U.S. patent application number 16/736846 was filed with the patent office on 2020-05-07 for curvilinear golf ball dimples and methods of making same.
This patent application is currently assigned to Acushnet Company. The applicant listed for this patent is Acushnet Company. Invention is credited to Michael R. Madson, Nicholas M. Nardacci.
Application Number | 20200139196 16/736846 |
Document ID | / |
Family ID | 70460056 |
Filed Date | 2020-05-07 |
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United States Patent
Application |
20200139196 |
Kind Code |
A1 |
Madson; Michael R. ; et
al. |
May 7, 2020 |
CURVILINEAR GOLF BALL DIMPLES AND METHODS OF MAKING SAME
Abstract
The present invention is directed to golf balls having surface
textures with unique appearances and improved aerodynamic
characteristics due, at least in part, to the use of curvilinear
dimple plan shapes. In particular, the present invention is
directed to a golf ball that includes at least a portion of its
dimples having a plan shape defined by a number of convex or
concave arcs that are derived from the vertices of a regular
n-sided polygon, for example, an equilateral triangle or
square.
Inventors: |
Madson; Michael R.; (Easton,
MA) ; Nardacci; Nicholas M.; (Barrington,
RI) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Acushnet Company |
Fairhaven |
MA |
US |
|
|
Assignee: |
Acushnet Company
Fairhaven
MA
|
Family ID: |
70460056 |
Appl. No.: |
16/736846 |
Filed: |
January 8, 2020 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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15849932 |
Dec 21, 2017 |
10532250 |
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16736846 |
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15726615 |
Oct 6, 2017 |
10195485 |
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15849932 |
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14941916 |
Nov 16, 2015 |
9782629 |
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15726615 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
A63B 37/002 20130101;
A63B 37/0007 20130101; A63B 37/0006 20130101; A63B 2102/32
20151001 |
International
Class: |
A63B 37/00 20060101
A63B037/00 |
Claims
1. A golf ball having an outer surface comprising a plurality of
dimples disposed thereon, wherein a majority of the dimples are
curvilinear dimples having a non-isodiametrical plan shape defined
by at least three circular arcs, each circular arc defining an edge
of the dimple and having two discontinuous endpoints that define
adjacent vertices of a base polygon, and wherein: the curvilinear
dimples include dimples having at least two different equivalent
dimple diameters, including a maximum equivalent dimple diameter
and a minimum equivalent dimple diameter; and the difference
between the maximum equivalent dimple diameter and the minimum
equivalent dimple diameter is about 0.080 inches or less.
2. The golf ball of claim 1, wherein the curvilinear dimples
include dimples having three edges and dimples having four
edges.
3. The golf ball of claim 1, wherein the golf ball has a dimple
surface coverage of greater than about 73.0%.
4. The golf ball of claim 1, wherein the minimum equivalent dimple
diameter of the curvilinear dimples is about 0.120 inches or
greater.
5. The golf ball of claim 1, wherein the maximum equivalent dimple
diameter of the curvilinear dimples is about 0.200 inches or
less.
6. The golf ball of claim 1, wherein each of the curvilinear
dimples having the maximum equivalent dimple diameter has three
edges.
7. The golf ball of claim 1, wherein each of the curvilinear
dimples having the maximum equivalent dimple diameter has four
edges.
8. The golf ball of claim 1, wherein each of the curvilinear
dimples having the minimum equivalent dimple diameter has three
edges.
9. The golf ball of claim 1, wherein each of the curvilinear
dimples having the minimum equivalent dimple diameter has four
edges.
10. The golf ball of claim 1, wherein the plurality of dimples
includes at least one spherical dimple having a circular plan shape
and a profile shape based on a spherical function.
11. The golf ball of claim 1, wherein the plurality of dimples
consists of curvilinear dimples.
12. The golf ball of claim 1, wherein each edge of every
curvilinear dimple is concave-out.
13. The golf ball of claim 1, wherein each curvilinear dimple has a
plan shape perimeter ratio of greater than about 1.00 and less than
about 1.10.
14. The golf ball of claim 1, wherein each curvilinear dimple has a
maximum absolute distance of from about 0.003 inches to about 0.020
inches.
15. The golf ball of claim 1, wherein the circular arcs defining
the edges of the curvilinear dimples have substantially the same
radius.
16. A golf ball having an outer surface comprising a plurality of
dimples disposed thereon, wherein a majority of the dimples are
curvilinear dimples having a non-isodiametrical plan shape defined
by at least three circular arcs, each circular arc defining an edge
of the dimple and having two discontinuous endpoints that define
adjacent vertices of a base polygon, and wherein: a majority of the
curvilinear dimples have three edges; the curvilinear dimples
include dimples having at least two different equivalent dimple
diameters, including a maximum equivalent dimple diameter and a
minimum equivalent dimple diameter; and the difference between the
maximum equivalent dimple diameter and the minimum equivalent
dimple diameter is about 0.080 inches or less.
17. The golf ball of claim 16, wherein at least one curvilinear
dimple has four edges.
18. The golf ball of claim 16, wherein the minimum equivalent
dimple diameter of the curvilinear dimples is about 0.120 inches or
greater.
19. The golf ball of claim 16, wherein the maximum equivalent
dimple diameter of the curvilinear dimples is about 0.200 inches or
less.
20. The golf ball of claim 16, wherein each of the curvilinear
dimples having the maximum equivalent dimple diameter has three
edges.
21. The golf ball of claim 16, wherein each of the curvilinear
dimples having the maximum equivalent dimple diameter has four
edges.
22. The golf ball of claim 16, wherein each of the curvilinear
dimples having the minimum equivalent dimple diameter has three
edges.
23. The golf ball of claim 16, wherein each of the curvilinear
dimples having the minimum equivalent dimple diameter has four
edges.
24. The golf ball of claim 16, wherein each curvilinear dimple has
a plan shape perimeter ratio of greater than about 1.00 and less
than about 1.10.
25. The golf ball of claim 16, wherein each curvilinear dimple has
a maximum absolute distance of from about 0.003 inches to about
0.020 inches.
26. The golf ball of claim 16, wherein the circular arcs defining
the edges of the curvilinear dimples have substantially the same
radius.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation-in-part of U.S. patent
application Ser. No. 15/849,932, filed Dec. 21, 2017, which is a
continuation-in-part of U.S. patent application Ser. No.
15/726,615, filed Oct. 6, 2017, now U.S. Pat. No. 10,195,485, which
is a continuation-in-part of U.S. patent application Ser. No.
14/941,916, filed Nov. 16, 2015, now U.S. Pat. No. 9,782,629, the
entire disclosures of which are hereby incorporated herein by
reference.
FIELD OF THE INVENTION
[0002] The present invention relates to golf ball dimples having a
non-isodiametrical, curvilinear plan shape defined by circular
arcs. In particular, the present invention relates to golf ball
dimples having plan shapes defined by a number of convex or concave
arcs derived from a regular n-sided polygon. When utilized on golf
balls, the golf ball dimples of the present invention provide
surface textures with unique appearances, while maintaining
desirable aerodynamic characteristics.
BACKGROUND OF THE INVENTION
[0003] Golf balls generally include a spherical outer surface with
a plurality of dimples formed thereon. The dimples on a golf ball
improve the aerodynamic characteristics of a golf ball and,
therefore, golf ball manufacturers have researched dimple patterns,
shape, volume, and cross-section in order to improve the
aerodynamic performance of a golf ball. Determining specific dimple
arrangements and dimple shapes that result in an aerodynamic
advantage requires an understanding of how a golf ball travels
through air.
[0004] Aerodynamic forces acting on a golf ball are typically
resolved into orthogonal components of lift (F.sub.L) and drag
(F.sub.D). Lift is defined as the aerodynamic force component
acting perpendicular to the flight path. It results from a
difference in pressure that is created by a distortion in the air
flow that results from the back spin of the ball. Due to the back
spin, the top of the ball moves with the air flow, which delays the
separation to a point further aft. Conversely, the bottom of the
ball moves against the air flow, moving the separation point
forward. This asymmetrical separation creates an arch in the flow
pattern, requiring the air over the top of the ball to move faster,
and thus have lower pressure than the air underneath the ball.
[0005] Drag is defined as the aerodynamic force component acting
opposite to the ball flight direction. As the ball travels through
the air, the air surrounding the ball has different velocities and,
thus, different pressures. The air exerts maximum pressure at the
stagnation point on the front of the ball. The air then flows over
the sides of the ball and has increased velocity and reduced
pressure. The air separates from the surface of the ball, leaving a
large turbulent flow area with low pressure, i.e., the wake. The
difference between the high pressure in front of the ball and the
low pressure behind the ball reduces the ball speed and acts as the
primary source of drag.
[0006] Lift and drag, among other aerodynamic characteristics of a
golf ball, are influenced by the external surface geometry of the
ball, which includes the dimples thereon. As such, the dimples on a
golf ball play an important role in controlling those
parameters.
[0007] Recently, a number of golf ball products in the market place
have been introduced with golf ball surfaces featuring visually
distinct dimple patterns. Golf balls featuring these visually
distinct dimple patterns are most prevalent in the premium distance
category. Existing examples of such golf balls include, but are not
limited to, the Dunlop XXiO XD Aero, the Bridgestone Tourstage
PHYZ, and the Saso Kaede. While these golf ball designs possess a
unique visual appearance, the dimple patterns utilized on the golf
balls, when compared to conventional dimple patterns, are less
aerodynamically efficient.
[0008] Other unique dimple designs have also been introduced. For
example, isodiametrical dimples, such as those disclosed in U.S.
Pat. No. 5,377,989, provide for visually distinct dimple shapes.
However, due to the nature of the curvatures in forming the
isodiametric shape, these dimples limit surface coverage uniformity
and packing efficiency when utilized on golf balls. Accordingly,
there remains a need for a dimple geometry that provides a visually
distinct golf ball surface texture, while providing improved
aerodynamic characteristics and maximized packing efficiency.
SUMMARY OF THE INVENTION
[0009] The present invention is directed to a golf ball having a
substantially spherical surface, including a plurality of dimples
on the spherical surface, wherein at least a portion of the
plurality of dimples, for example, about 50 percent or more,
include a curvilinear plan shape defined by at least 3 circular
arcs, wherein each circular arc includes two endpoints that define
adjacent vertices of a regular polygon. In one embodiment, the
curvilinear plan shape is defined by 3 to 12 circular arcs. In
another embodiment, the regular polygon is an equilateral polygon
comprising from 3 to 12 sides. In still another embodiment, the
number of circular arcs is equivalent to the number of sides of the
regular polygon. The circular arcs may include concave arcs, convex
arcs, or combinations thereof. For example, the plan shape may be
defined by an even number of alternating convex and concave
circular arcs less than or equal to 12. In yet another embodiment,
the portion of the plurality of dimples has a plan shape area ratio
of about 0.35 to about 1.75.
[0010] The present invention is also directed to a golf ball having
a substantially spherical surface, including a plurality of dimples
on the spherical surface, wherein at least a portion of the
plurality of dimples, for example, about 70 percent or more,
include a curvilinear plan shape defined by a plurality of arc
segments having endpoints that define adjacent vertices of a
polygon including n sides, wherein each arc segment includes an arc
center outside of the polygon, and wherein the plurality of arc
segments is equal to n. In one embodiment, n ranges from 3 to 12,
and more preferably, from 3 to 8. In another embodiment, the
plurality of arc segments has identical lengths and radii.
Conversely, the arc segments may each have a different length and
radius. In still another embodiment, the plurality of arc segments
includes both concave and convex circular arcs. For example, the
plan shape may be defined by alternating convex and concave
circular arcs. In yet another embodiment, the portion of the
plurality of dimples has a plan shape perimeter ratio of less than
1.10.
[0011] The present invention is further directed to a golf ball
dimple having a perimeter defined by a plurality of convex or
concave circular arcs having identical lengths and radii, wherein
each circular arc has two endpoints that define consecutive
vertices of a regular n-sided polygon. In one embodiment, the
perimeter of the dimple is defined by at least 3 circular arcs, for
example, 3 to 12 circular arcs. In this aspect, the perimeter may
be defined by a plurality of concave circular arcs and a plurality
of convex circular arcs. In another embodiment, the regular n-sided
polygon is selected from the group consisting of triangles,
squares, pentagons, hexagons, heptagons, octagons, nonagons,
decagons, hendecagons, and dodecagons.
