U.S. patent application number 13/672910 was filed with the patent office on 2013-03-14 for dimple patterns for golf balls.
This patent application is currently assigned to ACUSHNET COMPANY. The applicant listed for this patent is ACUSHNET COMPANY. Invention is credited to Chris Hixenbaugh, Michael R. Madson, Nicholas M. Nardacci.
Application Number | 20130065708 13/672910 |
Document ID | / |
Family ID | 47830353 |
Filed Date | 2013-03-14 |
United States Patent
Application |
20130065708 |
Kind Code |
A1 |
Hixenbaugh; Chris ; et
al. |
March 14, 2013 |
DIMPLE PATTERNS FOR GOLF BALLS
Abstract
The present invention provides a method for arranging dimples on
a golf ball surface that significantly improves aerodynamic
symmetry and minimizes parting line visibility by arranging the
dimples in a pattern derived from at least one irregular domain
generated from a regular or non-regular polyhedron. One or more
irregular domains may have an initial dimple sub-pattern of nearest
neighbor dimples wherein the dimple sub-pattern is packed in one or
more irregular domains; and the unfilled regions of the irregular
domains are packed with dimples and the irregular domains are
tessellated around the golf ball surface.
Inventors: |
Hixenbaugh; Chris;
(Dartmouth, MA) ; Nardacci; Nicholas M.; (Bristol,
RI) ; Madson; Michael R.; (Wrentham, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
ACUSHNET COMPANY; |
Fairhaven |
MA |
US |
|
|
Assignee: |
ACUSHNET COMPANY
Fairhaven
MA
|
Family ID: |
47830353 |
Appl. No.: |
13/672910 |
Filed: |
November 9, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13251590 |
Oct 3, 2011 |
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13672910 |
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12262464 |
Oct 31, 2008 |
8029388 |
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13251590 |
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Current U.S.
Class: |
473/379 ;
473/378; 473/380; 473/381; 473/382; 473/384 |
Current CPC
Class: |
A63B 37/0004 20130101;
A63B 37/0006 20130101; A63B 37/0007 20130101; A63B 45/00
20130101 |
Class at
Publication: |
473/379 ;
473/378; 473/384; 473/382; 473/381; 473/380 |
International
Class: |
A63B 37/14 20060101
A63B037/14; A63B 37/12 20060101 A63B037/12 |
Claims
1. A golf ball surface having a polyhedral arrangement of dimples
comprising: one or more irregular domains containing dimples; and
an initial sub-pattern of nearest neighbor dimples within at least
one of the irregular domain(s).
2. The golf ball according to claim 1, wherein a dimple sub-pattern
is packed within the edges of one or more irregular domains, and
the unfilled regions of the irregular domains are packed with
dimples and the irregular domains are tessellated around the golf
ball surface.
3. The golf ball according to claim 1, wherein a dimple sub-pattern
is packed on the edges of one or more irregular domains, and the
unfilled regions of the irregular domains are packed with dimples
and the irregular domains are tessellated around the golf ball
surface.
4. The golf ball according to claim 1, wherein a dimple sub-pattern
includes being packed, both on the edges and within the edges of
one or more irregular domains, and the unfilled regions of the
irregular domains are packed with dimples and the irregular domains
are tessellated around the golf ball surface.
5. The golf ball according to claim 1, wherein a dimple sub-pattern
is packed in a first irregular domain; and the unfilled region of
the first irregular domain is packed with dimples surrounding the
sub-pattern; additional irregular domains are packed with an
arrangement of dimples and the irregular domains are tessellated
around the golf ball surface.
6. The golf ball according to claim 1, wherein a dimple sub-pattern
is packed in a first and second irregular domain; the unfilled
regions of the first and second irregular domains are packed with
dimples surrounding the sub-pattern; and the irregular domains are
tessellated around the ball surface.
7. The golf ball according to claim 2, wherein the sub-pattern of
nearest neighbor dimples is visually distinct from the other packed
dimples.
8. The golf ball according to claim 7, wherein the sub-pattern of
nearest neighbor dimples exhibit different perimeter shape, or
dimple profile, or color, or texture, or grooves, or brambles or a
combination therein from the dimples not contained within the
sub-pattern.
9. The golf ball according to claim 6, wherein the sub-pattern of
nearest neighbor dimples has a circular perimeter with a diameter
ranging between 0.100 to 0.220 inches.
10. The golf ball according to claim 8, wherein the sub-pattern of
nearest neighbor dimples have non-circular perimeters which if
circumscribed by a circle are in a diameter range between 0.100 to
0.270 inches.
11. The golf ball according to claim 2, wherein each sub-pattern
contains 2 to 80 nearest neighbor dimples within the irregular
domain.
12. The golf ball according to claim 2, wherein the base geometry
of each irregular domain contains 10 to 115 dimples.
13. The golf ball according to claim 2, wherein the surface
coverage of dimples on the golf ball is between 70 to 90
percent.
14. The golf ball according to claim 2, wherein the surface
coverage of the sub-pattern of nearest neighbor dimples is between
10 to 60 percent.
15. The golf ball according to claim 8, wherein the dimple profile
is selected from a group consisting of spherical, Gabriel's horn,
catenary, conical, Witch of Agnesi, ellipse, superposition of two
curves or spherically weighted profiles.
16. The golf ball according to claim 8, wherein the dimple profile
is selected from a group consisting of circular, polygonal, or
elliptical.
17. The golf ball according to claim 1, wherein the polyhedron is
selected from a group consisting of tetrahedron, or cube, or
octahedron, or dodecahedron, or icosahedron.
18. The golf ball according to claim 1, wherein a parting line of
the golf ball intersects two edges of each sub-pattern section.
19. The golf ball according to claim 1, wherein the dimples are
arranged to create a staggered parting line through the segment.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a Continuation-in-Part of co-pending
U.S. patent application Ser. No. 13/251,590, filed Oct. 3, 2011,
which is a Divisional of U.S. patent application Ser. No.
