Patent ID: 12208313

DETAILED DESCRIPTION

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. The method includes choosing control points of a polyhedron, connecting the control points with a non-straight sketch line, patterning the sketch line in a first manner to generate an irregular domain, optionally patterning the sketch line in a second manner to create an additional irregular domain, packing the irregular domain(s) with dimples, and tessellating the irregular domain(s) to cover the surface of the golf ball in a uniform pattern. 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 or eliminating great circles due to parting lines from the molding process.

In a particular embodiment, illustrated inFIG.1A, the present invention comprises a golf ball10comprising dimples12. Dimples12are arranged by packing irregular domains14with dimples, as seen best inFIG.1D. Irregular domains14are created in such a way that, when tessellated on the surface of golf ball10, they impart greater orders of symmetry to the surface than prior art balls. The irregular shape of domains14additionally 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.

For purposes of the present invention, the term “irregular domains” refers to domains wherein at least one, and preferably all, of the segments defining the borders of the domain is not a straight line.

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 1Vertices of Circumscribed Sphere based on CorrespondingPolyhedron VerticesType ofPolyhedronVerticesTetrahedron(+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 + √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.2shows an exemplary face16of 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 face16. 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: Center to midpoint (C→M); Center to center (C→C); Center to vertex (C→V); Midpoint to midpoint (M→M); Midpoint to Vertex (M→V); and 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 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.

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 toFIGS.1A-1D, the center to vertex method yields one domain that tessellates to cover the surface of golf ball10. The domain is defined as follows:1. A regular polyhedron is chosen (FIGS.1A-1Duse an icosahedron);2. A single face16of the regular polyhedron is chosen, as shown inFIG.1B;3. Center C of face16, and a first vertex V1of face16are connected with any non-linear sketch line, hereinafter referred to as a segment18;4. A copy20of segment18is rotated about center C, such that copy20connects center C with vertex V2adjacent to vertex V1. The two segments18and20and the edge E connecting vertices V1and V2define an element22, as shown best inFIG.1C; and5. Element22is rotated about midpoint M of edge E to create a domain14, as shown best inFIG.1D.

When domain14is tessellated to cover the surface of golf ball10, as shown inFIG.1A, a different number of total domains14will result depending on the regular polyhedron chosen as the basis for control points C and V1. The number of domains14used to cover the surface of golf ball10is equal to the number of faces PFof the polyhedron chosen times the number of edges PEper face of the polyhedron divided by 2, as shown below in Table 2.

TABLE 2Domains Resulting From Use of Specific PolyhedraWhen Using the Center to Vertex MethodType ofNumber ofNumber ofNumber ofPolyhedronFaces, PFEdges, PEDomains 14Tetrahedron436Cube6412Octahedron8312Dodecahedron12530Icosahedron20330
The Center to Midpoint Method

Referring toFIGS.3A-3D, the center to midpoint method yields a single irregular domain that can be tessellated to cover the surface of golf ball10. The domain is defined as follows:1. A regular polyhedron is chosen (FIGS.3A-3Duse a dodecahedron);2. A single face16of the regular polyhedron is chosen, as shown inFIG.3A;3. Center C of face16, and midpoint M1of a first edge E1of face16are connected with a segment18;4. A copy20of segment18is rotated about center C, such that copy20connects center C with a midpoint M2of a second edge E2adjacent to first edge E1. The two segments16and18and the portions of edge E1and edge E2between midpoints M1and M2define an element22; and5. Element22is patterned about vertex V of face16which is contained in element22and connects edges E1and E2to create a domain14.

When domain14is tessellated around a golf ball10to cover the surface of golf ball10, as shown inFIG.3D, a different number of total domains14will result depending on the regular polyhedron chosen as the basis for control points C and M1. The number of domains14used to cover the surface of golf ball10is equal to the number of vertices PVof the chosen polyhedron, as shown below in Table 3.

TABLE 3Domains Resulting From Use of Specific PolyhedraWhen Using the Center to Midpoint MethodType of PolyhedronNumber of Vertices, PVNumber of Domains 14Tetrahedron44Cube88Octahedron66Dodecahedron2020Icosahedron1212
The Center to Center Method

Referring toFIGS.4A-4D, the center to center method yields two domains that can be tessellated to cover the surface of golf ball10. The domains are defined as follows:1. A regular polyhedron is chosen (FIGS.4A-4Duse a dodecahedron);2. Two adjacent faces16aand16bof the regular polyhedron are chosen, as shown inFIG.4A;3. Center C1of face16a, and center C2of face16bare connected with a segment18;4. A copy20of segment18is rotated 180 degrees about the midpoint M between centers C1and C2, such that copy20also connects center C1with center C2, as shown inFIG.4B. The two segments16and18define a first domain14a; and5. Segment18is rotated equally about vertex V to define a second domain14b, as shown inFIG.4C.

When first domain14aand second domain14bare tessellated to cover the surface of golf ball10, as shown inFIG.4D, a different number of total domains14aand14bwill result depending on the regular polyhedron chosen as the basis for control points C1and C2. The number of first and second domains14aand14bused to cover the surface of golf ball10is PF*PE/2 for first domain14aand PVfor second domain14b, as shown below in Table 4.

TABLE 4Domains Resulting From Use of Specific Polyhedra WhenUsing the Center to Center MethodNumberNumberNumberNumberNumber ofofof FirstofofSecondType ofVertices,DomainsFaces,Edges,DomainsPolyhedronPV14aPFPE14bTetrahedron46434Cube812648Octahedron69836Dodecahedron203012520Icosahedron121820312
The Midpoint to Midpoint Method

Referring toFIGS.5A-5D,11A-11AI,14A-14I,15A-15C,16A-16C, and17A-17C, the midpoint to midpoint method yields two domains that tessellate to cover the surface of golf ball10. The domains are defined as follows:1. A regular polyhedron is chosen (FIGS.5A-5Duse a dodecahedron;FIGS.11A-11AI,14A-14I,15A-15C,16A-16C, and17A-17Cuse an octahedron);2. A single face16of the regular polyhedron is projected onto a sphere, as shown inFIGS.5A and11A;3. The midpoint M1of a first edge E1of face16, and the midpoint M2of a second edge E2adjacent to first edge E1are connected with a segment18, as shown inFIGS.5A and11A;4. Segment18is patterned around center C of face16, at an angle of rotation equal to 360/PE, to form a first domain14a, as shown inFIGS.5B and11B;5. Segment18, along with the portions of first edge E1and second edge E2between midpoints M1and M2, define an element22, as shown inFIGS.5B and11B; and6. Element22is patterned about the vertex V which connects edges E1and E2to create a second domain14b, as shown inFIGS.5C and11C. The number of segments in the pattern that forms the second domain is equal to PF*PE/PV.

When first domain14aand second domain14bare tessellated to cover the surface of golf ball10, as shown inFIGS.5D and11D, a different number of total domains14aand14bwill result depending on the regular polyhedron chosen as the basis for control points M1and M2. The number of first and second domains14aand14bused to cover the surface of golf ball10is PFfor first domain14aand PVfor second domain14b, as shown below in Table 5.

In a particular aspect of the embodiment shown inFIGS.11A-11AI,14A-14I,15A-15C,16A-16C, and17A-17C, segment18forms a portion of a real or false parting line of golf ball10. Thus, segment18, along with each copy thereof that is produced by steps 4 and 6 above, produce the real and three false parting lines of the ball when the domains are tessellated to cover the ball's surface.

TABLE 5Domains Resulting From Use of Specific PolyhedraWhen Using the Midpoint to Midpoint MethodNumberNumberNumber ofNumber ofType ofofof FirstVertices,SecondPolyhedronFaces, PFDomains 14aPVDomains 14bTetrahedron4444Cube6688Octahedron8866Dodecahedron12122020Icosahedron20201212
The Midpoint to Vertex Method

Referring toFIGS.6A-6D, the midpoint to vertex method yields one domain that tessellates to cover the surface of golf ball10. The domain is defined as follows:1. A regular polyhedron is chosen (FIGS.6A-6Duse a dodecahedron);2. A single face16of the regular polyhedron is chosen, as shown inFIG.6A;3. A midpoint M1of edge E1of face16and a vertex V1on edge E1are connected with a segment18;4. Copies20of segment18is patterned about center C of face16, one for each midpoint M2and vertex V2of face16, to define a portion of domain14, as shown inFIG.6B; and5. Segment18and copies20are then each rotated 180 degrees about their respective midpoints to complete domain14, as shown inFIG.6C.

When domain14is tessellated to cover the surface of golf ball10, as shown inFIG.6D, a different number of total domains14will result depending on the regular polyhedron chosen as the basis for control points M1and V1. The number of domains14used to cover the surface of golf ball10is PF, as shown in Table 6.

TABLE 6Domains Resulting From Use of Specific PolyhedraWhen Using the Midpoint to Vertex MethodType of PolyhedronNumber of Faces, PFNumber of Domains 14Tetrahedron44Cube66Octahedron88Dodecahedron1212Icosahedron2020
The Vertex to Vertex Method

Referring toFIGS.7A-7C, the vertex to vertex method yields two domains that tessellate to cover the surface of golf ball10. The domains are defined as follows:1. A regular polyhedron is chosen (FIGS.7A-7Cuse an icosahedron);2. A single face16of the regular polyhedron is chosen, as shown inFIG.7A;3. A first vertex V1face16, and a second vertex V2adjacent to first vertex V1are connected with a segment18;4. Segment18is patterned around center C of face16to form a first domain14a, as shown inFIG.7B;5. Segment18, along with edge E1between vertices V1and V2, defines an element22; and6. Element22is rotated around midpoint M1of edge E1to create a second domain14b.

When first domain14aand second domain14bare tessellated to cover the surface of golf ball10, as shown inFIG.7C, a different number of total domains14aand14bwill result depending on the regular polyhedron chosen as the basis for control points V1and V2. The number of first and second domains14aand14bused to cover the surface of golf ball10is PFfor first domain14aand PF*PE/2 for second domain14b, as shown below in Table 7.

