US20130150186A1 - Dimple patterns for golf balls - Google Patents

Dimple patterns for golf balls Download PDF

Info

Publication number
US20130150186A1
US20130150186A1 US13/765,986 US201313765986A US2013150186A1 US 20130150186 A1 US20130150186 A1 US 20130150186A1 US 201313765986 A US201313765986 A US 201313765986A US 2013150186 A1 US2013150186 A1 US 2013150186A1
Authority
US
United States
Prior art keywords
polyhedron
domain
domains
golf ball
vertex
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Abandoned
Application number
US13/765,986
Inventor
Nicholas M. Nardacci
Michael R. Madson
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Acushnet Co
Original Assignee
Acushnet Co
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority to US12/262,464 priority Critical patent/US8029388B2/en
Priority to US13/251,590 priority patent/US20120071276A1/en
Application filed by Acushnet Co filed Critical Acushnet Co
Priority to US13/765,986 priority patent/US20130150186A1/en
Assigned to ACUSHNET COMPANY reassignment ACUSHNET COMPANY ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: MADSON, MICHAEL R., NARDACCI, NICHOLAS M.
Publication of US20130150186A1 publication Critical patent/US20130150186A1/en
Assigned to KOREA DEVELOPMENT BANK, NEW YORK BRANCH reassignment KOREA DEVELOPMENT BANK, NEW YORK BRANCH SECURITY AGREEMENT Assignors: ACUSHNET COMPANY
Assigned to ACUSHNET COMPANY reassignment ACUSHNET COMPANY RELEASE OF SECURITY INTEREST IN PATENTS PREVIOUSLY RECORDED AT REEL/FRAME (031935/0395) Assignors: KOREA DEVELOPMENT BANK, NEW YORK BRANCH
Application status is Abandoned legal-status Critical

Links

Images

Classifications

    • AHUMAN NECESSITIES
    • A63SPORTS; GAMES; AMUSEMENTS
    • A63BAPPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003Golf balls
    • A63B37/0004Surface depressions or protrusions
    • A63B37/0006Arrangement or layout of dimples
    • AHUMAN NECESSITIES
    • A63SPORTS; GAMES; AMUSEMENTS
    • A63BAPPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003Golf balls
    • A63B37/0004Surface depressions or protrusions
    • AHUMAN NECESSITIES
    • A63SPORTS; GAMES; AMUSEMENTS
    • A63BAPPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003Golf balls
    • A63B37/0004Surface depressions or protrusions
    • A63B37/0007Non-circular dimples
    • AHUMAN NECESSITIES
    • A63SPORTS; GAMES; AMUSEMENTS
    • A63BAPPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B45/00Apparatus or methods for manufacturing balls

Abstract

The present invention provides a method for arranging dimples on a golf ball surface that significantly improves aerodynamic symmetry and minimizes parting line visibility by arranging the dimples in a pattern derived from at least one irregular domain generated from a regular or non-regular polyhedron. The method includes choosing control points of a polyhedron, generating an irregular domain based on those control points, packing the irregular domain with dimples, and tessellating the irregular domain to cover the surface of the golf ball. The control points include the center of a polyhedral face, a vertex of the polyhedron, a midpoint or other point on an edge of the polyhedron and others. The method ensures that the symmetry of the underlying polyhedron is preserved while eliminating great circles due to parting lines.

