HEPTAGONAL DIPYRAMID DIMPLE PATTERN FOR A GOLF BALL

A golf ball has a generally spherical surface and a plurality of dimples formed on the surface. The dimples are arranged in a dimple pattern defined by a heptagonal dipyramid projected on the surface. The pattern includes fourteen substantially identical dimple sections including seven dimple sections in a first hemisphere and seven dimple sections in a second hemisphere.

FIELD OF THE INVENTION

The present disclosure relates to golf ball dimple patterns, and, more particularly, golf ball dimple patterns that are defined by the projection of a heptagonal dipyramid onto a sphere.

BACKGROUND OF THE INVENTION

Historically, dimple patterns for golf balls have had an enormous 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, which overcome the force of gravity, are lift and drag. 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 and 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 form or 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. In order to minimize pressure drag, dimples provide a means to energize the flow field and delay the separation of flow, or reduce the low-pressure region behind the ball. However, the penalty for reducing pressure drag is skin friction. Skin friction is a viscous effect residing close to the surface of the ball within the boundary layer. The dimples provide an optimal amount of disturbance, triggering the laminar turbulent flow transition while maintaining a sufficiently thin boundary layer region for viscous drag to occur.

The United States Golf Association (U.S.G.A.) requires 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.

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 three of five existing Platonic Solids including Icosahedron, Dodecahedron, or Octahedron. 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. Thus, there is a continuing need for novel dimple patterns incorporating unique combinations of dimple properties such as size, shape, number, volume, or arrangement, in order to provide a golf ball that has distinctive characteristics.

SUMMARY OF THE INVENTION

The present disclosure describes a golf ball including a plurality of dimples. The dimples may be arranged in a dimple pattern defined by a heptagonal dipyramid projected on a spherical outer surface of the golf ball. The pattern includes fourteen substantially identical dimple sections including seven dimple sections in a first hemisphere and seven dimple sections in a second hemisphere.

In other aspects, the present disclosure further describes the dimple sections that make up the dimple pattern. A boundary of each of the dimple sections may consist of two linear side edges and a linear or non-linear base edge. The side edges are defined such that each dimple section consists of a plurality of shared non-polar dimples each of which has a centroid that lies on a side edge of the dimple section, a plurality of dimples that are not intersected by a side edge, and, optionally, a shared polar dimple having a centroid that lies at the vertex of the two linear side edges of the section.

In another aspect, the present disclosure further describes exemplary dimples that make up the dimple sections and overall dimple pattern. For example, dimples having a polar angle of greater than or equal to 2° and less than or equal to 20° may have a planar area satisfying the following condition for a given polar angle x:

In another example, the dimple pattern may include 370-390 dimples and provide surface coverage greater than 75% on the outer surface of the golf ball. Each dimple may have a diameter of 0.110 inches or greater. Each of the dimple sections may comprise at least five different dimple diameters. The centroids of at least three dimples may lie on each side edge of each dimple section. The dimple pattern within each dimple section may have mirror symmetry across a symmetry line that extends from an intersection of the two side edges to a midpoint of the base edge. The centroids of at least six non-polar dimples may lie on either (i) every symmetry line of every dimple section, or (ii) every side edge of every dimple section. The six (or more) non-polar dimples may include three dimples that lie closest to a vertex of the side edges that all have the same dimple diameter. The six (or more) non-polar dimples may include at least four different dimple diameters. The six (or more) non-polar dimples may include one dimple that lies closest to the base edge that has the smallest diameter of all of the dimples in the dimple section. The dimples within each dimple section that are located adjacent to the base edge of the section may have diameters that are different by 0.005 inches or less.

In another aspect of the present disclosure, a golf ball has two identical hemispheres connected at their bases to form the spherical shape. The dimple sections of the first hemisphere may be aligned with the dimple sections of the second hemisphere, or may be rotated with respect to the dimple sections of the second hemisphere. In some embodiments, some of the dimples of the first hemisphere may be interdigitated with some of the dimples of the second hemisphere to provide a staggered parting line. With a staggered parting line, the golf ball has no dimple-free great circles.