[0012] The present invention may also be directed to a golf ball
having a substantially spherical surface, including a plurality of
dimples on the spherical surface, wherein at least a portion of the
plurality of dimples include a convex curvilinear plan shape
defined by circular arcs, wherein each circular arc comprises two
endpoints that define adjacent vertices of a regular polygon having
three or four sides, for example, an equilateral triangle or a
square, wherein each vertex of the regular polygon has an arc
vertex angle .theta..sub.v defined by the following equation:
180 ( n - 2 n ) < .theta. v < 180 ( n - 2 n ) + R
##EQU00001##
wherein n is the number of sides of the regular polygon and R is
about 5 to 35. In one embodiment, each circular arc comprises an
arc center outside of the regular polygon. In another embodiment,
each side of the regular polygon is about 0.085 inches to about
0.350 inches in length. In still another embodiment, the regular
polygon has an inradius of about 0.025 inches to about 0.100 inches
and a circumradius of about 0.050 inches to about 0.200 inches.
[0013] The present invention is further directed to a golf ball
having a substantially spherical surface, including a plurality of
dimples on the spherical surface, wherein at least a portion of the
plurality of dimples include one or more non-isodiametrical plan
shapes, wherein each non-isodiametrical plan shape is defined by a
plurality of convex are segments having endpoints that define
adjacent vertices of a regular polygon comprising n sides, wherein
the plurality of arc segments is equal to n, wherein n is three or
four, wherein each vertex of the regular polygon has an arc vertex
angle .theta..sub.v defined by the following equation:
180 ( n - 2 n ) < .theta. v < 180 ( n - 2 n ) + R
##EQU00002##
wherein n is the number of sides of the regular polygon and R is
about 5 to 35, and wherein each arc segment includes an arc center
outside of the regular polygon. In one embodiment, each dimple has
a plan shape perimeter ratio of less than 1.10. In another
embodiment, in the portion of the plurality of dimples, each dimple
has a plan shape area of about 0.0025 in.sup.2 to about 0.045
in.sup.2. In still another embodiment, in the portion of the
plurality of dimples, each dimple has a plan shape area ratio of
greater than 1 and less than 1.75. In yet another embodiment, in
the portion of the plurality of dimples, each dimple has a maximum
absolute distance of about 0.0005 inches to about 0.040 inches. In
another embodiment, in the portion of the plurality of dimples, a
first number of dimples include a non-isodiametrical plan shape
defined by a plurality of convex arc segments having endpoints that
define adjacent vertices of a polygon including three sides and a
second number of dimples include a non-isodiametrical plan shape
defined by a plurality of convex arc segments having endpoints that
define adjacent vertices of a polygon including four sides. In this
aspect, the first number of dimples and the second number of
dimples may have different plan shape perimeter ratios and
different plan shape areas. In yet another embodiment, each arc
segment has the same radius.
[0014] The present invention may also be directed to a golf ball
dimple having a non-isodiametrical plan shape defined by a
plurality of convex circular arcs, wherein each circular arc has a
pair of endpoints that define consecutive vertices of a regular
three-sided or four-sided polygon, wherein each circular arc
includes an arc center outside of the polygon, wherein each pair of
endpoints define consecutive vertices on the same polygon, and
wherein each vertex of the polygon has an arc vertex angle
.theta..sub.v defined by the following equation:
180 ( n - 2 n ) < .theta. v < 180 ( n - 2 n ) + R
##EQU00003##
wherein n is the number of sides of the regular polygon and R is
about 5 to 35. In one embodiment, the golf ball dimple has an
equivalent dimple diameter of about 0.080 inches to about 0.220
inches. In another embodiment, the golf ball dimple has a plan
shape area of about 0.005 in.sup.2 to about 0.035 in.sup.2. In
still another embodiment, the golf ball dimple has a dimple surface
volume of about 0.5.times.10.sup.-4 in.sup.3 to about
3.0.times.10.sup.-4 in.sup.3. In yet another embodiment, the
regular polygon has a circumradius and an inradius, and wherein
each circular arc has a radius at least twice the circumradius of
the regular polygon. In still another embodiment, the regular
polygon has an inradius of about 0.025 inches to about 0.100 inches
and a circumradius of about 0.050 inches to about 0.200 inches.
[0015] The present invention is also directed to a golf ball having
a substantially spherical surface, including a plurality of dimples
on the spherical surface, wherein at least a portion of the
plurality of dimples include a non-isodiametrical plan shape
defined by at least three circular arcs, wherein each circular arc
defines an edge of the dimple and includes two discontinuous
endpoints that define adjacent vertices of a base polygon, wherein
at least one dimple pair in the portion of the plurality of dimples
includes a first dimple having a first edge and a second dimple
having a second edge that is adjacent to the first edge, and
wherein the first edge is defined by a concave circular arc and the
second edge is defined by a convex circular arc, and the maximum
integration distance between the first edge and the second edge is
about 0.020 inches or less. In another embodiment, the first edge
and the second edge have substantially equal arc edge radii. In
still another embodiment, the first edge and the second edge each
have a maximum distance between the circular arc and the base
polygon of about 0.005 inches to about 0.030 inches. In one
embodiment, the first edge and the second edge have the same
maximum distances. In another embodiment, the first edge has a
first maximum distance, the second edge has a second maximum
distance, and the difference between the first maximum distance and
the second maximum distance is less than or equal to about 0.01
inches. In yet another embodiment, the maximum integration distance
between the first edge and the second edge is about 0.010 inches or
less. In another embodiment, the at least a portion of the
plurality of dimples include a non-isodiametrical plan shape
defined by three or four circular arcs.
[0016] The present invention is further directed to a golf ball
having a substantially spherical surface, including a plurality of
dimples on the spherical surface, wherein at least a portion of the
plurality of dimples include a non-isodiametrical plan shape
defined by at least three circular arcs, wherein each circular arc
defines an edge of the dimple and includes two discontinuous
endpoints that define adjacent vertices of a regular polygon,
wherein at least one dimple in the portion of the plurality of
dimples includes at least one edge that is adjacent to a respective
edge of at least one other dimple in the portion of the plurality
of dimples, wherein the at least one edge has a first concavity,
the respective edge has a second concavity, and the first concavity
is different from the second concavity, wherein the maximum
integration distance between the at least one edge and the
respective edge is about 0.020 inches or less, and wherein the at
least one edge and the respective edge are unified. In one
embodiment, the at least one edge and the respective edge have
substantially equal arc edge radii. In another embodiment, the
first concavity and the second concavity are selected from
concave-in or concave-out. For example, the first concavity may be
concave-in and the second concavity may be concave-out. In still
another embodiment, the maximum integration distance between the
first edge and the second edge is about 0.010 inches or less, for
instance, about 0.005 inches or less. In yet another embodiment, at
least about 25 percent, for example, at least about 50 percent, of
the dimples on the golf ball include at least one unified edge.
[0017] The present invention may also be directed to a golf ball
having a substantially spherical surface, including a plurality of
dimples on the spherical surface, wherein at least a portion of the
plurality of dimples include a non-isodiametrical plan shape
defined by at least three circular arcs, wherein each circular arc
defines an edge of the dimple and includes two discontinuous
endpoints that define adjacent vertices of a regular polygon,
wherein at least one dimple in the portion of the plurality of
dimples includes at least two edges that are adjacent to respective
edges of at least two other dimples in the portion of the plurality
of dimples, wherein the at least two edges each have a first
concavity, the respective edges of the at least two other dimples
each have a second concavity, and the first concavity is different
from the second concavity, wherein the maximum integration distance
between each of the at least two edges and the respective edges is
about 0.010 inches or less, and wherein the at least two edges and
the respective edges are unified. In this aspect, the first
concavity and the second concavity are selected from concave-in or
concave-out. In another embodiment, at least about 50 percent of
the dimples on the golf ball include at least two unified edges. In
yet another embodiment, at least about 10 percent, for instance, at
least about 50 percent, of the edges defined by circular arcs are
unified.
[0018] In a particular aspect of the embodiments disclosed herein,
the curvilinear dimples include dimples having at least two
different equivalent dimple diameters, including a maximum
equivalent dimple diameter and a minimum equivalent dimple
diameter, and the difference between the maximum equivalent dimple
diameter and the minimum equivalent dimple diameter is about 0.080
inches or less.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] Further features and advantages of the invention can be
ascertained from the following detailed description that is
provided in connection with the drawings described below:
[0020] FIG. 1 is a flowchart illustrating the steps according to a
method of forming a dimple plan shape of the present invention;
[0021] FIG. 2 illustrates a regular polygon defined in a
two-dimensional plane according to one embodiment of the present
invention;
[0022] FIG. 3 illustrates a defined first convex arc segment and
associated center point of the regular polygon of FIG. 2 according
to one embodiment of the present invention;
[0023] FIG. 4A illustrates all defined convex arc segments and
associated center points of the regular polygon of FIG. 2 according
to one embodiment of the present invention;
[0024] FIG. 4B illustrates all defined arc segments of FIG. 4A as
convex arcs according to one embodiment of the present
invention;
[0025] FIG. 5 illustrates a dimple plan shape constructed from the
arc segments of FIG. 4A-B according to one embodiment of the
present invention;
[0026] FIG. 6 illustrates a defined first concave arc segment and
associated center point of the regular polygon of FIG. 2 according
to one embodiment of the present invention;
[0027] FIG. 7A illustrates all defined concave arc segments and
associated center points of the regular polygon of FIG. 2 according
to one embodiment of the present invention;
[0028] FIG. 7B illustrates all defined arc segments of FIG. 7A as
concave arcs according to one embodiment of the present
invention;
[0029] FIG. 8 illustrates a dimple plan shape constructed from the
arc segments of FIG. 7A-B according to one embodiment of the
present invention;
[0030] FIGS. 9-11 illustrate various embodiments of golf ball
dimple patterns constructed from a plurality of dimple plan shapes
according to the present invention;
[0031] FIG. 12A is a graphical representation illustrating dimple
surface volumes for golf balls produced in accordance with the
present invention;
[0032] FIG. 12B is a graphical representation illustrating
preferred dimple surface volumes for golf balls produced in
accordance with the present invention;
[0033] FIG. 13 illustrates a golf ball dimple plan shape defined by
concave arcs that are created from the vertices of a regular
5-sided polygon according to one embodiment of the present
invention;
[0034] FIG. 14 illustrates a golf ball dimple plan shape defined by
convex arcs that are created from the vertices of a regular 6-sided
polygon according to one embodiment of the present invention;
[0035] FIG. 15 illustrates a golf ball dimple plan shape defined by
a random arrangement of convex and concave arcs that are created
from the vertices of a regular 5-sided polygon according to one
embodiment of the present invention;
[0036] FIG. 16 illustrates a golf ball dimple plan shape defined by
alternating convex and concave arcs that are created from the
vertices of a regular 6-sided polygon according to one embodiment
of the present invention;
[0037] FIG. 17 illustrates a golf ball dimple plan shape defined by
convex arcs having different radii that are created from the
vertices of a regular 4-sided polygon according to one embodiment
of the present invention;
[0038] FIG. 18 illustrates a golf ball dimple plan shape according
to one embodiment of the present invention;
[0039] FIG. 19 illustrates a golf ball dimple plan shape according
to another embodiment of the present invention;
[0040] FIGS. 20 and 21 illustrate various embodiments of golf ball
dimple patterns constructed from a plurality of dimple plan shapes
according to the present invention;
[0041] FIG. 22 is a graphical representation illustrating preferred
dimple surface volumes for golf balls produced in accordance with
one embodiment of the present invention;
[0042] FIGS. 23 and 24 illustrate various dimple base patterns
having plan shapes contemplated by the present invention;
[0043] FIG. 25 shows a dimple pair according to one embodiment of
the present invention where adjacent edges are unified and have
opposite concavity;
[0044] FIGS. 26A and 26B show an arrangement of four dimples having
the disclosed plan shapes and unified edges according to one
embodiment of the present invention;
[0045] FIG. 27 illustrates a dimple pattern having cohesively
integrated dimples according to one embodiment of the present
invention;
[0046] FIGS. 28A and 28B show an arrangement of four dimples having
the disclosed plan shapes and unified edges according to another
embodiment of the present invention; and
[0047] FIG. 29 illustrates a dimple pattern having cohesively
integrated dimples according to another embodiment of the present
invention.
[0048] FIG. 30A illustrate a dimple base pattern having plan shapes
contemplated by the present invention.
[0049] FIG. 30B illustrates a dimple pattern contemplated by the
present invention.
DETAILED DESCRIPTION
[0050] The present invention is directed to golf balls having
surface textures with unique appearances and improved aerodynamic
characteristics due, at least in part, to the use of noncircular
dimple plan shapes. In particular, the present invention is
directed to a golf ball that includes at least a portion of its
dimples having a curvilinear plan shape defined by a number of
convex or concave arcs that are derived from a regular n-sided
polygon.
[0051] Advantageously, in one embodiment, golf balls including
dimple plan shapes produced in accordance with the present
invention have visually distinct surface textures. Indeed, the
dimple plan shapes of the present invention possess a unique visual
appearance. In another embodiment, the dimple plan shapes of the
present invention allow the dimples to be arranged according to
spherically tiled dimple designs. The spherical tiling layouts
utilizing the dimple plan shapes of the present invention provide
improved symmetry including multiple axes of symmetry on each golf
ball. As a result, golf balls including the dimple plan shapes of
the present invention exhibit improved aerodynamic performance in
addition to providing visually distinct dimple patterns.