Description

    CROSS REFERENCE TO RELATED APPLICATIONS
  • This application is a Divisional of co-pending U.S. patent application Ser. No. 13/251,590, filed Oct. 3, 2011, which is a Divisional of co-pending U.S. patent application Ser. No. 12/262,464 filed Oct. 31, 2008, now U.S. Pat. No. 8,029,388, the disclosures of which are incorporated by reference herein in their entirety.
  • FIELD OF THE INVENTION
  • This invention relates to golf balls, particularly to golf balls having improved dimple patterns. More particularly, the invention relates to methods of arranging dimples on a golf ball by generating irregular domains based on polyhedrons, packing the irregular domains with dimples, and tessellating the domains onto the surface of the golf ball.
  • BACKGROUND OF THE INVENTION
  • Historically, dimple patterns for golf balls have had a variety of geometric shapes, patterns, and configurations. Primarily, patterns are laid out in order to provide desired performance characteristics based on the particular ball construction, material attributes, and player characteristics influencing the ball's initial launch angle and spin conditions. Therefore, pattern development is a secondary design step that is used to achieve the appropriate aerodynamic behavior, thereby tailoring ball flight characteristics and performance.
  • Aerodynamic forces generated by a ball in flight are a result of its velocity and spin. These forces can be represented by a lift force and a drag force. Lift force is perpendicular to the direction of flight and is a result of air velocity differences above and below the rotating ball. This phenomenon is attributed to Magnus, who described it in 1853 after studying the aerodynamic forces on spinning spheres and cylinders, and is described by Bernoulli's Equation, a simplification of the first law of thermodynamics. Bernoulli's equation relates pressure and velocity where pressure is inversely proportional to the square of velocity. The velocity differential, due to faster moving air on top and slower moving air on the bottom, results in lower air pressure on top and an upward directed force on the ball.
  • Drag is opposite in sense to the direction of flight and orthogonal to lift. The drag force on a ball is attributed to parasitic drag forces, which consist of pressure drag and viscous or skin friction drag. A sphere is a bluff body, which is an inefficient aerodynamic shape. As a result, the accelerating flow field around the ball causes a large pressure differential with high-pressure forward and low-pressure behind the ball. The low pressure area behind the ball is also known as the wake. In order to minimize pressure drag, dimples provide a means to energize the flow field and delay the separation of flow, or reduce the wake region behind the ball. Skin friction is a viscous effect residing close to the surface of the ball within the boundary layer.
  • The industry has seen many efforts to maximize the aerodynamics of golf balls, through dimple disturbance and other methods, though they are closely controlled by golf's national governing body, the United States Golf Association (U.S.G.A.). One U.S.G.A. requirement is that golf balls have aerodynamic symmetry. Aerodynamic symmetry allows the ball to fly with a very small amount of variation no matter how the golf ball is placed on the tee or ground. Preferably, dimples cover the maximum surface area of the golf ball without detrimentally affecting the aerodynamic symmetry of the golf ball.
  • In attempts to improve aerodynamic symmetry, many dimple patterns are based on geometric shapes. These may include circles, hexagons, triangles, and the like. Other dimple patterns are based in general on the five Platonic Solids including icosahedron, dodecahedron, octahedron, cube, or tetrahedron. Yet other dimple patterns are based on the thirteen Archimedian Solids, such as the small icosidodecahedron, rhomicosidodecahedron, small rhombicuboctahedron, snub cube, snub dodecahedron, or truncated icosahedron. Furthermore, other dimple patterns are based on hexagonal dipyramids. Because the number of symmetric solid plane systems is limited, it is difficult to devise new symmetric patterns. Moreover, dimple patterns based some of these geometric shapes result in less than optimal surface coverage and other disadvantageous dimple arrangements. Therefore, dimple properties such as number, shape, size, and arrangement are often manipulated in an attempt to generate a golf ball that has better aerodynamic properties.
  • U.S. Pat. No. 5,562,552 to Thurman discloses a golf ball with an icosahedral dimple pattern, wherein each triangular face of the icosahedron is split by a three straight lines which each bisect a corner of the face to form 3 triangular faces for each icosahedral face, wherein the dimples are arranged consistently on the icosahedral faces.
  • U.S. Pat. No. 5,046,742 to Mackey discloses a golf ball with dimples packed into a 32-sided polyhedron composed of hexagons and pentagons, wherein the dimple packing is the same in each hexagon and in each pentagon.
  • U.S. Pat. No. 4,998,733 to Lee discloses a golf ball formed of ten “spherical” hexagons each split into six equilateral triangles, wherein each triangle is split by a bisecting line extending between a vertex of the triangle and the midpoint of the side opposite the vertex, and the bisecting lines are oriented to achieve improved symmetry.
  • U.S. Pat. No. 6,682,442 to Winfield discloses the use of polygons as packing elements for dimples to introduce predictable variance into the dimple pattern. The polygons extend from the poles of the ball to a parting line. Any space not filled with dimples from the polygons is filled with other dimples.
  • A continuing need exists for a dimple pattern whose dimple arrangement results in a maximized surface coverage and desirable aerodynamic characteristics, including improved symmetry.
  • SUMMARY OF THE INVENTION