DETAILED DESCRIPTION OF THE INVENTION

Disclosed embodiments include golf ball dimple patterns having multi-fold rotational symmetry around a polar axis of the golf ball. An exemplary embodiment uses the projected edges of a heptagonal pyramid as a means of arranging dimples on the surface of a hemisphere such that the hemisphere exhibits seven-fold rotational symmetry about the polar axis. The resulting rotationally-symmetrical dimple pattern may be applied to each of two hemispheres connected at an equatorial plane to create a dimple pattern for an entire spherical golf ball. The projected edges divide the dimple pattern into dimple sections, with each of the dimple sections being substantially identical. The edges that define the dimple sections are used to characterize the dimple pattern but are not physically present on the golf ball. The dimple pattern within each dimple section may be arranged to provide desired dimple surface coverage for the golf ball while maintaining the seven-fold rotational symmetry. In some embodiments, the dimple pattern of each dimple section may also exhibit mirror symmetry across a line within the boundaries of the dimple section.

As a result of basing the boundary lines on a heptagonal pyramid, the dimple sections each include two side edges and a base edge, similar to the edges of the triangular faces of the corresponding pyramid. For example, dimple sections may consist of two linear side edges and a linear or non-linear base edge. The two linear side edges of the dimple sections correspond to the linear side edges of each face of the dipyramid. Each side edge runs longitudinally from a base edge to the pole of a hemisphere. As discussed further below, the side edges may intersect one or more dimples. The base edges of the dimple sections are defined such that the base edges do not intersect any dimples. For example, the side edges may be defined such that each dimple section consists of a plurality of shared non-polar dimples each of which has a centroid that lies along a side edge of the dimple section, a plurality of dimples that are not intersected by a side edge, and, optionally, a shared polar dimple having a centroid that lies at the vertex of the two linear side edges of the dimple section. As used herein, a dimple centroid may be considered to lie on a line on a golf ball surface even though the centroid of the dimple technically lies in the empty volume defined by the dimple phantom surface. For the purposes of this disclosure, a dimple centroid is considered to lie on a line on a golf ball surface when the centroid is on a plane that also includes that line.

In one embodiment, the golf ball has a planar parting line wherein no dimples intersect the equatorial plane, and the base edges are straight lines corresponding to the linear base edges of the dipyramid on which the dimple pattern is based. In another embodiment, the golf ball has a non-planar parting line wherein at least a portion of the dimples located adjacent to the equator intersect the equatorial plane, and the base edges are curved segments drawn along the corresponding linear base edges of the dipyramid such that no dimples are intersected.

Dimples may be located entirely within a dimple section (i.e., the dimple perimeter is not intersected by a side edge or base edge) or dimples may be shared between two or more sections (also referred to herein as “shared dimples”). For every dimple that is not located entirely within a dimple section, the centroid of the dimple is located either at a hemispherical pole or on a side edge. Disclosed dimple patterns may include at least one dimple that lies on each of the side edges of the dimple sections. In some embodiments, the dimple pattern also includes at least one dimple that lies on a line of mirror symmetry of each dimple section (also referred to herein as a “symmetry line”).

A heptagonal dipyramid is a polyhedron formed from two heptagonal pyramids joined at their bases. The resulting solid has fourteen triangular faces, nine vertices, and twenty-one edges. InFIG.1, a heptagonal dipyramid10is formed from a first heptagonal pyramid12and a second heptagonal pyramid14. Each of the fourteen triangular faces16has two side edges18and a base edge20. Adjacent faces16share a side edge18. The base edges20are connected around a centerline of the heptagonal dipyramid10. In the disclosed figures, the reference numerals are included and point to examples of corresponding components, even though more are shown. The description of one feature that is repeated can be equally applied to the same features throughout the embodiment. For example, in the depicted embodiment, all of the faces16and edges18shown on the dipyramid10are the same or similar and thus are represented by face16and its side edges18and base edge20.