TABLE 7Domains Resulting From Use of Specific PolyhedraWhen Using the Vertex to Vertex MethodTypeNumberNumberNumber ofNumberofofof FirstEdgesof SecondPolyhedronFaces, PFDomains 14aper Face, PEDomains 14bTetrahedron4436Cube66412Octahedron88312Dodecahedron1212530Icosahedron2020330

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 toFIGS.8A-8E, the midpoint to center to vertex method yields one domain that tessellates to cover the surface of golf ball10. The domain is defined as follows:1. A regular polyhedron is chosen (FIGS.8A-8Euse an icosahedron);2. A single face16of the regular polyhedron is chosen, as shown inFIG.8A;3. A midpoint M1on edge E1of face16, Center C of face16and a vertex V1on edge E1are connected with a segment18, and segment18and the portion of edge E1between midpoint M1and vertex V1define a first element22a, as shown inFIG.8A;4. A copy20of segment18is rotated about center C, such that copy20connects 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 segment18between midpoint M1and center C, the portion of copy20between vertex V2and center C, and the portion of edge E1between midpoint M1and vertex V2define a second element22b, as shown inFIG.8B;5. First element22aand second element22bare rotated about midpoint M1of edge E1, as seen inFIG.8C, to define two domains14, wherein a single domain14is bounded solely by portions of segment18and copy20and the rotation18′ of segment18, as seen inFIG.8D.

When domain14is tessellated to cover the surface of golf ball10, as shown inFIG.8E, a different number of total domains14will result depending on the regular polyhedron chosen as the basis for control points M, C, and V. The number of domains14used to cover the surface of golf ball10is equal to the number of faces PFof the polyhedron chosen times the number of edges PEper face of the polyhedron, as shown below in Table 8.

TABLE 8Domains Resulting From Use of Specific PolyhedraWhen Using the Midpoint to Center to Vertex MethodType ofNumber ofNumber ofNumber ofPolyhedronFaces, PFEdges, PEDomains 14Tetrahedron4312Cube6424Octahedron8324Dodecahedron12560Icosahedron20360

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 toFIGS.9A-9E, the center to edge method yields one domain that tessellates to cover the surface of golf ball10. The domain is defined as follows:1. A regular polyhedron is chosen (FIGS.9A-9Euse an icosahedron);2. A single face16of the regular polyhedron is chosen, as shown inFIG.9A;3. Center C of face16, and a point P1on edge E1are connected with a segment18;4. A copy20of segment18is rotated about center C, such that copy20connects 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 segments18and20and the portions of edges E1and E2between points P1and P2, respectively, and a vertex V, which connects edges E1and E2, define an element22, as shown best inFIG.9B; and5. Element22is rotated about midpoint M1of edge E1or midpoint M2of edge whichever is located within element22, as seen inFIGS.9B-9C, to create a domain14, as seen inFIG.9D.

When domain14is tessellated to cover the surface of golf ball10, as shown inFIG.9E, a different number of total domains14will result depending on the regular polyhedron chosen as the basis for control points C and P1. The number of domains14used to cover the surface of golf ball10is equal to the number of faces PFof the polyhedron chosen times the number of edges PEper face of the polyhedron divided by 2, as shown below in Table 9.

TABLE 9Domains Resulting From Use of Specific Polyhedra When Using theCenter to Edge MethodType ofNumber ofNumber ofNumber ofPolyhedronFaces, PFEdges, PEDomains 14Tetrahedron436Cube6412Octahedron8312Dodecahedron12530Icosahedron20330

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 toFIGS.10A-10E, a vertex to vertex method based on a rhombic dodecahedron yields one domain that tessellates to cover the surface of golf ball10. The domain is defined as follows:1. A single face16of the rhombic dodecahedron is chosen, as shown inFIG.10A;2. A first vertex V1face16, and a second vertex V2adjacent to first vertex V1are connected with a segment18, as shown inFIG.10B;3. A first copy20of segment18is rotated about vertex V2, such that it connects vertex V2to vertex V3of face16, a second copy24of segment18is rotated about center C, such that it connects vertex V3and vertex V4of face16, and a third copy26of segment18is rotated about vertex V1such that it connects vertex V1to vertex V4, all as shown inFIG.10C, to form a domain14, as shown inFIG.10D;

When domain14is tessellated to cover the surface of golf ball10, as shown inFIG.10E, twelve domains will be used to cover the surface of golf ball10, one for each face of the rhombic dodecahedron.

After the irregular domain(s) are created using any of the above methods, the domain(s) may be packed with dimples in order to be usable in creating golf ball10.

InFIGS.11E-11AL14A-14I,15A-15C,16A-16C, and17A-17C, a first domain and a second domain are created using the midpoint to midpoint method based on an octahedron.FIG.11Eshows a first domain14aand a portion of a second domain14bpacked with dimples, with the dimples of the first domain14adesignated by the letter a.FIG.11Fshows a second domain14band a portion of a first domain14apacked with dimples, with the dimples of the second domain14bdesignated by the letter b.FIG.11Gshows a first domain14aand a second domain14bpacked with dimples and tessellated to cover the surface of golf ball10.FIG.11Hshows a first domain14apacked with dimples and a portion of a second domain14bpacked with dimples, but the dimples are packed within the domains in different patterns than those shown inFIG.11E. InFIG.11H, the first domain14ais designated by shading.FIG.11Ishows the second domain14band the first domain14awith the dimples packed within the domains in the same pattern as that shown inFIG.11H. InFIG.11I, the second domain14bis designated by shading.FIG.11Jshows the first and second domains packed with dimples according to the embodiment shown inFIGS.11H and11Itessellated to cover the surface of golf ball10.

FIG.11Kshows a first domain14apacked with dimples and a portion of a second domain14bpacked with dimples, but the dimples are packed within the domains in different patterns than those shown inFIGS.11E and11H. InFIG.11K, the first domain14ais designated by shading.FIG.11Lshows the second domain14band the first domain14awith the dimples packed within the domains in the same pattern as that shown inFIG.11K. InFIG.11L, the second domain14bis designated by shading.FIG.11Mshows the first and second domains packed with dimples according to the embodiment shown inFIGS.11K and11Ltessellated to cover the surface of golf ball10.

FIG.11Nshows a first domain14apacked with dimples and a portion of a second domain14b.FIG.11Oshows the second domain14bpacked with dimples and a portion of the first domain14a.FIG.11Pshows the first and second domains packed with dimples according to the embodiments shown inFIGS.11N and11O.

FIG.11Qshows a first domain14apacked with dimples and a portion of a second domain14b.FIG.11Rshows the second domain14bpacked with dimples and a portion of the first domain14a.FIG.11Sshows the first and second domains packed with dimples according to the embodiments shown inFIGS.11Q and11R.

FIG.11Vshows a first domain14apacked with perimeter dimples and a portion of a second domain14bpacked with perimeter dimples.FIG.11Wshows the second domain14bpacked with perimeter dimples and a portion of the first domain14apacked with perimeter dimples.FIG.11Xshows the first and second domains packed with perimeter dimples according to the embodiments shown inFIGS.11V and11W.

FIG.11Yshows a first domain14apacked with perimeter dimples and a portion of a second domain14bpacked with perimeter dimples.FIG.11Zshows the second domain14bpacked with perimeter dimples and a portion of the first domain14apacked with perimeter dimples.FIG.11AAshows the first and second domains packed with perimeter dimples according to the embodiments shown inFIGS.11Y and11Z.

FIGS.11AB,11AC,11AF and11AGshow a first domain14apacked with dimples and a portion of a second domain14b, according to two different embodiments of the present invention.FIGS.11AD,11AE,11AH and11AIshow a second domain14bpacked with dimples and a first domain, according to two different embodiments of the present invention.

FIG.14Ashows a first domain14apacked with dimples and a portion of a second domain14b.FIG.14Bshows the second domain14bpacked with dimples and a portion of the first domain14a.FIG.14Cshows the first and second domains packed with dimples according to the embodiments shown inFIGS.14A and14B.

FIG.14Dshows a first domain14apacked with dimples and a portion of a second domain14b.FIG.14Eshows the second domain14bpacked with dimples and a portion of the first domain14a.FIG.14Fshows the first and second domains packed with dimples according to the embodiments shown inFIGS.14D and14E.

FIG.14Gshows a first domain14apacked with dimples and a portion of a second domain14b.FIG.14Hshows the second domain14bpacked with dimples and a portion of the first domain14a.FIG.14Ishows the first and second domains packed with dimples according to the embodiments shown inFIGS.14G and14H.

FIG.15Ashows a first domain14apacked with dimples and a portion of a second domain14bpacked with dimples. InFIG.15A, the first domain14ais designated by shading.FIG.15Bshows the second domain14band the first domain14awith the dimples packed within the domains in the same pattern as that shown inFIG.15A. InFIG.15B, the second domain14bis designated by shading.FIG.15Cshows the first and second domains packed with dimples according to the embodiment shown inFIGS.15A and15Btessellated to cover the surface of golf ball10.

FIG.16Ashows a first domain14apacked with dimples and a portion of a second domain14b.FIG.16Bshows the second domain14bpacked with dimples and a portion of the first domain14a.FIG.16Cshows the first and second domains packed with dimples according to the embodiments shown inFIGS.16A and16B.

FIG.17Ashows a first domain14apacked with dimples and a portion of a second domain14b.FIG.17Bshows the second domain14bpacked with dimples and a portion of the first domain14a.FIG.17Cshows the first and second domains packed with dimples according to the embodiments shown inFIGS.17A and17B.

In a particular embodiment, as illustrated inFIGS.11E-11S,11U-11AI,14A-14I,15A-15C,16A-16C, and17A-17C, the dimple pattern of the first domain has three-way rotational symmetry about the central point of the first domain, and the dimple pattern of the second domain has four-way rotational symmetry about the central point of the second domain.

In one embodiment, there are no limitations on how the dimples are packed. In another embodiment, the dimples are packed such that no dimple intersects a line segment.

