Dimple Patterns for Golf Balls

This application is a continuation of U.S. patent application Ser. No. 18/086,824, filed Dec. 22, 2022, which is a continuation-in-part of U.S. patent application Ser. No. 17/743,580, filed May 13, 2022, which is a continuation of U.S. patent application Ser. No. 16/953,540, filed Nov. 20, 2020, now U.S. Pat. No. 11,406,876, the entire disclosures of which are incorporated by reference herein.

The present disclosure relates generally to golf balls. More particularly, the present disclosure relates to golf ball dimple patterns that are arranged in dipyramid layouts and have low surface coverages.

The flight performance of a golf ball is affected by a variety of factors including the weight, size, materials, dimple pattern, and external shape of the golf ball. Golf ball manufacturers seek to maximize aerodynamic efficiency and improve the performance of golf balls by adjusting the materials and construction of the ball as well as the dimple pattern and dimple shape.

The aerodynamic forces acting on a golf ball are typically resolved into orthogonal components of lift (F) and drag (F). Lift is defined as the aerodynamic force component acting perpendicular to the flight path. It results from a difference in pressure that is created by a distortion in the air flow that results from the back spin of the ball. Due to the back spin, the top of the ball moves with the air flow, which delays the separation to a point further aft. Conversely, the bottom of the ball moves against the air flow, moving the separation point forward. This asymmetrical separation creates an arch in the flow pattern, requiring the air over the top of the ball to move faster, and thus have lower pressure than the air underneath the ball.

Drag is defined as the aerodynamic force component acting parallel to the ball flight direction. As the ball travels through the air, the air surrounding the ball has different velocities and, thus, different pressures. The air exerts maximum pressure at the stagnation point on the front of the ball. The air then flows over the sides of the ball and has increased velocity and reduced pressure. The air separates from the surface of the ball, leaving a large turbulent flow area with low pressure, i.e., the wake. The difference between the high pressure in front of the ball and the low pressure behind the ball reduces the ball speed and acts as the primary source of drag.

Recently, there has been an increased desire to manipulate these aerodynamic forces to produce reduced-flight golf balls (i.e., golf balls that are designed to travel a distance that is shorter than the distance traveled by standard golf balls). Advances in golf ball compositions and dimple designs have caused high-performance golf balls to exceed the maximum distance allowed by the United States Golf Association (USGA). Some industry experts have called for the USGA to roll back the distance standard for golf balls to preserve the game.

Golf ball manufacturers have developed ways to reduce the distance traveled by the golf ball. For example, some manufacturers have created inefficient dimple patterns or have modified the compositions of the golf ball core to reduce the flight of the ball. Inefficient dimple patterns with low surface coverages have been used for many years. For example, the Atti pattern, which is an octahedron pattern split into eight concentric straight-line rows and covering 66 percent of the ball, was the predominant pattern utilized on golf balls for most of the 20th century. These dimple patterns were composed of substantially uniform dimples (for example, dimples having only one or two dimple diameters) and lacked aerodynamic efficiency. As dimple designers moved toward patterns with increased surface coverages, many more dimple sizes (for example, dimple diameters) were needed to achieve increased coverages and improved aerodynamics, such as increased distance. While these high-performance golf balls have improved aerodynamic consistency, the golf balls will not adhere to a shorter USGA maximum distance.

Accordingly, there remains a need to fine-tune the dimple patterns and dimple dimensions on these high-performance golf balls to reduce the flight distance, while also maintaining the appearance of a high-performance trajectory.

High-performance golf balls having reduced flight distance are disclosed. In some embodiments, a golf ball having a substantially spherical surface, including a plurality of dimples disposed thereon, wherein the dimples are arranged in a dipyramid pattern including at least six substantially identical dimple sections, wherein each dimple section is defined by a spherical triangle, wherein the dimple arrangement within each substantially identical dimple section is asymmetric, and wherein the dimples cover about 70 percent or less of the substantially spherical surface. In one embodiment, the dipyramid pattern includes six, eight, ten, twelve, or fourteen substantially identical dimple sections. In another embodiment, the dipyramid pattern includes eight substantially identical dimple sections. In still another embodiment, the dimple arrangement within each substantially identical dimple section is at least one of: not rotationally symmetric about a center of the dimple section or non-mirror symmetric about a central plane of the dimple section. In yet another embodiment, the dimples in each of the substantially identical dimple sections include at least two different dimple diameters including a minimum dimple diameter and a maximum dimple diameter. In still another embodiment, a dimple is located at a single vertex of each substantially identical dimple section.