FIG.2is a hemisphere22including a projection of the edges16,18of the first heptagonal pyramid12onto the outer surface of the hemisphere22. The hemisphere22is thus divided into seven sections24by the projected edges. It should be understood that the projected edges are boundary lines (e.g., define a boundary) for dividing the hemisphere22into seven identical sections24, but are not physical edges or otherwise present on the hemisphere22. Each section24of the hemisphere22includes a boundary defined by two side edges26and a base edge28. The two side edges26are straight lines corresponding to the linear side edges of the first heptagonal pyramid12. The side edges26and other similar edges disclosed herein are considered to be “linear” for the purposes of this disclosure, as they follow a straight path on the surface of the golf ball (i.e., a longitudinal or latitudinal line on the golf ball). For example, each side edge26runs longitudinally from the base edge28to a pole30of the hemisphere22.

FIG.3Ais a hemisphere32including projected edges that define a boundary dividing the hemisphere32into seven dimple sections34, much like the hemisphere22. The hemisphere32has generally spherical outer surface36. The boundary of each dimple section34includes side edges38and base edges40. The side edges38intersect at a vertex at the pole42of the hemisphere32. Each dimple section34is defined by two side edges38and the base edge40that connects the two side edges38to each other.

The hemisphere32additionally includes a plurality of dimples44formed on the surface36. The plurality of dimples44include all of the dimples on the surface36of the hemisphere32, of which only three include reference numerals. The plurality of dimples44are arranged in a dimple pattern. The plurality of dimples may44may include a polar dimple with a centroid at the pole42. The dimples44that do not lie at the pole42may be considered non-polar dimples. Some of the dimples44may lie on the side edges38and as such are shared dimples between two dimple sections34. More particularly, the centroid of some dimples44lie on a plane that includes the side edge38, and thus may be considered to lie on the side edge38in accordance with the present disclosure. The dimple pattern is arranged such that each of the seven dimple sections34are substantially identical. The dimples44are configured such that the projected area of each dimple plan shape is within an appropriate design range in order to accommodate the seven-fold symmetry and provide desirable aerodynamic performance. For example, the dimple planar area may be dependent on one or more of the volume of the dimple or the location of the dimple on the golf ball.

InFIG.3A, the dimples44are arranged such that a pattern is repeated around the hemisphere32seven times, resulting in the seven substantially identical dimple sections34. The dimple sections34in the depicted embodiment include mirror symmetry across a line of symmetry46. More particularly, a plane of mirror symmetry divides each dimple section34in half and the line of symmetry46is a line on the surface36where the plane of mirror symmetry intersects the surface36. The lines of symmetry46extend longitudinally from a vertex at the pole42to the midpoint of each base edge40. The lines of symmetry46intersect the centroid of some of the dimples44. More particularly, the centroid of some dimples44lie on a line of symmetry46(i.e., the centroid of some dimples11lie on a plane of mirror symmetry that includes a line of symmetry46).

The pattern of dimples44in the depicted embodiment is configured such that the there are two options for drawing the side edges38to create substantially identical dimple sections while maintaining the criteria that dimples44are either entirely within the boundaries of the dimple sections or have centroids that lie on the side edges38or on the pole42.FIG.3Adepicts the first arrangement of side edges38(shown in solid lines), with the lines of symmetry46(shown in dashed lines) within dimple sections34.FIG.3Bdepicts the second arrangement in which the lines of symmetry46fromFIG.3Aare considered side edges38A (shown in solid lines) of dimple sections34A and the side edges38fromFIG.3Aare considered lines of symmetry46A (shown in dashed lines). The base edges40A are shifted relative to the base edges40in order to connect the side edges38A. The dimples44are arranged in the exact same pattern inFIGS.3A and3B, with the only difference being the characterization of the dimple sections34,34A. The dimples44that lie on the side edges38inFIG.3Alie on the lines of symmetry46A inFIG.3B. The dimples44that lie on the lines of symmetry46inFIG.3Alie on the side edges38inFIG.3B.