In a particular embodiment, the dimples are packed such that all nearest neighbor dimples are separated by substantially the same distance, δ, wherein the average of all δ values is from 0.002 inches to 0.020 inches, and wherein any individual δ value can vary from the mean by ±0.005 inches. For purposes of the present invention, nearest neighbor dimples are determined according to the following method. A reference dimple and a potential nearest neighbor dimple are selected such that the reference dimple has substantially the same diameter or a smaller diameter than the potential nearest neighbor dimple. Two tangency lines are drawn from the center of the reference dimple to the potential nearest neighbor dimple. A line segment is then drawn connecting the center of the reference dimple to the center of the potential nearest neighbor dimple. If the two tangency lines and the line segment do not intersect any other dimple edges, then those dimples are considered to be nearest neighbors. For example, as shown inFIG.12A, two tangency lines3A and3B are drawn from the center of a reference dimple1to a potential nearest neighbor dimple2. Line segment4is then drawn connecting the center of reference dimple1to the center of potential nearest neighbor dimple2. Tangency lines3A and3B and line segment4do not intersect any other dimple edges, so dimple1and dimple2are considered nearest neighbors. InFIG.12B, two tangency lines3A and3B are drawn from the center of a reference dimple1to a potential nearest neighbor dimple2. Line segment4is then drawn connecting the center of reference dimple1to the center of potential nearest neighbor dimple2. Tangency lines3A and3B intersect an alternative dimple, so dimple1and dimple2are not considered nearest neighbors. Those skilled in the art will recognize that the line segments do not actually have to be drawn on the golf ball. Rather, a computer modeling program capable of performing this operation automatically is preferably used.

Each dimple typically has a diameter of 0.050 or 0.075 or 0.080 or 0.090 or 0.100 or 0.110 or 0.115 or 0.120 or 0.150 or 0.160 or 0.170 or 0.180 or 0.185 or 0.190 or 0.200 or 0.205 or 0.250 or 0.300 or 0.350 inches, or a diameter within a range having a lower limit and an upper limit selected from these values. The diameter of a dimple having a non-circular plan shape is defined by its equivalent diameter, de, which calculated as:

de=2⁢Aπ
where A is the plan shape area of the dimple. Diameter measurements are determined on finished golf balls according toFIG.13. Generally, it may be difficult to measure a dimple's diameter due to the indistinct nature of the boundary dividing the dimple from the ball's undisturbed land surface. Due to the effect of paint and/or the dimple design itself, the junction between the land surface and dimple may not be a sharp corner and is therefore indistinct. This can make the measurement of a dimple's diameter somewhat ambiguous. To resolve this problem, dimple diameter on a finished golf ball is measured according to the method shown inFIG.13.FIG.13shows a dimple half-profile34, extending from the dimple centerline31to the land surface outside of the dimple33. A ball phantom surface32is constructed above the dimple as a continuation of the land surface33. A first tangent line T1is then constructed at a point on the dimple sidewall that is spaced 0.003 inches radially inward from the phantom surface32. T1intersects phantom surface32at a point P1, which defines a nominal dimple edge position. A second tangent line T2is then constructed, tangent to the phantom surface32, at P1. The edge angle is the angle between T1and T2. The dimple diameter is the distance between P1and its equivalent point diametrically opposite along the dimple perimeter. Alternatively, it is twice the distance between P1and the dimple centerline31, measured in a direction perpendicular to centerline31. The dimple depth is the distance measured along a ball radius from the phantom surface of the ball to the deepest point on the dimple. The dimple surface volume is the space enclosed between the phantom surface32and the dimple surface34(extended along T1until it intersects the phantom surface). The dimple plan shape area is based on a planar view of the dimple plan shape, such that the viewing plane is normal to an axis connecting the center of the ball to the centroid of the dimple.

In a particular embodiment, all of the dimples on the outer surface of the ball have the same diameter. It should be understood that “same diameter” dimples includes dimples on a finished ball having respective diameters that differ by less than 0.005 inches due to manufacturing variances.

In another particular embodiment, there are two or more different dimple diameters on the outer surface of the ball, including a minimum dimple diameter, a maximum dimple diameter, and, optionally, one or more additional dimple diameters. The dimples are arranged in multiple copies of a first domain and a second domain formed according to the midpoint to midpoint method based on an octahedron wherein the first domain and the second domain are tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles. The overall dimple pattern consists of eight first domains and six second domains. The dimple pattern within the first domain is different from the dimple pattern within the second domain. Each of the first domain and the second domain consists of perimeter dimples and interior dimples.

In a first particular aspect of this embodiment, as illustrated inFIGS.11N-11Pwhich are further described below, the perimeter dimples of the first domain consist of dimples having at least two different diameters, the perimeter dimples of the second domain consist of dimples having no more than two different diameters, and the diameter of at least one perimeter dimple is the maximum dimple diameter. The dimples optionally have one or more of the following additional characteristics:a) the first domain has three-way rotational symmetry about the central point of the first domain, and the second domain has four-way rotational symmetry about the central point of the second domain;b) the diameter of at least one perimeter dimple of the first domain is the maximum dimple diameter;c) none of the perimeter dimples of the first domain have a diameter that is the minimum dimple diameter;d) none of the perimeter dimples of the second domain have a diameter that is the maximum dimple diameter;e) the diameter of at least one perimeter dimple of the second domain is the minimum dimple diameter;f) the diameter of at least one interior dimple is the maximum dimple diameter;g) none of the interior dimples of the first domain have a diameter that is the maximum dimple diameter;h) the diameter of at least one interior dimple of the first domain is the minimum dimple diameter;i) the diameter of at least one interior dimple of the second domain is the maximum dimple diameter;j) none of the interior dimples of the second domain have a diameter that is the minimum dimple diameter;k) there are three or more different dimple diameters on the outer surface of the ball;l) there are four or more different dimple diameters on the outer surface of the ball;m) there are five or more different dimple diameters on the outer surface of the ball;n) the perimeter dimples of the first domain consist of dimples having at least three different dimple diameters;o) the interior dimples of the first domain consist of dimples having no more than two different diameters;p) the interior dimples of the second domain consist of dimples having no more than two different diameters; andq) the number of different dimple diameters, D, on the outer surface is related to the total number of dimples, N, on the outer surface according to one of the particular embodiments further disclosed below.

In a second particular aspect of this embodiment, as illustrated inFIGS.11Q-11Swhich are further described below, there are three or more different dimple diameters on the outer surface of the ball, the interior dimples of the first domain consist of dimples having no more than two different diameters, the interior dimples of the second domain consist of dimples having at least three different diameters, the diameter of at least one dimple in the first domain is the minimum dimple diameter, and the diameter of at least one dimple in the second domain is the minimum dimple diameter. The dimples optionally have one or more of the following additional characteristics:a) the first domain has three-way rotational symmetry about the central point of the first domain, and the second domain has four-way rotational symmetry about the central point of the second domain;b) there are four or more different dimple diameters on the outer surface of the ball;c) there are five or more different dimple diameters on the outer surface of the ball;d) there are six or more different dimple diameters on the outer surface of the ball;e) none of the perimeter dimples of the first domain has a diameter that is the maximum dimple diameter;f) the diameter of at least one of the perimeter dimples of the first domain is the minimum dimple diameter;g) none of the perimeter dimples of the second domain have a diameter that is the maximum dimple diameter;h) the diameter of at least one of the perimeter dimples of the second domain is the minimum dimple diameter;i) the diameter of at least one interior dimple is the maximum dimple diameter;j) none of the interior dimples of the first domain have a diameter that is the maximum dimple diameter;k) none of the interior dimples of the first domain have a diameter that is the minimum dimple diameter;l) the diameter of at least one of the interior dimples of the second domain is the maximum dimple diameter;m) none of the interior dimples of the second domain have a diameter that is the minimum dimple diameter;n) the perimeter dimples of the first domain consist of dimples having at least three different dimple diameters;o) the interior dimples of the first domain consist of dimples having only one dimple diameter;p) the perimeter dimples of the second domain consist of dimples having at least two different diameters; andq) the number of different dimple diameters, D, on the outer surface is related to the total number of dimples, N, on the outer surface according to one of the particular embodiments further disclosed below.

It should be understood that manufacturing variances are to be taken into account when determining the number of different dimple diameters. The placement of the dimple in the overall pattern should also be taken into account. Specifically, dimples located in the same location within the multiple copies of the domain(s) that are tessellated to form the dimple pattern are assumed to be same diameter dimples, unless they have a difference in diameter of 0.005 inches or greater.

For purposes of the present disclosure, each dimple on the outer surface of the golf ball is either a perimeter dimple or an interior dimple and is positioned entirely within a single domain. Perimeter dimples are those dimples located directly adjacent to a border segment. The perimeter dimples of a given domain are those located inside of that domain, and, in a particular embodiment, form an axially symmetric pattern about the geometric center of the domain. Interior dimples are those dimples not located directly adjacent to a border segment. The interior dimples of a given domain are those located within the domain, and, in a particular embodiment, form an axially symmetric pattern about the geometric center of the domain. Nearest neighbor dimples can also be used to determine whether a given dimple is a perimeter dimple or an interior dimple. If at least one of a particular dimple's nearest neighbors is located in a different domain than that particular dimple, then that particular dimple is a perimeter dimple. If all of a particular dimple's nearest neighbor dimples are located in the same domain as that particular dimple, then that particular dimple is an interior dimple.

In the embodiments shown inFIGS.11N and11Q, the shaded dimples represent the perimeter dimples of the first domain14a, and the unshaded dimples represent the interior dimples of the first domain14a. In the embodiments shown inFIGS.11O and11R, the shaded dimples represent the perimeter dimples of the second domain14b, and the unshaded dimples represent the interior dimples of the second domain14b. Thus, inFIGS.11P and11S, which show the first domain14aand the second domain14bpacked with dimples according to the embodiments shown inFIGS.11N-11O and11Q-11R, respectively, the shaded dimples represent the perimeter dimples and the unshaded dimples represent the interior dimples.