Dimple Plan Shape
[0052] A dimple plan shape, as used herein, refers to the perimeter
of the dimple as seen from a top view of the dimple, or the
demarcation between the dimple and the outer surface of the golf
ball or fret surface. The present invention contemplates dimples
having a curvilinear plan shape.
[0053] The present invention contemplates curvilinear dimple plan
shapes defined by circular arcs that form a simple closed path. A
"simple closed path," as used herein, includes a curve that starts
and ends at the same point without traversing any defining point or
edge along the path more than once. In particular, the dimple plan
shapes of the present invention include a number of convex or
concave circular arcs having endpoints that define the vertices of
a regular n-sided polygon. That is, the plan shapes of the present
invention are defined by arc segments created from a regular
n-sided polygon. Indeed, the present invention contemplates
non-smooth plan shapes having discontinuities at the endpoints of
each arc segment. As used herein, a plan shape has "discontinuities
at the endpoints" or "discontinuous endpoints" if two dimple edges
meet at a point making the plan shape non-differentiable at that
point.
[0054] The present invention contemplates plan shapes defined by a
plurality of arc segments that are derived from the sides of a
regular n-sided polygon. In one embodiment, the arc segments are
created by arcs of circles centered outside of a regular polygon.
As discussed in greater detail below, the location of the centers
of the circles is dependent on whether the number of sides of the
polygon is odd or even. For example, when the number of sides of
the polygon is even, the centers of the circles lie on an axis
defined by the center of the polygonal inradius and the side
mid-point. In another embodiment, when the number of sides of the
polygon is odd, the centers of the circles lie on an axis defined
by the center of the polygonal inradius and the vertex. Indeed, the
circular arcs are designed to sweep the sides of the regular
polygon such that arc segments are created between each vertex of
the regular polygon in a convex or concave manner.
[0055] In one embodiment, the plan shape may be defined by a
plurality of convex arcs. For example, the plan shape may include a
plurality of arc segments that curve in an outwardly direction. In
another embodiment, the plan shape may be defined by a plurality of
concave arcs. For example, the plan shape may include a plurality
of arc segments that curve in an inwardly direction.
[0056] In still another embodiment, the plan shape may be defined
by a combination of convex and concave arcs. For example, the plan
shape may include one or more convex arcs and one or more concave
arcs such that each arc segment is created between each vertex of
the regular polygon in a concave or convex manner.
[0057] In yet another embodiment, the plan shape may be defined by
alternating convex and concave arcs. For example, the plan shape
may include a plurality of arc segments that alternate between
convex arcs and concave arcs. In this embodiment, the number of
sides of the polygon is even.
[0058] The number of arc segments is equivalent to the number of
sides of the regular polygon. For example, a plan shape including
three arc segments may correspond to a three-sided polygon or a
triangle. In another embodiment, a plan shape including four arc
segments may correspond to a four-sided polygon or a square. In
still another embodiment, a plan shape including five arc segments
may correspond to a five-sided polygon or a pentagon. In yet
another embodiment, a plan shape including six arc segments may
correspond to a six-sided polygon or a hexagon.
[0059] In this aspect, the present invention contemplates the use
of any regular n-sided polygon. By the term, "regular n-sided
polygon," it is meant a polygon that is equiangular (i.e., all
angles are equal in measure) and equilateral (i.e., all sides have
the same length). In one embodiment, the present invention
contemplates regular n-sided polygons, where n is equal to or
greater than 3. Indeed, the present invention contemplates regular
polygons having at least 3 or more equal length sides. While
polygons having a higher number of sides may be employed,
increasing the number of sides produces plan shapes which closely
approximate a circular perimeter. Thus, it is preferable to utilize
polygons having smaller values of n.
[0060] For example, the present invention contemplates the use of
regular n-sided polygons having from 3 to about 50 equal length
sides. In another embodiment, the polygon of the present invention
has from 3 to about 26 equal length sides. In still another
embodiment, the polygon of the present invention has from 3 to
about 12 equal length sides. In yet another embodiment, the polygon
of the present invention has from 3 to about 8 equal length sides.
For example, the polygon may have 4 equal length sides.
[0061] Suitable examples of regular n-sided polygons contemplated
by the present invention include, but are not limited to,
triangles, squares, pentagons, hexagons, heptagons, octagons,
nonagons, decagons, hendecagons, and dodecagons. In one embodiment,
the regular n-sided polygon is a triangle. In another embodiment,
the regular n-sided polygon is a square.
[0062] The overall dimensions of the regular n-sided polygon may
vary. In this aspect, the dimensions of the polygon may be defined
by the length of the sides of the polygon. As noted above, the
polygons of the present invention are equilateral (i.e., all sides
have the same length). In this aspect, the length of each side of
the polygon may be at least about 0.085 inches. In one embodiment,
the length of each side of the polygon is about 0.350 inches or
less. For example, the length of each side of the polygon may range
from about 0.085 inches to about 0.350 inches. In another
embodiment, the length of each side of the polygon ranges from
about 0.085 inches to about 0.260 inches. For example, the length
of each side may range from about 0.100 inches to about 0.250
inches. In another embodiment, the length of each side may range
from about 0.125 inches to about 0.225 inches. In still another
embodiment, the length of each side may range from about 0.150
inches to about 0.200 inches.
[0063] In another embodiment, the dimensions of the polygon may be
defined by the inradius of the regular polygon. For purposes of the
present invention, the term, "inradius," refers to the radius of a
polygon's incircle, or the radius of the largest circle that fits
inside of the polygon and is tangent to each side. The inradius of
a regular polygon with n sides and side length .alpha. is given by
equation (1), denoted below:
r = 1 2 a cot ( .pi. n ) . ( 1 ) ##EQU00004##
In this aspect, the present invention contemplates regular polygons
having an inradius of at least about 0.020 inches. In one
embodiment, the inradius is about 0.175 inches or less. In another
embodiment, the inradius is about 0.125 inches or less. In yet
another embodiment, the inradius is about 0.115 inches or less. In
still another embodiment, the inradius is about 0.010 inches or
less. For example, the inradius may range from about 0.025 inches
to about 0.150 inches. In one embodiment, the polygon of the
present invention has an inradius of about 0.050 inches to about
0.125 inches. In another embodiment, the polygon of the present
invention has an inradius of about 0.075 inches to about 0.115
inches. In still another embodiment, the polygon of the present
invention has an inradius of about 0.080 inches to about 0.100
inches. For example, the polygon of the present invention may have
an inradius of about 0.025 inches to about 0.100 inches.
[0064] In still another embodiment, the dimensions of the polygon
may be defined by the circumradius of the regular polygon. For
purposes of the present invention, the term, "circumradius," refers
to the radius of the polygon's circumcircle, or the radius of the
circle that passes through each vertex of the regular polygon.
Indeed, the circumradius will approach the inradius as n approaches
infinity. For example, when n=3, the circumradius is twice the
inradius.
[0065] In this aspect, the present invention contemplates regular
polygons having a circumradius of at least about 0.05 inches.
Likewise, the circumradius may be about 0.300 inches or less. In
one embodiment, the circumradius ranges from about 0.050 inches to
about 0.300 inches. For example, the polygon of the present
invention may have a circumradius of about 0.075 inches to about
0.275 inches. In another embodiment, the polygon of the present
invention may have a circumradius of about 0.100 inches to about
0.250 inches. In still another embodiment, the polygon of the
present invention may have a circumradius of about 0.125 inches to
about 0.225 inches. In yet another embodiment, the polygon of the
present invention may have a circumradius of about 0.150 inches to
about 0.200 inches. For example, the polygon of the present
invention may have a circumradius of about 0.050 inches to about
0.200 inches.
[0066] The length and radii of the curvature of each arc segment
will vary based on the selected dimensions of the regular n-sided
polygon. However, in one embodiment, the arc segments of the plan
shape have equal curvatures. That is, each arc segment of the plan
shape has an identical length and radii. In another embodiment, the
arc segments of the plan shape have different lengths and radii.
For instance, each arc segment may have a different radii. In still
another embodiment, at least one of the arc segments may have
different radii.
[0067] FIG. 1 illustrates one embodiment of a method of forming a
dimple plan shape in accordance with the present invention. For
example, step 101 includes selecting the regular polygon and its
overall dimensions, and defining the regular polygon in a
two-dimensional plane. Indeed, any of the regular n-sided polygons
discussed above are contemplated in this aspect of the present
invention. In one embodiment, the dimensions of the regular polygon
may be defined by specifying the length of each side of the
polygon. In another embodiment, the dimensions of the polygon may
be defined by specifying the inradius or circumradius of the
regular polygon. However, the dimensions of the polygon, including
the length of each side, the inradius, and the circumradius, should
be selected such that the values are in accordance with the
parameters discussed above. FIG. 2 illustrates a regular polygon
defined in a two-dimensional plane. As shown in FIG. 2, the regular
polygon 5 has four equal sides that meet at four vertices, V.sub.1,
V.sub.2, V.sub.3, and V.sub.4. The four-sided regular polygon 5 is
referred to, hereinafter, as a square.
[0068] Once the base polygon is chosen, each arc segment is
constructed. According to the present invention, the number of arc
segments is equivalent to the number of sides of the regular
polygon. For example, if the regular polygon has four sides, the
plan shape of the present invention will be defined by four arc
segments. To construct the first arc segment, an arc center is
determined (step 102). The arc center, C, may be defined as any
point lying outside the polygonal boundary. Indeed, each arc center
should lie outside the convex hull of the base polygon.
[0069] In this aspect, the location of the arc center, C, will vary
depending on the number of sides of the polygon. In one embodiment,
when the number of sides of the polygon is even, the arc center
lies on an axis that extends radially from the inradius center and
bisects the opposing side of the polygon. In another embodiment,
when the number of sides of the polygon is odd, the arc center lies
on an axis that extends radially from the inradius center and
through the opposing vertex. For example, if the polygon is a
triangle, the arc centers lie on axes defined by the inradius
center and the opposing vertex. In contrast, if the polygon is a
square, the arc centers lie on axes defined by the inradius center
and the opposing side mid-point.
[0070] After the arc center has been defined, at step 103, an arc
is swept around the arc center to create a circle. In one
embodiment, the circle should sweep one side of the regular polygon
such that an arc segment is defined having endpoints at two
consecutive vertices of the polygon. In this regard, to ensure that
the circle sweeps the interior or exterior of a side of the
polygon, the radius, r, of the circle should, at a minimum, be
greater than twice the circumradius, r.sub.c, of the selected
polygon. For example, the radius, r, of the circle should satisfy
the following inequality, denoted as equation (2) below:
2 r c < r < 2 r c * ( a * sin ( .pi. / n ) n .beta. + 1 ) , (
2 ) ##EQU00005##
where constants, .alpha. and .beta., define the upper bound on the
radius. In one embodiment, .alpha. is a value between about 50 and
about 100, while .beta. is a value between about 2 and about 4. For
example, .alpha. may be between about 60 and about 90. In one
embodiment, .alpha. is between about 75 and about 85. In another
embodiment, .alpha. is between about 50 and 65. In yet another
embodiment, .alpha. is between about 85 and 100.
[0071] FIG. 3 demonstrates a defined first arc segment and
associated center point using the square 5 as the regular polygon.
For example, the arc center, C1, is defined as a point lying
outside the boundary of the square 5. The radius, r.sub.i, of the
circle, A1, is determined such that the radius is at least twice
the circumradius of the square 5 and satisfies the inequality of
equation (2). The circle, A1, is swept around the arc center, C1,
such that the circle sweeps one side of the square 5. As a result,
arc segment, S1, is defined such that its endpoints are at
consecutive vertices, V.sub.1 and V.sub.2, of the square 5.
[0072] Steps 102 and 103, as described above, are repeated for each
arc segment of the plan shape (step 104). Indeed, an arc segment
should be constructed for each side of the selected regular
polygon. In this aspect, the remaining arc centers should be
defined around the regular polygon such that each side of the
polygon is utilized in constructing an arc segment. For example,
FIG. 4A shows all four defined arc segments and associated center
points of the square 5. As shown in FIG. 4A, the arc center, C2, is
defined as a point lying outside the boundary of the square
polygon. The radius, r.sub.2, of the circle, A2, is determined such
that the radius is at least twice the circumradius of the square 5
and satisfies the inequality of equation (2). The circle, A2, is
swept around the arc center, C2, to define arc segment, S2, having
endpoints at consecutive vertices, V.sub.2 and V.sub.3, of the
square.