According to disclosed embodiments, the seven dimple sections (e.g., dimple sections34,34A) that make up the dimple pattern on each hemisphere are substantially identical to each other. In an exemplary embodiment of a spherical golf ball having two hemispheres, all fourteen dimple sections on the ball are substantially identical to each other. For purposes of the present disclosure, dimple sections are “substantially identical” if they have substantially the same dimple arrangement (i.e., the relative positions of their dimples' centroids are about the same) and substantially the same dimple characteristics (e.g., plan shape, cross-sectional shape, diameter, edge angle, etc.). Thus, for each dimple located entirely within a particular section on a hemisphere, there is a corresponding dimple in each of the other six dimple sections of that hemisphere. For dimples having a centroid located on a side edge, there is a corresponding dimple located on each of the other six side edges of that hemisphere. Dimples that are not located at the pole of a hemisphere may be considered non-polar dimples. Polar dimples, which may be, but are not necessarily present in dimple patterns of the present disclosure, are shared between all seven sections on a hemisphere, and, thus, have no corresponding dimple on that hemisphere. For each set of corresponding dimples, the relative positions of the dimple centroids within their respective sections are about the same, and each of the dimples within that set of corresponding dimples has substantially the same characteristics.

Dimples of the present invention may have a variety of plan shapes, including, but not limited to, circular, polygonal, oval, or irregular shapes, and a variety of profile shapes, including, but not limited to, circular, catenary, elliptical, or conical shapes. Suitable non-spherical dimples preferably have a plan shape area and dimple volume within a range having a lower limit and an upper limit selected from the values within the region shown inFIG.4, which is a graphical representation of the relationship between dimple volume and plan shape area of non-spherical dimples according to an embodiment of the present invention.

The plan shape area is based on a planer view of the dimple plan shape, such that the viewing plane is normal to an axis connecting the center of the ball to the point of the calculated surface depth. The dimple volume is the total volume encompassed by the dimple shape and the surface of the golf ball. The preferred dimple volume will be less than the upper limit volume calculated by

and greater than the lower limit calculated by

where x is the dimple plan shape area and x is between 0.0025 and 0.045 inclusive.

For purposes of the present disclosure, the plan shape area of a non-spherical dimple is based on a planar view of the dimple plan shape, such that the viewing plane is normal to an axis connecting the center of the ball to the point of the calculated surface depth. The dimple volume is the total volume encompassed by the dimple shape and the surface of the golf ball.

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 toFIG.5. Generally, it may be difficult to measure a dimple's diameter due to the indistinct nature of the boundary dividing the dimple from the ball's undisturbed land surface. Due to the effect of paint and/or the dimple design itself, the junction between the land surface and dimple may not be a sharp corner and is therefore indistinct. This can make the measurement of a dimple's diameter somewhat ambiguous. To resolve this problem, the diameter of a dimple100on a finished golf ball is measured according to the method shown inFIG.5.

FIG.5shows a cross-sectional profile of a dimple surface110of the dimple100, extending from the dimple centerline120to the land surface130outside of the dimple100. A ball phantom surface140is constructed above the dimple100as a continuation of the land surface130. A first tangent line T1is then constructed at a point on the dimple sidewall that is spaced 0.003 inches radially inward from the phantom surface140. T1intersects phantom surface140at a point P1, which defines a nominal dimple edge position. A second tangent line T2is then constructed, tangent to the phantom surface140, at P1. The edge angle of the dimple100is the angle between T1and T2. The diameter of the dimple100is the distance between P1and its equivalent point diametrically opposite along the dimple perimeter. Alternatively, the dimple diameter is twice the distance between P1and the dimple centerline120, measured in a direction perpendicular to centerline120. The depth of the dimple100is the distance measured along a ball radius from the phantom surface140of the ball to the deepest point on the dimple100. The volume of the dimple100is the space enclosed between the phantom surface140and the dimple surface110(extended along T1until it intersects the phantom surface).