  • The present invention provides a method for arranging dimples on a golf ball surface that significantly improves aerodynamic symmetry and minimizes parting line visibility by arranging the dimples in a pattern derived from at least one irregular domain generated from a regular or non-regular polyhedron. The method includes choosing control points of a polyhedron, generating an irregular domain based on those control points, packing the irregular domain with dimples, and tessellating the irregular domain to cover the surface of the golf ball. The control points include the center of a polyhedral face, a vertex of the polyhedron, a midpoint or other point on an edge of the polyhedron and others. The method ensures that the symmetry of the underlying polyhedron is preserved while minimizing great circles due to parting lines from the molding process.
  • The present invention provides methods for generating an irregular domain based on two or more control points. These methods include connecting the control points with a non-linear sketch line, patterning the sketch line in a first manner to create a first irregular domain, and optionally patterning the sketch line in a second manner to create a second irregular domain.
  • The present invention also provides methods for generating one or more irregular domains based on each set of control points. The center to vertex method, the center to midpoint method, the vertex to midpoint method, the center to edge method, and the midpoint to center to vertex method each provide a single irregular domain that can be tessellated to cover a golf ball. The center to center method, the midpoint to midpoint method, and the vertex to vertex method each provide two irregular domains that can be tessellated to cover a golf ball. In each case, the irregular domains cover the surface of the golf ball in a uniform pattern.
  • BRIEF DESCRIPTION OF THE DRAWINGS
  • In the accompanying drawings which form a part of the specification and are to be read in conjunction therewith and in which like reference numerals are used to indicate like parts in the various views:
  • FIG. 1A illustrates a golf ball having dimples arranged by a method of the present invention; FIG. 1B illustrates a polyhedron face; FIG. 1C illustrates an element of the present invention in the polyhedron face of FIG. 1B; FIG. 1D illustrates a domain formed by a methods of the present invention packed with dimples and formed from two elements of FIG. 1C;
  • FIG. 2 illustrates a single face of a polyhedron having control points thereon;
  • FIG. 3A illustrates a polyhedron face; FIG. 3B illustrates an element of the present invention packed with dimples; FIG. 3C illustrates a domain of the present invention packed with dimples formed from elements of FIG. 3B; FIG. 3D illustrates a golf ball formed by a method of the present invention formed of the domain of FIG. 3C;
  • FIG. 4A illustrates two polyhedron faces; FIG. 4B illustrates a first domain of the present invention in the two polyhedron faces of FIG. 4A; FIG. 4C illustrates a first domain and a second domain of the present invention in three polyhedron faces; FIG. 4D illustrates a golf ball formed by a method of the present invention formed of the domains of FIG. 4C;
  • FIG. 5A illustrates a polyhedron face; FIG. 5B illustrates a first domain of the present invention in a polyhedron face; FIG. 5C illustrates a first domain and a second domain of the present invention in three polyhedron faces; FIG. 5D illustrates a golf ball formed using a method of the present invention formed of the domains of FIG. 5C;
  • FIG. 6A illustrates a polyhedron face; FIG. 6B illustrates a portion of a domain of the present invention in the polyhedron face of FIG. 6A; FIG. 6C illustrates a domain formed by the methods of the present invention; FIG. 6D illustrates a golf ball formed using the methods of the present invention formed of domains of FIG. 6C;
  • FIG. 7A illustrates a polyhedron face; FIG. 7B illustrates a domain of the present invention in the polyhedron face of FIG. 7A; FIG. 7C illustrates a golf ball formed by a method of the present invention;
  • FIG. 8A illustrates a first element of the present invention in a polyhedron face; FIG. 8B illustrates a first and a second element of the present invention in the polyhedron face of FIG. 8A; FIG. 8C illustrates two domains of the present invention composed of first and second elements of FIG. 8B; FIG. 8D illustrates a single domain of the present invention based on the two domains of FIG. 8C; FIG. 8E illustrates a golf ball formed using a method of the present invention formed of the domains of FIG. 8D;
  • FIG. 9A illustrates a polyhedron face; FIG. 9B illustrates an element of the present invention in the polyhedron face of FIG. 9A; FIG. 9C illustrates two elements of FIG. 9B combining to form a domain of the present invention; FIG. 9D illustrates a domain formed by the methods of the present invention based on the elements of FIG. 9C; FIG. 9E illustrates a golf ball formed using a method of the present invention formed of domains of FIG. 9D;
  • FIG. 10A illustrates a face of a rhombic dodecahedron; FIG. 10B illustrates a segment of the present invention in the face of FIG. 10A; FIG. 10C illustrates the segment of FIG. 10B and copies thereof forming a domain of the present invention; FIG. 10D illustrates a domain formed by a method of the present invention based on the segments of FIG. 10C; and FIG. 10E illustrates a golf ball formed by a method of the present invention formed of domains of FIG. 10D.
  • DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
  • In one embodiment, illustrated in FIG. 1A, the present invention comprises a golf ball 10 comprising dimples 12. Dimples 12 are arranged by packing irregular domains 14 with dimples, as seen best in FIG. 1D. Irregular domains 14 are created in such a way that, when tessellated on the surface of golf ball 10, they impart greater orders of symmetry to the surface than prior art balls. The irregular shape of domains 14 additionally minimize the appearance and effect of the golf ball parting line from the molding process, and allows greater flexibility in arranging dimples than would be available with regularly shaped domains.
  • The irregular domains can be defined through the use of any one of the exemplary methods described herein. Each method produces one or more unique domains based on circumscribing a sphere with the vertices of a regular polyhedron. The vertices of the circumscribed sphere based on the vertices of the corresponding polyhedron with origin (0,0,0) are defined below in Table 1.