[0073] Similarly, the arc center, C3, is defined as a point lying
outside the boundary of the square polygon. The radius, r.sub.3, of
the circle, A3, is determined such that the radius is at least
twice the circumradius of the square 5 and satisfies the inequality
of equation (2). The circle, A3, is swept around the arc center,
C3, to define arc segment, S3, having endpoints at consecutive
vertices, V.sub.3 and V.sub.4, of the square.
[0074] Further, arc center, C4, is defined as a point lying outside
the boundary of the square polygon. The radius, r.sub.4, of the
circle, A4, is determined such that the radius is at least twice
the circumradius of the square 5 and satisfies the inequality of
equation (2). The circle, A4, is swept around the arc center, C4,
to define arc segment, S4, having endpoints at consecutive
vertices, V.sub.4 and V.sub.1, of the square. In this embodiment,
the circles, the radii, the arc segments, and the Euclidean
distance of the arc centers from the incenter of the polygon, are
equivalent.
[0075] As discussed briefly above, the arc segments of the present
invention may be convex or concave. In this aspect of the
invention, the location of the arc center relative to the arc will
determine whether the arc segment is convex or concave. For
example, when forming a convex arc, the arc center should lie on
the side opposite to the side of the polygon where the convex arc
segment is formed. Conversely, when forming a concave arc, the arc
center should lie on the same side as the side of the polygon where
the concave arc segment is formed.
[0076] FIGS. 2-4B demonstrate the use of convex arc segments.
Indeed, FIG. 3 shows the arc center C1 positioned on the side
opposite to the side of the polygon where the convex arc segment
will be formed (i.e., between V1 and V2). FIG. 4B exemplifies arc
segments, S1-S4, as convex arcs.
[0077] After each of the arc segments are constructed, the dimple
plan shape of the present invention is generated (step 105). FIG. 5
shows the final dimple plan shape constructed from arc segments,
S1-S4, defined in FIG. 4B. In particular, FIG. 5 illustrates a
curvilinear dimple plan shape 10 (represented by bold line)
contemplated by the present invention. Specifically, FIG. 5 shows a
convex dimple plan shape defined by circular arc segments and
created from a square (4-sided polygon). As can be seen by the
constructed curvilinear dimple plan shape of FIG. 5, the present
invention contemplates non-smooth plan shapes having
discontinuities at the endpoints of each arc segment. Indeed, the
discontinuity at each end point is maintained after constructing
the arcs such that the resulting plan shape is non-isodiametrical
in nature.
[0078] In certain embodiments, the present invention contemplates
dimple plan shapes defined by convex arc segments and created from
a square, such as the plan shape depicted in FIG. 5. In other
embodiments, the dimple plan shapes are defined by convex arc
segments and created from a triangle, such as the plan shape
depicted in FIG. 18. In this aspect of the invention, the square
and triangular convex dimple plan shapes may be formed from
equilateral polygons having any of the side lengths, inradius
values, and circumradius values discussed above. However, in one
embodiment, the square and triangular convex dimple plan shapes may
be formed from squares and triangles, respectively, having an
inradius of about 0.025 inches to about 0.100 inches. In another
embodiment, the inradius may be about 0.025 inches to about 0.085
inches. For instance, the squares and triangles may have an
inradius of about 0.045 inches to about 0.075 inches. Similarly,
the square and triangular convex dimple plan shapes may be formed
from squares and triangles, respectively, having a circumradius of
about 0.050 inches to about 0.200 inches. In one embodiment, the
square and triangles may have a circumradius of about 0.075 inches
to about 0.150 inches. In another embodiment, the circumradius is
about 0.06 inches to about 0.130 inches. In yet another embodiment,
the circumradius is about 0.09 inches to about 0.125 inches.
[0079] The dimple plan shapes of the present invention also
maintain a maximum absolute distance or sagitta. For example, the
square and triangular convex dimple plan shapes maintain a maximum
absolute distance or sagitta. As used herein, the "maximum absolute
distance" or "sagitta" is defined as the maximum distance between
any point on the plan shape and the base polygon. FIG. 18 shows a
triangular convex dimple plan shape produced in accordance with the
present invention. As shown in FIG. 18, the maximum absolute
distance between the polygon (triangle) and the farthest point on
the plan shape from the polygonal boundary is represented by
d.sub.max. The distance d may be calculated according to the
following equation:
d= {square root over
((x.sub.polygon-x.sub.plan).sup.2+(y.sub.polygon-y.sub.plan).sup.2)}.
The maximum value, the sagitta, for all sides of the polygon is the
maximum absolute distance d.sub.max. In one embodiment, d.sub.max
is at least about 0.0005 inches. In another embodiment, d.sub.max
is at least about 0.001 inches. In yet another embodiment,
d.sub.max is at least about 0.003 inches. In still another
embodiment, d.sub.max is about 0.040 inches or less. In yet another
embodiment, d.sub.max is about 0.03 inches or less. In still
another embodiment, d.sub.max is about 0.020 inches or less. For
example, the maximum absolute distance, d.sub.max, or sagitta, may
range from about 0.0005 inches to about 0.040 inches. In another
embodiment, the maximum absolute distance, d.sub.max, or sagitta,
ranges from about 0.001 inches to about 0.030 inches. In still
another embodiment, the maximum absolute distance, d.sub.max, or
sagitta, ranges from about 0.003 inches to about 0.020 inches.
[0080] Furthermore, the convex dimple plan shapes of the present
invention include an arc vertex angle. For instance, each of the
square and triangular convex dimple plan shapes constructed in
accordance with the present invention includes an arc vertex angle.
As used herein, "arc vertex angle," is defined as the angle formed
by tangent lines drawn through the shared vertex of adjacent arc
segments of the plan shape. For instance, as shown in FIG. 19, the
curvilinear dimple plan shape 10 of FIG. 5 has an arc vertex angle
.theta..sub.v. The arc vertex angle .theta..sub.v, is the angle
formed by tangent line T1 and tangent line T2 drawn through the
shared vertex V4 of adjacent arc segments S1 and S2. The arc vertex
angle .theta..sub.v, may be defined by the following equation:
180 ( n - 2 n ) < .theta. v < 180 ( n - 2 n ) + R
##EQU00006##
wherein n is the is the number of sides of the regular polygon, R
is a constant, and .theta..sub.v, is the arc vertex angle. In one
embodiment, R has a value of about 5 to 35, for example, about 5 to
30, about 10 to 25, about 10 to 20, and about 15 to 20. In this
aspect, the arc vertex angle for a triangle may range from greater
than 60.degree. to less than 95.degree., for instance, from
65.degree. to 85.degree. or from 70.degree. to 80.degree..
Similarly, the arc vertex angle for a square may range from greater
than 90.degree. to less than 125.degree., for example, from
95.degree. to 120.degree. or from 100.degree. to 115.degree..
[0081] The process described above in FIG. 1 is also applicable to
forming a dimple plan shape having concave arc segments. For
example, steps 102-105 may be adjusted for the concave nature of
the arc. FIGS. 6-8, discussed in more detail below, exemplify the
process of
[0082] FIG. 1 for forming dimple plan shapes having concave arc
segments in accordance with the present invention.
[0083] As discussed above, step 101 includes selecting the regular
polygon and its overall dimensions, and defining the regular
polygon in a two-dimensional plane. For illustrative purposes, the
square 5 having four equal sides that meet at four vertices,
V.sub.1, V.sub.2, V.sub.3, and V.sub.4 (as shown in FIG. 2) will be
used.
[0084] To construct the first arc segment, an arc center is
determined (step 102). In this embodiment, since the number of
sides of the polygon is even, the arc center should lie on an axis
that extends radially from the polygonal incenter and through the
vertex. Additionally, because a concave arc segment is
contemplated, the arc center should lie on the same side as the
side of the polygon where the concave arc segment is formed. For
example, as shown in FIG. 6, the arc center C1 lies on the same
side as the side of the polygon where the first concave arc segment
will be formed (i.e., between V1 and V2).
[0085] FIG. 6 demonstrates a defined first concave arc segment and
associated center point using the square 5 as the regular polygon.
For example, the arc center, C1, is defined as a point lying
outside the boundary of the square 5, but on the same side of S1.
The radius, r.sub.1, of the circle, A1, is determined such that the
radius is at least twice the circumradius of the square 5 and
satisfies the inequality of equation (2). The circle, A1, is swept
around the arc center, C1, such that the circle sweeps one side of
the square 5. As a result, concave arc segment, S1, is defined such
that its endpoints are at consecutive vertices, V.sub.1 and
V.sub.2, of the square 5.
[0086] Steps 102 and 103, as described above, are repeated for each
arc segment of the plan shape (step 104). Indeed, an arc segment
should be constructed for each side of the selected regular
polygon. In this aspect, the remaining arc centers should be
defined around the regular polygon such that each side of the
polygon is utilized in constructing an arc segment. For example,
FIG. 7A shows all four defined concave arc segments and associated
center points of the square 5. As shown in FIG. 7A, the arc center,
C2, is defined as a point lying outside the boundary of the square
polygon, but located on the same side as S2. The radius, r.sub.2,
of the circle, A2, is determined such that the radius is at least
twice the circumradius of the square 5 and satisfies the inequality
of equation (2). The circle, A2, is swept around the arc center,
C2, to define arc segment, S2, having endpoints at consecutive
vertices, V.sub.2 and V.sub.3, of the square.
[0087] Similarly, the arc center, C3, is defined as a point lying
outside the boundary of the square polygon, but located on the same
side as S3. The radius, r.sub.3, of the circle, A3, is determined
such that the radius is at least twice the circumradius of the
square 5 and satisfies the inequality of equation (2). The circle,
A3, is swept around the arc center, C3, to define arc segment, S3,
having endpoints at consecutive vertices, V.sub.3 and V.sub.4, of
the square.
[0088] Further, arc center, C4, is defined as a point lying outside
the boundary of the square polygon, but located on the same side as
S4. The radius, r.sub.4, of the circle, A4, is determined such that
the radius is at least twice the circumradius of the square 5 and
satisfies the inequality of equation (2). The circle, A4, is swept
around the arc center, C4, to define arc segment, S4, having
endpoints at consecutive vertices, V.sub.4 and V.sub.1, of the
square. FIG. 7B exemplifies arc segments, S1-S4, as concave
arcs.
[0089] After each of the arc segments are constructed, the dimple
plan shape of the present invention is generated (step 105). FIG. 8
shows the final dimple plan shape constructed from arc segments,
S1-S4, defined in FIG. 7B. In particular, FIG. 8 illustrates a
curvilinear dimple plan shape 20 (represented by bold line)
contemplated by the present invention. Specifically,
[0090] FIG. 8 shows a concave dimple plan shape defined by circular
arc segments and created from a square (4-sided polygon).
[0091] In still another embodiment, the process described above in
FIG. 1 may be applicable to designing dimple plan shapes having
both concave and convex arc segments. Indeed, the process may be
adjusted to design a dimple plan shape having a random combination
of both concave and convex arcs. In another embodiment, the process
may be adjusted to design a dimple plan shape having alternating
convex arcs and concave arcs.
[0092] After the dimple plan shape has been generated, at step 106,
the plan shape can be used in designing geometries for dimple
patterns of a golf ball. For example, the plan shapes generated in
accordance with the present invention can be imported into a CAD
program and used to define dimple geometries and tool paths for
fabricating tooling for golf ball manufacture. The various dimple
geometries can then be used in constructing dimple patterns that
provide surface textures with unique appearances and improved
aerodynamic characteristics.
[0093] At step 107, the resulting dimple pattern can be transformed
to the outer surface of a golf ball. Similarly, the negative of the
resulting dimple pattern may be used to form the interior surface
of the cavity of a golf ball mold. For example, the negative of the
resulting golf ball dimple pattern can be applied to the interior
of a golf ball mold, which can then be used in an injection
molding, compression molding, or casting process to form a cover
layer comprising the golf ball dimple pattern.
Dimple Patterns & Packing
[0094] The golf ball dimples of the present invention may be
tailored to maximize surface coverage uniformity and packing
efficiency by altering the plan shape of the dimple. For example,
in one embodiment, the convex and concave edges of the dimple plan
shapes according to the present invention can be designed such that
the dimples are packed more closely together to reduce the width of
the land portions adjacent to each dimple. In this aspect, each
individual dimple may have a different plan shape so that the space
between each dimple can be reduced. Thus, the surface edges of the
dimples of the present invention allow for maximizing the dimple
coverage on the surface of a golf ball by reducing the land portion
located between adjacent dimples.
[0095] In another embodiment, the golf ball dimple plan shapes of
the present invention can be tailored to maximize surface coverage
uniformity and packing efficiency by selecting a regular n-sided
polygon having a number of sides that is equivalent to the number
of neighboring dimples. For example, if the dimple plan shape is
constructed using a regular polygon having 5 sides, the present
invention contemplates that the dimple will be surrounded by 5
neighboring dimples. In another embodiment, the number of sides of
the regular polygon is a scalar multiple of the number of
neighboring dimples. For example, if the number of neighboring
dimples is 4, the present invention contemplates a dimple plan
shape created from a regular polygon having 8 or 12 sides.