In an exemplary embodiment, a majority of the dimples on the outer surface of golf balls of the present disclosure are spherical dimples, i.e., dimples having a circular plan shape and a profile shape based on a spherical function. In a particular aspect of this embodiment, the spherical dimples have one or more properties/characteristics selected from:a) the edge angle of each spherical dimple is 10 or 11 or 12 or 13 or 14 or 15 or 16 degrees, or is within a range having a lower limit and an upper limit selected from these values;b) the maximum difference in edge angle between any two of the spherical dimples is 1 degree;c) the edge angle of all of the spherical dimples is substantially the same (For purposes of the present disclosure, edge angles on a finished ball are substantially the same if they differ by less than 0.25 degrees.); andd) the average edge angle of the spherical dimples is from 12 to 15 degrees; and The dimples may include subsets of like dimples having the same diameter. It should be understood that manufacturing variances are to be taken into account when determining the number of different dimple diameters. For purposes of the present disclosure, dimples having substantially the same diameter, also referred to herein as “same diameter” dimples, includes dimples on a finished ball having respective diameters that differ by less than 0.005 inches due to manufacturing variances.

The total number of dimples on the golf ball may also be varied according to the present embodiments. The total number of dimples may be based on, for example, the number of differently sized dimples, the maximum and minimum diameters of the dimples, the dimple arrangement, and the like. In an exemplary, the total number of dimples is between about 250 and about 500. In a more particular embodiment, the total number of dimples is between about 300-450 dimples. In another embodiment, the total number of dimples is between about 350-400 dimples. In a more particular embodiment, the total number of dimples is between about 370-390 dimples. In a particular embodiment, the total number of dimples is 380. In other exemplary embodiments, the total number of dimples is 252 or 254 or 264 or 266 or 276 or 278 or 288 or 290 or 300 or 302 or 312 or 314 or 324 or 326 or 336 or 338 or 348 or 350 or 360 or 362 or 372 or 374 or 384 or 386 or 396 or 398 or 408 or 410 or 420 or 422 or the total number of dimples is within a range having a lower limit and an upper limit selected from these values.

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

Golf balls of the present disclosure are not limited by a particular golf ball construction. The golf ball may have any type of core, such as solid, liquid, wound, and the like, and may be a one-piece, two-piece, or multilayer ball. Each layer of the golf ball may be constructed from any suitable thermoset or thermoplastic material known to those of ordinary skill in the art. When desirable, the cover may be coated with any number of layers, such as a base coat, top coat, paint, or any other desired coating.

FIG.6Adepicts a golf ball48having a plurality of dimples49in a dimple pattern based on a heptagonal dipyramid. The golf ball48is a generally spherical body having a first hemisphere50and a second hemisphere52connected at an equatorial plane. The first hemisphere50includes seven dimple sections54, similar to or the same as the hemisphere32and dimple sections34inFIG.3A. Each dimple section54includes a subset of the plurality of dimples49, including some dimples that are shared with one or more other dimple sections54. The dimple sections54include a boundary defined by side edges56and a base edge58. It should be understood that the golf ball48is not physically divided into sections and that the side edges56and base edge58are boundaries that delineate the symmetry of the dimple pattern on the surface of the golf ball48. The first hemisphere50includes seven dimple sections54that each include an identical dimple pattern inside the boundaries of the side edges56and base edge58. As a result, the first hemisphere50of the golf ball48has seven-fold rotational symmetry (also referred to as axial symmetry) around a polar axis60. In other words, the hemisphere50has an identical dimple pattern at seven different locations when the hemisphere50is rotated 2π/7 radians (approximately 51.43°) around the polar axis60. The polar axis60is defined as the axis connecting the pole of the first hemisphere50to the pole of the second hemisphere52.

The second hemisphere52also includes seven dimple sections62. The hemisphere52may be the same as the hemisphere50, only flipped to the opposite side of the spherical golf ball48such that the pole of the first hemisphere50and the pole of the second hemisphere52are poles of the golf ball48, connected by the polar axis60. The dimple sections62are bounded by side edges64and a base edge66. InFIG.6A, the dimple sections54are aligned with the dimple sections62such that the side edges56are collinear with the side edges64and the base edges58completely overlap the base edges66.FIG.6Bis an alternative golf ball48A in which hemispheres50A,52A include dimple sections54A,62A, respectively, which are the same as the hemispheres50,52and dimple sections54,62, except that the hemisphere52A is rotated around the polar axis60with respect to the hemisphere50A. In the example ofFIG.6B, the hemisphere52A is rotated 2π/14 radians (approximately 25.71°) around the polar axis60such that each side edge56A or64A bisects a base edge58A or66A of a dimple section on the opposite hemisphere. In other embodiments, the hemisphere52may be rotated any amount between 0 and 2π/7 radians with respect to the hemisphere50.