12/262,464 filed Oct. 31, 2008, now U.S. Pat. No. 8,029,388, the
disclosures of which are incorporated by reference herein in their
entirety.
FIELD OF THE INVENTION
[0002] This invention relates to golf balls, particularly to golf
balls having improved dimple patterns. More particularly, the
invention relates to methods of arranging dimples on a golf ball by
generating irregular domains based on polyhedrons, packing the
irregular domains with dimples, and tessellating the domains onto
the surface of the golf ball.
BACKGROUND OF THE INVENTION
[0003] Historically, dimple patterns for golf balls have had a
variety of geometric shapes, patterns, and configurations.
Primarily, patterns are laid out in order to provide desired
performance characteristics based on the particular ball
construction, material attributes, and player characteristics
influencing the ball's initial launch angle and spin conditions.
Therefore, pattern development is a secondary design step that is
used to achieve the appropriate aerodynamic behavior, thereby
tailoring ball flight characteristics and performance.
[0004] Aerodynamic forces generated by a ball in flight are a
result of its velocity and spin. These forces can be represented by
a lift force and a drag force. Lift force is perpendicular to the
direction of flight and is a result of air velocity differences
above and below the rotating ball. This phenomenon is attributed to
Magnus, who described it in 1853 after studying the aerodynamic
forces on spinning spheres and cylinders, and is described by
Bernoulli's Equation, a simplification of the first law of
thermodynamics. Bernoulli's equation relates pressure and velocity
where pressure is inversely proportional to the square of velocity.
The velocity differential, due to faster moving air on top and
slower moving air on the bottom, results in lower air pressure on
top and an upward directed force on the ball.
[0005] Drag is opposite in sense to the direction of flight and
orthogonal to lift. The drag force on a ball is attributed to
parasitic drag forces, which consist of pressure drag and viscous
or skin friction drag. A sphere is a bluff body, which is an
inefficient aerodynamic shape. As a result, the accelerating flow
field around the ball causes a large pressure differential with
high-pressure forward and low-pressure behind the ball. The low
pressure area behind the ball is also known as the wake. In order
to minimize pressure drag, dimples provide a means to energize the
flow field and delay the separation of flow, or reduce the wake
region behind the ball. Skin friction is a viscous effect residing
close to the surface of the ball within the boundary layer. The
industry has seen many efforts to maximize the aerodynamics of golf
balls, through dimple disturbance and other methods, though they
are closely controlled by golf's national governing body, the
United States Golf Association (U.S.G.A.). One U.S.G.A. requirement
is that golf balls have aerodynamic symmetry. Aerodynamic symmetry
allows the ball to fly with a very small amount of variation no
matter how the golf ball is placed on the tee or ground.
Preferably, dimples cover the maximum surface area of the golf ball
without detrimentally affecting the aerodynamic symmetry of the
golf ball.
[0006] In attempts to improve aerodynamic symmetry, many dimple
patterns are based on geometric shapes. These may include circles,
hexagons, triangles, and the like. Other dimple patterns are based
in general on the five Platonic Solids including icosahedron,
dodecahedron, octahedron, cube, or tetrahedron. Yet other dimple
patterns are based on the thirteen Archimedean Solids, such as the
small icosidodecahedron, rhomicosidodecahedron, small
rhombicuboctahedron, snub cube, snub dodecahedron, or truncated
icosahedron. Furthermore, other dimple patterns are based on
hexagonal dipyramids. Because the number of symmetric solid plane
systems is limited, it is difficult to devise new symmetric
patterns. Moreover, dimple patterns based some of these geometric
shapes result in less than optimal surface coverage and other
disadvantageous dimple arrangements. Therefore, dimple properties
such as number, shape, size, and arrangement are often manipulated
in an attempt to generate a golf ball that has better aerodynamic
properties.
[0007] U.S. Pat. No. 5,562,552 to Thurman discloses a golf ball
with an icosahedral dimple pattern, wherein each triangular face of
the icosahedron is split by a three straight lines which each
bisect a corner of the face to form 3 triangular faces for each
icosahedral face, wherein the dimples are arranged consistently on
the icosahedral faces.
[0008] U.S. Pat. No. 5,046,742 to Mackey discloses a golf ball with
dimples packed into a 32-sided polyhedron composed of hexagons and
pentagons, wherein the dimple packing is the same in each hexagon
and in each pentagon. U.S. Pat. No. 4,998,733 to Lee discloses a
golf ball formed of ten "spherical" hexagons each split into six
equilateral triangles, wherein each triangle is split by a
bisecting line extending between a vertex of the triangle and the
midpoint of the side opposite the vertex, and the bisecting lines
are oriented to achieve improved symmetry.
[0009] U.S. Pat. No. 6,682,442 to Winfield discloses the use of
polygons as packing elements for dimples to introduce predictable
variance into the dimple pattern. The polygons extend from the
poles of the ball to a parting line. Any space not filled with
dimples from the polygons is filled with other dimples.
[0010] A continuing need exists for a dimple pattern whose dimple
arrangement results in a maximized surface coverage and desirable
aerodynamic characteristics, including improved symmetry.
SUMMARY OF THE INVENTION
[0011] The present invention provides a method for arranging
dimples on a golf ball surface that significantly improves
aerodynamic symmetry and minimizes parting line visibility by
arranging the dimples in a pattern derived from at least one
irregular domain generated from a regular or non-regular
polyhedron. The method includes choosing control points of a
polyhedron, generating an irregular domain based on those control
points, packing the irregular domain with dimples, and tessellating
the irregular domain to cover the surface of the golf ball.
[0012] One embodiment of the present invention provides for an
initial dimple sub-pattern contained in the irregular domain(s).
The dimple sub-pattern may be defined as nearest neighbor dimples
on or within edges of one or more of the irregular domains. Once
the sub-pattern is defined, the remaining unpacked spherical region
is packed with dimples around the initial sub-pattern of dimples.
The irregular domains are then tessellated around the ball surface.
The sub-pattern dimples can be packed within any number of the
irregular domains.