[0096] FIGS. 9-11 demonstrate various dimple patterns created in
accordance with the present invention. In particular, FIG. 9
illustrates a golf ball dimple pattern 110 made up of hexagonal
alternating convex/concave plan shapes 115. Indeed, FIG. 9
illustrates dimple plan shapes 115 defined by alternating
convex/concave arcs and created from a 6-sided regular polygon
(i.e., hexagon). In addition, FIG. 10 illustrates a golf ball
dimple pattern 120 made up of heptagonal concave plan shapes 125.
FIG. 10 illustrates dimple plan shapes 125 defined by concave arcs
and created from a 7-sided regular polygon (i.e., heptagon).
Further, FIG. 11 illustrates a golf ball dimple pattern 130 made up
of pentagonal concave plan shapes 135. For example, FIG. 11 shows
dimple plan shapes 135 defined by concave arcs and created from a
5-sided regular polygon (i.e., pentagon). As demonstrated in FIGS.
9-11, the present invention provides for the possibility of
interdigitation amongst neighboring dimples, a characteristic not
possible with conventional circular dimples. This creates the
opportunity for additional dimple packing arrangements and dimple
distribution on the golf ball surface.
[0097] As discussed above, the present invention contemplates
dimple plan shapes defined by convex arc segments and created from
a three- or four-sided polygon, e.g., a triangle or a square. Such
convex dimple plan shapes of the present invention may be utilized
in various dimple patterns. For example, in some embodiments, the
dimple patterns of the present invention may utilize only square
convex dimple plan shapes. In other embodiments, the dimple
patterns of the present invention may utilize only triangular
convex dimple plan shapes. In other embodiments, the dimple
patterns may utilize a combination of square and triangular convex
dimple plan shapes. In this aspect, the dimple patterns may include
about 1 to about 99 percent of the dimples created from square
convex dimple plan shapes with the remainder of the dimples created
from triangle convex dimple plan shapes. For example, a suitable
dimple pattern may include about 10 to about 90 percent of the
dimples created from square convex dimple plan shapes with the
remainder of the dimples created from triangle convex dimple plan
shapes.
[0098] In this aspect, the opposing hemispheres of the golf balls
may have the same or different dimple patterns/layouts. The
specific arrangement or packing of the dimples within the
hemispheres may vary. For example, each hemisphere may include a
base pattern that is rotated about the polar axis and which forms
the overall dimple pattern. In other embodiments, each hemisphere
may be composed of a single base pattern that is not rotated about
the polar axis. The dimples arranged in each hemisphere may be of
varying designs and dimensions. For example, each hemisphere may be
composed of dimples having square and triangular convex plan shapes
and varying profile shapes, dimple diameters, plan shape perimeter
ratios, plan shape area ratios, and maximum absolute distances
(sagittas).
[0099] In some embodiments, the dimple patterns of the present
invention may be composed of dimples having the same plan shape
type and having identical or differing dimensions. For instance,
the dimple patterns may be composed of a number of triangular
convex plan shapes having varying or identical equivalent dimple
diameters (as defined below), depths, plan shape perimeter ratios,
plan shape area ratios, and maximum absolute distances (sagittas).
In another embodiment, the dimple patterns of the present invention
may be composed of dimples having different plan shape types, where
each plan shape type has identical or differing dimensions.
[0100] FIGS. 20 and 21 demonstrate dimple patterns utilizing the
triangular and square convex dimple plan shapes of the present
invention. FIG. 20 illustrates a golf ball dimple pattern made up
of a combination of triangular and square convex dimple plan
shapes. As shown in FIG. 20, the golf ball dimple pattern 710 is
composed of curvilinear convex plan shapes created from a regular
three-sided polygon, i.e., an equilateral triangle, 715 and
curvilinear convex plan shapes created from a regular four-sided
polygon, i.e., a square, 720. In addition, FIG. 21 illustrates a
golf ball dimple pattern made up of solely square convex dimple
plan shapes. More specifically, as shown in FIG. 21, the golf ball
dimple pattern 810 is composed of curvilinear convex plan shapes
created from a regular four-sided polygon, i.e., a square, 815. In
each of FIGS. 20 and 21, the opposing hemispheres of the golf ball
have the same dimple pattern/layout. However, this invention also
contemplates golf balls where the opposing hemispheres have
different dimple patterns/layouts.
[0101] While the dimple plan shapes of the present invention may be
used for at least a portion of the dimples on a golf ball, it is
not necessary that the dimple plan shapes be used on every dimple
of a golf ball. In general, it is preferred that a sufficient
number of dimples on the ball are constructed in accordance with
the present invention so that the aerodynamic characteristics of
the ball may be altered. For example, at least about 30 percent of
the dimples on a golf ball include plan shapes according to the
present invention. In another embodiment, at least about 50 percent
of the dimples on a golf ball include plan shapes according to the
present invention. In still another embodiment, at least about 70
percent of the dimples on a golf ball include plan shapes according
to the present invention. In yet another embodiment, at least about
90 percent of the dimples on a golf ball include the plan shapes of
the present invention. Indeed, 100 percent of the dimples on a golf
ball may include the plan shapes of the present invention.
[0102] While the present invention is not limited by any particular
dimple pattern, dimples having plan shapes according to the present
invention are arranged preferably along parting lines or equatorial
lines, in proximity to the poles, or along the outlines of a
geodesic or polyhedron pattern. Conventional dimples, or those
dimples that do not include the plan shapes of the present
invention, may occupy the remaining spaces. The reverse arrangement
is also suitable.
[0103] In addition, the dimples in each hemisphere should be packed
such that the golf ball does not have any dimple free great
circles. As will be apparent to those of ordinary skill in the art,
a golf ball having no "dimple free great circles" refers to a golf
ball having an outer surface that does not contain a great circle
which is free of dimples.
[0104] Suitable dimple patterns include, but are not limited to,
polyhedron-based patterns (e.g., tetrahedron, icosahedron,
octahedron, dodecahedron, icosidodecahedron, cuboctahedron, and
triangular dipyramid), phyllotaxis-based patterns, spherical tiling
patterns, and random arrangements. In one embodiment, the dimples
are arranged according to a spherical tiling pattern. For example,
the dimples of the present invention may be arranged according to
spherical tiling patterns described in U.S. Pat. No. 8,029,388 and
U.S. Publication No. 2013/0065708, the entire disclosures of which
are incorporated by reference herein.
[0105] The dimple patterns of the present invention may be of any
count. In one embodiment, the dimple count ranges from about 300 to
about 400. In another embodiment, the dimple count is about 312. In
still another embodiment, the dimple count is about 330, for
example, about 332. In yet another embodiment, the dimple count is
about 392. In addition, the dimple pattern may include any number
of dimple sizes. In one embodiment, the number of dimple sizes
range from about 1 to about 30. In another embodiment, the number
of dimple sizes range from about 5 to about 20.
Dimple Patterns Having Cohesively Integrated Dimples
[0106] The present invention also contemplates dimple patterns
composed of cohesively integrated dimples having the disclosed plan
shapes. As discussed above, the dimples of the present invention
have a curvilinear plan shape defined by at least three convex
and/or concave arcs. The term, "cohesively integrated dimples,"
refers to an arrangement of adjacent dimples having the disclosed
plan shapes where at least one arc edge of the plan shape of a
first dimple is adjacent to an arc edge of the plan shape of a
second dimple and the two adjacent arc edges are unified. In other
words, the two adjacent arc edges are substantially equal in
radius, have opposite concavity, and maintain a pre-determined
maximum integration distance. The cohesively integrated dimples of
the present invention provide improved packing efficiency. For
example, the unified edges of the dimple plan shapes according to
the present invention provide integrated or opposing concavity,
which allows for the dimples to be packed more closely together to
reduce the width of the land portions adjacent to each dimple.
[0107] In one embodiment, the cohesively integrated dimples of the
present invention include adjacent edges that are unified. In this
aspect, to be considered "unified," the adjacent edges have
opposite concavity. That is, one of the adjacent arc edges curves
inward while the opposing adjacent arc edge curve outwards. For
example, if the dimple edge of the first dimple is a concave arc,
the adjacent dimple edge of the second dimple should be a convex
arc. Similarly, if the dimple edge of the first dimple is a convex
arc, the adjacent dimple edge of the second dimple should be a
concave arc. The concavity of the arcs may also be referred to as
"concave-in" (which is intended to refer to concave arcs) and
"concave-out" (which is intended to refer to convex arcs). In this
aspect, the concavity of the dimple edge of the first dimple is
different from the concavity of the adjacent dimple edge of the
second dimple.
[0108] FIG. 25 shows an example of a dimple pair where the adjacent
edges are unified and have opposite concavity. As shown in FIG. 25,
the two dimples have adjacent edges, 151 and 152. The edge of the
first dimple 151 is a concave arc and the adjacent edge of the
second dimple is a convex arc 152. In other words, the edge of the
first dimple 151 is concave-in and the adjacent edge of the second
dimple is concave-out relative to the centroid of the dimple plan
shape. The difference in concavity allows for the adjacent edges to
be unified. In another embodiment, to be considered "unified," the
two adjacent edges must have a pre-determined maximum integration
distance ("MID"). The MID represents the maximum distance between
the two adjacent edges (i.e., the dimple edge of the first dimple
and the adjacent dimple edge of the second dimple). To determine
the MID between the two adjacent edges, the center of the arc
forming the concave edge is identified. For instance, in the pair
of adjacent edges shown in FIG. 25, the first dimple has the
concave edge (represented by 151). The center of the concave arc
that forms edge 151 is determined according to the methods
described above. In FIG. 25, the center of the concave arc that
forms the edge 151 is represented by 153.
[0109] Upon determination of the location of the center of the arc
forming the concave edge, three reference lines are drawn that are
utilized in calculating the MID. In one embodiment, the first
reference line is drawn from the center of the concave arc (as
determined from above) to the center point on the concave edge. In
this aspect, the first reference line should intersect the adjacent
convex edge of the opposing dimple without intersecting any other
dimple edges first. For instance, as shown in FIG. 25, the first
reference line 154 extends from the center of the concave arc
(represented by 153) to the center point on the concave edge 151,
which is represented by 154a. The first reference line 154
intersects the adjacent convex edge 152. The second reference line
is drawn from the center of the concave arc (as determined from
above) to a first vertex of the concave edge. In some embodiments,
the first vertex represents the top vertex of the concave edge. As
demonstrated in FIG. 25, the second reference line 155 extends from
the center of the concave arc (represented by 153) to the top
vertex of the concave edge 151, which is represented by 155a. The
third reference line is drawn from the center of the concave arc
(as determined from above) to a second vertex of the concave edge.
In some embodiments, the second vertex represents the bottom vertex
of the concave edge. As shown in FIG. 25, the third reference line
156 extends from the center of the concave arc (represented by 153)
to the bottom vertex of the concave edge 151, which is represented
by 156a.
[0110] The MID between the two adjacent edges (i.e., the dimple
edge of the first dimple and the adjacent dimple edge of the second
dimple) is determined from the reference lines. In one embodiment,
if the adjacent convex edge of the opposing dimple only intersects
the first reference line, the MID between the two adjacent edges is
the distance between the center point on the concave edge and the
point of intersection between the first reference line and the
adjacent convex edge of the opposing dimple. While the adjacent
convex edge 152 in FIG. 25 does not intersect only the first
reference line 153, for exemplary purposes, if the adjacent convex
edge 152 intersected only the first reference line 153, the MID
would be the distance between the center point on the concave edge
154a and the point of intersection between the first reference line
154 and the adjacent convex edge 152 which is represented by 157.
In another embodiment, if the adjacent convex edge of the opposing
dimple intersects the first reference line in addition to the
second reference line and/or the third reference line, the MID
between the two adjacent edges is the largest of the following
three distances: [0111] i. the distance between the center point on
the concave edge and the point of intersection between the first
reference line and the adjacent convex edge of the opposing dimple;
[0112] ii. the distance between the first vertex of the concave
edge and the point of intersection between the second reference
line and the adjacent convex edge of the opposing dimple; or [0113]
iii. the distance between the second vertex of the concave edge and
the point of intersection between the third reference line and the
adjacent convex edge of the opposing dimple.
[0114] For instance, in FIG. 25, the adjacent convex edge 152 of
the opposing dimple intersects the first reference line 154, the
second reference line 155, and the third reference line 156.
