U.S. patent application number 13/765986 was filed with the patent office on 2013-06-13 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 Michael R. Madson, Nicholas M. Nardacci.
Application Number | 20130150186 13/765986 |
Document ID | / |
Family ID | 42132119 |
Filed Date | 2013-06-13 |
United States Patent
Application |
20130150186 |
Kind Code |
A1 |
Nardacci; Nicholas M. ; et
al. |
June 13, 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. 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. The control points
include the center of a polyhedral face, a vertex of the
polyhedron, a midpoint or other point on an edge of the polyhedron
and others. The method ensures that the symmetry of the underlying
polyhedron is preserved while eliminating great circles due to
parting lines.
Inventors: |
Nardacci; Nicholas M.;
(Bristol, RI) ; Madson; Michael R.; (Pawtucket,
RI) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Acushnet Company; |
Fairthaven |
MA |
US |
|
|
Assignee: |
Acushnet Company
Fairhaven
MA
|
Family ID: |
42132119 |
Appl. No.: |
13/765986 |
Filed: |
February 13, 2013 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
13251590 |
Oct 3, 2011 |
|
|
|
13765986 |
|
|
|
|
12262464 |
Oct 31, 2008 |
8029388 |
|
|
13251590 |
|
|
|
|
Current U.S.
Class: |
473/378 |
Current CPC
Class: |
A63B 37/0007 20130101;
A63B 45/00 20130101; A63B 37/0006 20130101; A63B 37/0004
20130101 |
Class at
Publication: |
473/378 |
International
Class: |
A63B 37/00 20060101
A63B037/00 |
Claims
1. A golf ball having dimples based on a polyhedron pattern,
wherein the dimples are arranged in irregular domains comprised of
non-linear segments, wherein the irregular domains are tessellated
over a surface of the golf ball and are defined by a non-linear
line from a first vertex of a face of the polyhedron to a second
vertex.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a Divisional of co-pending U.S. patent
application Ser. No. 13/251,590, filed Oct. 3, 2011, which is a
Divisional of co-pending 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.
[0006] 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.
[0007] 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 Archimedian 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.
[0008] 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.
[0009] 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.
[0010] 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.
[0011] 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.
[0012] 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
[0013] 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. The
control points include the center of a polyhedral face, a vertex of
the polyhedron, a midpoint or other point on an edge of the
polyhedron and others. The method ensures that the symmetry of the
underlying polyhedron is preserved while minimizing great circles
due to parting lines from the molding process.
[0014] The present invention provides methods for generating an
irregular domain based on two or more control points. These methods
include connecting the control points with a non-linear sketch
line, patterning the sketch line in a first manner to create a
first irregular domain, and optionally patterning the sketch line
in a second manner to create a second irregular domain.
[0015] The present invention also provides methods for generating
one or more irregular domains based on each set of control points.
The center to vertex method, the center to midpoint method, the
vertex to midpoint method, the center to edge method, and the
midpoint to center to vertex method each provide a single irregular
domain that can be tessellated to cover a golf ball. The center to
center method, the midpoint to midpoint method, and the vertex to
vertex method each provide two irregular domains that can be
tessellated to cover a golf ball. In each case, the irregular
domains cover the surface of the golf ball in a uniform
pattern.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] 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:
[0017] FIG. 1A illustrates a golf ball having dimples arranged by a
method of the present invention; FIG. 1B illustrates a polyhedron
face; FIG. 1C illustrates an element of the present invention in
the polyhedron face of FIG. 1B; FIG. 1D illustrates a domain formed
by a methods of the present invention packed with dimples and
formed from two elements of FIG. 1C;
[0018] FIG. 2 illustrates a single face of a polyhedron having
control points thereon;
[0019] FIG. 3A illustrates a polyhedron face; FIG. 3B illustrates
an element of the present invention packed with dimples; FIG. 3C
illustrates a domain of the present invention packed with dimples
formed from elements of FIG. 3B; FIG. 3D illustrates a golf ball
formed by a method of the present invention formed of the domain of
FIG. 3C;
[0020] FIG. 4A illustrates two polyhedron faces; FIG. 4B
illustrates a first domain of the present invention in the two
polyhedron faces of FIG. 4A; FIG. 4C illustrates a first domain and
a second domain of the present invention in three polyhedron faces;
FIG. 4D illustrates a golf ball formed by a method of the present
invention formed of the domains of FIG. 4C;
[0021] FIG. 5A illustrates a polyhedron face; FIG. 5B illustrates a
first domain of the present invention in a polyhedron face; FIG. 5C
illustrates a first domain and a second domain of the present
invention in three polyhedron faces; FIG. 5D illustrates a golf
ball formed using a method of the present invention formed of the
domains of FIG. 5C;
[0022] FIG. 6A illustrates a polyhedron face; FIG. 6B illustrates a
portion of a domain of the present invention in the polyhedron face
of FIG. 6A; FIG. 6C illustrates a domain formed by the methods of
the present invention; FIG. 6D illustrates a golf ball formed using
the methods of the present invention formed of domains of FIG.
