum
tolerance allows for an initial velocity of 255 per second) and the overall
distance to
280 yards (256m) plus a six percent tolerance for a total distance of 296.8
yards (the six
percent tolerance may be lowered to four percent). A complete description of
the
Rules of Golf are available on the USGA web page at www.usga.org. Thus, the
initial
velocity and overall distance of a golf ball must not exceed these limits in
order to
conform to the Rules of Golf. Therefore, the golf ball 20 has a dimple pattern
that
enables the golf ball 20 to meet, yet not exceed, these limits.