  • TABLE 1 Vertices of Circumscribed Sphere based on Corresponding Polyhedron Vertices Type of Polyhedron Vertices Tetrahedron (+1, +1, +1); (−1, −1, +1); (−1, +1, −1); (+1, −1, −1) Cube (±1, ±1, ±1) Octahedron (±1, 0, 0); (0, ±1, 0); (0, 0, ±1) Dodecahedron (±1, ±1, ±1); (0, ±1/φ, ±φ); (±1/φ, ±φ, 0); (±φ, 0, ±1/φ)* Icosahedron (0, ±1, ±φ); (±1, ±φ, 0); (±φ, 0, ±1)* *φ = (1 + √5)/2
  • Each method has a unique set of rules which are followed for the domain to be symmetrically patterned on the surface of the golf ball. Each method is defined by the combination of at least two control points. These control points, which are taken from one or more faces of a regular or non-regular polyhedron, consist of at least three different types: the center C of a polyhedron face; a vertex V of a face of a regular polyhedron; and the midpoint M of an edge of a face of the polyhedron. FIG. 2 shows an exemplary face 16 of a polyhedron (a regular dodecahedron in this case) and one of each a center C, a midpoint M, a vertex V, and an edge E on face 16. The two control points C, M, or V may be of the same or different types. Accordingly, six types of methods for use with regular polyhedrons are defined as follows:
  • 1. Center to midpoint (C→M);
  • 2. Center to center (C→C);
  • 3. Center to vertex (C→V);
  • 4. Midpoint to midpoint (M→M);
  • 5. Midpoint to Vertex (M→V); and
  • 6. Vertex to Vertex (V→V).
  • While each method differs in its particulars, they all follow the same basic scheme. First, a non-linear sketch line is drawn connecting the two control points. This sketch line may have any shape, including, but not limited, to an arc, a spline, two or more straight or 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 to FIGS. 1A-1D, the center to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:
      • 1. A regular polyhedron is chosen (FIGS. 1A-1D use an icosahedron);
      • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 1B;
      • 3. Center C of face 16, and a first vertex V1 of face 16 are connected with any non-linear sketch line, hereinafter referred to as a segment 18;
      • 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with vertex V2 adjacent to vertex V1. The two segments 18 and 20 and the edge E connecting vertices V1 and V2 define an element 22, as shown best in FIG. 1C; and
      • 5. Element 22 is rotated about midpoint M of edge E to create a domain 14, as shown best in FIG. 1D.
  • When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 1A, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and V1. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces PF of the polyhedron chosen times the number of edges PE per face of the polyhedron divided by 2, as shown below in Table 2.
  • Domains Resulting from Use of Specific Polyhedra When Using the Center to Vertex Method
  • Number Type of of Faces, Number of Edges, Number of Domains Polyhedron PF PE 14 Tetrahedron 4 3 6 Cube 6 4 12 Octahedron 8 3 12 Dodecahedron 12 5 30 Icosahedron 20 3 30
  • The Center to Midpoint Method
  • Referring to FIGS. 3A-3D, the center to midpoint method yields a single irregular domain that can be tessellated to cover the surface of golf ball 10. The domain is defined as follows:
      • 1. A regular polyhedron is chosen (FIGS. 3A-3D use a dodecahedron);
      • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 3A;
      • 3. Center C of face 16, and midpoint M1 of a first edge E1 of face 16 are connected with a segment 18;
      • 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M2 of a second edge E2 adjacent to first edge E1. The two segments 16 and 18 and the portions of edge E1 and edge E2 between midpoints M1 and M2 define an element 22; and
      • 5. Element 22 is patterned about vertex V of face 16 which is contained in element 22 and connects edges E1 and E2 to create a domain 14.
  • When domain 14 is tessellated around a golf ball 10 to cover the surface of golf ball 10, as shown in FIG. 3D, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and M1. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of vertices PV of the chosen polyhedron, as shown below in Table 3.
  • TABLE 3 Domains Resulting From Use of Specific Polyhedra When Using the Center to Midpoint Method Type of Polyhedron Number of Vertices, PV Number of Domains 14 Tetrahedron 4 4 Cube 8 8 Octahedron 6 6 Dodecahedron 20 20 Icosahedron 12 12
  • The Center to Center Method
  • Referring to FIGS. 4A-4D, the center to center method yields two domains that can be tessellated to cover the surface of golf ball 10. The domains are defined as follows:
      • 1. A regular polyhedron is chosen (FIGS. 4A-4D use a dodecahedron);
      • 2. Two adjacent faces 16 a and 16 b of the regular polyhedron are chosen, as shown in FIG. 4A;
      • 3. Center C1 of face 16 a, and center C2 of face 16 b are connected with a segment 18;
      • 4. A copy 20 of segment 18 is rotated 180 degrees about the midpoint M between centers C1 and C2, such that copy 20 also connects center C1 with center C2, as shown in FIG. 4B. The two segments 16 and 18 define a first domain 14 a; and
      • 5. Segment 18 is rotated equally about vertex V to define a second domain 14 b, as shown in FIG. 4C.
  • When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIG. 4D, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points C1 and C2. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is PF*PE/2 for first domain 14 a and PV for second domain 14 b, as shown below in Table 4.
  • TABLE 4 Domains Resulting From Use of Specific Polyhedra When Using the Center to Center Method Number of Number Number of Number of First Number of Second Type of Vertices, Domains of Faces, Edges, Domains Polyhedron PV 14a PF PE 14b Tetrahedron 4 6 4 3 4 Cube 8 12 6 4 8 Octahedron 6 9 8 3 6 Dodecahedron 20 30 12 5 20 Icosahedron 12 18 20 3 12
  • The Midpoint to Midpoint Method
  • Referring to FIGS. 5A-5D, the midpoint to midpoint method yields two domains that tessellate to cover the surface of golf ball 10. The domains are defined as follows:
      • 1. A regular polyhedron is chosen (FIGS. 5A-5D use a dodecahedron);
      • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 5A;
      • 3. The midpoint M1 of a first edge E1 of face 16, and the midpoint M2 of a second edge E2 adjacent to first edge E1 are connected with a segment 18;
      • 4. Segment 18 is patterned around center C of face 16 to form a first domain 14 a, as shown in FIG. 5B;
      • 5. Segment 18, along with the portions of first edge E1 and second edge E2 between midpoints M1 and M2, define an element 22; and
      • 6. Element 22 is patterned about vertex V which is contained in element 22 and connects edges E1 and E2 to create a second domain 14 b, as shown in FIG. 5C.
  • When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIG. 5D, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points M1 and M2. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is PF for first domain 14 a and PV for second domain 14 b, as shown below in Table 5.
  • TABLE 5 Domains Resulting From Use of Specific Polyhedra When Using the Center to Center Method Number of Number of Second Type of Number of Number of First Vertices, Domains Polyhedron Faces, PF Domains 14a PV 14b Tetrahedron 4 4 4 4 Cube 6 6 8 8 Octahedron 8 8 6 6 Dodecahedron 12 12 20 20 Icosahedron 20 20 12 12
  • The Midpoint to Vertex Method
  • Referring to FIGS. 6A-6D, the midpoint to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:
      • 1. A regular polyhedron is chosen (FIGS. 6A-6D use a dodecahedron);
      • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 6A;
      • 3. A midpoint M1 of edge E1 of face 16 and a vertex V1 on edge E1 are connected with a segment 18;
      • 4. Copies 20 of segment 18 is patterned about center C of face 16, one for each midpoint M2 and vertex V2 of face 16, to define a portion of domain 14, as shown in FIG. 6B; and
      • 5. Segment 18 and copies 20 are then each rotated 180 degrees about their respective midpoints to complete domain 14, as shown in FIG. 6C.
  • When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 6D, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points M1 and V1. The number of domains 14 used to cover the surface of golf ball 10 is PF, as shown in Table 6.
  • TABLE 6 Domains Resulting From Use of Specific Polyhedra When Using the Midpoint to Vertex Method Type of Polyhedron Number of Faces, PF Number of Domains 14 Tetrahedron 4 4 Cube 6 6 Octahedron 8 8 Dodecahedron 12 12 Icosahedron 20 20
  • The Vertex to Vertex Method
  • Referring to FIGS. 7A-7C, the vertex to vertex method yields two domains that tessellate to cover the surface of golf ball 10. The domains are defined as follows:
      • 1. A regular polyhedron is chosen (FIGS. 7A-7C use an icosahedron);
      • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 7A;
      • 3. A first vertex V1 face 16, and a second vertex V2 adjacent to first vertex V1 are connected with a segment 18;
      • 4. Segment 18 is patterned around center C of face 16 to form a first domain 14 a, as shown in FIG. 7B;
      • 5. Segment 18, along with edge E1 between vertices V1 and V2, defines an element 22; and
      • 6. Element 22 is rotated around midpoint M1 of edge E1 to create a second domain 14 b.
  • When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIG. 7C, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points V1 and V2. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is PF for first domain 14 a and PF*PE/2 for second domain 14 b, as shown below in Table 7.
  • TABLE 7 Domains Resulting From Use of Specific Polyhedra When Using the Vertex to Vertex Method Number of Number Number of Second Type of Number of of First Edges per Face, Domains Polyhedron Faces, PF Domains 14a PE 14b Tetrahedron 4 4 3 6 Cube 6 6 4 12 Octahedron 8 8 3 12 Dodecahedron 12 12 5 30 Icosahedron 20 20 3 30
  • While the six methods previously described each make use of two control points, it is possible to create irregular domains based on more than two control points. For example, three, or even more, control points may be used. The use of additional control points allows for potentially different shapes for irregular domains. An exemplary method using a midpoint M, a center C and a vertex V as three control points for creating one irregular domain is described below.
  • The Midpoint to Center to Vertex Method
  • Referring to FIGS. 8A-8E, the midpoint to center to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:
      • 1. A regular polyhedron is chosen (FIGS. 8A-8E use an icosahedron);
      • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 8A;
      • 3. A midpoint M1 on edge E1 of face 16, Center C of face 16 and a vertex V1 on edge E1 are connected with a segment 18, and segment 18 and the portion of edge E1 between midpoint M1 and vertex V1 define a first element 22 a, as shown in FIG. 8A;
      • 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M2 on edge E2 adjacent to edge E1, and connects center C with a vertex V2 at the intersection of edges E1 and E2, and the portion of segment 18 between midpoint M1 and center C, the portion of copy 20 between vertex V2 and center C, and the portion of edge E1 between midpoint M1 and vertex V2 define a second element 22 b, as shown in FIG. 8B; 5. First element 22 a and second element 22 b are rotated about midpoint M1 of edge E1, as seen in FIGS. 8C, to define two domains 14, wherein a single domain 14 is bounded solely by portions of segment 18 and copy 20 and the rotation 18′ of segment 18, as seen in FIG. 8D. When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 8E, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points M, C, and V. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces PF of the polyhedron chosen times the number of edges PE per face of the polyhedron, as shown below in Table 8.
  • TABLE 8 Domains Resulting From Use of Specific Polyhedra When Using the Midpoint to Center to Vertex Method Type of Number of Number of Edges, Number of Domains Polyhedron Faces, PF PE 14 Tetrahedron 4 3 12 Cube 6 4 24 Octahedron 8 3 24 Dodecahedron 12 5 60 Icosahedron 20 3 60