FIGS.11N-11Pillustrate a first domain14aand a second domain14bformed according to the midpoint to midpoint method based on an octahedron. The alphabetical labels within the dimples designate same diameter dimples; i.e., all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.11N-11P, the dimples labelled A have a diameter of about 0.110 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled C have a diameter of about 0.160 inches, the dimples labelled D have a diameter of about 0.170 inches, and the dimples labelled E have a diameter of about 0.180 inches. Thus, according to the embodiment shown inFIGS.11N-11P, tessellating first domain14aand second domain14babout the outer surface of a golf ball results in an overall dimple pattern having a total of 350 dimples arranged within eight copies of first domain14aand six copies of second domain14b, the dimples having five different dimple diameters, including a minimum diameter of 0.110 inches, a maximum diameter of 0.180 inches, and three additional dimple diameters, with the first domain having four different dimple diameters (A, B, C, E) and the second domain having four different dimple diameters (A, B, D, E).

FIGS.11Q-11Sillustrate a first domain14aand a second domain14bformed according to the midpoint to midpoint method based on an octahedron. The alphabetical labels within the dimples designate same diameter dimples; i.e., all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.11Q-11S, the dimples labelled A have a diameter of about 0.120 inches, the dimples labelled B have a diameter of about 0.140 inches, the dimples labelled C have a diameter of about 0.160 inches, the dimples labelled D have a diameter of about 0.170 inches, the dimples labelled E have a diameter of about 0.180 inches, and the dimples labelled F have a diameter of about 0.190 inches. Thus, according to the embodiment shown inFIGS.11Q-11S, tessellating first domain14aand second domain14babout the outer surface of a golf ball results in an overall dimple pattern having a total of 342 dimples arranged within eight copies of first domain14aand six copies of second domain14b, the dimples having six different dimple diameters, including a minimum diameter of 0.120 inches, a maximum diameter of 0.190 inches, and four additional dimple diameters, with the first domain having three different dimple diameters (A, D, E) and the second domain having six different dimple diameters (A, B, C, D, E, F).

In a third particular aspect of this embodiment, the perimeter dimples within each domain have a particular diameter relationship as follows. As stated above, in the present embodiment, the domains are generated using the midpoint to midpoint method based on an octahedron. Thus, as illustrated, for example, inFIGS.11A-11D, each first domain14ais defined by three irregular segments, i.e., an irregular segment18and two copies thereof, and each second domain14bis defined by four irregular segments, i.e., an irregular segment18and three copies thereof. The three or four irregular segments defining a given domain are connected at their endpoints which correspond to the midpoints of the edges of the faces of the base octahedron used to generate the domains, for example, M1and M2inFIGS.11A-11C. The perimeter dimples of a given domain are positioned adjacent to the three or four irregular segments defining that domain. Each perimeter dimple is positioned adjacent to a single irregular segment, except in the case where a domain has one perimeter dimple located at each of its vertices, in which case the perimeter dimple located at each vertex is adjacent to two irregular segments. Domains having a single perimeter dimple located at the vertices of the domain are illustrated, for example, as domain14aofFIGS.11E,11H,11K,11N,11Q,11V and11Y, and domain14bofFIGS.11F,11I,11L,11O,11R,11U,11W and11Z.

For each one of the three or four irregular segments defining a domain, a reference line is drawn connecting endpoints of the irregular segment in the plane that is normal to the axis of symmetry of that domain. For example,FIG.11Tshows a first domain14adefined by three irregular segments, a second domain14bdefined by four irregular segments, and one of the four reference lines that can be drawn connecting two endpoints of the irregular segments defining the second domain14b.FIG.11Ushows the perimeter dimples of the first domain14a, the perimeter dimples of the second domain14b, and the reference line shown inFIG.11T. InFIG.11U, all of the perimeter dimples positioned adjacent to a common irregular segment of the second domain14bare intersected by the reference line connecting the endpoints of the common irregular segment; however, in some embodiments, a portion of the perimeter dimples positioned adjacent to a common irregular segment of a given domain are not intersected by the reference line connecting the endpoints of the common irregular segment.

In the third particular aspect of this embodiment, all of the perimeter dimples within a domain that are positioned adjacent to a common irregular segment have a diameter relationship wherein their respective diameters get progressively smaller (or, alternatively, progressively larger) as the distance gets larger from each dimple's centroid to the midpoint of the reference line connecting the endpoints of the common irregular segment. For example,FIGS.11V-11X, discussed further below, illustrate an embodiment wherein all of the perimeter dimples within a given domain that are positioned adjacent to a common irregular segment defining that domain have a diameter relationship wherein their respective diameters get progressively smaller as the distance from each dimple's centroid to the midpoint of the reference line connecting the endpoints of the common irregular segment gets larger. In other words, all of the perimeter dimples within a given domain have a diameter relationship wherein

if xdimple a>xdimple b, then ddimple a<ddimple bk,

where dimple a and dimple b are any two perimeter dimples of the given domain positioned adjacent to a common irregular segment defining the given domain, d is the dimple diameter, and x is the distance from the center of the dimple to the midpoint of a reference line connecting the endpoints of the common irregular segment.

Alternatively,FIGS.11Y-11AA, discussed further below, illustrate an embodiment wherein all of the perimeter dimples within a given domain that are positioned adjacent to a common irregular segment defining that domain have a diameter relationship wherein their respective diameters get progressively larger as the distance from each dimple's centroid to the midpoint of the reference line connecting the endpoints of the common irregular segment gets larger. In other words, all of the perimeter dimples within a given domain have a diameter relationship wherein

if xdimple a>xdimple b, then ddimple a>ddimple b,

where dimple a and dimple b are any two perimeter dimples of the given domain positioned adjacent to a common irregular segment defining the given domain, d is the dimple diameter, and x is the distance from the center of the dimple to the midpoint of a reference line connecting the endpoints of the common irregular segment.

Referring now toFIGS.11V-11X, only the perimeter dimples are shown. The interior dimples of the first domain are positioned within the domain in any suitable pattern that has three-way rotational symmetry about the central point of the domain. The interior dimples of the second domain are positioned within the domain in any suitable pattern that has four-way rotational symmetry about the central point of the domain. The alphabetical labels within the dimples designate same diameter dimples. For example, all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.11V-11X, the dimples labelled A have a diameter of about 0.110 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled C have a diameter of about 0.160 inches, the dimples labelled D have a diameter of about 0.170 inches, and the dimples labelled E have a diameter of about 0.185 inches.

InFIG.11W, for the perimeter dimples positioned adjacent to a common irregular segment defining the second domain14b, the dimples labelled D have the largest diameter and are positioned closest to the midpoint of the reference line connecting the endpoints of the common irregular segment; the dimples labelled B have a smaller diameter than the dimples labelled D and are positioned second closest to the midpoint of the reference line; and the dimples labelled A have the smallest diameter and are positioned furthest from the midpoint of the reference line. Thus, all of the perimeter dimples of the second domain have a diameter relationship wherein

if xdimple 1>xdimple 2

then ddimple 1<ddimple 2,

where dimple1and dimple2are any two perimeter dimples of the second domain positioned adjacent to a common irregular segment, d is the dimple diameter, and x is the distance from the center of the dimple to the midpoint of a reference line connecting the endpoints of the common irregular segment.

InFIG.11V, for the perimeter dimples positioned adjacent to a common irregular segment defining the first domain14a, the dimple labelled E has the largest diameter and is positioned closest to the midpoint of the reference line connecting the endpoints of the common irregular segment; the dimples labelled C have a smaller diameter than the dimple labelled E and are positioned second closest to the midpoint of the reference line; and the dimples labelled B have the smallest diameter and are positioned furthest from the midpoint of the reference line. Thus, all of the perimeter dimples of the first domain have a diameter relationship wherein

if xdimple 3>xdimple 4

then ddimple 3<ddimple 4,

where dimple3and dimple4are any two perimeter dimples of the first domain positioned adjacent to a common irregular segment, d is the dimple diameter, and x is the distance from the center of the dimple to the midpoint of a reference line connecting the endpoints of the common irregular segment.

Referring now toFIGS.11Y-11AA, only the perimeter dimples are shown. The interior dimples of the first domain are positioned within the domain in any suitable pattern that has three-way rotational symmetry about the central point of the domain. The interior dimples of the second domain are positioned within the domain in any suitable pattern that has four-way rotational symmetry about the central point of the domain. The alphabetical labels within the dimples designate same diameter dimples. For example, all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.11Y-11AA, the dimples labelled A have a diameter of about 0.175 inches, the dimples labelled B have a diameter of about 0.180 inches, the dimples labelled C have a diameter of about 0.185 inches, and the dimples labelled D have a diameter of about 0.195 inches.

InFIG.11Z, for the perimeter dimples positioned adjacent to a common irregular segment defining the second domain14b, the dimple labelled A has the smallest diameter and is positioned closest to the midpoint of the reference line connecting the endpoints of the common irregular segment; the dimples labelled C have a larger diameter than the dimples labelled A and are positioned second closest to the midpoint of the reference line; and the dimples labelled D have the largest diameter and are positioned furthest from the midpoint of the reference line. Thus, all of the perimeter dimples of the second domain have a diameter relationship wherein

if xdimple 1>xdimple 2

then ddimple 1>ddimple 2,

where dimple1and dimple2are any two perimeter dimples of the second domain positioned adjacent to a common irregular segment, d is the dimple diameter, and x is the distance from the center of the dimple to the midpoint of a reference line connecting the endpoints of the common irregular segment.

InFIG.11Y, for the perimeter dimples positioned adjacent to a common irregular segment defining the first domain14a, the dimples labelled B have the smallest diameter and are positioned closest to the midpoint of the reference line connecting the endpoints of the common irregular segment; and the dimples labelled D have the largest diameter and are positioned furthest from the midpoint of the reference line. Thus, all of the perimeter dimples of the first domain have a diameter relationship wherein

if xdimple 3>xdimple 4

then ddimple 3>ddimple 4,

where dimple3and dimple4are any two perimeter dimples of the first domain positioned adjacent to a common irregular segment, d is the dimple diameter, and x is the distance from the center of the dimple to the midpoint of a reference line connecting the endpoints of the common irregular segment.