[0013] The method of determining nearest neighbor dimples is
illustrated in FIG. 11C, wherein two tangency lines T.sub.L are
drawn from the center of a first dimple to a potential nearest
neighbor dimple. Additionally, a line segment L.sub.S is drawn
connecting the center of the first dimple to the center of the
potential nearest neighbor dimple. If there is no line segment that
is intersected by another dimple, or portion of a dimple, then
those dimples are considered to be nearest neighbor dimples.
[0014] The golf ball produced by the method of the present
invention has a sub-pattern of nearest neighbor dimples that are
visually distinct from the other packed dimples. The sub-pattern of
nearest neighbor dimples may exhibit different perimeter shape, or
dimple profile, or color, or texture, or grooves, or brambles or a
combination therein from the packed dimples of the initial base
geometry. The sub-pattern of nearest neighbor dimples may have
circular perimeters with diameters ranging between 0.100 to 0.220
inches. In golf balls wherein the sub-pattern of nearest neighbor
dimples have non-circular perimeters; the diameter range is between
0.120 to 0.270 inches when the non-circular perimeters are
circumscribed by a circle.
[0015] The present invention provides for a golf ball wherein each
sub-pattern contains 2 to 80 nearest neighbor dimples, and wherein
the base geometry of each irregular domain contains 10 to 115
dimples. The surface coverage of dimples is between 70 to 90
percent, including surface coverage of sub-pattern nearest neighbor
dimples between 10 to 60 percent.
[0016] Other embodiments of the present invention may have dimple
profiles that are spherical, Gabriel's horn, catenary, conical,
Witch of Agnesi, ellipse, or any other profile defined by the
superposition of two or more curves or spherically weighted
profiles. Further these dimples can have perimeters such as
circular, or polygonal, or elliptical.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] In the accompanying drawings which form a part of the
specification and are to be read in conjunction therewith and in
which like reference numerals are used to indicate like parts in
the various views:
[0018] FIG. 1A illustrates a golf ball having dimples arranged by a
method of the invention; FIG. 1B illustrates a polyhedron face;
FIG. 1C illustrates an element of the invention in the polyhedron
face of FIG. 1B; and FIG. 1D illustrates a domain formed by a
methods of the invention packed with dimples and formed from two
elements of FIG. 1C;
[0019] FIG. 2 illustrates a single face of a polyhedron having
control points thereon;
[0020] FIG. 3A illustrates a polyhedron face; FIG. 3B illustrates
an element of the invention packed with dimples; FIG. 3C
illustrates a domain of the invention packed with dimples formed
from elements of FIG. 3B; and FIG. 3D illustrates a golf ball
formed by a method of the invention formed of the domain of FIG.
3C;
[0021] FIG. 4A illustrates two polyhedron faces; FIG. 4B
illustrates a first domain of the invention in the two polyhedron
faces of FIG. 4A; FIG. 4C illustrates a first domain and a second
domain of the invention in three polyhedron faces; FIG. 4D
illustrates a golf ball formed by a method of the invention formed
of the domains of FIG. 4C;
[0022] FIG. 5A illustrates a polyhedron face; FIG. 5B illustrates a
first domain of the invention in a polyhedron face; FIG. 5C
illustrates a first domain and a second domain of the invention in
three polyhedron faces; and FIG. 5D illustrates a golf ball formed
using a method of the invention formed of the domains of FIG.
5C;
[0023] FIG. 6A illustrates a polyhedron face; FIG. 6B illustrates a
portion of a domain of the invention in the polyhedron face of FIG.
6A; FIG. 6C illustrates a domain formed by the methods of the
invention; and FIG. 6D illustrates a golf ball formed using the
methods of the invention formed of domains of FIG. 6C;
[0024] FIG. 7A illustrates a polyhedron face; FIG. 7B illustrates a
domain of the invention in the polyhedron face of FIG. 7A; and FIG.
7C illustrates a golf ball formed by a method of the invention;
[0025] FIG. 8A illustrates a first element of the invention in a
polyhedron face; FIG. 8B illustrates a first and a second element
of the invention in the polyhedron face of FIG. 8A; FIG. 8C
illustrates two domains of the invention composed of first and
second elements of FIG. 8B; FIG. 8D illustrates a single domain of
the invention based on the two domains of FIG. 8C; and FIG. 8E
illustrates a golf ball formed using a method of the invention
formed of the domains of FIG. 8D;
[0026] FIG. 9A illustrates a polyhedron face; FIG. 9B illustrates
an element of the invention in the polyhedron face of FIG. 9A; FIG.
9C illustrates two elements of FIG. 9B combining to form a domain
of the invention; FIG. 9D illustrates a domain formed by the
methods of the invention based on the elements of FIG. 9C; and FIG.
9E illustrates a golf ball formed using a method formed of domains
of FIG. 9D;
[0027] FIG. 10A illustrates a face of a rhombic dodecahedron; FIG.
10B illustrates a segment of the present invention in the face of
FIG. 10A; FIG. 10C illustrates the segment of FIG. 10B and copies
thereof forming a domain of the present invention; FIG. 10D
illustrates a domain formed by a method of the present invention
based on the segments of FIG. 10C; and FIG. 10E illustrates a golf
ball formed by a method of the present invention formed of domains
of FIG. 10D;
[0028] FIG. 11A utilizes the mid-point to mid-point tiling method
to illustrate irregular domains of the present invention;
[0029] FIG. 11B utilizes the mid-point to mid-point tiling method
to illustrate irregular domains of the present invention;
[0030] FIG. 11C depicts a dimple sub-pattern wherein they are shown
as nearest neighbor dimples within edges of one of the irregular
domains;
[0031] FIG. 11D depicts a dimple sub-pattern wherein they are shown
as nearest neighbor dimples within edges of another of the
irregular domains;
[0032] FIG. 11E shows the domains of FIG. 11C and FIG. 11D
tessellated around a golf ball sphere;
[0033] FIG. 12A utilizes the mid-point to mid-point tiling method
to illustrate irregular domains of the present invention;
[0034] FIG. 12B depicts a dimple sub-pattern wherein they are shown
as nearest neighbor dimples within edges of one of the irregular
domains;
[0035] FIG. 12C shows the domains of FIG. 12B tessellated around a
golf ball sphere;
[0036] FIG. 13A depicts a dimple sub-pattern wherein they are shown
as nearest neighbor dimples within edges of one of the irregular
domains; and
[0037] FIG. 13B shows the domains of FIG. 13A tessellated around a
golf ball sphere.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0038] The present invention provides a method for arranging
dimples on a golf ball surface in a pattern derived from at least
one irregular domain generated from a regular or non-regular
polyhedron. In the invention as described below extends the method
of spherical tiling to include sub-patterns of dimples within the
base geometry dimple packing. Unique patterns are thus created with
improved aerodynamics and visual aesthetics.