  • While the methods described previously provide a framework for the use of center C, vertex V, and midpoint M as the only control points, other control points are usable. For example, a control point may be any point P on an edge E of the chosen polyhedron face. When this type of control point is used, additional types of domains may be generated, though the mechanism for creating the irregular domain(s) may be different. An exemplary method, using a center C and a point P on an edge, for creating one such irregular domain is described below.
  • The Center to Edge Method
  • Referring to FIGS. 9A-9E, the center to edge method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:
      • 1. A regular polyhedron is chosen (FIGS. 9A-9E use an icosahedron);
      • 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 9A;
      • 3. Center C of face 16, and a point P1 on edge E1 are connected with a segment 18,
      • 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a point P2 on edge E2 adjacent to edge E1, where point P2 is positioned identically relative to edge E2 as point P1 is positioned relative to edge E1, such that the two segments 18 and 20 and the portions of edges E1 and E2 between points P1 and P2, respectively, and a vertex V, which connects edges E1 and E2, define an element 22, as shown best in FIG. 9B; and
      • 5. Element 22 is rotated about midpoint M1 of edge E1 or midpoint M2 of edge E2, whichever is located within element 22, as seen in FIGS. 9B-9C, to create a domain 14, as seen in FIG. 9D.
  • When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 9E, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and P1. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces PF of the polyhedron chosen times the number of edges PE per face of the polyhedron divided by 2, as shown below in Table 9.
  • TABLE 9 Domains Resulting From Use of Specific Polyhedra When Using the Center to Edge Method Type of Number of Number of Edges, Number of Domains Polyhedron Faces, PF PE 14 Tetrahedron 4 3 6 Cube 6 4 12 Octahedron 8 3 12 Dodecahedron 12 5 30 Icosahedron 20 3 30
  • Though each of the above described methods has been explained with reference to regular polyhedrons, they may also be used with certain non-regular polyhedrons, such as Archimedean Solids, Catalan Solids, or others. The methods used to derive the irregular domains will generally require some modification in order to account for the non-regular face shapes of the non-regular solids. An exemplary method for use with a Catalan Solid, specifically a rhombic dodecahedron, is described below.
  • A Vertex to Vertex Method for a Rhombic Dodecahedron
  • Referring to FIGS. 10A-10E, a vertex to vertex method based on a rhombic dodecahedron yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:
      • 1. A single face 16 of the rhombic dodecahedron is chosen, as shown in FIG. 10A;
      • 2. A first vertex V1 face 16, and a second vertex V2 adjacent to first vertex V1 are connected with a segment 18, as shown in FIG. 10B;
      • 3. A first copy 20 of segment 18 is rotated about vertex V2, such that it connects vertex V2 to vertex V3 of face 16, a second copy 24 of segment 18 is rotated about center C, such that it connects vertex V3 and vertex V4 of face 16, and a third copy 26 of segment 18 is rotated about vertex V1 such that it connects vertex V1 to vertex V4, all as shown in FIG. 10C, to form a domain 14, as shown in FIG. 10D;
  • When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 10E, twelve domains will be used to cover the surface of golf ball 10, one for each face of the rhombic dodecahedron.
  • After the irregular domain(s) is created using any of the above methods, the domain(s) may be packed with dimples in order to be usable in creating golf ball 10. There are no limitations on how the dimples are packed. There are likewise no limitations to the dimple shapes or profiles selected to pack the domains. Though the present invention includes substantially circular dimples in one embodiment, dimples or protrusions (brambles) having any desired characteristics and/or properties may be used. For example, in one embodiment the dimples may have a variety of shapes and sizes including different depths and widths. In particular, the dimples may be concave hemispheres, or they may be triangular, square, hexagonal, catenary, polygonal or any other shape known to those skilled in the art. They may also have straight, curved, or sloped edges or sides. To summarize, any type of dimple or protrusion (bramble) known to those skilled in the art may be used with the present invention. The dimples may all fit within each domain, as seen in FIGS. 1A and 1D, or dimples may be shared between one or more domains, as seen in FIGS. 3C-3D, so long as the dimple arrangement on each independent domain remains consistent across all copies of that domain on the surface of a particular golf ball. Alternatively, the tessellation can create a pattern that covers more than about 60%, preferably more than about 70% and preferably more than about 80% of the golf ball surface without using dimples.
  • 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 exceeding 12. The order of symmetry of a golf ball produced using the method of the current invention will depend on the regular or non-regular polygon on which the irregular domain is based. The order and type of symmetry for golf balls produced based on the five regular polyhedra are listed below in Table 10.
  • TABLE 10 Symmetry of Golf Ball of the Present Invention as a Function of Polyhedron Type of Polyhedron Type of Symmetry Symmetrical Order Tetrahedron Chiral Tetrahedral Symmetry 12 Cube Chiral Octahedral Symmetry 24 Octahedron Chiral Octahedral Symmetry 24 Dodecahedron Chiral Icosahedral Symmetry 60 Icosahedron Chiral Icosahedral Symmetry 60
  • 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.
  • While the preferred embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not of limitation. It will be apparent to persons skilled in the relevant art that various changes in form and detail can be made therein without departing from the spirit and scope of the invention. For example, while the preferred polyhedral shapes have been provided above, other polyhedral shapes could also be used. Thus the present invention should not be limited by the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims (1)