WhileFIGS.11V-11AAillustrate embodiments wherein the perimeter dimples of the first and second domains have the same diameter relationship (i.e., in both domains the diameters get progressively smaller going from the midpoint to each endpoint of the reference line, or in both domains the diameters get progressively larger going from the midpoint to each endpoint of the reference line), the present invention includes embodiments wherein the perimeter dimples of only one of the two domains have a diameter relationship wherein the diameters get progressively smaller or larger going from the midpoint to each endpoint of the reference line. The present invention also includes embodiments wherein the perimeter dimples of one domain have a diameter relationship wherein the diameters get progressively smaller and the perimeter dimples of the other domain have a diameter relationship wherein the diameters get progressively larger, going from the midpoint to each endpoint of the reference line.

In a further aspect of this particular embodiment, the dimples additionally have one or more of the following additional characteristics:a) the number of first domain perimeter dimples positioned adjacent to a common irregular segment defining the first domain is not equal to the number of second domain perimeter dimples positioned adjacent to a common irregular segment defining the second domain;b) the number of first domain perimeter dimples positioned adjacent to a common irregular segment defining the first domain is equal to the number of second domain perimeter dimples positioned adjacent to a common irregular segment defining the second domain;c) at least one perimeter dimple of the first domain has substantially the same diameter as at least one of its nearest neighbor dimples located in the second domain;d) the first domain has a dimple positioned at each of its vertices, the second domain has a dimple positioned at each of its vertices, the dimples positioned at the vertices of the first domain have the same diameter as the dimples positioned at the vertices of the second domain; ande) the first domain has a dimple positioned at each of its vertices, the second domain has a dimple positioned at each of its vertices, the dimples positioned at the vertices of the first domain do not have the same diameter as the dimples positioned at the vertices of the second domain.

In a fourth particular aspect of this embodiment, as illustrated inFIGS.11AB,11AC,11AF and11AG, the dimples are arranged within the first domain as follows. As stated above, in the present embodiment, the domains are generated using the midpoint to midpoint method based on an octahedron. Thus, the first domain has three-way rotational symmetry about the central point of the first domain. In this fourth particular aspect of the present embodiment, the dimples of the first domain, other than a center dimple if present, are arranged along the sides of a plurality of reference triangles. The reference triangles are concentric triangles having a common center that is coincident with the central point of the first domain. Each reference triangle is located entirely within a domain, and is entirely surrounded by or entirely surrounds another reference triangle. If a center dimple is present, the dimples of the first domain, other than the center dimple, are arranged along the sides of at least two reference triangles. If no center dimple is present, the dimples of the first domain are arranged along the sides of at least three reference triangles. A center dimple is defined herein as a dimple having a center that is coincident with the central point of a domain. For purposes of the present invention, a dimple is said to be arranged along the side of a reference triangle if at least one side of the reference triangle intersects the dimple. In this particular embodiment, center dimples are not intersected by any side of any reference triangle. Every dimple in the first domain that is not a center dimple is intersected by a single reference triangle. It should be understood that the reference triangles are imaginary lines that can be drawn on the surface of the golf ball to describe a dimple arrangement, and do not necessarily exist on the final golf ball.

For example,FIGS.11AB and11ACillustrate an embodiment wherein the first domain14aincludes a center dimple having a center that is coincident with the central point of the first domain14a, and the dimples of the first domain14a, other than the center dimple, are arranged along the sides of two reference triangles36and38. The alphabetical labels within the dimples designate same diameter dimples. For example, all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.11AB and11AC, the dimple labelled A has a diameter of about 0.110 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled C have a diameter of about 0.160 inches, and the dimples labelled E have a diameter of about 0.185 inches.

Similarly,FIGS.11AF and11AGillustrate an embodiment wherein the first domain14aincludes a center dimple having a center that is coincident with the central point of the first domain14a, and the dimples of the first domain14a, other than the center dimple, are arranged along the sides of two reference triangles36and38. The alphabetical labels within the dimples designate same diameter dimples. For example, all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.11AF and11AG, the dimple labelled A has a diameter of about 0.110 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled C have a diameter of about 0.160 inches, and the dimples labelled D have a diameter of about 0.180 inches.

In the embodiment of the present invention wherein the dimples of the first domain are arranged along reference triangles, the dimples of the first domain optionally have one or more of the following characteristics:a) the maximum difference between the dimple diameters of any two dimples arranged along the sides of one of the reference triangles is 0.100 inches, or the maximum difference is 0.070 inches, or the maximum difference is 0.050 inches;b) the first domain includes dimples having at least three different dimple diameters;c) the dimples arranged along the sides of at least one of the reference triangles include dimples having at least three different diameters;d) for every reference triangle, the average dimple diameter of the dimples arranged along said reference triangle is within a range having a lower limit of 0.100 or 0.110 inches and an upper limit of 0.180 or 0.200 inches;e) the first domain includes at least one dimple having the minimum dimple diameter;f) the first domain includes at least one dimple having the maximum dimple diameter; andg) at least one dimple diameter is present in more than one reference triangle.

In a fifth particular aspect of this embodiment, as illustrated inFIGS.11AD,11AE,11AH and11AI, the dimples are arranged within the second domain as follows. As stated above, in the present embodiment, the domains are generated using the midpoint to midpoint method based on an octahedron. Thus, the second domain has four-way rotational symmetry about the central point of the second domain. In this further particular aspect of the present embodiment, the dimples of the second domain, other than an optional center dimple, are arranged along the sides of at least three reference quadrilaterals. The reference quadrilaterals are concentric quadrilaterals having a common center that is coincident with the central point of the second domain. Each reference quadrilateral is located entirely within a domain, and is entirely surrounded by or entirely surrounds another reference quadrilateral. For purposes of the present invention, a dimple is said to be arranged along the side of a reference quadrilateral if at least one side of the reference quadrilateral intersects the dimple. In this particular embodiment, center dimples are not intersected by any side of any reference quadrilateral. Every dimple in the second domain that is not a center dimple is intersected by a single reference quadrilateral. It should be understood that the reference quadrilaterals are imaginary lines that can be drawn on the surface of the golf ball to describe a dimple arrangement, and do not necessarily exist on the final golf ball.

For example,FIGS.11AD and11AEillustrate an embodiment wherein the second domain14bincludes a center dimple having a center that is coincident with the central point of the second domain14b, and the dimples of the second domain14b, other than the center dimple, are arranged along the sides of two reference quadrilaterals42,44and46. The alphabetical labels within the dimples designate same diameter dimples. For example, all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.11AD and11AE, the dimples labelled A has a diameter of about 0.110 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled D have a diameter of about 0.170 inches, and the dimples labelled E have a diameter of about 0.185 inches.

Similarly,FIGS.11AH and11AIillustrate an embodiment wherein the second domain14bincludes a center dimple having a center that is coincident with the central point of the second domain14b, and the dimples of the second domain14b, other than the center dimple, are arranged along the sides of two reference quadrilaterals42,44and46. The alphabetical labels within the dimples designate same diameter dimples. For example, all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.11AH and11AI, the dimples labelled A has a diameter of about 0.110 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled C have a diameter of about 0.160 inches, and the dimples labelled D have a diameter of about 0.180 inches.

In the embodiments of the present invention wherein the dimples of the second domain are arranged along reference quadrilaterals, the dimples of the second domain optionally have one or more of the following characteristics:a) the maximum difference between the dimple diameters of any two dimples arranged along the sides of one of the reference quadrilaterals is 0.100 inches, or the maximum difference is 0.080 inches;b) the second domain includes dimples having at least three different dimple diameters, or at least four different dimple diameters;c) the dimples arranged along the sides of at least one of the reference quadrilaterals include dimples having at least three different diameters;d) for every reference quadrilateral, the average dimple diameter of the dimples arranged along said reference quadrilateral is within a range having a lower limit of 0.100 or 0.110 inches and an upper limit of 0.180 or 0.200 inches;e) the second domain includes at least one dimple having the minimum dimple diameter;f) the second domain includes at least one dimple having the maximum dimple diameter;g) at least two of the reference quadrilaterals include a dimple having the minimum dimple diameter; andh) at least two of the reference quadrilaterals include a dimple having the maximum dimple diameter.

In another particular embodiment, as illustrated inFIGS.17A-17C, the dimples are arranged within the first and second domains as follows. The domains are generated using the midpoint to midpoint method based on an octahedron. Thus, the first domain has three-way rotational symmetry about the central point of the first domain, and the second domain has four-way rotational symmetry about the central point of the second domain. The first domain and the second domain are tessellated to cover the outer surface of the golf ball in a uniform pattern having no dimple-free great circles and consisting of eight first domains and six second domains. The first domain includes a center dimple having a centroid that is coincident with the central point of the first domain, and the second domain includes a center dimple having a centroid that is coincident with the central point of the second domain.

In this embodiment, the dimples of the first domain, other than the center dimple, are arranged along the sides of a plurality of reference triangles. The reference triangles are concentric triangles having a common center that is coincident with the central point of the first domain. Each reference triangle is located entirely within a domain, and is entirely surrounded by or entirely surrounds another reference triangle. For purposes of the present invention, a dimple is said to be arranged along the side of a reference triangle if the dimple is not a center dimple and the dimple is intersected by at least one side of the reference triangle.

It should be understood that the reference triangles are imaginary lines that can be drawn on the surface of the golf ball to describe a dimple arrangement, and do not necessarily exist on the final golf ball.

In this embodiment, the dimples of the second domain, other than the center dimple, are arranged along the sides of a plurality of reference quadrilaterals. The reference quadrilaterals are concentric quadrilaterals having a common center that is coincident with the central point of the second domain. Each reference quadrilateral is located entirely within a domain, and is entirely surrounded by or entirely surrounds another reference quadrilateral. For purposes of the present invention, a dimple is said to be arranged along the side of a reference quadrilateral if the dimple is not a center dimple and the dimple is intersected by a least one side of the reference quadrilateral. It should be understood that the reference quadrilaterals are imaginary lines that can be drawn on the surface of the golf ball to describe a dimple arrangement, and do not necessarily exist on the final golf ball.