Accordingly, the MID between the two adjacent edges in FIG. 25 is
the largest of: [0115] i. the distance between the center point on
the concave edge 154a and the point of intersection 157 between the
first reference line 154 and the adjacent convex edge of the
opposing dimple 152; [0116] ii. the distance between the first
vertex of the concave edge 155a and the point of intersection 158
between the second reference line 155 and the adjacent convex edge
of the opposing dimple 152; or [0117] iii. the distance between the
second vertex of the concave edge 156a and the point of
intersection 159 between the third reference line 156 and the
adjacent convex edge of the opposing dimple 152.
[0118] The above-described procedure for calculating the MID
between two adjacent edges should be repeated for each dimple edge
that is to be unified. For instance, if a dimple has two unified
edges, the above-described procedure should be utilized to
determine the MID between the first pair of adjacent edges and the
second pair of adjacent edges. Likewise, if a dimple has three
unified edges, the above-described procedure should be utilized to
determine the MID between the first pair of adjacent edges, the
second pair of adjacent edges, and the third pair of adjacent
edges.
[0119] In this aspect, to consider the two adjacent edges unified,
the MID between the two adjacent edges (i.e., the concave dimple
edge and the adjacent convex dimple edge) is less than or equal to
about 0.020 inches. In another embodiment, the MID between the
unified adjacent edges is less than or equal to about 0.010 inches.
In still another embodiment, the MID between the unified adjacent
edges is less than or equal to about 0.005 inches. In yet another
embodiment, the MID between the unified adjacent edges is less than
or equal to about 0.0025 inches. However, as will be apparent to
one of ordinary skill in the art, the MID must be greater than
zero. In another embodiment, the MID between the unified adjacent
edges ranges from about 0.0025 inches to about 0.020 inches. For
example, the MID between the unified adjacent edges ranges from
about 0.005 inches to about 0.010 inches.
[0120] In another embodiment, the adjacent edges have substantially
equal arc edge radii. The term, "arc edge radius," refers to the
radius of each of the arc edges of the disclosed curvilinear plan
shapes. For example, each adjacent edge may have an arc edge radius
that is greater than twice the inradius of the base polygon and
less than five times the inradius of the base polygon. In another
embodiment, each adjacent edge may have an arc edge radius that is
greater than three times the inradius of the base polygon and less
than five times the inradius of the base polygon.
[0121] As used herein, "substantially equal arc edge radii" means
each radius measurement differs by less than 0.10 inches. In
another embodiment, "substantially equal arc edge radii" means each
radius measurement differs by less than about 0.08 inches. In still
another embodiment, "substantially equal are edge radii" means each
radius measurement differs by less than about 0.05 inches. In yet
another embodiment, "substantially equal arc edge radii" means each
radius measurement differs by less than about 0.01 inches. In
another embodiment, the adjacent edges have identical radii.
[0122] In still another embodiment, each of the adjacent edges
maintains a maximum absolute distance or sagitta. The maximum
absolute distance ("d.sub.max"), as defined above, represents the
maximum distance between the circular arc and the base polygon.
Each of the unified adjacent edges has a d.sub.max of about 0.005
inches to about 0.030 inches. In another embodiment, each of the
unified adjacent edges has a d.sub.max of about 0.010 inches to
about 0.025 inches. In yet another embodiment, each of the unified
adjacent edges has a d.sub.max of about 0.015 inches to about 0.020
inches.
[0123] In one embodiment, the unified adjacent edges have the same
maximum absolute distance. In another embodiment, the unified
adjacent edges have different maximum absolute distances. In this
aspect, the difference between the maximum absolute distances of
each of the two adjacent edges should be less than or equal to
about 0.01 inches. In another embodiment, the difference between
the maximum absolute distances of each of the two adjacent edges
should be less than or equal to about 0.005 inches. In still
another embodiment, the difference between the maximum absolute
distances of each of the two adjacent edges should be less than or
equal to about 0.0025 inches. In yet another embodiment, the
difference between the maximum absolute distances of each of the
two adjacent edges should be less than or equal to about 0.0015
inches.
[0124] Any of the disclosed dimple plan shapes may have unified
adjacent edges as discussed above. That is, cohesively integrated
dimples of the present invention may include any of the disclosed
dimples having a curvilinear plan shape defined by at least three
convex and/or concave arcs. For example, in one embodiment, the
cohesively integrated dimples may include dimples having a
curvilinear plan shape defined by three convex and/or concave arcs.
In another embodiment, the cohesively integrated dimples may
include dimples having a curvilinear plan shape defined by four
convex and/or concave arcs. In still another embodiment, the
cohesively integrated dimples may include dimples having a
curvilinear plan shape defined by five convex and/or concave arcs.
In yet another embodiment, the cohesively integrated dimples may
include dimples having a curvilinear plan shape defined by six or
more convex and/or concave arcs.
[0125] In another embodiment, the cohesively integrated dimples may
include combinations of dimples having varying curvilinear plan
shapes. For example, the cohesively integrated dimples may be
arranged such that a dimple having a curvilinear plan shape defined
by three concave arcs has an edge that is unified with an adjacent
edge of a curvilinear plan shape defined by four convex arcs.
[0126] In one embodiment, each cohesively integrated dimple may
include more than one edge that has unified arcs. For instance, a
first cohesively integrated dimple may include a first edge that is
unified with an adjacent edge of a second dimple and the first
dimple may include a second edge that is unified with an adjacent
edge of a third dimple. In one embodiment, the cohesively
integrated dimple may include at least two edges that have unified
arcs (for example, at least two unified edges). In another
embodiment, the cohesively integrated dimple may include at least
three edges that have unified arcs (for example, at least three
unified edges). In still another embodiment, the cohesively
integrated dimple may include at least four edges that have unified
arcs (for example, at least four unified edges).
[0127] While at least a portion of the dimples on a golf ball are
cohesively integrated, it is not necessary that every dimple on the
golf ball be cohesively integrated. In one embodiment, less than
about 10 percent of the dimples on a golf ball having the disclosed
curvilinear plan shapes include at least one edge that has unified
arcs (for example, unified edges). In another embodiment, more than
about 10 percent of the dimples on a golf ball having the disclosed
curvilinear plan shapes may include at least one edge that has
unified arcs (for example, unified edges). For instance, at least
about 25 percent of the dimples on a golf ball having the disclosed
curvilinear plan shapes include at least one edge that has unified
arcs (for example, unified edges). In another embodiment, at least
about 50 percent of the dimples on a golf ball having the disclosed
curvilinear plan shapes include at least one unified edge. In still
another embodiment, at least about 75 percent of the dimples on a
golf ball having the disclosed curvilinear plan shapes include at
least one unified edge. In yet another embodiment, at least about
90 percent of the dimples on a golf ball having the disclosed
curvilinear plan shapes include at least one unified edge. Indeed,
100 percent of the dimples on a golf ball having the disclosed
curvilinear plan shapes may include at least one unified edge.
[0128] In this aspect, the present invention contemplates dimple
patterns composed of dimples having the disclosed curvilinear plan
shapes where at least about 10 percent of all edges defined by
circular arcs are unified. In another embodiment, the present
invention contemplates dimple patterns composed of dimples having
the disclosed curvilinear plan shapes where at least about 25
percent of all edges defined by circular arcs are unified. In still
another embodiment, the present invention contemplates dimple
patterns composed of dimples having the disclosed curvilinear plan
shapes where at least about 50 percent of all edges defined by
circular arcs are unified. In yet another embodiment, the present
invention contemplates dimple patterns composed of dimples having
the disclosed curvilinear plan shapes where at least about 75
percent of all edges defined by circular arcs are unified. In
another embodiment, the present invention contemplates dimple
patterns composed of dimples having the disclosed curvilinear plan
shapes where at least about 90 percent of all edges defined by
circular arcs are unified.
[0129] FIGS. 27 and 29 demonstrate dimple patterns composed of
cohesively integrated dimples having the disclosed plan shapes.
That is, FIGS. 27 and 29 illustrate dimple patterns of the present
invention that are composed of a plurality of dimples having
curvilinear plan shapes defined by at least three convex and/or
concave arcs and having unified edges. FIG. 27 shows an arrangement
of four dimples having the disclosed plan shapes and unified edges
(represented by 900) in a dimple pattern on a golf ball with
dimples having circular plan shapes. Each arrangement 900 includes
a center dimple having three edges defined by concave circular arcs
where all three edges are unified and three surrounding dimples,
each having three edges defined by convex circular arcs where only
one edge is unified.
[0130] FIG. 29 shows a dimple pattern composed entirely of dimples
having the disclosed plan shapes (for example, plan shapes defined
by circular arcs). The dimple pattern shown in FIG. 29 (represented
by 940) includes dimples having three edges defined by convex
circular arcs (represented by 935). The dimple pattern 940 also
includes dimples having four edges defined by concave circular arcs
(represented by 936) and dimples having four edges defined by
convex circular arcs (represented by 937). Each of the four edges
of dimples 936 and 937 are unified.
Dimple Dimensions
[0131] The dimples on the golf balls of the present invention may
comprise any width, depth, depth profile, edge angle, or edge
radius and the patterns may comprise multitudes of dimples having
different widths, depths, depth profiles, edge angles, or edge
radii. Since the plan shape perimeters of the present invention are
noncircular, the plan shapes are defined by an effective dimple
diameter which is twice the average radial dimension of the set of
points defining the plan shape from the plan shape centroid. For
example, in one embodiment, dimples according to the present
invention have an effective dimple diameter within a range of about
0.050 inches to about 0.300 inches. In another embodiment, the
dimples have an effective dimple diameter of about 0.100 inches to
about 0.250 inches. In still another embodiment, the dimples have
an effective dimple diameter of about 0.110 inches to about 0.225
inches. In yet another embodiment, the dimples have an effective
dimple diameter of about 0.125 inches to about 0.200 inches.
[0132] The dimples of the present invention also have an equivalent
dimple diameter. As used herein, "equivalent dimple diameter" is
defined as the equivalent circular spherical dimple diameter equal
to the specific curvilinear dimple plan shape area. The equivalent
dimple diameter may be calculated according to the following
formula:
d e = 2 A .pi. ##EQU00007##
[0133] where d.sub.e is the equivalent dimple diameter and A is the
plan shape area of the curvilinear dimple. In one embodiment, the
equivalent dimple diameter is at least about 0.08 inches, or at
least about 0.09 inches, or at least about 0.100 inches, or at
least about 0.110 inches, or at least about 0.120 inches. In
another embodiment, the equivalent dimple diameter is about 0.220
inches or less, or about 0.210 inches or less, or about 0.200
inches or less, or about 0.190 inches or less. For example, when
the dimples have square and triangular convex dimple plan shapes,
the dimples may have equivalent dimple diameters ranging from about
0.080 inches to about 0.220 inches. In another embodiment, the
dimples may have equivalent dimple diameters ranging from about
0.090 inches to about 0.210 inches. In still another embodiment,
the dimples may have equivalent dimple diameters ranging from about
0.100 inches to about 0.200 inches. In yet another embodiment, the
dimples may have equivalent dimple diameters ranging from about
0.110 inches to about 0.190 inches.
[0134] In a particular embodiment, the curvilinear dimples within a
dimple pattern include dimples having at least two different
equivalent dimple diameters, including a maximum equivalent dimple
diameter and a minimum equivalent dimple diameter, and the
difference between the maximum equivalent dimple diameter and the
minimum equivalent dimple diameter is about 0.080 inches or less,
or about 0.060 inches or less, or about 0.040 inches or less. In a
particular aspect of this embodiment, the dimple pattern provides
for a dimple surface coverage on the golf ball of about 73.0% or
greater.
[0135] The surface depth for dimples of the present invention is
within a range of about 0.003 inches to about 0.025 inches. In one
embodiment, the surface depth is about 0.005 inches to about 0.020
inches. In another embodiment, the surface depth is about 0.006
inches to about 0.017 inches.
[0136] The dimples of the present invention have a plan shape
perimeter ratio. The plan shape perimeter ratio is defined as the
ratio of the plan shape perimeter to that of the regular n-sided
polygon perimeter. The perimeter is defined as the distance around
a two-dimensional shape, and thus, the length of the boundary line
defining the plan shape. In one embodiment, dimples of the present
invention have a plan shape perimeter ratio of less than 1.10. In
another embodiment, the dimples of the present invention have a
plan shape perimeter ratio of less than 1.07. In another
embodiment, the dimples of the present invention have a plan shape
perimeter ratio of less than 1.05. In another embodiment, the
dimples of the present invention have a plan shape perimeter ratio
of less than 1.10 and greater than 1.00.
[0137] For example, when the dimples have triangular convex dimple
plan shapes, the dimples may have a plan shape perimeter ratio of
less than 1.10, less than 1.05, or less than 1.01. Similarly, when
the dimples have square convex dimple plan shapes, the dimples may
have a plan shape perimeter ratio of less than 1.10, less than
1.05, or less than 1.01.