In further embodiments, a golf ball having a substantially spherical surface, including a plurality of dimples disposed thereon, wherein the dimples are arranged in a dipyramid pattern including at least six substantially identical dimple sections, wherein each dimple section is defined by a spherical triangle, wherein the dimple arrangement within each substantially identical dimple section lacks at least one of: rotational symmetry about a center of the dimple section or mirror symmetry about a central plane of the dimple section, and wherein the dimples cover about 65 percent or less of the substantially spherical surface. In one embodiment, the dipyramid pattern includes six, eight, ten, twelve, or fourteen substantially identical dimple sections. In another embodiment, the dipyramid pattern includes eight substantially identical dimple sections. In still another embodiment, the dimple arrangement within each substantially identical dimple section lacks both rotational symmetry about the center of the dimple section and mirror symmetry about the central plane of the dimple section. In yet another embodiment, the dimples cover about 60 percent or less of the substantially spherical surface. In another embodiment, the dimples in each of the substantially identical dimple sections include at least three different dimple diameters including a minimum dimple diameter, a maximum dimple diameter, and an additional dimple diameter. In still another embodiment, the dimples in each of the substantially identical dimple sections include at least seven different dimple diameters including a minimum dimple diameter, a maximum dimple diameter, and at least five additional dimple diameters. In yet another embodiment, each of the at least seven different dimple diameters range from about 0.100 inches to about 0.200 inches.

In still further embodiments, a golf ball having a substantially spherical surface, including a plurality of dimples disposed thereon, wherein the dimples are arranged in a dipyramid pattern including at least eight substantially identical dimple sections, wherein each dimple section is defined by a spherical triangle, wherein the dimples in each of the substantially identical dimple sections include at least three different dimple diameters including a minimum dimple diameter, a maximum dimple diameter, and at least one additional dimple diameter, wherein the dimple arrangement within each substantially identical dimple section is not rotationally symmetric about a center of the dimple section and the dimple arrangement is non-mirror symmetric about a central plane of the dimple section, and wherein the dimples cover about 60 percent or less of the substantially spherical surface. In one embodiment, the dipyramid pattern includes eight, ten, twelve, or fourteen substantially identical dimple sections. In another embodiment, the dipyramid pattern has eight substantially identical dimple sections. In still another embodiment, the dimples in each of the substantially identical dimple sections include at least seven different dimple diameters including a minimum dimple diameter, a maximum dimple diameter, and at least five additional dimple diameters. In yet another embodiment, each of the at least seven different dimple diameters range from about 0.100 inches to about 0.200 inches. In another embodiment, the minimum difference in diameter between any two dimples within each dimple section is about 0.010 inches or more.

Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art of this disclosure. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the specification and should not be interpreted in an idealized or overly formal sense unless expressly so defined herein. Well known functions or constructions may not be described in detail for brevity or clarity.

The terms “about” and “approximately” shall generally mean an acceptable degree of error or variation for the quantity measured given the nature or precision of the measurements. Numerical quantities given in this description are approximate unless stated otherwise, meaning that the term “about” or “approximately” can be inferred when not expressly stated.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well (i.e., at least one of whatever the article modifies), unless the context clearly indicates otherwise.

The present disclosure provides reduced-flight golf balls. That is, golf balls designed to travel a distance that is shorter than the distance traveled by current performance balls. The golf balls of the present disclosure have low dimple surface coverage and dimple patterns composed of multiple dimple sizes and edge angles that correlate with the surface coverage. Advantageously, by using multiple dimple sizes, for instance, different dimple diameters, edge angles, and dimple depths, the dimple patterns disclosed herein can be optimized to help reduce the flight of the ball while providing improved aerodynamic consistency and maintaining the appearance of a high-performance trajectory.

The golf ball dimple patterns of the present disclosure are arranged in dipyramid layouts. According to the dipyramid layouts, there are two identical hemispheres on the golf ball separated by an equator. Each hemisphere may include three, four, five, six, or seven triangular segments such that there are six, eight, ten, twelve, or fourteen identical sections, respectively, on the golf ball. In one embodiment, each section is in the shape of a spherical triangle. As used herein, “spherical triangle” refers to a figure formed on the surface of a sphere by three circular arcs intersecting pairwise at three vertices. The three circular arcs each represent an edge of the spherical triangle. In some embodiments, each spherical triangle has a base edge located at the equator of the golf ball and two side edges that run longitudinally from the base edge to the pole of the hemisphere. A spherical triangle in the northern hemisphere may be joined with a spherical triangle in the southern hemisphere at their base edges to form a “dipyramid.”

In one embodiment, the golf ball dimple patterns may be arranged in a triangular dipyramid layout such that there are three spherical triangles on each of the two hemispheres of the golf ball. In this embodiment, the triangular dipyramid layout includes a total of six identical dimple sections on the golf ball. In another embodiment, the golf ball dimple patterns may be arranged in a quadrilateral dipyramid layout such that there are four spherical triangles on each of the two hemispheres of the golf ball. In this embodiment, the quadrilateral dipyramid layout includes a total of eight identical dimple sections on the golf ball. In still another embodiment, the golf ball dimple patterns may be arranged in a pentagonal dipyramid layout such that there are five spherical triangles on each of the two hemispheres of the golf ball. In this embodiment, the pentagonal dipyramid layout includes a total of ten identical dimple sections on the golf ball. In yet another embodiment, the golf ball dimple patterns may be arranged in a hexagonal dipyramid layout such that there are six spherical triangles on each of the two hemispheres of the golf ball. In this embodiment, the hexagonal dipyramid layout includes a total of twelve identical dimple sections on the golf ball. In still another embodiment, the golf ball dimple patterns may be arranged in a heptagonal dipyramid layout such that there seven spherical triangles on each of the two hemispheres of the golf ball. In this embodiment, the heptagonal dipyramid layout includes a total of fourteen identical dimple sections.