For example,FIGS.17A-17Cillustrate an embodiment wherein the first domain14aincludes a center dimple having a centroid that is coincident with the central point of the first domain14a, and the second domain14bincludes a center dimple having a centroid that is coincident with the central point of the second domain14b. The dimples of the first domain14a, other than the center dimple, are arranged along the sides of two reference triangles36and38. The dimples of the second domain14b, other than the center dimple, are arranged along the sides of three reference triangles42,44, and46. The alphabetical labels within the dimples designate same diameter dimples. For example, all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.17A-17C, the dimples labelled A have a diameter of about 0.100 inches, the dimples labelled B have a diameter of about 0.115 inches, the dimples labelled C have a diameter of about 0.125 inches, the dimples labelled D have a diameter of about 0.145 inches, the dimples labelled E have a diameter of about 0.165 inches, the dimples labelled F have a diameter of about 0.185 inches, the dimples labelled G have a diameter of about 0.195 inches, and the dimple labelled H has a diameter of about 0.210 inches.

In a particular aspect of this embodiment wherein the first domain includes a center dimple and the remaining dimples of the first domain are arranged along the sides of a plurality of reference triangles, and the second domain includes a center dimple and the remaining dimples of the second domain are arranged along the sides of a plurality of reference quadrilaterals, the dimples optionally have one or more of the following characteristics:a) there are at least three, or at least four, or at least five, or at least six, or at least seven, or at least eight, different dimple diameters present on the outer surface of the ball;b) there are at least six different dimple diameters present in the second domain;c) the dimple diameter of the center dimple of the first domain is not the minimum dimple diameter;d) the dimple diameter of the center dimple of the first domain is 0.175 inches or greater;e) the dimple diameter of the center dimple of the second domain is the maximum dimple diameter;f) the first domain does not include any dimples having the minimum dimple diameter;g) the first domain does not include any dimples having the maximum dimple diameter;h) for at least one of the reference triangles of the first domain, all of the dimples arranged along the sides of the triangle are same diameter dimples;i) for at least one of the reference triangles of the first domain, the dimples arranged along the sides of the triangle include dimples having a difference in diameter of 0.025 inches or greater;j) for at least one of the reference quadrilaterals of the second domain, all of the dimples arranged along the sides of the quadrilateral are same diameter dimples;k) for at least one of the reference quadrilaterals of the second domain, the dimples arranged along the sides of the quadrilateral include dimples having a difference in diameter of 0.025 inches or greater, or a difference in diameter of 0.050 or greater;l) the second domain includes four vertex dimples, each vertex dimple having a centroid that is coincident with one of the four vertices of the largest reference quadrilateral;m) the dimple diameter of each of the four vertex dimples of the second domain is the minimum dimple diameter;n) for at least six of the different dimple diameters on the outer surface of the ball, either SD1=0 or SD2=0, where SD1 represents the number of dimples having a given diameter positioned within the first domain and SD2 represents the number of dimples having a given diameter positioned within the second domain;o) SD1=0 for at least two of the different dimple diameters on the outer surface of the ball;p) SD2=0 for at least two of the different dimple diameters on the outer surface of the ball; andq) the ratio of the number of different dimple diameters having an SD1 value of 0 to the number of different dimple diameters having an SD2 value of 0 is 0.50 or greater.

In another particular embodiment, there are two or more different dimple diameters on the outer surface of the ball, including a minimum dimple diameter, a maximum dimple diameter, and, optionally, one or more additional dimple diameters. The dimples are arranged in multiple copies of a first domain and a second domain formed according to the midpoint to midpoint method based on an octahedron wherein the first domain and the second domain are tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles. The overall dimple pattern consists of eight first domains and six second domains. Each of the two or more different dimple diameters on the ball has a first domain diameter ratio defined by the equation:

first⁢domain⁢diameter⁢ratio=S⁢D⁢1S⁢D⁢1+S⁢D⁢2
and a second domain diameter ratio defined by the equation:

second⁢domain⁢diameter⁢ratio⁢=S⁢D⁢2S⁢D⁢1+S⁢D⁢2
where SD1 is the number of same diameter dimples positioned within the first domain having said diameter, and SD2 is the number of same diameter dimples positioned within the second domain having said diameter.

In a particular aspect of this embodiment, for the minimum dimple diameter,
SD1min≤½(SD2min)
where SD1minis the number of dimples positioned within the first domain having the minimum dimple diameter, and SD2minis the number of dimples positioned within the second domain having the minimum dimple diameter. In another particular aspect of this embodiment, for the maximum dimple diameter,
SD1max≤½(SD2max)
where SD1maxis the number of dimples positioned within the first domain having the maximum dimple diameter, and SD2maxis the number of dimples positioned within the second domain having the maximum dimple diameter. The dimple pattern optionally has one or more of the following additional characteristics:a) the first domain has three-way rotational symmetry about the central point of the first domain, and the second domain has four-way rotational symmetry about the central point of the second domain;b) the number of different dimple diameters in the first domain is the same as the number of different dimple diameters in the second domain;c) the number of different dimple diameters in the first domain is different from the number of different dimple diameters in the second domain;d) the first domain includes at least one dimple having the minimum dimple diameter and at least one dimple having the maximum dimple diameter;e) the second domain includes at least one dimple having the minimum dimple diameter and at least one dimple having the maximum dimple diameter;f) there are at least four, or at least five, different dimple diameters on the outer surface of the ball;g) every different dimple diameter on the ball is present in the first domain;h) at least one of the different dimple diameters on the ball is not present in the first domain;i) every different dimple diameter on the ball is present in the second domain;j) at least one of the different dimple diameters on the ball is not present in the second domain;k) SD1min≤¼(SD2min); andl) SD1max≤¼(SD2max).

For example,FIGS.14A-14Cillustrate a first domain14aand a second domain14bformed according to the midpoint to midpoint method based on an octahedron. The alphabetical labels within the dimples designate same diameter dimples; i.e., all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.14A-14C, the dimples labelled A have a diameter of about 0.110 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled C have a diameter of about 0.160 inches, the dimples labelled D have a diameter of about 0.170 inches, and the dimples labelled E have a diameter of about 0.185 inches. Thus, according to the embodiment shown inFIGS.14A-14C, tessellating first domain14aand second domain14babout the outer surface of a golf ball results in an overall dimple pattern having a total of 350 dimples arranged within eight copies of first domain14aand six copies of second domain14b, the dimples having five different dimple diameters, including a minimum diameter of 0.110 inches, a maximum diameter of 0.185 inches, and three additional dimple diameters, with the first domain having four different dimple diameters (A, B, C, E) and the second domain having four different dimple diameters (A, B, D, E). SD1, SD2, the first domain diameter ratio, and the second domain diameter ratio, for each of the five different dimple diameters are given in Table 10 below.

TABLE 10Dimple Diameter (alphabetical label)Dimple Diameter (inches)SD1SD2first domain diameter ratio =SD⁢1SD⁢1+SD⁢2second domain diameter ratio =SD⁢2SD⁢1+SD2A0.110141545B0.150692535C0.1606010D0.17001601E0.18538311811

Thus, in the embodiment shown inFIGS.14A-14C,

SD1≥1, SD2≥1, and SD1≤½(SD2) for the minimum dimple diameter A;

SD1≥1, and SD2≥1, for the first additional dimple diameter B;

SD1≥1, and SD2=0, for the second additional dimple diameter C;

SD1=0, and SD2≥1, for the third additional dimple diameter D; and

SD1≥1, SD2≥1, and SD1≤½(SD2) for the maximum dimple diameter E.

FIGS.14D-14Falso illustrate a first domain14aand a second domain14bformed according to the midpoint to midpoint method based on an octahedron. The alphabetical labels within the dimples designate same diameter dimples; i.e., all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.14D-14F, the dimples labelled A have a diameter of about 0.110 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled C have a diameter of about 0.160 inches, and the dimples labelled D have a diameter of about 0.180 inches. Thus, according to the embodiment shown inFIGS.14D-14F, tessellating first domain14aand second domain14babout the outer surface of a golf ball results in an overall dimple pattern having a total of 374 dimples arranged within eight copies of first domain14aand six copies of second domain14b, the dimples having four different dimple diameters, including a minimum diameter of 0.110 inches, a maximum diameter of 0.180 inches, and two additional dimple diameters, with the first domain and the second domain each having all four different dimple diameters (A, B, C, D). SD1, SD2, the first domain diameter ratio, and the second domain diameter ratio, for each of the four different dimple diameters are given in Table 11 below.

TABLE 11Dimple Diameter (alphabetical label)Dimple Diameter (inches)SD1SD2first domain diameter ratio =SD⁢1SD⁢1+SD⁢2second domain diameter ratio =SD⁢2SD⁢1+SD⁢2A0.11011211⁢31⁢21⁢3B0.150692535C0.160683747D0.1803121545
Thus, in the embodiment shown inFIGS.14D-14F,

SD1≥1, SD2≥1, and SD1≤½(SD2) for the minimum dimple diameter A;

SD1≥1, and SD2≥1, for the first additional dimple diameter B;

SD1≥1, and SD2≥1, for the second additional dimple diameter C; and

SD1≥1, SD2≥1, and SD1≤½(SD2) for the maximum dimple diameter D.

In another particular aspect of this embodiment, for the minimum dimple diameter,

SD1min≥2(SD2min)

where SD1minis the number of dimples positioned within the first domain having the minimum dimple diameter, and SD2minis the number of dimples positioned within the second domain having the minimum dimple diameter. In another particular aspect of this embodiment, for the maximum dimple diameter,

SD1max≥ 3/2(SD2max)

where SD1maxis the number of dimples positioned within the first domain having the maximum dimple diameter, and SD2maxis the number of dimples positioned within the second domain having the maximum dimple diameter. The dimple pattern optionally has one or more of the following additional characteristics:a) the first domain has three-way rotational symmetry about the central point of the first domain, and the second domain has four-way rotational symmetry about the central point of the second domain;b) the number of different dimple diameters in the first domain is the same as the number of different dimple diameters in the second domain;c) the number of different dimple diameters in the first domain is different from the number of different dimple diameters in the second domain;d) the first domain and the second domain each include at least one dimple having the minimum dimple diameter;e) the first domain and the second domain each include at least one dimple having the maximum dimple diameter;f) there are at least four, or at least five, or at least six, or at least seven, different dimple diameters on the outer surface of the ball;g) the first domain comprises dimples having at least four different diameters, or the first domain consists of dimples having four different diameters;h) the second domain comprises dimples having at least four different diameters, or the second domain consists of dimples having six different diameters;i) every different dimple diameter on the ball is present in the first domain;j) at least one, or at least two, or at least three, of the different dimple diameters on the ball is not present in the first domain;k) every different dimple diameter on the ball is present in the second domain;l) at least one, or at least two, or at least three, of the different dimple diameters on the ball is not present in the second domain.