[0039] In one embodiment, illustrated in FIG. 1A, the present
invention comprises a golf ball 10 comprising dimples 12. Dimples
12 are arranged by packing irregular domains 14 with dimples, as
seen best in FIG. 1D. Irregular domains 14 are created in such a
way that, when tessellated on the surface of golf ball 10, they
impart greater orders of symmetry to the surface than prior art
balls. The irregular shape of domains 14 additionally minimize the
appearance and effect of the golf ball parting line from the
molding process, and allows greater flexibility in arranging
dimples than would be available with regularly shaped domains.
[0040] The irregular domains can be defined through the use of any
one of the exemplary methods described herein. Each method produces
one or more unique domains based on circumscribing a sphere with
the vertices of a regular polyhedron. The vertices of the
circumscribed sphere based on the vertices of the corresponding
polyhedron with origin (0,0,0) are defined below in Table 1.
TABLE-US-00001 TABLE 1 Vertices of Circumscribed Sphere based on
Corresponding Polyhedron Vertices Type of Polyhedron Vertices
Tetrahedron (+1, +1, +1); (-1, -1, +1); (-1, +1, -1); (+1, -1, -1)
Cube (.+-.1, .+-.1, .+-.1) Octahedron (.+-.1, 0, 0); (0, .+-.1, 0);
(0, 0, .+-.1) Dodecahedron (.+-.1, .+-.1, .+-.1); (0, .+-.1/.phi.,
.+-..phi.); (.+-.1/.phi., .+-..phi., 0); (.+-..phi., 0,
.+-.1/.phi.)* Icosahedron (0, .+-.1, .+-..phi.); (.+-.1, .+-..phi.,
0); (.+-..phi., 0, .+-.1)* *.phi. = (1 + {square root over
(5)})/2
[0041] Each method has a unique set of rules which are followed for
the domain to be symmetrically patterned on the surface of the golf
ball. Each method is defined by the combination of at least two
control points. These control points, which are taken from one or
more faces of a regular or non-regular polyhedron, consist of at
least three different types: the center C of a polyhedron face; a
vertex V of a face of a regular polyhedron; and the midpoint M of
an edge of a face of the polyhedron. FIG. 2 shows an exemplary face
16 of a polyhedron (a regular dodecahedron in this case) and one of
each a center C, a midpoint M, a vertex V, and an edge E on face
16. The two control points C, M, or V may be of the same or
different types. Accordingly, six types of methods for use with
regular polyhedrons are defined as follows:
[0042] 1. Center to midpoint (C.fwdarw.M);
[0043] 2. Center to center (C.fwdarw.C);
[0044] 3. Center to vertex (C.fwdarw.V);
[0045] 4. Midpoint to midpoint (M.fwdarw.M);
[0046] 5. Midpoint to Vertex (M.fwdarw.V); and
[0047] 6. Vertex to Vertex (V.fwdarw.V).
[0048] While each method differs in its particulars, they all
follow the same basic scheme. First, a non-linear sketch line is
drawn connecting the two control points. This sketch line may have
any shape, including, but not limited, to an arc, a spline, two or
more straight or acute lines or curves, or a combination thereof.
Second, the sketch line is patterned in a method specific manner to
create a domain, as discussed below. Third, when necessary, the
sketch line is patterned in a second fashion to create a second
domain.
[0049] While the basic scheme is consistent for each of the six
methods, each method preferably follows different steps in order to
generate the domains from a sketch line between the two control
points, as described below with reference to each of the methods
individually.
The Center to Vertex Method
[0050] Referring again to FIGS. 1A-1D, the center to vertex method
yields a domain that tessellates to cover the surface of golf ball
10. The domain is defined as follows: [0051] 1. A regular
polyhedron is chosen (FIGS. 1A-1D use an icosahedron); [0052] 2. A
single face 16 of the regular polyhedron is chosen, as shown in
FIG. 1B; [0053] 3. Center C of face 16, and a first vertex V.sub.1
of face 16 are connected with any non-linear sketch line,
hereinafter referred to as a segment 18; [0054] 4. A copy 20 of
segment 18 is rotated about center C, such that copy 20 connects
center C with vertex V.sub.2 adjacent to vertex V.sub.1. The two
segments 18 and 20 and the edge E connecting vertices V.sub.1 and
V.sub.2 define an element 22, as shown best in FIG. 1C; and [0055]
5. Element 22 is rotated about midpoint M of edge E to create a
domain 14, as shown best in FIG. 1D.
[0056] When domain 14 is tessellated to cover the surface of golf
ball 10, as shown in FIG. 1A, a different number of total domains
14 will result depending on the regular polyhedron chosen as the
basis for control points C and V.sub.1. The number of domains 14
used to cover the surface of golf ball 10 is equal to the number of
faces P.sub.F of the polyhedron chosen times the number of edges
P.sub.E per face of the polyhedron divided by 2, as shown below in
Table 2.