6C;
[0023] FIG. 7A illustrates a polyhedron face; FIG. 7B illustrates a
domain of the present invention in the polyhedron face of FIG. 7A;
FIG. 7C illustrates a golf ball formed by a method of the present
invention;
[0024] FIG. 8A illustrates a first element of the present invention
in a polyhedron face; FIG. 8B illustrates a first and a second
element of the present invention in the polyhedron face of FIG. 8A;
FIG. 8C illustrates two domains of the present invention composed
of first and second elements of FIG. 8B; FIG. 8D illustrates a
single domain of the present invention based on the two domains of
FIG. 8C; FIG. 8E illustrates a golf ball formed using a method of
the present invention formed of the domains of FIG. 8D;
[0025] FIG. 9A illustrates a polyhedron face; FIG. 9B illustrates
an element of the present invention in the polyhedron face of FIG.
9A; FIG. 9C illustrates two elements of FIG. 9B combining to form a
domain of the present invention; FIG. 9D illustrates a domain
formed by the methods of the present invention based on the
elements of FIG. 9C; FIG. 9E illustrates a golf ball formed using a
method of the present invention formed of domains of FIG. 9D;
[0026] 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.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0027] 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.
[0028] 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 + 5)/2
[0029] 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:
[0030] 1. Center to midpoint (C.fwdarw.M);
[0031] 2. Center to center (C.fwdarw.C);
[0032] 3. Center to vertex (C.fwdarw.V);
[0033] 4. Midpoint to midpoint (M.fwdarw.M);
[0034] 5. Midpoint to Vertex (M.fwdarw.V); and
[0035] 6. Vertex to Vertex (V.fwdarw.V).
[0036] 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 arcuate 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.
[0037] 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
[0038] Referring again to FIGS. 1A-1D, the center to vertex method
yields one domain that tessellates to cover the surface of golf
ball 10. The domain is defined as follows: [0039] 1. A regular
polyhedron is chosen (FIGS. 1A-1D use an icosahedron); [0040] 2. A
single face 16 of the regular polyhedron is chosen, as shown in
FIG. 1B; [0041] 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; [0042] 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 [0043]
5. Element 22 is rotated about midpoint M of edge E to create a
domain 14, as shown best in FIG. 1D.
[0044] 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.
Domains Resulting from Use of Specific Polyhedra When Using the
Center to Vertex Method
TABLE-US-00002 Number Type of of Faces, Number of Edges, Number of
Domains Polyhedron P.sub.F 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
[0045] 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:
[0046] 1. A regular polyhedron is chosen (FIGS. 3A-3D use a
dodecahedron); [0047] 2. A single face 16 of the regular polyhedron
is chosen, as shown in FIG. 3A; [0048] 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; [0049] 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 [0050] 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.
[0051] 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
[0052] 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: [0053] 1. A regular
polyhedron is chosen (FIGS. 4A-4D use a dodecahedron); [0054] 2.
Two adjacent faces 16a and 16b of the regular polyhedron are
chosen, as shown in FIG. 4A; [0055] 3. Center C.sub.1 of face 16a,
and center C.sub.2 of face 16b are connected with a segment 18;
[0056] 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
[0057] 5. Segment 18 is rotated equally about vertex V to define a
second domain 14b, as shown in FIG. 4C.