As shown inFIGS.6A and6B, the parting line between the hemispheres of the golf balls48,48A may be flat. With a flat parting line, the base edges66,66A are linear (i.e., follow a straight path on the surface of the golf ball) and lie in and/or parallel to the equatorial plane. In other embodiments, a golf ball having a disclosed heptagonal dipyramid dimple pattern may include a staggered parting line.FIG.6Cis an example of a golf ball68having a plurality of dimples70arranged in a dimple pattern based on a heptagonal dipyramid and also having a staggered parting line. The dimples70are arranged in dimple sections72,74that are similar to the dimple sections54A,62A of the golf ball48A (dimple sections72in a first hemisphere, dimple sections74in a second hemisphere, with the second hemisphere being offset by 2π/14 radians). In particular, the dimple patterns within dimple sections72,74are substantially identical to the dimple patterns within the dimple sections54A,62A ofFIG.6B. However, the golf ball68does not include any dimple-free great circles, including at the equator. The dimples70in dimple sections72that are adjacent to the equator of the golf ball68are interdigitated with dimples70in dimple sections74that are adjacent to the equator. In order to accommodate the interdigitated dimples70, the dimple sections72are defined with linear side edges76and a curved base edge78. For the purpose of this disclosure, the curved base edge78and other similar base edges disclosed herein, are considered “non-linear” base edges to differentiate from the “linear” side and base edges also disclosed herein. A “non-linear” base edge connects side edges to each other but does not follow a straight path on the surface. A “non-linear” base edge may have an “average” that is approximated by a straight path. For instance, the curved base edge78may have equal amplitudes above and below a line equivalent to a linear base edge. The dimple sections74similarly include linear side edges80and curved base edges82. The side edges76,80are similar to the side edges56A,64A extending longitudinally from a pole to the base edges78,82. The curved base edges78,82follow a sinusoidal/wavy path between the dimples70that are adjacent to the equatorial plane. In this way, the dimples70are arranged in a dimple pattern that satisfies the criteria that the dimples70are either entirely within the boundaries of the dimple sections72,74or have centroids on the side edges76,80or at a pole of one of the hemispheres.

FIGS.7A and7Bare a side and perspective view of an exemplary section84of a sphere. The section84may correspond to a dimple section of a golf ball as described in the present disclosure, such as a section of a heptagonal dipyramid projected onto a sphere The section84intersects a polar axis86and includes side edges88and a base edge90. The polar axis86and side edges88intersect at a vertex92(which would be a pole of a complete hemisphere having seven of the sections84and/or a complete sphere having fourteen of the sections84). The section84further includes a surface94. The surface94is the surface of a complete sphere including the section84and include would include dimples in a golf ball having fourteen of the sections84. One way to describe the location of a dimple on the surface94is by identifying the polar angle θ of the dimple. The polar angle θ of any dimple is the angle between the polar axis86and the dimple centroid. For example, a dimple having a centroid at the vertex92would have a polar angle θ of 0° and a dimple having a centroid on the base edge90would have a polar angle θ of 90°.

In some embodiments, the acceptable planar area of any one dimple on the surface94depends on its polar angle location. In some embodiments, the dependency on the polar angle may be limited to a particular surface area, such as a polar area96. The polar area96may be, for example, an area from approximately 2° to 20° in polar angle. In an exemplary embodiment, the planar area of a dimple in the polar area96satisfies the following condition for a given polar angle x:

FIG.8includes a graph of planar area to polar angle for the above range. For dimples having centroids with a polar angle greater to or equal to 2° and less than or equal to 20°, the planar area falls on or between the lines shown in the graph. In an exemplary embodiment, any dimple outside of the 2-20° range has a planar area greater than or equal to 0.0018 in2and less than or equal to 0.052 in2.