TABLE-US-00002 TABLE 2 Domains Resulting From Use of Specific
Polyhedra When Using the Center to Vertex Method Type of Number of
Faces, Number of Number of Domains Polyhedron P.sub.F Edges,
P.sub.E 14 Tetrahedron 4 3 6 Cube 6 4 12 Octahedron 8 3 12
Dodecahedron 12 5 30 Icosahedron 20 3 30
The Center to Midpoint Method
[0057] Referring to FIGS. 3A-3D, the center to midpoint method
yields a single irregular domain that can be tessellated to cover
the surface of golf ball 10. The domain is defined as follows:
[0058] 1. A regular polyhedron is chosen (FIGS. 3A-3D use a
dodecahedron); [0059] 2. A single face 16 of the regular polyhedron
is chosen, shown in FIG. 3A; [0060] 3. Center C of face 16, and
midpoint M.sub.1 of a first edge E.sub.1 of face 16 are connected
with a segment 18; [0061] 4. A copy 20 of segment 18 is rotated
about center C, such that copy 20 connects center C with a midpoint
M.sub.2 of a second edge E.sub.2 adjacent to first edge E.sub.1.
The two segments 16 and 18 and the portions of edge E.sub.1 and
edge E.sub.2 between midpoints M.sub.1 and M.sub.2 define an
element 22; and [0062] 5. Element 22 is patterned about vertex V of
face 16 which is contained in element 22 and connects edges E.sub.1
and E.sub.2 to create a domain 14.
[0063] When domain 14 is tessellated around a golf ball 10 to cover
the surface of golf ball 10, as shown in FIG. 3D, a different
number of total domains 14 will result depending on the regular
polyhedron chosen as the basis for control points C and M.sub.1.
The number of domains 14 used to cover the surface of golf ball 10
is equal to the number of vertices P.sub.V of the chosen
polyhedron, as shown below in Table 3.
TABLE-US-00003 TABLE 3 Domains resulting from use of specific
Polyhedra when using the Center to Midpoint Method Type of
Polyhedron Number of Vertices, P.sub.V Number of Domains 14
Tetrahedron 4 4 Cube 8 8 Octahedron 6 6 Dodecahedron 20 20
Icosahedron 12 12
The Center to Center Method
[0064] Referring to FIGS. 4A-4D, the center to center method yields
two domains that can be tessellated to cover the surface of golf
ball 10. The domains are defined as follows: [0065] 1. A regular
polyhedron is chosen (FIGS. 4A-4D use a dodecahedron); [0066] 2.
Two adjacent faces 16a and 16b of the regular polyhedron are
chosen, as shown in FIG. 4A; [0067] 3. Center C.sub.1 of face 16a,
and center C.sub.2 of face 16b are connected with a segment 18;
[0068] 4. A copy 20 of segment 18 is rotated 180 degrees about the
midpoint M between centers C.sub.1 and C.sub.2, such that copy 20
also connects center C.sub.1 with center C.sub.2, as shown in FIG.
4B. The two segments 16 and 18 define a first domain 14a; and
[0069] 5. Segment 18 is rotated equally about vertex V to define a
second domain 14b, as shown in FIG. 4C.
[0070] When first domain 14a and second domain 14b are tessellated
to cover the surface of golf ball 10, as shown in FIG. 4D, a
different number of total domains 14a and 14b will result depending
on the regular polyhedron chosen as the basis for control points
C.sub.1 and C.sub.2. The number of first and second domains 14a and
14b used to cover the surface of golf ball 10 is P.sub.F*P.sub.E/2
for first domain 14a and P.sub.V for second domain 14b, as shown
below in Table 4.
TABLE-US-00004 TABLE 4 Domains Resulting From Use of Specific
Polyhedra When Using the Center to Center Method Number of Number
Number of Number of First of Second Type of Vertices, Domains
Faces, Number of Domains Polyhedron P.sub.V 14a P.sub.F Edges,
P.sub.E 14b Tetrahedron 4 6 4 3 4 Cube 8 12 6 4 8 Octahedron 6 9 8
3 6 Dodecahedron 20 30 12 5 20 Icosahedron 12 18 20 3 12
The Midpoint to Midpoint Method
[0071] Referring to FIGS. 5A-5D, the midpoint to midpoint method
yields two domains that tessellate to cover the surface of golf
ball 10. The domains are defined as follows: [0072] 1. A regular
polyhedron is chosen (FIGS. 5A-5D use a dodecahedron); [0073] 2. A
single face 16 of the regular polyhedron is chosen, as shown in
FIG. 5A; [0074] 3. The midpoint M.sub.1 of a first edge E.sub.1 of
face 16, and the midpoint M.sub.2 of a second edge E.sub.2 adjacent
to first edge E.sub.1 are connected with a segment 18; [0075] 4.
Segment 18 is patterned around center C of face 16 to form a first
domain 14a, as shown in FIG. 5B; [0076] 5. Segment 18, along with
the portions of first edge E.sub.1 and second edge E.sub.2 between
midpoints M.sub.1 and M.sub.2, define an element 22; and [0077] 6.
Element 22 is patterned about vertex V which is contained in
element 22 and connects edges E.sub.1 and E.sub.2 to create a
second domain 14b, as shown in FIG. 5C.
[0078] When first domain 14a and second domain 14b are tessellated
to cover the surface of golf ball 10, as shown in FIG. 5D, a
different number of total domains 14a and 14b will result depending
on the regular polyhedron chosen as the basis for control points
M.sub.1 and M.sub.2. The number of first and second domains 14a and
14b used to cover the surface of golf ball 10 is P.sub.F for first
domain 14a and P.sub.V for second domain 14b, as shown below in
Table 5.