For example,FIGS.14G-14Iillustrate a first domain14aand a second domain14bformed according to the midpoint to midpoint method based on an octahedron. The alphabetical labels within the dimples designate same diameter dimples; i.e., all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.14G-14I, the dimples labelled A have a diameter of about 0.130 inches, the dimples labelled B have a diameter of about 0.140 inches, the dimples labelled C have a diameter of about 0.150 inches, the dimples labelled D have a diameter of about 0.160 inches, the dimples labelled E have a diameter of about 0.170 inches, the dimples labelled F have a diameter of about 0.180 inches, and the dimples labelled G have a diameter of about 0.190 inches. Thus, according to the embodiment shown inFIGS.14G-14I, tessellating first domain14aand second domain14babout the outer surface of a golf ball results in an overall dimple pattern having a total of 342 dimples arranged within eight copies of first domain14aand six copies of second domain14b, the dimples having seven different dimple diameters, including a minimum diameter of 0.130 inches, a maximum diameter of 0.190 inches, and five additional dimple diameters, with the first domain having four different dimple diameters (A, D, E, G) and the second domain having six different dimple diameters (A, B, C, D, F, G). For each of the seven different dimple diameters, Table 12 below gives the number of same diameter dimples positioned within the first domain having that given diameter (SD1), the number of same diameter dimples positioned within the second domain having that given diameter (SD2), the first domain diameter ratio, and the second domain diameter ratio.

TABLE 12Dimple Diameter (alphabetical label)Dimple Diameter (inches)SD1SD2first domain diameter ratio =SD⁢1SD⁢1+SD⁢2second domain diameter ratio =SD⁢2SD⁢1+SD⁢2A0.130313414B0.1400120121212C0.150080888D0.1603831⁢181⁢1E0.170303303F0.180040444G0.19064610410

Thus, in the embodiment shown inFIGS.14G-14I,SD1≥0, SD2≥0, and SD1≥2(SD2) for the minimum dimple diameter A;SD1=0 and SD2≥0, for the first additional dimple diameter B;SD1=0 and SD2≥0, for the second additional dimple diameter C;SD1≥0 and SD2≥0, for the third additional dimple diameter D;SD1≥0 and SD2=0, for the fourth additional dimple diameter E;SD1=0 and SD2≥0, for the fifth additional dimple diameter F; andSD1≥0, SD2>0, and SD1≥(SD2) for the maximum dimple diameter G.

In another particular aspect of this embodiment, for the minimum dimple diameter, SD1min+SD2min≥5, where SD1minis the number of dimples positioned within the first domain having the minimum dimple diameter, SD2minis the number of dimples positioned within the second domain having the minimum dimple diameter, and either SD1min=0 or SD2min=0. In another particular aspect of this embodiment, for the maximum dimple diameter, SD1max+SD2max≤3, where SD1maxis the number of dimples positioned within the first domain having the maximum dimple diameter and SD2maxis the number of dimples positioned within the second domain having the maximum dimple diameter. The dimple pattern optionally has one or more of the following additional characteristics:a) the first domain has three-way rotational symmetry about the central point of the first domain, and the second domain has four-way rotational symmetry about the central point of the second domain;b) SD1min+SD2min≥8, or SD1min+SD2min≥10;c) either SD1max=0 or SD2max=0;d) SD1max+SD2max=1;e) the first domain does not include any dimples having the minimum dimple diameter or the maximum dimple diameter;f) there are at least three, or at least four, or at least five different dimple diameters on the outer surface of the ball; andg) every different dimple diameter on the ball is present in the second domain. For example,FIGS.16A-16Cillustrate a first domain14aand a second domain14bformed according to the midpoint to midpoint method based on an octahedron. The alphabetical labels within the dimples designate same diameter dimples; i.e., all dimples labelled A have the same diameter, all dimples labelled B have the same diameter, and so on. In a particular aspect of the embodiment illustrated inFIGS.16A-16C, the dimples labelled A have a diameter of about 0.120 inches, the dimples labelled B have a diameter of about 0.150 inches, the dimples labelled C have a diameter of about 0.155 inches, the dimples labelled D have a diameter of about 0.170 inches, and the dimples labelled E have a diameter of about 0.185 inches. Thus, according to the embodiment shown inFIGS.16A-16C, tessellating first domain14aand second domain14babout the outer surface of a golf ball results in an overall dimple pattern having a total of 390 dimples arranged within eight copies of first domain14aand six copies of second domain14b, the dimples having five different dimple diameters, including a minimum diameter of 0.120 inches, a maximum diameter of 0.185 inches, and three additional dimple diameters, with the first domain having three different dimple diameters (B, C, D) and the second domain having five different dimple diameters (A, B, C, D, E). For each of the five different dimple diameters, Table 13 below gives the number of same diameter dimples positioned within the first domain having that given diameter (SD1), the number of same diameter dimples positioned within the second domain having that given diameter (SM), the first domain diameter ratio, and the second domain diameter ratio.

TABLE 13Dimple Diameter (alphabetical label)Dimple Diameter (inches)SD1SD2first domain diameter ratio =SD⁢1SD⁢1+SD⁢2second domain diameter ratio =SD⁢2SD⁢1+SD⁢2A0.12001201⁢21⁢21⁢2B0.15031231⁢51215C0.15568614814D0.17061261⁢81⁢21⁢8E0.185010111

Thus, in the embodiment shown inFIGS.16A-16C,SD1=0 and SD2=12 for the minimum dimple diameter A; andSD1=0 and SD2=1 for the maximum dimple diameter E.

In a particular aspect of the embodiments disclosed herein wherein there are two or more different dimple diameters on the outer surface of the ball, the number of different dimple diameters, D, on the outer surface is related to the total number of dimples, N, on the outer surface, such that: if N<350, then D>5; and if N≥350, then D>6. In a further particular aspect of this embodiment, the dimples are arranged in multiple copies of a first domain and a second domain formed according to the midpoint to midpoint method based on an octahedron wherein the first domain and the second domain are tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles. The overall dimple pattern consists of eight first domains having three-way rotational symmetry about the central point of the first domain and six second domains having four-way symmetry about the central point of the second domain. The dimple pattern within the first domain is different from the dimple pattern within the second domain. Each of the first domain and the second domain consists of perimeter dimples and interior dimples. The dimples optionally have one or more of the following additional characteristics:a) each of the perimeter dimples has at least two nearest neighbor dimples that are located in a domain other than the domain of that perimeter dimple;b) for each perimeter dimple, the difference in diameter between the perimeter dimple and each of its nearest neighbor dimples located in a different domain is 0.08 inches or less, or 0.06 inches or less, or 0.04 inches or less; andc) at least one perimeter dimple in each domain is a same diameter dimple with respect to at least one of its nearest neighbor dimples located in a different domain.

In another particular aspect of the embodiments disclosed herein wherein there are two or more different dimple diameters on the outer surface of the ball, the number of different dimple diameters, D, on the outer surface is related to the total number of dimples, N, on the outer surface, such that: if N<302, then D≤5; if N=302, then D≤4; if 302<N<350, then D≤5; and if N≥350, then D≤6. In a further particular aspect of this embodiment, the sample standard deviation is less than 0.025, or less than 0.020, or less than 0.0175. Sample standard deviation, s, is defined by the equation:

s=Σi=1N(xi-x¯)2N-1
where xiis the diameter of any given dimple on the outer surface of the ball,xis the average dimple diameter, and N is the total number of dimples on the outer surface of the ball.

In another further particular aspect of this embodiment, the dimples are arranged in multiple copies of a first domain and a second domain formed according to the midpoint to midpoint method based on an octahedron wherein the first domain and the second domain are tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles. The overall dimple pattern consists of eight first domains having three-way rotational symmetry about the central point of the first domain and six second domains having four-way symmetry about the central point of the second domain. The dimple pattern within the first domain is different from the dimple pattern within the second domain. Each of the first domain and the second domain consists of perimeter dimples and interior dimples. The dimples optionally have one or more of the following additional characteristics:a) each of the perimeter dimples has at least two nearest neighbor dimples that are located in a domain other than the domain of that perimeter dimple;b) for each perimeter dimple, the difference in diameter between the perimeter dimple and each of its nearest neighbor dimples located in a different domain is 0.08 inches or less, or 0.06 inches or less, or 0.04 inches or less; andc) at least one perimeter dimple in each domain is a same diameter dimple with respect to at least one of its nearest neighbor dimples located in a different domain.

For example, in the embodiment shown inFIG.11H, each of the dimples labelled4or6or9is a perimeter dimple of the first domain14a, and each of the dimples labelled1or5is an interior dimple of the first domain14a. In the embodiment shown inFIG.11I, each of the dimples labelled3or7or8is a perimeter dimple of the second domain14b, and each of the dimples labelled2or4or9or10is an interior dimple of the second domain14b.

In the embodiment shown inFIG.11J, the total number of dimples on the outer surface of the ball is 350, and the number of different dimple diameters is 10. InFIGS.11H and11I, the numerical labels within the dimples designate same diameter dimples. For example, all dimples labelled1have the same diameter; all dimples labelled2have the same diameter; and so on. In a particular aspect of the embodiment illustrated inFIGS.11H and11I, the dimples labelled1have a diameter of about 0.090 inches, the dimples labelled2have a diameter of about 0.110 inches, the dimples labelled3have a diameter of about 0.115 inches, the dimples labelled4have a diameter of about 0.150 inches, the dimples labelled5have a diameter of about 0.160 inches, the dimples labelled6have a diameter of about 0.165 inches, the dimples labelled7have a diameter of about 0.170 inches, the dimples labelled8have a diameter of about 0.175 inches, the dimples labelled9have a diameter of about 0.185 inches, and the dimples labelled10have a diameter of about 0.205 inches.