[0058] 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 Number of Second Type of Vertices,
Domains of Faces, Edges, Domains Polyhedron P.sub.V 14a P.sub.F
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
[0059] 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: [0060] 1. A regular
polyhedron is chosen (FIGS. 5A-5D use a dodecahedron); [0061] 2. A
single face 16 of the regular polyhedron is chosen, as shown in
FIG. 5A; [0062] 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; [0063] 4.
Segment 18 is patterned around center C of face 16 to form a first
domain 14a, as shown in FIG. 5B; [0064] 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 [0065] 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.
[0066] 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 of Number
of Second Type of Number of Number of First Vertices, 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
[0067] 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: [0068] 1. A regular
polyhedron is chosen (FIGS. 6A-6D use a dodecahedron); [0069] 2. A
single face 16 of the regular polyhedron is chosen, as shown in
FIG. 6A; [0070] 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; [0071] 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
[0072] 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.
[0073] 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
[0074] 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: [0075] 1. A regular polyhedron
is chosen (FIGS. 7A-7C use an icosahedron); [0076] 2. A single face
16 of the regular polyhedron is chosen, as shown in FIG. 7A; [0077]
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;
[0078] 4. Segment 18 is patterned around center C of face 16 to
form a first domain 14a, as shown in FIG. 7B; [0079] 5. Segment 18,
along with edge E.sub.1 between vertices V.sub.1 and V.sub.2,
defines an element 22; and [0080] 6. Element 22 is rotated around
midpoint M.sub.1 of edge E.sub.1 to create a second domain 14b.
[0081] 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 of Number
Number of Second Type of Number of of First Edges per Face, Domains
Polyhedron Faces, P.sub.F Domains 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
[0082] 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
[0083] 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: [0084] 1. A regular
polyhedron is chosen (FIGS. 8A-8E use an icosahedron); [0085] 2. A
single face 16 of the regular polyhedron is chosen, as shown in
FIG. 8A; [0086] 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; [0087] 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; 5. First element 22a and second element
22b are rotated about midpoint M.sub.1 of edge E.sub.1, as seen in
FIGS. 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 [0087] TABLE 8 Domains Resulting From Use of
Specific Polyhedra When Using the Midpoint to Center to Vertex
Method Type of Number of Number of Edges, Number of Domains
Polyhedron Faces, P.sub.F P.sub.E 14 Tetrahedron 4 3 12 Cube 6 4 24
Octahedron 8 3 24 Dodecahedron 12 5 60 Icosahedron 20 3 60
[0088] 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 usable. 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
[0089] 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: [0090] 1. A regular polyhedron is
chosen (FIGS. 9A-9E use an icosahedron); [0091] 2. A single face 16
of the regular polyhedron is chosen, as shown in FIG. 9A; [0092] 3.
Center C of face 16, and a point P.sub.1 on edge E.sub.1 are
connected with a segment 18, [0093] 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 [0094] 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.
[0095] 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
Number of Edges, Number of Domains Polyhedron Faces, P.sub.F
P.sub.E 14 Tetrahedron 4 3 6 Cube 6 4 12 Octahedron 8 3 12
Dodecahedron 12 5 30 Icosahedron 20 3 30
[0096] 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
[0097] 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: [0098] 1. A single face 16 of the rhombic dodecahedron is
chosen, as shown in FIG. 10A; [0099] 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; [0100] 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;
[0101] 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.
[0102] After the irregular domain(s) is created using any of the
above methods, the domain(s) may be packed with dimples in order to
be usable in creating golf ball 10. 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. To summarize, any type of dimple or protrusion
(bramble) known to those skilled in the art may be used with the
present invention. The dimples may all fit within each domain, as
seen in FIGS. 1A and 1D, or dimples may be shared between one or
more domains, as seen in FIGS. 3C-3D, so long as the dimple
arrangement on each independent domain remains consistent across
all copies of that domain on the surface of a particular golf ball.
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 without using
dimples.
[0103] 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.
Alternatively, the borders of the irregular domains may comprise
ridges or channels and the domains are packed with dimples.
[0104] 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
[0105] These high orders of symmetry have several benefits,
including 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.
[0106] 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.
[0107] 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.
* * * * *