TABLE-US-00005 TABLE 5 Domains resulting from use of specific
polyhedra when using the Center to Center Method Number Number of
Number of Type of Number of of First Vertices, Second Domains
Polyhedron Faces, P.sub.F Domains 14a P.sub.V 14b Tetrahedron 4 4 4
4 Cube 6 6 8 8 Octahedron 8 8 6 6 Dodecahedron 12 12 20 20
Icosahedron 20 20 12 12
The Midpoint to Vertex Method
[0079] Referring to FIGS. 6A-6D, the midpoint to vertex method
yields one domain that tessellates to cover the surface of golf
ball 10. The domain is defined as follows: [0080] 1. A regular
polyhedron is chosen (FIGS. 6A-6D use a dodecahedron); [0081] 2. A
single face 16 of the regular polyhedron is chosen, as in FIG. 6A;
[0082] 3. A midpoint M.sub.1 of edge E.sub.1 of face 16 and a
vertex V.sub.1 on edge E.sub.1 are connected with a segment 18;
[0083] 4. Copies 20 of segment 18 is patterned about center C of
face 16, one for each midpoint M.sub.2 and vertex V.sub.2 of face
16, to define a portion of domain 14, as shown in FIG. 6B; and
[0084] 5. Segment 18 and copies 20 are then each rotated 180
degrees about their respective midpoints to complete domain 14, as
shown in FIG. 6C.
[0085] When domain 14 is tessellated to cover the surface of golf
ball 10, as shown in FIG. 6D, a different number of total domains
14 will result depending on the regular polyhedron chosen as the
basis for control points M.sub.1 and V.sub.1. The number of domains
14 used to cover the surface of golf ball 10 is P.sub.F, as shown
in Table 6.
TABLE-US-00006 TABLE 6 Domains resulting from use of specific
polyhedra when using the Midpoint to Vertex Method Type of
Polyhedron Number of Faces, P.sub.F Number of Domains 14
Tetrahedron 4 4 Cube 6 6 Octahedron 8 8 Dodecahedron 12 12
Icosahedron 20 20
The Vertex to Vertex Method
[0086] Referring to FIGS. 7A-7C, the vertex to vertex method yields
two domains that tessellate to cover the surface of golf ball 10.
The domains are defined as follows: [0087] 1. A regular polyhedron
is chosen (FIGS. 7A-7C use an icosahedron); [0088] 2. A single face
16 of the regular polyhedron is chosen, as in FIG. 7A; [0089] 3. A
first vertex V.sub.1 face 16, and a second vertex V.sub.2 adjacent
to first vertex V.sub.1 are connected with a segment 18; [0090] 4.
Segment 18 is patterned around center C of face 16 to form a first
domain 14a, as shown in FIG. 7B; [0091] 5. Segment 18, along with
edge E.sub.1 between vertices V.sub.1 and V.sub.2, defines an
element 22; and [0092] 6. Element 22 is rotated around midpoint
M.sub.1 of edge E.sub.1 to create a second domain 14b.
[0093] When first domain 14a and second domain 14b are tessellated
to cover the surface of golf ball 10, as shown in FIG. 7C, a
different number of total domains 14a and 14b will result depending
on the regular polyhedron chosen as the basis for control points
V.sub.1 and V.sub.2. The number of first and second domains 14a and
14b used to cover the surface of golf ball 10 is P.sub.F for first
domain 14a and P.sub.F*P.sub.E/2 for second domain 14b, as shown
below in Table 7.
TABLE-US-00007 TABLE 7 Domains resulting from use of specific
polyhedra when using the Vertex to Vertex Method Number Number of
of First Edges Number of Type of Number of Domains per Face, Second
Domains Polyhedron Faces, P.sub.F 14a P.sub.E 14b Tetrahedron 4 4 3
6 Cube 6 6 4 12 Octahedron 8 8 3 12 Dodecahedron 12 12 5 30
Icosahedron 20 20 3 30
[0094] While the six methods previously described each make use of
two control points, it is possible to create irregular domains
based on more than two control points. For example, three, or even
more, control points may be used. The use of additional control
points allows for potentially different shapes for irregular
domains. An exemplary method using a midpoint M, a center C and a
vertex V as three control points for creating one irregular domain
is described below.
The Midpoint to Center to Vertex Method
[0095] Referring to FIGS. 8A-8E, the midpoint to center to vertex
method yields one domain that tessellates to cover the surface of
golf ball 10. The domain is defined as follows: [0096] 1. A regular
polyhedron is chosen (FIGS. 8A-8E use an icosahedron); [0097] 2. A
single face 16 of the regular polyhedron is chosen, as in FIG. 8A;
[0098] 3. A midpoint M.sub.1 on edge E.sub.1 of face 16, Center C
of face 16 and a vertex V.sub.1 on edge E.sub.1 are connected with
a segment 18, and segment 18 and the portion of edge E.sub.1
between midpoint M.sub.1 and vertex V.sub.1 define a first element
22a, as shown in FIG. 8A; [0099] 4. A copy 20 of segment 18 is
rotated about center C, such that copy 20 connects center C with a
midpoint M.sub.2 on edge E.sub.2 adjacent to edge E.sub.1, and
connects center C with a vertex V.sub.2 at the intersection of
edges E.sub.1 and E.sub.2, and the portion of segment 18 between
midpoint M.sub.1 and center C, the portion of copy 20 between
vertex V.sub.2 and center C, and the portion of edge E.sub.1
between midpoint M.sub.1 and vertex V.sub.2 define a second element
22b, as shown in FIG. 8B; [0100] 5. First element 22a and second
element 22b are rotated about midpoint M.sub.1 of edge E.sub.1, as
seen in FIG. 8C, to define two domains 14, wherein a single domain
14 is bounded solely by portions of segment 18 and copy 20 and the
rotation 18' of segment 18, as seen in FIG. 8D. When domain 14 is
tessellated to cover the surface of golf ball 10, as shown in FIG.
8E, a different number of total domains 14 will result depending on
the regular polyhedron chosen as the basis for control points M, C,
and V. The number of domains 14 used to cover the surface of golf
ball 10 is equal to the number of faces P.sub.F of the polyhedron
chosen times the number of edges P.sub.E per face of the
polyhedron, as shown below in Table 8.
