US20130065708A1

US20130065708A1 - Dimple patterns for golf balls

Info

Publication number: US20130065708A1
Application number: US13/672,910
Authority: US
Inventors: Chris Hixenbaugh; Nicholas M. Nardacci; Michael R. Madson
Original assignee: Acushnet Co
Current assignee: Acushnet Co
Priority date: 2008-10-31
Filing date: 2012-11-09
Publication date: 2013-03-14

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.

Description

CROSS REFERENCE TO RELATED APPLICATIONS

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

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

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.
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.
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.
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.
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.
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.
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.
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

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.
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.
The method of determining nearest neighbor dimples is illustrated in FIG. 11C, wherein two tangency lines T_Lare drawn from the center of a first dimple to a potential nearest neighbor dimple. Additionally, a line segment L_Sis 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.
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.
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.
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

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:

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;

FIG. 2 illustrates a single face of a polyhedron having control points thereon;

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;

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;

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;

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;

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;

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;

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;

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;

FIG. 11A utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

FIG. 11B utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

FIG. 11C depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains;

FIG. 11D depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of another of the irregular domains;

FIG. 11E shows the domains of FIG. 11C and FIG. 11D tessellated around a golf ball sphere;

FIG. 12A utilizes the mid-point to mid-point tiling method to illustrate irregular domains of the present invention;

FIG. 12B depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains;

FIG. 12C shows the domains of FIG. 12B tessellated around a golf ball sphere;

FIG. 13A depicts a dimple sub-pattern wherein they are shown as nearest neighbor dimples within edges of one of the irregular domains; and

FIG. 13B shows the domains of FIG. 13A tessellated around a golf ball sphere.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

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.
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.
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 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/φ, ±φ); (±1/φ, ±φ, 0); (±φ, 0, ±1/φ)*
Icosahedron	(0, ±1, ±φ); (±1, ±φ, 0); (±φ, 0, ±1)*

*φ = (1 + {square root over (5)})/2

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:
1. Center to midpoint (C→M);
2. Center to center (C→C);
3. Center to vertex (C→V);
4. Midpoint to midpoint (M→M);
5. Midpoint to Vertex (M→V); and
6. Vertex to Vertex (V→V).
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.
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

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:

- 1. A regular polyhedron is chosen (FIGS. 1A-1D use an icosahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 1B;
- 3. Center C of face 16, and a first vertex V₁of face 16 are connected with any non-linear sketch line, hereinafter referred to as a segment 18;
- 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with vertex V₂adjacent to vertex V₁. The two segments 18 and 20 and the edge E connecting vertices V₁and V₂define an element 22, as shown best in FIG. 1C; and
- 5. Element 22 is rotated about midpoint M of edge E to create a domain 14, as shown best in FIG. 1D.

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 V₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P_Fof the polyhedron chosen times the number of edges P_Eper face of the polyhedron divided by 2, as shown below in Table 2.

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_F	Edges, P _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

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:

- 1. A regular polyhedron is chosen (FIGS. 3A-3D use a dodecahedron);
- 2. A single face 16 of the regular polyhedron is chosen, shown in FIG. 3A;
- 3. Center C of face 16, and midpoint M₁of a first edge E₁of face 16 are connected with a segment 18;
- 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M₂of a second edge E₂adjacent to first edge E₁. The two segments 16 and 18 and the portions of edge E₁and edge E₂between midpoints M₁and M₂define an element 22; and
- 5. Element 22 is patterned about vertex V of face 16 which is contained in element 22 and connects edges E₁and E₂to create a domain 14.

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 M₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of vertices P_Vof the chosen polyhedron, as shown below in Table 3.

TABLE 3

Domains resulting from use of specific Polyhedra when using the
Center to Midpoint Method

Type of Polyhedron	Number of Vertices, P_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

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:

- 1. A regular polyhedron is chosen (FIGS. 4A-4D use a dodecahedron);
- 2. Two adjacent faces 16 a and 16 b of the regular polyhedron are chosen, as shown in FIG. 4A;
- 3. Center C₁of face 16 a, and center C₂of face 16 b are connected with a segment 18;
- 4. A copy 20 of segment 18 is rotated 180 degrees about the midpoint M between centers C₁and C₂, such that copy 20 also connects center C₁with center C₂, as shown in FIG. 4B. The two segments 16 and 18 define a first domain 14 a; and
- 5. Segment 18 is rotated equally about vertex V to define a second domain 14 b, as shown in FIG. 4C.

When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIG. 4D, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points C₁and C₂. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is P_F*P_E/2 for first domain 14 a and P_Vfor second domain 14 b, as shown below in Table 4.

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
_V	14a	P_F	Edges, P _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

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:

- 1. A regular polyhedron is chosen (FIGS. 5A-5D use a dodecahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 5A;
- 3. The midpoint M₁of a first edge E₁of face 16, and the midpoint M₂of a second edge E₂adjacent to first edge E₁are connected with a segment 18;
- 4. Segment 18 is patterned around center C of face 16 to form a first domain 14 a, as shown in FIG. 5B;
- 5. Segment 18, along with the portions of first edge E₁and second edge E₂between midpoints M₁and M₂, define an element 22; and
- 6. Element 22 is patterned about vertex V which is contained in element 22 and connects edges E₁and E₂to create a second domain 14 b, as shown in FIG. 5C.