In the embodiment shown inFIG.11K, each of the dimples labelled2is a perimeter dimple of the first domain14a, as is each of the nine dimples labelled3that are directly adjacent to one of the three border segments. Each of the three dimples labelled3that are not directly adjacent to one or the three border segments is an interior dimple of the first domain14a. In the embodiment shown inFIG.11L, each of the dimples labelled1or3is a perimeter dimple of the second domain14b, and each of the dimples labelled2or4is an interior dimple of the second domain14b.

In the embodiment shown inFIG.11M, the total number of dimples on the outer surface of the ball is342, and the number of different dimple diameters is 4. InFIGS.11K and11L, the numerical labels within the dimples designate same diameter dimples. For example, all dimples labelled1have the same diameter; all dimples labelled2have the same diameter; and so on. In a particular aspect of the embodiment illustrated inFIGS.11K and11L, the dimples labelled1have a diameter of about 0.110 inches, the dimples labelled2have a diameter of about 0.150 inches, the dimples labelled3have a diameter of about 0.170 inches, and the dimples labelled4have a diameter of about 0.185 inches. The sample standard deviation is 0.0182. The maximum difference in diameter between nearest neighbor dimples located in different domains is 0.04 inches.

There are 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 perimeters. 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 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 or dimples may be shared between domains, so long as the dimple arrangement on each 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%, or more than about 70%, or more than about 80% of the ball surface without using dimples.

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.

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 exceeding12. 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 14.

TABLE 14Symmetry of Golf Ball of the Present Invention as aFunction of PolyhedronType of PolyhedronType of SymmetrySymmetrical OrderTetrahedronChiral Tetrahedral Symmetry12CubeChiral Octahedral Symmetry24OctahedronChiral Octahedral Symmetry24DodecahedronChiral Icosahedral Symmetry60IcosahedronChiral Icosahedral Symmetry60

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.

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.

Dimple patterns of the present invention are particularly suitable for packing dimples on seamless golf balls. Seamless golf balls and methods of producing such are further disclosed, for example, in U.S. Pat. Nos. 6,849,007 and 7,422,529, the entire disclosures of which are hereby incorporated herein by reference.

In a particular aspect of the embodiments disclosed herein, golf balls of the present invention have a total number of dimples, N, on the outer surface thereof, of302or306or320or336or342or350or360or374or384or390or432.

In another particular aspect of the embodiments disclosed herein, golf balls of the present invention are oversized golf balls, having a diameter of greater than 1.69 inches, or a diameter of greater than 1.70 inches, or a diameter of greater than 1.82 inches, or a diameter of 1.70 inches or 1.72 inches or 1.74 inches or 1.78 inches or 1.82 inches, or a diameter within a range having a lower limit and an upper limit selected from these values. In a first further particular aspect of this embodiment, the diameter of the golf ball is from 1.70 inches to 1.82 inches, and the average plan shape area of the dimples, AAVE, in inch2, relates to the total number of dimples, N, on the outer surface of the golf ball, such that:
AAVE>1.617×10−7(N2)−1.685×10−4(N)+0.05729,AAVE<2.251×10−7(N2)−2.345×10−4(N)+0.07973, and 250<N<450.

In a second further particular aspect of this embodiment, the diameter of the golf ball is from 1.70 inches to 1.74 inches, and the average plan shape area of the dimples, AAVE, in inch2, relates to the total number of dimples, N, on the outer surface of the golf ball, such that:
AAVE>1.617×10−7(N2)−1.685×10−4(N)+0.05729, AAVE<2.057×10−7(N2)−2.143×10−4(N)+0.07288, and 250<N<450.
In a third further particular aspect of this embodiment, the diameter of the golf ball is from 1.74 inches to 1.78 inches, and the average plan shape area of the dimples, AAVE, in inch2, relates to the total number of dimples, N, on the outer surface of the golf ball, such that:
AAVE>1.694×10−7(N2)−1.765×10−4(N)+0.06002,AAVE<2.153×10−7(N2)−2.243×10−4(N)+0.07627, and 250<N<450.
In a fourth further particular aspect of this embodiment, the diameter of the golf ball is from 1.78 inches to 1.82 inches, and the average plan shape area of the dimples, AAVE, in inch2, relates to the total number of dimples, N, on the outer surface of the golf ball, such that:
AAVE>1.773×10−7(N2)−1.847×10−4(N)+0.06281, AAVE<2.251×10−7(N2)−2.345×10−4(N)+0.07973, and 250<N<450.
In a fifth further particular aspect of this embodiment, the golf ball has a diameter of greater than 1.82 inches, and the average plan shape area of the dimples, AAVE, in inch2, relates to the total number of dimples, N, on the outer surface of the golf ball such that:
AAVE>1.854×10−7(N2)−1.931×10−4(N)+0.06566, and 250<N<450.

FIGS.15A-15Cillustrate an example of a dimple pattern for oversized golf balls according to an embodiment of the present invention. InFIGS.15A-15C, the dimples are spherical dimples having a circular plan shape and a cross-sectional profile defined by a spherical function, and numerical labels within the dimples designate same diameter dimples. For example, all dimples labelled1have the same diameter; all dimples labelled2have the same diameter; and so on. Table 15 below gives illustrative values for dimple diameter, plan shape area, edge angle, dimple depth, and dimple volume for each given dimple size according to a non-limiting example of the embodiment shown inFIGS.15A-15C.

TABLE 15Non-limiting Example of Dimple Properties for the Dimples of FIGS. 15A-15CDimple Pattern Generated Using the Midpoint to Midpoint Method Based on an OctahedronDOMAIN 1 (labelled 14a in FIGS. 15A-15B)DimplePlan ShapeEdgeDimpleNumber of DimplesDimpleDiameterAreaAngleDepthDimple Volumelocated inLabel(in)(in2)(°)(in)(in3)Domain 120.1330.013914.50.00805.57 × 10−5330.1640.021114.50.00981.04 × 10−412DOMAIN 2 (labelled 14b in FIGS. 15A-15B)DimplePlan ShapeEdgeDimpleNumber of DimplesDimpleDiameterAreaAngleDepthDimple Volumelocated inLabel(in)(in2)(°)(in)(in3)Domain 210.1150.010414.50.00733.820 × 10−5420.1570.019414.50.01009.674 × 10−5930.1780.024914.50.01131.408 × 10−41640.1940.029514.50.01231.814 × 10−48

An overall golf ball dimple pattern is formed by tessellating multiple copies of the first domain and the second domain to cover the outer surface of the golf ball in a uniform pattern having no great circles. The resulting dimple pattern consists of eight first domains having three-way rotational symmetry about the central point of the first domain, and six second domains having four-way rotational symmetry about the central point of the second domain. In a particular embodiment of the example illustrated inFIGS.15A-15C, the golf ball has a diameter of 1.76 inches, the overall golf ball dimple pattern consists of 342 dimples, and the average plan shape area of the dimples is 0.0218 in2.

Aerodynamic characteristics of golf balls of the present invention can be described by aerodynamic coefficient magnitude and aerodynamic force angle. Based on a dimple pattern generated according to the present invention, in one embodiment, the golf ball achieves an aerodynamic coefficient magnitude of from 0.25 to 0.32 and an aerodynamic force angle of from 30° to 38° at a Reynolds Number of 230000 and a spin ratio of 0.085. Based on a dimple pattern generated according to the present invention, in another embodiment, the golf ball achieves an aerodynamic coefficient magnitude of from 0.26 to 0.33 and an aerodynamic force angle of from 32° to 40° at a Reynolds Number of 180000 and a spin ratio of 0.101. Based on a dimple pattern generated according to the present invention, in another embodiment, the golf ball achieves an aerodynamic coefficient magnitude of from 0.27 to 0.37 and an aerodynamic force angle of from 35° to 44° at a Reynolds Number of 133000 and a spin ratio of 0.133. Based on a dimple pattern generated according to the present invention, in another embodiment, the golf ball achieves an aerodynamic coefficient magnitude of from 0.32 to 0.45 and an aerodynamic force angle of from 39° to 45° at a Reynolds Number of 89000 and a spin ratio of 0.183. For purposes of the present disclosure, aerodynamic coefficient magnitude (Cmag) is defined by Cmag=(CL2+CD2)1/2and aerodynamic force angle (Cangle) is defined by Cangle=tan−1(CL/CD), where CLis a lift coefficient and CDis a drag coefficient. Aerodynamic characteristics of a golf ball, including aerodynamic coefficient magnitude and aerodynamic force angle, are disclosed, for example, in U.S. Pat. No. 6,729,976 to Bissonnette et al., the entire disclosure of which is hereby incorporated herein by reference. Aerodynamic coefficient magnitude and aerodynamic force angle values are calculated using the average lift and drag values obtained when 30 balls are tested in a random orientation. Reynolds number is an average value for the test and can vary by plus or minus 3%. Spin ratio is an average value for the test and can vary by plus or minus 5%.

When numerical lower limits and numerical upper limits are set forth herein, it is contemplated that any combination of these values may be used. All patents, publications, test procedures, and other references cited herein, including priority documents, are fully incorporated by reference to the extent such disclosure is not inconsistent with this invention and for all jurisdictions in which such incorporation is permitted. While the illustrative embodiments of the invention have been described with particularity, it will be understood that various other modifications will be apparent to and can be readily made by those of ordinary skill in the art without departing from the spirit and scope of the invention. Accordingly, it is not intended that the scope of the claims appended hereto be limited to the examples and descriptions set forth herein, but rather that the claims be construed as encompassing all of the features of patentable novelty which reside in the present invention, including all features which would be treated as equivalents thereof by those of ordinary skill in the art to which the invention pertains.