We claim:
1. A golf ball having dimples based on a polyhedron pattern, wherein the dimples are arranged in irregular domains comprised of non-linear segments, wherein the irregular domains are tessellated over a surface of the golf ball and are defined by a non-linear line from a first vertex of a face of the polyhedron to a second vertex.
US13/765,986 2008-10-31 2013-02-13 Dimple patterns for golf balls Abandoned US20130150186A1 (en)

Priority Applications (3)

Application Number Priority Date Filing Date Title
US12/262,464 US8029388B2 (en) 2008-10-31 2008-10-31 Dimple patterns for golf balls
US13/251,590 US20120071276A1 (en) 2008-10-31 2011-10-03 Dimple patterns for golf balls
US13/765,986 US20130150186A1 (en) 2008-10-31 2013-02-13 Dimple patterns for golf balls

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US13/765,986 US20130150186A1 (en) 2008-10-31 2013-02-13 Dimple patterns for golf balls

Related Parent Applications (1)

Application Number Title Priority Date Filing Date
US13/251,590 Division US20120071276A1 (en) 2008-10-31 2011-10-03 Dimple patterns for golf balls

Publications (1)

Publication Number Publication Date
US20130150186A1 true US20130150186A1 (en) 2013-06-13

Family

ID=42132119

Family Applications (3)

Application Number Title Priority Date Filing Date
US12/262,464 Active 2029-05-17 US8029388B2 (en) 2008-10-31 2008-10-31 Dimple patterns for golf balls
US13/251,590 Abandoned US20120071276A1 (en) 2008-10-31 2011-10-03 Dimple patterns for golf balls
US13/765,986 Abandoned US20130150186A1 (en) 2008-10-31 2013-02-13 Dimple patterns for golf balls

Family Applications Before (2)

Application Number Title Priority Date Filing Date
US12/262,464 Active 2029-05-17 US8029388B2 (en) 2008-10-31 2008-10-31 Dimple patterns for golf balls
US13/251,590 Abandoned US20120071276A1 (en) 2008-10-31 2011-10-03 Dimple patterns for golf balls

Country Status (1)

Country Link
US (3) US8029388B2 (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20130065708A1 (en) * 2008-10-31 2013-03-14 Acushnet Company Dimple patterns for golf balls

Families Citing this family (34)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20110021292A1 (en) 2008-10-31 2011-01-27 Madson Michael R Dimple patterns for golf balls
US9440115B2 (en) * 2008-10-31 2016-09-13 Acushnet Company Dimple patterns for golf balls
US10080923B2 (en) 2008-10-31 2018-09-25 Acushnet Company Dimple patterns for golf balls
US10188907B2 (en) 2008-10-31 2019-01-29 Acushnet Company Dimple patterns for golf balls
US9855465B2 (en) 2008-10-31 2018-01-02 Acushnet Company Dimple patterns for golf balls
US10315076B2 (en) 2008-10-31 2019-06-11 Acushnet Company Dimple patterns for golf balls
US10150006B2 (en) 2008-10-31 2018-12-11 Acushnet Company Dimple patterns for golf balls
US9901781B2 (en) 2008-10-31 2018-02-27 Acushnet Company Dimple patterns for golf balls
US10076682B2 (en) 2008-10-31 2018-09-18 Acushnet Company Dimple patterns for golf balls
US10213651B2 (en) 2008-10-31 2019-02-26 Acushnet Company Dimple patterns for golf balls
US20170246509A1 (en) * 2008-10-31 2017-08-31 Acushnet Company Dimple patterns for golf balls
US9833664B2 (en) 2008-10-31 2017-12-05 Acushnet Company Dimple patterns for golf balls
KR20140002812U (en) * 2012-11-02 2014-05-12 애쿠쉬네트캄파니 Dimple patterns for golf balls
CN103801059B (en) * 2012-11-13 2018-07-20 阿库施耐特公司 The patterns of indentations of golf
US10076683B2 (en) 2008-10-31 2018-09-18 Acushnet Company Dimple patterns for golf balls
US9808674B2 (en) 2008-10-31 2017-11-07 Acushnet Company Dimple patterns for golf balls
US9873021B2 (en) 2008-10-31 2018-01-23 Acushnet Company Dimple patterns for golf balls
US10398942B2 (en) 2008-10-31 2019-09-03 Acushnet Company Dimple patterns for golf balls
US9795833B2 (en) 2008-10-31 2017-10-24 Acushnet Company Dimple patterns for golf balls
US10124212B2 (en) 2008-10-31 2018-11-13 Acushnet Company Dimple patterns for golf balls
US10293212B2 (en) 2008-10-31 2019-05-21 Acushnet Company Dimple patterns for golf balls
US9925418B2 (en) 2008-10-31 2018-03-27 Achushnet Company Dimple patterns for golf balls
US9873020B2 (en) 2008-10-31 2018-01-23 Acushnet Company Dimple patterns for golf balls
US10213652B2 (en) 2008-10-31 2019-02-26 Acushnet Company Dimple patterns for golf balls
JP5827531B2 (en) * 2010-09-30 2015-12-02 アクシュネット カンパニーAcushnet Company Golf ball dimple pattern
US9504877B2 (en) 2008-10-31 2016-11-29 Achushnet Company Dimple patterns for golf balls
US20170225041A1 (en) * 2008-10-31 2017-08-10 Acushnet Company Dimple patterns for golf balls
US20170225040A1 (en) * 2008-10-31 2017-08-10 Acushnet Company Dimple patterns for golf balls
US8529816B2 (en) 2010-10-05 2013-09-10 Acushnet Company Mold frames and cavities for making dimpled golf balls
EP2738742B1 (en) * 2012-11-07 2018-07-25 Sumitomo Rubber Industries, Ltd. Process for designing rugged pattern on golf ball surface
US10195485B2 (en) 2015-11-16 2019-02-05 Acushnet Company Curvilinear golf ball dimples and methods of making same
US9782629B2 (en) 2015-11-16 2017-10-10 Acushnet Company Curvilinear golf ball dimples and methods of making same
USD786375S1 (en) * 2015-12-28 2017-05-09 Nike, Inc. Ball with surface ornamentation pattern
USD786374S1 (en) * 2015-12-28 2017-05-09 Nike, Inc. Ball with surface ornamentation pattern