[0138] The dimples of the present invention also have a plan shape
area. By the term, "plan shape area," it is meant the area based on
a planar view of the dimple plan shape, such that the viewing plane
is normal to an axis connecting the center of the golf ball to the
point of the calculated surface depth. In one embodiment, dimples
of the present invention have a plan shape area ranging from about
0.0025 in.sup.2 to about 0.045 in.sup.2. In another embodiment,
dimples of the present invention have a plan shape area ranging
from about 0.005 in.sup.2 to about 0.035 in.sup.2. In still another
embodiment, dimples of the present invention have a plan shape area
ranging from about 0.010 in.sup.2 to about 0.030 in.sup.2.
[0139] The dimples of the present invention are further defined to
have a plan shape area ratio. The plan shape area ratio is defined
as the ratio of the plan shape area to that of the regular n-sided
polygon area. In one embodiment, dimples of the present invention
have a plan shape area ratio ranging from about 0.35 to about 1.75.
In another embodiment, the plan shape area ratio ranges from about
0.40 to about 1.65. In still another embodiment, the plan shape
perimeter ratio ranges from about 0.45 to about 1.55.
[0140] For example, when the dimples have triangular convex dimple
plan shapes, the dimples may have a plan shape area ratio of
greater than 1.0. In one embodiment, when the dimples have
triangular convex dimple plan shapes, the dimples may have a plan
shape area ratio of equal to or less than 1.75. In another
embodiment, the dimples having triangular convex dimple plan shapes
may have a plan shape area ratio of equal to or less than 1.65. In
still another embodiment, the dimples having triangular convex
dimple plan shapes may have a plan shape area ratio of equal to or
less than 1.55. In one embodiment, the plan shape area ratio is
between 1.0 and 1.75, 1.0 and 1.65, or 1.0 and 1.55.
[0141] Similarly, when the dimples have square convex dimple plan
shapes, the dimples may have a plan shape area ratio of greater
than 1.0. In one embodiment, the dimples having square convex
dimple plan shapes have a plan shape area ratio of 1.75 or less,
1.65 or less, or 1.55 or less. For example, the dimples having
square convex dimple plan shapes may have a plan shape area ratio
of more than 1.0, but no more than 1.75.
[0142] Further, dimples of the present invention have a dimple
surface volume. By the term, "dimple surface volume," it is meant
the total volume encompassed by the dimple shape and the surface of
the golf ball. FIGS. 12A and 12B illustrate graphical
representations of dimple surface volumes contemplated for dimples
produced in accordance with the present invention. For example,
FIGS. 12A and 12B demonstrate contemplated dimple surface volumes
over a range of plan shape areas. In one embodiment, dimples
produced in accordance with the present invention have a plan shape
area and dimple surface volume falling within the ranges shown in
FIG. 12A. For example, a dimple having a plan shape area of about
0.01 in.sup.2 may have a surface volume of about
0.20.times.10.sup.-4 in.sup.3 to about 0.50.times.10.sup.-4
in.sup.3. In another embodiment, a dimple having a plan shape area
of about 0.025 in.sup.2 may have a surface volume of about
0.80.times.10.sup.-4 in.sup.3 to about 1.75.times.10.sup.-4
in.sup.3. In still another embodiment, a dimple having a plan shape
area of about 0.030 in.sup.2 may have a surface volume of about
1.20.times.10.sup.-4 in.sup.3 to about 2.40.times.10.sup.-4
in.sup.3. In yet another embodiment, a dimple having a plan shape
area of about 0.045 in.sup.2 may have a surface volume of about
2.10.times.10.sup.-4 in.sup.3 to about 4.25.times.10.sup.-4
in.sup.3.
[0143] In another embodiment, dimples produced in accordance with
the present invention have a plan shape area and dimple surface
volume falling within the ranges shown in FIG. 12B. For example, a
dimple having a plan shape area of about 0.01 in.sup.2 may have a
surface volume of about 0.25.times.10.sup.-4 in.sup.3 to about
0.35.times.10.sup.-4 in.sup.3. In another embodiment, a dimple
having a plan shape area of about 0.025 in.sup.2 may have a surface
volume of about 1.10.times.10.sup.-4 in.sup.3 to about
1.45.times.10.sup.-4 in.sup.3. In yet another embodiment, a dimple
having a plan shape area of about 0.030 in.sup.2 may have a surface
volume of about 1.40.times.10.sup.-4 in.sup.3 to about
1.90.times.10.sup.-4 in.sup.3.
[0144] In still another embodiment, when the dimples have square or
triangular convex dimple plan shapes, the dimples may have a plan
shape area and dimple surface volume falling within the ranges show
in FIG. 22. FIG. 22 illustrates a graphical representation of
dimple surface volumes contemplated for dimples having square and
triangular convex dimple plan shapes. The dimple volumes should be
less than the upper limit volume calculated by
V.sub.S=-0.0464A.sup.2+0.0135A-1.00.times.10.sup.-5
and greater than the lower limit calculated by
V.sub.S=0.0703A.sup.2+0.0016A-3.00.times.10.sup.-6,
where A is the dimple plan shape area. In one embodiment, the
dimple plan shape area (A) may range from 0.0025 in.sup.2 to 0.045
in.sup.2. In another embodiment, the dimple plan shape area (A) may
range from 0.0050 in.sup.2 to 0.035 in.sup.2. In yet another
embodiment, the dimple plan shape area (A) may range from 0.0050
in.sup.2 to 0.030 in.sup.2. In still another embodiment, the dimple
plan shape area (A) may range from 0.0075 in.sup.2 to 0.020
in.sup.2. In yet another embodiment, the dimple plan shape area (A)
may range from 0.010 in.sup.2 to 0.015 in.sup.2. In still another
embodiment, the dimple plan shape area (A) may range from 0.010
in.sup.2 to 0.030 in.sup.2.
[0145] Based on the above equations and the contemplated dimple
plan shape areas, the surface volumes of dimples having square or
triangular convex dimple plan shapes may range from about
0.014.times.10.sup.-4 in.sup.3 to about 5.035.times.10.sup.-4
in.sup.3. In another embodiment, the surface volumes may range from
about 0.50.times.10.sup.-4 in.sup.3 to about 4.50.times.10.sup.-4
in.sup.3. For example, the surface volume may range from about
0.50.times.10.sup.-4 in.sup.3 to about 3.0.times.10.sup.-4 in.sup.3
or about 0.50.times.10.sup.-4 in.sup.3 to about 2.0.times.10.sup.-4
in.sup.3. In still another embodiment, the surface volumes may
range from about 1.5.times.10.sup.-4 in.sup.3 to about
4.0.times.10.sup.-4 in.sup.3. In yet another embodiment, the
surface volumes may range from about 2.0.times.10.sup.-4 in.sup.3
to about 3.5.times.10.sup.-4 in.sup.3.
Dimple Profile
[0146] In addition to varying the size of the dimples, the
cross-sectional profile of the dimples may be varied. The
cross-sectional profile of the dimples according to the present
invention may be based on any known dimple profile shape. In one
embodiment, the profile of the dimples corresponds to a curve. For
example, the dimples of the present invention may be defined by the
revolution of a catenary curve about an axis, such as that
disclosed in U.S. Pat. Nos. 6,796,912 and 6,729,976, the entire
disclosures of which are incorporated by reference herein. In
another embodiment, the dimple profiles correspond to polynomial
curves, ellipses, spherical curves, saucer-shapes, truncated cones,
trigonometric, exponential, frequency, or logarithmic curves and
flattened trapezoids. In still another embodiment, the dimples of
the present invention may have dimple profiles that are conical. In
yet another embodiment, the dimple profiles may be created from a
set of mathematical functions including polynomial, exponential,
and trigonometric functions or combinations thereof.
[0147] The profile of the dimple may also aid in the design of the
aerodynamics of the golf ball. For example, shallow dimple depths,
such as those in U.S. Pat. No. 5,566,943, the entire disclosure of
which is incorporated by reference herein, may be used to obtain a
golf ball with high lift and low drag coefficients. Conversely, a
relatively deep dimple depth may aid in obtaining a golf ball with
low lift and low drag coefficients.
[0148] The dimple profile may also be defined by combining a
spherical curve and a different curve, such as a cosine curve, a
frequency curve or a catenary curve, as disclosed in U.S. Patent
Publication No. 2012/0165130, which is incorporated in its entirety
by reference herein. In another embodiment, the dimple profile can
result from the superposition of three or more different curves. In
still another embodiment, one or more of the superposed curves can
be a functionally weighted curve, as disclosed in U.S. Patent
Publication No. 2013/0172123, which is incorporated in its entirety
by reference herein.
Golf Ball Construction
[0149] The dimples of the present invention may be used with
practically any type of ball construction. For instance, the golf
ball may have a two-piece design, a double cover, or two-component
dual core construction depending on the type of performance desired
of the ball. Other suitable golf ball constructions include solid,
wound, liquid-filled, and/or dual cores, and multiple intermediate
layers.
[0150] Different materials may be used in the construction of the
golf balls made with the present invention. For example, the cover
of the ball may be made of a thermoset or thermoplastic, a castable
or non-castable polyurethane and polyurea, an ionomer resin,
balata, or any other suitable cover material known to those skilled
in the art. Conventional and non-conventional materials may be used
for forming core and intermediate layers of the ball including
polybutadiene and other rubber-based core formulations, ionomer
resins, highly neutralized polymers, and the like.
EXAMPLE
[0151] The following non-limiting examples demonstrate golf ball
dimple plan shapes made in accordance with the present invention.
The examples are merely illustrative of the preferred embodiments
of the present invention, and are not to be construed as limiting
the invention, the scope of which is defined by the appended
claims.
[0152] Examples 1-5 demonstrate various curvilinear dimple plan
shapes defined by circular arcs that are derived from regular
n-sided polygons. As demonstrated by the following examples, the
present invention provides for a number of different visually
distinct dimple plan shapes and surface textures.
Example 1
[0153] The following example illustrates a golf ball dimple plan
shape produced in accordance with the present invention. In
particular, FIG. 13 illustrates a concave plan shape 30
(represented by bold line) derived from a regular five-sided
polygon, or a pentagon, 202. As shown in FIG. 13, the plan shape 30
is defined by five concave arcs originating from centers C1-C5 and
having equal radii, r.sub.i, with respective indices 1 through 5.
The circumradius 201 and inradius 200 for the pentagon 202 are
illustrated as dashed lines centered about the origin, O. The
dimple plan shape 30 is further defined as having a plan shape
perimeter ratio of 1.0045 and a plan shape area ratio of
0.9206.
Example 2
[0154] The following example illustrates a golf ball dimple plan
shape produced in accordance with the present invention. In
particular, FIG. 14 illustrates a convex plan shape 40 (represented
by bold line) derived from a regular six-sided polygon, or a
hexagon, 302. As shown in FIG. 14, the plan shape 40 is defined by
six convex arcs originating from centers C1-C6 and having equal
radii, r.sub.i, with respective indices 1 through 6. The
circumradius 301 and inradius 300 for the hexagon 302 are
illustrated as dashed lines centered about the origin, O. The
dimple plan shape 40 is further defined as having a plan shape
perimeter ratio of 1.0107 and a plan shape area ratio of
1.0976.
Example 3
[0155] The following example illustrates a golf ball dimple plan
shape produced in accordance with the present invention. In
particular, FIG. 15 illustrates a plan shape 50 (represented by
bold line) created from a random arrangement of convex and concave
arcs derived from a regular five-sided polygon, or a pentagon, 402.
As shown in FIG. 15, the plan shape 50 is defined by five
convex/concave arcs originating from centers C1-C5 and having equal
radii, r.sub.i, with respective indices 1 through 5. The
circumradius 401 and inradius 400 for the pentagon 402 are
illustrated as dashed lines centered about the origin, O. The
dimple plan shape 50 is further defined as having a plan shape
perimeter ratio of 1.0056 and a plan shape area ratio of
1.0177.
Example 4
[0156] The following example illustrates a golf ball dimple plan
shape produced in accordance with the present invention. In
particular, FIG. 16 illustrates a plan shape 60 (represented by
bold line) created from alternating convex and concave arcs derived
from a regular six-sided polygon, or a hexagon, 502. As shown in
FIG. 16, the plan shape 60 is defined by six alternating convex and
concave arcs originating from centers C1-C6 and having equal radii,
r.sub.i, with respective indices 1 through 6. The circumradius 501
and inradius 500 for the hexagon 502 are illustrated as dashed
lines centered about the origin, O. The dimple plan shape 60 is
further defined as having a plan shape perimeter ratio of 1.0079
and a plan shape area ratio of 1.000. Dimple plan shapes in
accordance with this embodiment of the present invention are
limited to regular n-sided polygons having an even number of
sides.