TABLE-US-00008 [0100] TABLE 8 Domains resulting from use of
specific polyhedra when using the Midpoint to Center to Vertex
Method Type of Number of Faces, Number of Number of Domains
Polyhedron P.sub.F Edges, P.sub.E 14 Tetrahedron 4 3 12 Cube 6 4 24
Octahedron 8 3 24 Dodecahedron 12 5 60 Icosahedron 20 3 60
[0101] While the methods described previously provide a framework
for the use of center C, vertex V, and midpoint M as the only
control points, other control points are useable. For example, a
control point may be any point P on an edge E of the chosen
polyhedron face. When this type of control point is used,
additional types of domains may be generated, though the mechanism
for creating the irregular domain(s) may be different. An exemplary
method, using a center C and a point P on an edge, for creating one
such irregular domain is described below.
The Center to Edge Method
[0102] Referring to FIGS. 9A-9E, the center to edge method yields
one domain that tessellates to cover the surface of golf ball 10.
The domain is defined as follows: [0103] 1. A regular polyhedron is
chosen (FIGS. 9A-9E use an icosahedron); [0104] 2. A single face 16
of the regular polyhedron is chosen, as shown in FIG. 9A; [0105] 3.
Center C of face 16, and a point P.sub.1 on edge E.sub.1 are
connected with a segment 18; [0106] 4. A copy 20 of segment 18 is
rotated about center C, such that copy 20 connects center C with a
point P.sub.2 on edge E.sub.2 adjacent to edge E.sub.1, where point
P.sub.2 is positioned identically relative to edge E.sub.2 as point
P.sub.1 is positioned relative to edge E.sub.1, such that the two
segments 18 and 20 and the portions of edges E.sub.1 and E.sub.2
between points P.sub.1 and P.sub.2, respectively, and a vertex V,
which connects edges E.sub.1 and E.sub.2, define an element 22, as
shown best in FIG. 9B; and [0107] 5. Element 22 is rotated about
midpoint M.sub.1 of edge E.sub.1 or midpoint M.sub.2 of edge
E.sub.2, whichever is located within element 22, as seen in FIGS.
9B-9C, to create a domain 14, as seen in FIG. 9D.
[0108] When domain 14 is tessellated to cover the surface of golf
ball 10, as shown in FIG. 9E, a different number of total domains
14 will result depending on the regular polyhedron chosen as the
basis for control points C and P.sub.1. The number of domains 14
used to cover the surface of golf ball 10 is equal to the number of
faces P.sub.F of the polyhedron chosen times the number of edges
P.sub.E per face of the polyhedron divided by 2, as shown below in
Table 9.
TABLE-US-00009 TABLE 9 Domains resulting from use of specific
polyhedra when using the Center to Edge Method Type of Number of
Faces, Number of Number of Domains Polyhedron P.sub.F Edges,
P.sub.E 14 Tetrahedron 4 3 6 Cube 6 4 12 Octahedron 8 3 12
Dodecahedron 12 5 30 Icosahedron 20 3 30
[0109] Though each of the above described methods has been
explained with reference to regular polyhedrons, they may also be
used with certain non-regular polyhedrons, such as Archimedean
Solids, Catalan Solids, or others. The methods used to derive the
irregular domains will generally require some modification in order
to account for the non-regular face shapes of the non-regular
solids. An exemplary method for use with a Catalan Solid,
specifically a rhombic dodecahedron, is described below.
A Vertex to Vertex Method for a Rhombic Dodecahedron
[0110] Referring to FIGS. 10A-10E, a vertex to vertex method based
on a rhombic dodecahedron yields one domain that tessellates to
cover the surface of golf ball 10. The domain is defined as
follows: [0111] 1. A single face 16 of the rhombic dodecahedron, as
in FIG. 10A; [0112] 2. A first vertex V.sub.1 face 16, and a second
vertex V.sub.2 adjacent to first vertex V.sub.1 are connected with
a segment 18, as shown in FIG. 10B; [0113] 3. A first copy 20 of
segment 18 is rotated about vertex V.sub.2, such that it connects
vertex V.sub.2 to vertex V3 of face 16, a second copy 24 of segment
18 is rotated about center C, such that it connects vertex V.sub.3
and vertex V.sub.4 of face 16, and a third copy 26 of segment 18 is
rotated about vertex V.sub.1 such that it connects vertex V.sub.1
to vertex V.sub.4, all as shown in FIG. 10C, to form a domain 14,
as shown in FIG. 10D;
[0114] When domain 14 is tessellated to cover the surface of golf
ball 10, as shown in FIG. 10E, twelve domains will be used to cover
the surface of golf ball 10, one for each face of the rhombic
dodecahedron.
[0115] One additional embodiment to the above methods of spherical
tiling extends these methods to include sub-patterns of dimples
within the irregular domain(s) dimple packing 101. The method
includes choosing a spherical tiling base geometry and tiling
method, defining a sub-pattern of nearest neighbor dimples 102
within the irregular domain(s), and packing dimples within the
remaining un-dimpled region. Until the present invention, arranging
dimples on the surface of a golf ball has previously been done
solely working within a segment of the desired dimple pattern
geometry. The present invention is novel because a sub-pattern of
nearest neighbor dimples is first defined on the blank spherical
segment of the irregular domain(s). The remaining un-dimpled
regions are then packed around the initial defining sub-pattern of
nearest neighbor dimples. This can yield both aesthetic and
aerodynamic performance advantages.
[0116] The process is started with a spherical section, which is
circumscribed using the vertices of a regular polyhedron (as
previously shown in Table 1), and it should be understood that any
of the polyhedron types listed in Table 1 can be used. Illustrative
examples, shown here consist of a tetrahedron and an icosahedron.
Using the mid-point to mid-point tiling method and a tetrahedral
base, the irregular domains 101 illustrated in FIG. 11A and FIG.
11B are created.
[0117] The dimple sub-pattern can be defined as nearest neighbor
dimples on or within edges of one or more of the irregular domains.
