Patent Grant
11376473
This invention relates to golf balls, particularly to golf balls possessing uniquely packed 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.
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 aerodynamic efficiency 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, volume, and arrangement are often manipulated in an attempt to generate a golf ball that has improved 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.
Oversized golf balls, i.e., golf balls having a diameter of greater than 1.69 inches, require dimple layouts specifically optimized for the size of the ball in order to maximize driver distance. In order to maximize distance as the ball gets larger, the ball must fly higher in the air. By the present invention, a method for achieving maximum distance for different golf ball sizes has been discovered.
In one embodiment, the present invention is directed to a golf ball having an outer surface comprising a real parting line, a plurality of false parting lines, and a plurality of dimples. The dimples are arranged in multiple copies of one or more irregular domain(s) covering the outer surface in a uniform pattern. The irregular domain(s) are defined by non-straight segments, and one of the non-straight segments of each of the multiple copies of the irregular domain(s) forms either a portion of the real parting line or a portion of one of the plurality of false parting lines.
In another embodiment, the present invention is directed to a method for arranging a plurality of dimples on a golf ball surface. The method comprises generating a first and a second irregular domain based on an octahedron using a midpoint to midpoint method, mapping the first and second irregular domains onto a sphere, packing the first and second irregular domains with dimples, and tessellating the first and second domains to cover the sphere in a uniform pattern. The midpoint to midpoint method comprises providing a single face of the octahedron, the face comprising a first edge connected to a second edge at a vertex; connecting the midpoint of the first edge with the midpoint of the second edge with a non-straight segment; rotating copies of the segment about the center of the face such that the segment and the copies fully surround the center and form the first irregular domain bounded by the segment and the copies; and rotating subsequent copies of the segment about the vertex such that the segment and the subsequent copies fully surround the vertex and form the second irregular domain bounded by the segment and the subsequent copies.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples, wherein the dimples are arranged by a method comprising generating a first and a second irregular domain based on an octahedron using a midpoint to midpoint method, mapping the first and second irregular domains onto a sphere, packing the first and second irregular domains with dimples, and tessellating the first and second domains to cover the sphere in a uniform pattern.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting of eight first domains and six second domains. The first domain has three-way rotational symmetry about the central point of the first domain. The second domain has four-way rotational 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.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting 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. The plurality of dimples comprises dimples having at least two different diameters, including a minimum dimple diameter, a maximum dimple diameter, and, optionally, one or more additional dimple diameters. The first domain consists of perimeter dimples and interior dimples, the perimeter dimples of the first domain consisting of dimples having at least two different diameters. The second domain consists of perimeter dimples and interior dimples, the perimeter dimples of the second domain consisting of dimples having no more than two different diameters. The diameter of at least one perimeter dimple is the maximum dimple diameter.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting 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. The plurality of dimples comprises dimples having at least three different diameters including a minimum dimple diameter, a maximum dimple diameter, and at least one additional dimple diameter. The first domain consists of perimeter dimples and interior dimples, the interior dimples of the first domain consisting of dimples having no more than two different diameters. The second domain consists of perimeter dimples and interior dimples, the interior dimples of the second domain consisting of dimples having at least three different diameters. The diameter of at least one dimple in the first domain is the minimum dimple diameter. The diameter of at least one dimple in the second domain is the minimum dimple diameter.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting of eight first domains and six second domains. The first domain is defined by three irregular segments and has three-way rotational symmetry about the central point of the first domain. The second domain is defined by four irregular segments and has four-way rotational symmetry about the central point of the second domain. The first domain consists of perimeter dimples and interior dimples, the perimeter dimples of the first domain being positioned adjacent to the three irregular segments defining the first domain. The second domain consists of perimeter dimples and interior dimples, the perimeter dimples of the second domain being positioned adjacent to the four irregular segments defining the second domain.
In a particular aspect of this embodiment, all of the perimeter dimples of the second domain satisfy a diameter relationship such that
if xdimple 1>xdimple 2
then ddimple 1<ddimple 2,
where dimple 1 and dimple 2 are 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.