FIG.9Ashows a dimple section150including a subset of a plurality of dimples152formed on a surface. The dimple section150may correspond to the previously described dimple sections34,54. The dimple section150has two side edges154and a base edge156. The dimples152are arranged within the dimple section150such that the pattern exhibits mirror symmetry across a symmetry line158. As described above, the disclosed dimple pattern is arranged within the dimple sections such that, when repeated, the side edges that divide the dimple sections are interchangeable with the symmetry lines.

FIG.9Bshows a dimple section150A including another subset of the plurality of dimples152. The dimple section150A corresponds to the previously described dimple section34A. The dimple section150A has two side edges154A and a base edge156A. A side edge154A is equivalent to the symmetry line158. The subset of dimples152are arranged within the dimple section150A such that the pattern exhibits mirror symmetry across a symmetry line158A. The symmetry line158A is equivalent to the side edge154. Repeating the dimple sections150and150A seven times around a polar axis160results in identical hemispheres and dimple patterns (as mentioned, side and base edges described herein are not physically present on a disclosed golf ball). Thus, a description of a dimple152in relation to a side edge154could also be applied in relation to the symmetry line158, and vice versa.

FIG.10shows the dimple section150ofFIG.9Awith dimples152patterned around a hemisphere162that represents half of a golf ball.FIG.11Ashows the hemisphere162combined with an identical hemisphere164to form a golf ball166. Each hemisphere162,164includes seven dimple sections150. The golf ball166includes fourteen substantially identical dimple sections150. The golf ball166corresponds to the golf ball48inFIG.6A, with the hemisphere162being a first hemisphere and the hemisphere164being a second hemisphere, joined at its base to the base of the first hemisphere162. InFIG.11A, the first hemisphere162is aligned with the second hemisphere164. For example, the side edges154in the first hemisphere are continuous with side edges154of adjacent dimple sections in the second hemisphere164.

The alphabetic labels placed within the dimples152in the figures designate same diameter dimples; i.e., all dimples labeled A have substantially the same diameter, all dimples labeled B have substantially the same diameter, and so on. In particular, the alphabetic labels within the dimples in the figures designate dimples152having the same dimple diameter, edge angle, and chord depth. In an exemplary embodiment, the number of different dimple diameters on the outer surface of a disclosed golf ball is five or less. In a further particular aspect of the embodiment illustrated inFIGS.9A,9B,10,11A, and11B, the dimples152labeled A-E have the diameter, chord depth, and edge angle values given in Table 1 below:

Exemplary golf balls having dimples with properties according to Table 1 include five different dimple diameter sizes with a largest dimple diameter of 0.185 in. and a smallest dimple diameter of 0.110 in. The largest dimple diameter ratio is thus approximately 1.682, which is the dimple diameter ratio of the “A” and “E” dimples. The difference in diameter between the largest dimple diameter and the smallest dimple diameter is 0.075 in. The difference in chord depth between the smallest diameter dimple and the largest diameter dimple is 0.0013 in. In an exemplary embodiment, all of the dimples have the same edge angle For example, the dimples “A”−“E” all have an edge angle of 14°.

In the golf ball166, the linear side edges154intersect each other (i.e., create a vertex) at the pole168of the hemisphere162. In an exemplary embodiment, the centroid of a polar dimple170is located at the pole168, with a centroid of the polar dimple170at the vertex of the side edges154. Each dimple section150thus includes a 1/7thportion of the polar dimple170. In an exemplary embodiment, the polar dimple170has a largest diameter of the dimple diameters present on the golf ball166(e.g., an “E” dimple). For example, the polar dimple170has a diameter of approximately 0.185 in.