The sub-pattern 102 in the current example is defined within both
irregular domains. Once the sub-pattern is defined, the remaining
unpacked spherical region is packed around the initial sub-pattern
of dimples as illustrated in FIG. 11C and FIG. 11D, wherein the
sub-pattern dimples 102 are denoted by the gray color. Once the
sub-pattern is defined and the remaining unpacked spherical region
around the initial sub-pattern is packed with dimples, the dimpled
spherical region may then be tessellated, as seen in the golf ball
100 shown in FIG. 11E. The sub-pattern dimples may be packed within
any number of the irregular domains.
[0118] Although the dimple sub-pattern is defined by nearest
neighbor dimples, each instance of the sub-pattern may or may not
be continuously connected by sub-pattern nearest neighbor dimples
around the ball surface after the domains are tessellated.
[0119] The method of determining nearest neighbor dimples is
illustrated in FIG. 11C, wherein two tangency lines T.sub.L are
drawn from the center of a first dimple to a potential nearest
neighbor dimple. Additionally, a line segment L.sub.S is drawn
connecting the center of the first dimple to the center of the
potential nearest neighbor dimple. If there is no line segment that
is intersected by another dimple, or portion of a dimple, then
those dimples are considered to be nearest neighbor dimples.
[0120] Additional examples use an icosahedron as the base pattern
and the midpoint to midpoint method to create two irregular domains
101 in FIG. 12A. A sub-pattern of dimples 102 are defined within a
single domain in, FIG. 12B and FIG. 13A, and additional dimples are
defined within the unpacked region of the irregular domains. The
irregular domains are tessellated to create a golf ball 100 with a
sub-pattern that is connected throughout the tessellation (FIG.
13B) and a golf ball 100 with a sub-pattern that is disconnected
throughout the tessellation (FIG. 12C).
[0121] Visual distinction may be achieved between the sub-pattern
dimples and the remaining dimples, by exhibiting the sub-pattern
dimples with one or more of the following characteristics:
different perimeter shape; dimple profile; color; texture; grooves;
or brambles. Also, the dimples packing the remaining spherical
region, which is defined by the existing dimple sub-pattern, may
have different perimeter shape, dimple profile, color, or
texture.
[0122] Dimples with circular perimeters should have diameters that
fall within the range of 0.100 to 0.220 inches. Dimples with
non-circular perimeters should be circumscribed by a circle with a
diameter that falls within the range of 0.120 to 0.270 inches.
[0123] Each irregular domain preferably contains between 10 and 115
dimples, and the nearest initial sub-pattern of nearest neighbor
dimples preferably contains between 2 and 80 dimples.
[0124] Preferred high performance golf balls will usually have a
staggered parting line that passes through the section and normally
intersects two edges of the section.
[0125] The surface coverage of the dimples on the golf ball should
be between 70 to 90%, while the surface coverage of the nearest
neighbor sub-pattern of dimples should be between 10% and 60%.
[0126] Dimples may exhibit a contrasting color(s); the perimeter
shape may be circular, polygonal, or elliptical. Dimple profiles
can include, but are not limited to, spherical, Gabriel's horn,
catenary, conical, Witch of Agnesi, chalice, elliptical,
superposition of two curves, or any other spherically weighted
profile.
[0127] There are no limitations on how the dimples are packed.
There are likewise no limitations to the dimple shapes or profiles
selected to pack the domains. Though the present invention includes
substantially circular dimples in one embodiment, dimples or
protrusions (brambles) having any desired characteristics and/or
properties may be used. For example, in one embodiment the dimples
may have a variety of shapes and sizes including different depths
and widths. In particular, the dimples may be concave hemispheres,
or they may be triangular, square, hexagonal, catenary, polygonal
or any other shape known to those skilled in the art. They may also
have straight, curved, or sloped edges or sides. Any type of dimple
or protrusion (bramble) known to those skilled in the art may be
used with the present invention. Alternatively, the tessellation
can create a pattern that covers more than about 60%, preferably
more than about 70% and preferably more than about 80% of the golf
ball surface.
[0128] In other embodiments, the domains may not be packed with
dimples, and the borders of the irregular domains may instead
comprise ridges or channels. In golf balls having this type of
irregular domain, the one or more domains or sets of domains
preferably overlap to increase surface coverage of the
channels.
[0129] When the domain(s) is patterned onto the surface of a golf
ball, the arrangement of the domains dictated by their shape and
the underlying polyhedron ensures that the resulting golf ball has
a high order of symmetry, equaling or exceeding 12. The order of
symmetry of a golf ball produced using the method of the current
invention will depend on the regular or non-regular polygon on
which the irregular domain is based. The order and type of symmetry
for golf balls produced based on the five regular polyhedra are
listed below in Table 10.
TABLE-US-00010 TABLE 10 Symmetry of Golf Ball of the Present
Invention as a Function of Polyhedron Type of Polyhedron Type of
Symmetry Symmetrical Order Tetrahedron Chiral Tetrahedral Symmetry
12 Cube Chiral Octahedral Symmetry 24 Octahedron Chiral Octahedral
Symmetry 24 Dodecahedron Chiral Icosahedral Symmetry 60 Icosahedron
Chiral Icosahedral Symmetry 60
[0130] The benefits of these high orders of symmetry include more
even dimple distribution, the potential for higher packing
efficiency, and improved means to mask the ball parting line.
Further, dimple patterns generated in this manner may have improved
flight stability and symmetry as a result of the higher degrees of
symmetry.
[0131] In other embodiments, the irregular domains do not
completely cover the surface of the ball, and there are open spaces
between domains that may or may not be filled with dimples. This
allows dissymmetry to be incorporated into the ball. While the
preferred embodiments of the present invention have been described
above, it should be understood that they have been presented by way
of example only, and not of limitation. It will be apparent to
persons skilled in the relevant art that various changes in form
and detail can be made therein without departing from the spirit
and scope of the invention. For example, while the preferred
polyhedral shapes have been provided above, other polyhedral shapes
could also be used. Thus the present invention should not be
limited by the above-described exemplary embodiments, but should be
defined only in accordance with the following claims and their
equivalents.
* * * * *