In another particular aspect of this embodiment, all of the perimeter dimples of the second domain satisfy a diameter relationship such that
if xdimple 1>xdimple 2
then ddimple 1>ddimple 2,
where dimple 1 and dimple 2 are 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.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting of eight first domains and six second domains. The first domain has three-way rotational symmetry about the central point of the first domain. The second domain has four-way rotational symmetry about the central point of the second domain. The first domain includes a center dimple having a center that is coincident with the central point of the first domain. The dimples of the first domain, other than the center dimple, are arranged along the sides of at least two reference triangles, wherein the reference triangles are concentric triangles having a common center that is coincident with the central point of the first domain.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting of eight first domains and six second domains. The first domain has three-way rotational symmetry about the central point of the first domain. The second domain has four-way rotational symmetry about the central point of the second domain. The dimples of the first domain are arranged along the sides of at least three reference triangles, wherein the reference triangles are concentric triangles having a common center that is coincident with the central point of the first domain.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting 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. The plurality of dimples comprises dimples having at least two different diameters, including a minimum dimple diameter, a maximum dimple diameter, and, optionally, one or more additional dimple diameters. In a particular aspect of this embodiment, for the minimum dimple diameter, SD1min≤½ (SD2min), where SD1min is the number of dimples positioned within the first domain having the minimum dimple diameter, and SD2min is 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 SD1max is the number of dimples positioned within the first domain having the maximum dimple diameter, and SD2max is the number of dimples positioned within the second domain having the maximum dimple diameter.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting 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. The plurality of dimples comprises dimples having at least two different diameters, including a minimum dimple diameter, a maximum dimple diameter, and, optionally, one or more additional dimple diameters. In a particular aspect of this embodiment, for the minimum dimple diameter, SD1min≥2 (SD2min), where SD1min is the number of dimples positioned within the first domain having the minimum dimple diameter, SD2min is the number of dimples positioned within the second domain having the minimum dimple diameter, SD1min>0, and SD2min>0. In another particular aspect of this embodiment, for the maximum dimple diameter, SD1max 3/2 (SD2max), where SD1max is the number of dimples positioned within the first domain having the maximum dimple diameter, SD2max is the number of dimples positioned within the second domain having the maximum dimple diameter, SD1max>0, and SD2max>0.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting 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. The plurality of dimples comprises dimples having at least two different diameters, including a minimum dimple diameter, a maximum dimple diameter, and, optionally, one or more additional dimple diameters. In a particular aspect of this embodiment, for the minimum dimple diameter, SD1min+SD2min≥5, where SD1min is the number of dimples positioned within the first domain having the minimum dimple diameter, SD2min is 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 SD1max is the number of dimples positioned within the first domain having the maximum dimple diameter and SD2max is the number of dimples positioned within the second domain having the maximum dimple diameter.
In another embodiment, the present invention is directed to an oversized golf ball having a plurality of dimples disposed thereon, wherein the dimples are arranged in multiple copies of a first domain and a second domain, the first domain and the second domain being tessellated to cover the outer surface of the golf ball in a uniform pattern having no great circles and consisting of eight first domains and six second domains. The first domain has three-way rotational symmetry about the central point of the first domain. The second domain has four-way rotational symmetry about the central point of the second domain. In a particular aspect of this embodiment, the golf ball has a diameter of from 1.70 inches to 1.82 inches, and the average plan shape area of the dimples, AAVE, relates to the total number of dimples, 1V, 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 another particular aspect of this embodiment, the golf ball has a diameter of 1.82 inches or greater, or a diameter of greater than 1.82 inches, and the average plan shape area of the dimples, AAVE, 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.
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:
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 in
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.
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.
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
When domain 14 is tessellated to cover the surface of golf ball 10, as shown in
The Center to Midpoint Method
Referring to
When domain 14 is tessellated around a golf ball 10 to cover the surface of golf ball 10, as shown in
The Center to Center Method
Referring to
When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in
The Midpoint to Midpoint Method
Referring to
When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in
In a particular aspect of the embodiment shown in
The Midpoint to Vertex Method
Referring to
When domain 14 is tessellated to cover the surface of golf ball 10, as shown in
The Vertex to Vertex Method
Referring to
When first domain 14a and second domain 14b are tessellated to cover the surface of golf ball 10, as shown in
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
When domain 14 is tessellated to cover the surface of golf ball 10, as shown in
While the methods described previously provide a framework for the use of center C, vertex V, and midpoint M as the only control points, other control points are useable. For example, a control point may be any point P on an edge E of the chosen polyhedron face. When this type of control point is used, additional types of domains may be generated, though the mechanism for creating the irregular domain(s) may be different. An exemplary method, using a center C and a point P on an edge, for creating one such irregular domain is described below.
The Center to Edge Method
Referring to
When domain 14 is tessellated to cover the surface of golf ball 10, as shown in
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
When domain 14 is tessellated to cover the surface of golf ball 10, as shown in
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 ball 10.