Example 5
[0157] The following example illustrates a golf ball dimple plan
shape produced in accordance with the present invention. In
particular, FIG. 17 illustrates a plan shape 70 (represented by
bold line) created from convex arcs having different radii from a
regular four-sided polygon, or a square, 602. As shown in FIG. 17,
the plan shape 70 is defined by convex arcs of different radii
originating from centers C1-C4 and having radii, r.sub.i, with
respective indices 1 through 4. In this embodiment, r.sub.1=r.sub.3
and r.sub.2=r.sub.4. The circumradius 601 and inradius 600 for the
square 602 are illustrated as dashed lines centered about the
origin, O. The dimple plan shape 70 is further defined as having a
plan shape perimeter ratio of 1.0178 and a plan shape area ratio of
1.2144.
Example 6
[0158] The following example illustrates a golf ball dimple pattern
contemplated by the present invention. More particularly, the
following example illustrates a dimple base pattern utilizing
square and triangular convex plan shapes of varying sizes. FIG. 23
shows a dimple base pattern with curvilinear convex plan shapes
created from regular three- and four-sided polygons, i.e., an
equilateral triangle and a square, respectively. The dimple base
pattern of FIG. 23 may be used in a golf ball pattern having 302
dimples. While FIG. 23 illustrates the segment dimple pattern, FIG.
20 generally illustrates the overall golf ball dimple pattern.
[0159] Referring to FIG. 23, the dimples having plan shapes based
on three circular arcs or the triangular convex plan shapes are
represented by letter IDs: A, B, C, D, and E. Dimples A, B, C, D,
and E have a plan shape perimeter ratio of 1.0245 and a plan shape
area ratio of 1.4469 with equivalent dimple diameters ranging from
about 0.105 inches to about 0.195 inches. In addition, dimples A,
B, C, D, and E have maximum absolute distances, or sagittas,
ranging from about 0.011 inches to about 0.021 inches.
[0160] The dimples having plan shapes created from four circular
arcs or the square convex plan shapes are represented by letter ID:
F. Dimples F have a plan shape perimeter ratio of 1.0170 and a plan
shape area ratio of 1.2144 with an equivalent dimple diameter of
about 0.210 inches. In addition, dimples F have a maximum absolute
distance, or sagitta, of about 0.013 inches.
[0161] Although any dimple profile or profiles can be used, as
discussed above, the ideal dimple volumes should remain within the
preferred range defined in FIG. 22. Furthermore, for optimal flight
performance, the dimple volumes should be between about
0.5.times.10.sup.-4 in.sup.3 and 3.times.10.sup.-4 in.sup.3
depending on dimple plan shape area.
Example 7
[0162] The following example illustrates another golf ball dimple
pattern contemplated by the present invention. In particular, the
following example illustrates a dimple base pattern utilizing
square convex plan shapes. FIG. 24 shows a dimple base pattern with
curvilinear convex plan shapes created from regular four-sided
polygons, i.e., a square. The dimple base pattern of FIG. 24 may be
used in a golf ball pattern having 312 dimples. While FIG. 24
illustrates the segment dimple pattern, FIG. 21 illustrates the
overall golf ball dimple pattern.
[0163] Referring to FIG. 24, six types of dimples having four
circular arcs (square dimples), which account for all of the plan
shapes within the pattern, are represented by A, B, C, D, E, F, and
G. In this example, dimples A, B, C, D, E, F, and G are defined to
be identical regardless of their equivalent dimple diameters. Each
plan shape within the dimple pattern has a plan shape perimeter
ratio of 1.0068 and a plan shape area ratio of 1.1347 with
equivalent dimple diameters ranging from about 0.110 inches to
about 0.175 inches. Additionally, dimples A, B, C, D, E, F, and G
have maximum absolute distances, or sagittas, ranging from about
0.005 inches to about 0.007 inches.
[0164] Although any dimple profile or profiles can be used, as
discussed above, the ideal dimple volumes should remain within the
preferred range defined in FIG. 22. Furthermore, for optimal flight
performance, the dimple volumes should be between about
0.5.times.10.sup.-4 in.sup.3 and 2.times.10.sup.-4 in.sup.3
depending on dimple plan shape area.
Example 8
[0165] The following example illustrates a dimple pattern of the
present invention having cohesively integrated dimples. FIGS. 26A
and 26B show an arrangement of four dimples having the disclosed
plan shapes and unified edges (represented by 900). The center
dimple 901 has a plan shape composed of three concave circular
arcs. The center dimple 901 is surrounded by three adjacent dimples
902, 903, 904. Each of the adjacent dimples 902, 903, 904 has a
plan shape composed of three convex circular arcs. All of the
dimples in this example have the same maximum distance between the
circular arc and the base polygon (dmax) of approximately 0.015
inches.
[0166] When determining the maximum integration distance (MID) in
this example, the center of the arc forming the concave edge is
identified. In FIG. 26B, the center of the arc forming the concave
edge of dimple 901 is represented by 905. The first reference line
906 is drawn from the center of the concave arc 905 to the center
point on the concave edge of the center dimple 901. The second
reference line 907 is drawn from the center of the concave arc 905
to a top vertex of the concave edge of the center dimple 901. The
third reference line 908 is drawn from the center of the concave
arc 905 to a bottom vertex of the concave edge of the center dimple
901. The MID is the same at all three measurement points (909, 910,
and 911). In this example, the MID is equal to about 0.010
inches.
[0167] As can be seen in FIGS. 26A and 26B, the center dimple 901
has three edges defined by concave circular arcs and all three
edges are unified. That is, the center dimple 901 has a first edge
that is unified with an adjacent edge of dimple 902, a second edge
that is unified with an adjacent edge of dimple 903, and a third
edge that is unified with an adjacent edge of dimple 904. However,
the other dimples having three edges defined by convex circular
arcs 902, 903, 904 include only one unified edge. The remaining
edges of dimples 902, 903, 904 are not unified.
[0168] FIG. 27 shows the arrangement of the four dimples having the
disclosed plan shapes and unified edges (represented by 900) in a
dimple pattern on a golf ball with dimples having circular plan
shapes. The dimple pattern exemplified in FIG. 27 is composed of
350 dimples. The arrangement of dimples 900 is repeated eight times
around the golf ball, equating to 32 dimples having edges defined
by circular arcs. Of those 32 dimples, eight of the dimples have
three edges defined by concave circular arcs and 24 of the dimples
have three edges defined by convex circular arcs. In other words, a
total of 96 dimple edges on the golf ball are defined by circular
arcs. Of the 96 total arc edges, 48 arc edges are unified as
defined by the present invention. Accordingly, approximately 50
percent of the edges defined by circular arcs are unified.
Moreover, in relation to the total number of dimples on the golf
ball, 9.1 percent of the dimples on the golf ball have at least one
unified edge (i.e., 32 dimples out of the total 350 dimples). In
addition, 100 percent of all dimples having the disclosed
curvilinear plan shapes have at least one unified edge.
Example 9
[0169] The following example illustrates an arrangement of
cohesively integrated dimples according to the present invention.
FIGS. 28A and 28B show an arrangement of four dimples having the
disclosed plan shapes and unified edges (represented by 920). Two
of the dimples 921 and 924 have plan shapes composed of four convex
circular arcs. The other two dimples 922 and 923 have plan shapes
composed of four concave circular arcs. All of the dimples in this
example have the same maximum distance between the circular arc and
the base polygon (d.sub.max) of approximately 0.017 inches.
[0170] When determining the maximum integration distance (MID) in
this example, the center of the are forming the concave edge is
identified. In FIG. 28B, the center of the arc forming the concave
edge of dimple 922 is represented by 925. The first reference line
926 is drawn from the center of the concave arc 925 to the center
point on the concave edge of dimple 922. The second reference line
927 is drawn from the center of the concave arc 925 to a top vertex
of the concave edge of dimple 922. The third reference line 928 is
drawn from the center of the concave arc 925 to a bottom vertex of
the concave edge of dimple 922. The MID is the same at all three
measurement points (929, 930, and 931). In this example, the MID is
equal to about 0.012 inches.
[0171] As can be seen in FIGS. 28A and 28B, the two dimples having
plan shapes composed of four convex circular arcs 921 and 924
include two unified edges. That is, dimple 921 has a first edge
that is unified with an adjacent edge of dimple 922 and a second
edge that is unified with an adjacent edge of dimple 923.
Similarly, dimple 924 has a first edge that is unified with an
adjacent edge of dimple 922 and a second edge that is unified with
an adjacent edge of dimple 923. The two dimples having plan shapes
composed of four concave circular arcs 922 and 923 also include two
unified edges. Dimple 922 has a first edge that is unified with an
adjacent edge of dimple 921 and a second edge that is unified with
an adjacent edge of dimple 924. Likewise, dimple 923 has a first
edge that is unified with an adjacent edge of dimple 921 and a
second edge that is unified with an adjacent edge of dimple 924. In
this example, the remaining edges of dimples 921, 922, 923, 924 are
not unified.
Example 10
[0172] The following example illustrates a dimple pattern of the
present invention having cohesively integrated dimples. FIG. 29
shows a dimple pattern composed entirely of dimples having the
disclosed plan shapes (for example, plan shapes defined by circular
arcs). The dimple pattern shown in FIG. 29 (represented by 940) is
composed of 368 dimples. The dimple pattern 940 includes eight
dimples each having three edges defined by convex circular arcs.
These dimples are represented by 935. The dimple pattern 940 also
includes the arrangement of dimples described in Example 9 (shown
in the bolded circle in FIG. 29). More particularly, the dimple
pattern 940 includes 180 dimples each having four edges defined by
concave circular arcs (represented by 936) and 180 dimples each
having four edges defined by convex circular arcs (represented by
937). Each of the four edges of dimples 936 and 937 are unified.
This equates to 1,464 total dimple edges defined by circular arcs.
Of the total number of arc edges, 1,272 edges are unified as
defined by the present invention. Accordingly, approximately 87
percent of the edges defined by circular arcs are unified.
Moreover, in relation to the total number of dimples on the golf
ball, 97.8 percent of the dimples on the golf ball have at least
one unified edge (i.e., 360 dimples out of the total 368
dimples).
Example 11
[0173] FIG. 30A shows a dimple base pattern with curvilinear convex
plan shapes created from regular three- and four-sided polygons,
i.e., an equilateral triangle and a square, respectively. FIG. 30B
illustrates an overall golf ball dimple pattern formed by
tessellating multiple copies of the base pattern shown in FIG. 30A
to cover the outer surface of the golf ball in a uniform pattern.
The resulting dimple pattern consists of 302 dimples and provides
for a dimple surface coverage on the golf ball of about 74.8%.
[0174] In FIGS. 30A and 30B, the alphabetical labels within the
dimples designate dimples belonging to different dimple types,
i.e., dimples having the same alphabetical label have the same
dimple properties. For example, all dimples labelled A have
substantially the same plan shape, equivalent dimple diameter,
dimple surface volume, arc segment radii, maximum absolute
distance, and plan shape perimeter ratio. In the example
illustrated in FIGS. 30A and 30B, the dimple pattern consists of
three dimple types, including two dimple types having a plan shape
with three curvilinear edges (dimple types A and C) and one dimple
type having a plan shape with four curvilinear edges (dimple type
B). Table 1 below gives illustrative values for various dimple
properties for each of the three dimple types, according to a
non-limiting example of the embodiment shown in FIGS. 30A and
30B.
TABLE-US-00001 TABLE 1 Equiv- Plan Plan alent Dimple Arc Maximum
Shape Dimple Shape Dimple Surface Segment Absolute Perim- Type/
Area Diameter Volume Radii Distance eter Label (in.sup.2) (in)
(in.sup.3) (in) (in) Ratio A 0.02012 0.160 1.0229 .times. 10.sup.-4
0.400 0.012 1.01 B 0.02541 0.180 1.4503 .times. 10.sup.-4 0.400
0.007 1.01 C 0.02583 0.181 1.4766 .times. 10.sup.-4 0.400 0.014
1.01
[0175] Notwithstanding that the numerical ranges and parameters
setting forth the broad scope of the invention are approximations,
the numerical values set forth in the specific examples are
reported as precisely as possible. Any numerical value, however,
inherently contain certain errors necessarily resulting from the
standard deviation found in their respective testing measurements.
Furthermore, when numerical ranges of varying scope are set forth
herein, it is contemplated that any combination of these values
inclusive of the recited values may be used.
[0176] The invention described and claimed herein is not to be
limited in scope by the specific embodiments herein disclosed,
since these embodiments are intended as illustrations of several
aspects of the invention. Any equivalent embodiments are intended
to be within the scope of this invention. Indeed, various
modifications of the invention in addition to those shown and
described herein will become apparent to those skilled in the art
from the foregoing description. Such modifications are also
intended to fall within the scope of the appended claims. All
patents and patent applications cited in the foregoing text are
expressly incorporated herein by reference in their entirety.
* * * * *