In an exemplary embodiment, the dimple section150includes mirror symmetry across the symmetry line158. The symmetry line158extends from the intersection of the side edges154at the pole168to a midpoint of the base edge156. In at least some embodiments, the dimple section150includes at least some dimples152that have centroids that lie on a side edge154and at least some dimples that have centroids that lie on the symmetry line158. According to an exemplary embodiment, within a single dimple section150or150A, there are at least three dimples152on each side edge154and at least three dimples152on the symmetry line158(i.e., at least three dimples152lie on a first side edge154, at least three different dimples152lie on a second side edge154, and at least three different dimples152lie on the symmetry line158, for a total of at least nine dimples152lying on those lines combined). According to another aspect of the golf ball166, within each dimple section150or150A there are at least six dimples152on the symmetry line158(FIG.9A) or at least six dimples152on both side edges154A (FIG.9B). According to another aspect of the golf ball166, there are a total of at least twelve dimples152that lie on either a side edge154,154A or a symmetry line158,158A.

The dimples152include three dimples172that lie on the symmetry line158(or side edge154A) and are closest to the polar dimple170. The three dimples172are the same size and shape. For example, the three dimples172closest to the polar dimple170are “C” dimples (i.e., not the smallest or largest dimples in the dimple section150). The dimples152further include a dimple174, a dimple176, and a dimple178, all also having a centroid that lies on the symmetry line158(or side edge154A). The dimple174may be a “D” dimple, the dimple176may be an “E” dimple, and the dimple178may be an “A” dimple. In this way, the dimples172,174,176, and178that lie on the symmetry line158(or side edge154A) include at least four different dimple sizes. In an exemplary embodiment, the “A” dimple178may be the closest of the dimples172,174,176, and178to the base edge156.

The dimple section150may include at least twenty-four dimples that lie entirely within the boundaries of the dimple section150, including one “A” dimple, ten “B” dimples, three “C” dimples, seven “D” dimples, and three “E” dimples. The dimple section150A may include at least twenty-one dimples that lie entirely within the boundaries of the dimple section150A, including ten “B” dimples, two “C” dimples, seven “D” dimples, and two “E” dimples. The dimples152include five dimples180located adjacent to the base edge156(or156A). The dimples180include two different dimple diameters. In the dimple section150, the dimples180include four consecutive dimples that are the same size (e.g., “B” dimples). In the dimple section150A, the dimples180include a dimple that also lies on the symmetry line158A.

FIG.11Bshows a golf ball166A including dimples152A, according to another embodiment.FIG.11Bcorresponds to the golf ball48A inFIG.6B. The golf ball166A includes dimple sections150formed in hemispheres162A and164A, which are identical to hemispheres162,164, except for their relative position. Each hemisphere162A,164A includes seven dimple sections150, for a total of fourteen substantially identical dimple sections150in golf ball166A. In the golf ball166A, the hemisphere162A is rotated by 2π/14 radians with respect to the hemisphere164A around the polar axis160. As a result, the side edges154intersect the midpoint of an opposing base edge156.

FIG.11Cshows a golf ball182having dimples184, according to another embodiment.FIG.11Ccorresponds to the golf ball68inFIG.6C. The golf ball182includes hemispheres186and188, which are similar to the hemispheres162A,164A, except that the dimples184are adjusted (e.g., shifted in position) to produce a staggered parting line between the hemispheres186,188. The golf ball182includes a dimple section190. The dimple section190is repeated seven times in the hemisphere186and seven times in the hemisphere188for a total of fourteen dimple sections in the golf ball182. The dimples184in dimple section190include relative sizes that match the description of the section150(or150A). The dimple section190includes linear side edges192and a curved base edge194. In an exemplary embodiment, the above description of the dimples “A”-“E” may also apply to the golf ball182.

The disclosed golf balls166,166A, and182each have an overall dimple pattern including a total of 380 dimples. The dimples produce a surface coverage of the outer surface of the golf ball of greater than 75%. In an exemplary embodiment, the dimples152provide a surface coverage of the outer surface of the golf ball of about 81.7%.

The disclosed embodiments include golf ball dimple patterns based on the projection of a heptagonal dipyramid. The disclosed features are exemplary and can be used individually or in combination with other design features to provide an aerodynamically tuned golf ball satisfying desired design characteristics.

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.