In
In a particular embodiment, as illustrated in
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 in
Each dimple typically has a diameter within a range having a lower limit of 0.050 or 0.100 inches and an upper limit of 0.205 or 0.250 inches. The diameter of a dimple having a non-circular plan shape is defined by its equivalent diameter, de, which calculated as:
where A is the plan shape area of the dimple. Diameter measurements are determined on finished golf balls according to
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 in
In a second particular aspect of this embodiment, as illustrated in
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 in
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, in
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,
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,
if xdimple a>xdimple b, then ddimiple 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.
Alternatively,
if xdimple a>xdimple b, then ddimiple 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 to
In
if xdimple 1>xdimple 2
then ddimple 1<ddimple 2,
where dimple 1 and dimple 2 are 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.
In
if xdimple 3>xdimple 4
then ddimple 3<ddimple 4,
where dimple 3 and dimple 4 are 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 to
In
if xdimple 1>xdimple 2
then ddimiple 1>ddimple 2,
where dimple 1 and dimple 2 are 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.
In
if Xdimple 3>xdimple 4
then ddimple 3>ddimple 4,
where dimple 3 and dimple 4 are 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.
While
In a further aspect of this particular embodiment, the dimples additionally have one or more of the following additional characteristics:
In a fourth particular aspect of this embodiment, as illustrated in
For example,
Similarly,
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:
In a fifth particular aspect of this embodiment, as illustrated in
For example,
Similarly,
In the embodiment 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:
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:
and a second domain diameter ratio defined by the equation:
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 SD1min is the number of dimples positioned within the first domain having the minimum dimple diameter, and SD2min is 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 SD1max is the number of dimples positioned within the first domain having the maximum dimple diameter, and SD2max is 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:
For example,
Thus, in the embodiment shown in
Thus, in the embodiment shown in
In another particular aspect of this embodiment, for the minimum dimple diameter,
SD1min≥2(SD2min),
where SD1min is the number of dimples positioned within the first domain having the minimum dimple diameter, and SD2min is 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 SD1max is the number of dimples positioned within the first domain having the maximum dimple diameter, and SD2max is 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:
For example,
Thus, in the embodiment shown in
In another particular aspect of this embodiment, for the minimum dimple diameter, SD1min+SD2min≥5, where SD1min is the number of dimples positioned within the first domain having the minimum dimple diameter, SD2min is 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 SD1max is the number of dimples positioned within the first domain having the maximum dimple diameter and SD2max is 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:
For example,
Thus, in the embodiment shown in
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:
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:
where xi is the diameter of any given dimple 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:
For example, in the embodiment shown in
In the embodiment shown in
In the embodiment shown in
In the embodiment shown in
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 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
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 14.
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, of 302 or 306 or 320 or 336 or 342 or 350 or 360 or 374 or 384 or 390 or 432.
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 inch, 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.
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 in
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)1/2 and aerodynamic force angle (Cangle) is defined by Cangle=tan−1(CL/CD), where CL is a lift coefficient and CD is 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.