When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIG. 5D, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points M₁and M₂. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is P_Ffor first domain 14 a and P_Vfor second domain 14 b, as shown below in Table 5.

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_F	Domains 14a	P	_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

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:

- 1. A regular polyhedron is chosen (FIGS. 6A-6D use a dodecahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 6A;
- 3. A midpoint M₁of edge E₁of face 16 and a vertex V₁on edge E₁are connected with a segment 18;
- 4. Copies 20 of segment 18 is patterned about center C of face 16, one for each midpoint M₂and vertex V₂of face 16, to define a portion of domain 14, as shown in FIG. 6B; and
- 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.

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 M₁and V₁. The number of domains 14 used to cover the surface of golf ball 10 is P_F, as shown in Table 6.

TABLE 6

Domains resulting from use of specific polyhedra when using the
Midpoint to Vertex Method

Type of Polyhedron	Number of Faces, P_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

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:

- 1. A regular polyhedron is chosen (FIGS. 7A-7C use an icosahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 7A;
- 3. A first vertex V₁face 16, and a second vertex V₂adjacent to first vertex V₁are connected with a segment 18;
- 4. Segment 18 is patterned around center C of face 16 to form a first domain 14 a, as shown in FIG. 7B;
- 5. Segment 18, along with edge E₁between vertices V₁and V₂, defines an element 22; and
- 6. Element 22 is rotated around midpoint M₁of edge E₁to create a second domain 14 b.

When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIG. 7C, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points V₁and V₂. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is P_Ffor first domain 14 a and P_F*P_E/2 for second domain 14 b, as shown below in Table 7.

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 _F	14a	P_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

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

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:

- 1. A regular polyhedron is chosen (FIGS. 8A-8E use an icosahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as in FIG. 8A;
- 3. A midpoint M₁on edge E₁of face 16, Center C of face 16 and a vertex V₁on edge E₁are connected with a segment 18, and segment 18 and the portion of edge E₁between midpoint M₁and vertex V₁define a first element 22 a, as shown in FIG. 8A;
- 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M₂on edge E₂adjacent to edge E₁, and connects center C with a vertex V₂at the intersection of edges E₁and E₂, and the portion of segment 18 between midpoint M₁and center C, the portion of copy 20 between vertex V₂and center C, and the portion of edge E₁between midpoint M₁and vertex V₂define a second element 22 b, as shown in FIG. 8B;
- 5. First element 22 a and second element 22 b are rotated about midpoint M₁of edge E₁, 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_Fof the polyhedron chosen times the number of edges P_Eper face of the polyhedron, as shown below in Table 8.

TABLE 8

Domains resulting from use of specific polyhedra when using the
Midpoint to Center to Vertex Method

Tetrahedron	4	3	12
Cube	6	4	24
Octahedron	8	3	24
Dodecahedron	12	5	60
Icosahedron	20	3	60

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

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:

- 1. A regular polyhedron is chosen (FIGS. 9A-9E use an icosahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 9A;
- 3. Center C of face 16, and a point P₁on edge E₁are connected with a segment 18;
- 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a point P₂on edge E₂adjacent to edge E₁, where point P₂is positioned identically relative to edge E₂as point P₁is positioned relative to edge E₁, such that the two segments 18 and 20 and the portions of edges E₁and E₂between points P₁and P₂, respectively, and a vertex V, which connects edges E₁and E₂, define an element 22, as shown best in FIG. 9B; and
- 5. Element 22 is rotated about midpoint M₁of edge E₁or midpoint M₂of edge E₂, whichever is located within element 22, as seen in FIGS. 9B-9C, to create a domain 14, as seen in FIG. 9D.

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 P₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P_Fof the polyhedron chosen times the number of edges P_Eper face of the polyhedron divided by 2, as shown below in Table 9.

TABLE 9

Domains resulting from use of specific polyhedra when using the
Center to Edge Method

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

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:

- 1. A single face 16 of the rhombic dodecahedron, as in FIG. 10A;
- 2. A first vertex V₁face 16, and a second vertex V₂adjacent to first vertex V₁are connected with a segment 18, as shown in FIG. 10B;
- 3. A first copy 20 of segment 18 is rotated about vertex V₂, such that it connects vertex V₂to vertex V3 of face 16, a second copy 24 of segment 18 is rotated about center C, such that it connects vertex V₃and vertex V₄of face 16, and a third copy 26 of segment 18 is rotated about vertex V₁such that it connects vertex V₁to vertex V₄, all as shown in FIG. 10C, to form a domain 14, as shown in FIG. 10D;

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.
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.
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.
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.
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.
The method of determining nearest neighbor dimples is illustrated in FIG. 11C, wherein two tangency lines T_Lare drawn from the center of a first dimple to a potential nearest neighbor dimple. Additionally, a line segment L_Sis 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.
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).
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.
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.
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.
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.
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%.
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.
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.
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.
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 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

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.
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.

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.