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20060264271A1 (en) * 2005-05-23 2006-11-23 Callaway Golf Company Golf ball dimple pattern

Family Cites Families (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5046742A (en) 1988-11-15 1991-09-10 Gary T. Mackey Golf ball
KR920004349B1 (en) 1989-08-10 1992-06-04 강병중 Golf-ball
KR960016742B1 (en) * 1994-01-25 1996-12-20 이세권 Golf ball
US5562552A (en) 1994-09-06 1996-10-08 Wilson Sporting Goods Co. Geodesic icosahedral golf ball dimple pattern
KR970005338B1 (en) * 1994-09-06 1997-04-15 이세권 Golf ball
US5735756A (en) * 1996-09-10 1998-04-07 Lisco, Inc. Golf ball and dimple pattern forming process
EP1166830A3 (en) * 2000-06-19 2003-12-10 Dunlop Slazenger Group Americas Inc Distance golf ball
US20020016228A1 (en) * 2000-06-19 2002-02-07 Emerson Brent D. Control golf ball-DDH steel control
US6682442B2 (en) 2001-02-08 2004-01-27 Acushnet Company Dimple patterns on golf balls
JP4672210B2 (en) * 2001-08-21 2011-04-20 Sriスポーツ株式会社 Golf ball
JP2003260151A (en) * 2002-03-08 2003-09-16 Bridgestone Sports Co Ltd Golf ball
US6702696B1 (en) * 2002-09-10 2004-03-09 Acushnet Company Dimpled golf ball and dimple distributing method
US7594867B2 (en) * 2003-08-12 2009-09-29 Acushnet Company Surface pattern for golf balls

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20060264271A1 (en) * 2005-05-23 2006-11-23 Callaway Golf Company Golf ball dimple pattern

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20130065708A1 (en) * 2008-10-31 2013-03-14 Acushnet Company Dimple patterns for golf balls

Also Published As

Publication number Publication date
US20100113187A1 (en) 2010-05-06
US20120071276A1 (en) 2012-03-22
US8029388B2 (en) 2011-10-04

Similar Documents

Publication Publication Date Title
KR880002367B1 (en) Golf ball
US5078402A (en) Golf ball
CA2040205C (en) Golf ball
US5957786A (en) Golf ball dimple pattern
US6383092B1 (en) Golf ball with pyramidal protrusions
EP0484612B1 (en) Golf ball
EP1704900B1 (en) A golf ball having a tubular lattice pattern
JP2937494B2 (en) Golf ball
JP3694671B2 (en) Dimple pattern based on leaf mechanism
KR960016742B1 (en) Golf ball
US6224499B1 (en) Golf ball with multiple sets of dimples
KR920004349B1 (en) Golf-ball
US5009428A (en) Golf ball
JP2849713B2 (en) The golf ball of a multilayer structure having a plurality of protrusions on the surface of the inner cover
US6749525B2 (en) Golf balls dimples
CN1190245C (en) Golf ball dimples with curvature continuity
US5842937A (en) Golf ball with surface texture defined by fractal geometry
US20020151384A1 (en) Dimple patterns on golf balls
US5518234A (en) Game ball
AU598401B2 (en) Golf balls
US20070026971A1 (en) Golf ball dimples forming indicia
JP2843557B2 (en) Golf ball
US7618333B2 (en) Golf ball
US5562552A (en) Geodesic icosahedral golf ball dimple pattern
EP0587285A1 (en) Golf ball with novel dimple pattern

Legal Events

Date Code Title Description
AS Assignment

Owner name: ACUSHNET COMPANY, MASSACHUSETTS

Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:NARDACCI, NICHOLAS M.;MADSON, MICHAEL R.;REEL/FRAME:029810/0179

Effective date: 20081029

AS Assignment

Owner name: KOREA DEVELOPMENT BANK, NEW YORK BRANCH, NEW YORK

Free format text: SECURITY AGREEMENT;ASSIGNOR:ACUSHNET COMPANY;REEL/FRAME:031935/0395

Effective date: 20130603

STCB Information on status: application discontinuation

Free format text: ABANDONED -- FAILURE TO RESPOND TO AN OFFICE ACTION

AS Assignment

Owner name: ACUSHNET COMPANY, MASSACHUSETTS

Free format text: RELEASE OF SECURITY INTEREST IN PATENTS PREVIOUSLY RECORDED AT REEL/FRAME (031935/0395);ASSIGNOR:KOREA DEVELOPMENT BANK, NEW YORK BRANCH;REEL/FRAME:039939/0427

Effective date: 20160728