The present application is a continuation-in-part of U.S. patent application Ser. No. 16/712,855, filed Dec. 12, 2019, which is a continuation-in-part of U.S. patent application Ser. No. 16/137,609, filed Sep. 21, 2018, and U.S. patent application Ser. No. 16/214,207, filed Dec. 10, 2018, now U.S. Pat. No. 10,532,252, the entire disclosures of which are hereby incorporated herein by reference. U.S. patent application Ser. No. 16/137,609 is a continuation of U.S. patent application Ser. No. 15/707,079, filed Sep. 18, 2017, now U.S. Pat. No. 10,080,923, the entire disclosure of which is hereby incorporated herein by reference. U.S. patent application Ser. No. 15/707,079 is a continuation-in-part of U.S. patent application Ser. No. 15/262,213, filed Sep. 12, 2016, now U.S. Pat. No. 9,795,833, which is a continuation-in-part of U.S. patent application Ser. No. 13/046,823, filed Mar. 14, 2011, now U.S. Pat. No. 9,440,115, which is a continuation-in-part of U.S. patent application Ser. No. 12/262,464, filed Oct. 31, 2008, now U.S. Pat. No. 8,029,388, the entire disclosures of which are hereby incorporated herein by reference. U.S. application Ser. No. 15/707,079 is also a continuation-in-part of U.S. patent application Ser. No. 15/262,234, filed Sep. 12, 2016, now U.S. Pat. No. 9,873,020, which is a continuation-in-part of U.S. patent application Ser. No. 13/046,823, filed Mar. 14, 2011, now U.S. Pat. No. 9,440,115, which is a continuation-in-part of U.S. patent application Ser. No. 12/262,464, filed Oct. 31, 2008, now U.S. Pat. No. 8,029,388, the entire disclosures of which are hereby incorporated herein by reference. U.S. patent application Ser. No. 16/214,207 is a continuation-in-part of U.S. patent application Ser. No. 15/707,058, filed Sep. 18, 2017, now U.S. Pat. No. 10,150,006, the entire disclosures of which are hereby incorporated herein by reference, the entire disclosures of which are hereby incorporated herein by reference. U.S. patent application Ser. No. 15/707,058 is a continuation-in-part of U.S. patent application Ser. No. 15/262,213, filed Sep. 12, 2016, now U.S. Pat. No. 9,795,833, which is a continuation-in-part of U.S. patent application Ser. No. 13/046,823, filed Mar. 14, 2011, now U.S. Pat. No. 9,440,115, which is a continuation-in-part of U.S. patent application Ser. No. 12/262,464, filed Oct. 31, 2008, now U.S. Pat. No. 8,029,388, the entire disclosures of which are hereby incorporated herein by reference. U.S. patent application Ser. No. 15/707,058 is also a continuation-in-part of U.S. patent application Ser. No. 15/262,234, filed Sep. 12, 2016, now U.S. Pat. No. 9,873,020, which is a continuation-in-part of U.S. patent application Ser. No. 13/046,823, filed Mar. 14, 2011, now U.S. Pat. No. 9,440,115, which is a continuation-in-part of U.S. patent application Ser. No. 12/262,464, filed Oct. 31, 2008, now U.S. Pat. No. 8,029,388, the entire disclosures of which are hereby incorporated herein by reference.
| Number | Name | Date | Kind |
|---|---|---|---|
| 4998733 | Lee | Mar 1991 | A |
| 5046742 | Markey | Sep 1991 | A |
| 5562552 | Thurman | Oct 1996 | A |
| 5564708 | Hwang | Oct 1996 | A |
| 5575477 | Hwang | Nov 1996 | A |
| 6682442 | Winfield | Jan 2004 | B2 |
| 20020016227 | Emerson et al. | Feb 2002 | A1 |
| 20020016228 | Emerson et al. | Feb 2002 | A1 |
| 20030171167 | Kasashima | Sep 2003 | A1 |
| 20040152541 | Sajima | Aug 2004 | A1 |
| 20040171438 | Nardacci | Sep 2004 | A1 |
| 20050037871 | Nardacci | Feb 2005 | A1 |
| 20060142098 | Sajima | Jun 2006 | A1 |
| 20100113187 | Nardacci et al. | May 2010 | A1 |
| 20100261551 | Felker | Oct 2010 | A1 |
| 20120270684 | Sajima | Oct 2012 | A1 |
| Number | Date | Country | |
|---|---|---|---|
| 20200360767 A1 | Nov 2020 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 15707079 | Sep 2017 | US |
| Child | 16137609 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 16712855 | Dec 2019 | US |
| Child | 16984870 | US | |
| Parent | 16137609 | Sep 2018 | US |
| Child | 16712855 | US | |
| Parent | 15262213 | Sep 2016 | US |
| Child | 15707079 | US | |
| Parent | 13046823 | Mar 2011 | US |
| Child | 15262213 | US | |
| Parent | 12262464 | Oct 2008 | US |
| Child | 13046823 | US | |
| Parent | 15262234 | Sep 2016 | US |
| Child | 15707079 | US | |
| Parent | 13046823 | Mar 2011 | US |
| Child | 15262234 | US | |
| Parent | 12262464 | Oct 2008 | US |
| Child | 13046823 | US | |
| Parent | 16214207 | Dec 2018 | US |
| Child | 16712855 | US | |
| Parent | 15707058 | Sep 2017 | US |
| Child | 16214207 | US | |
| Parent | 15262213 | Sep 2016 | US |
| Child | 15707058 | US | |
| Parent | 13046823 | Mar 2011 | US |
| Child | 15262213 | US | |
| Parent | 12626464 | Oct 2008 | US |
| Child | 13046823 | US | |
| Parent | 15262234 | Sep 2016 | US |
| Child | 15707058 | US | |
| Parent | 13046823 | Mar 2011 | US |
| Child | 15262234 | US | |
| Parent | 12262464 | Oct 2008 | US |
| Child | 13046823 | US |