In one embodiment, the dimples may be located entirely within a dimple section. For example, the dimples may be arranged within the edges of the spherical triangle such that no dimples intersect an edge of the spherical triangle. In another embodiment, dimples may be shared between two or more dimples sections. In one aspect of this embodiment, for each dimple that is not located entirely within a dimple section, the centroid of the dimple is located along a side edge or at one or more vertices of the spherical triangle. In another aspect of this embodiment, dimples shared between two sections may include dimples that are positioned such that the centroid of the dimple does not lie along a side edge. For purposes of the present disclosure, the “centroid” of the dimple refers to the center of the dimple. In other embodiments, the base edges of the dimple sections are defined such that no dimples intersect the base edge.

In one embodiment of the present invention, the dimple pattern within each of the dimple sections may be arranged such that one or more dimples intersect a side edge of the spherical triangle. In a particular aspect of this embodiment, the side edge intersected by the one or more dimples runs through the centroid of the dimple such that half of the dimple is located within one spherical triangle and the other half is located within another spherical triangle. In another aspect of this embodiment, the side edge intersected by one or more dimples does not run through the centroid of the dimple. That is, less than half of the dimple is located within one spherical triangle and more than half of the dimple is located within an adjacent spherical triangle. In one embodiment, the dimple pattern within each of the dimple sections includes at least three dimples that intersect a side edge of the spherical triangle. In another embodiment, the dimple pattern within each of the dimple sections includes at least six dimples that intersect a side edge of the spherical triangle. In another embodiment, the dimple pattern within each of the dimple sections includes at least twelve dimples that intersect a side edge of the spherical triangle. In another embodiment, the dimple pattern within each of the dimple sections includes at least fifteen dimples that intersect a side edge of the spherical triangle.

In another embodiment, the dimple patterns of the present disclosure may be arranged such that a dimple lies at one or more vertices of the spherical triangle. In this embodiment, the centroid of the dimple is located at the vertex of the spherical triangle and a portion of the dimple is located within the other spherical triangles. That is, the dimple located at the vertex of the spherical triangle may be centered on the vertices of the spherical triangles. The dimple patterns of the present disclosure may include a dimple located at a single vertex of the spherical triangle. In another embodiment, the dimple patterns may include a dimple located at each of two vertices of the spherical triangle. In still another embodiment, the dimple patterns may include a dimple located at each of the three vertices of the spherical triangle.

The dimple patterns arranged in each of the dimple sections, for example, in each of the spherical triangles, are substantially identical to each other. For purposes of the present disclosure, dimple patterns are “substantially identical” if they have substantially the same dimple arrangement (i.e., the relative positions of each of the dimples' centroids are about the same) and substantially the same dimple characteristics (e.g., plan shape, cross-sectional shape, diameter, edge angle). Thus, for each dimple located entirely within a particular dimple section, for example, a particular spherical triangle, there is a corresponding dimple in each of the other dimple sections. For dimples having a centroid located along an edge of the dimple section, there is a corresponding dimple located along the same edge in the other dimple sections. For dimples located at the one or more vertices of the dimple sections, these dimples are shared between the other dimple sections.

The dimple patterns within each dimple section, for example, within each spherical triangle, include dimples having varying dimple diameters. In one embodiment, each dimple pattern has at least two different dimple diameters, including a minimum diameter dimple and a maximum diameter dimple. For example, the triangular and hexagonal dipyramid layouts disclosed herein may include dimple patterns having at least two different dimple diameters. For purposes of the present disclosure, dimples having substantially different diameters include dimples on a finished ball having respective diameters that differ by 0.005 inches or more. In another embodiment, each dimple pattern has at least three different dimple diameters, including a minimum diameter dimple, a maximum diameter dimple, and at least one additional diameter dimple. For instance, the quadrilateral and pentagonal dipyramid layouts disclosed herein may include dimple patterns having at least three different dimple diameters. In another embodiment, each dimple pattern has at least four different dimple diameters, including a minimum diameter dimple, a maximum diameter dimple, and at least two additional diameter dimples. In still another embodiment, each dimple pattern has at least five different dimple diameters, including a minimum diameter dimple, a maximum diameter dimple, and at least three additional diameter dimples. In yet another embodiment, each dimple pattern has at least six different dimple diameters, including a minimum diameter dimple, a maximum diameter dimple, and at least four additional diameter dimples. In still another embodiment, each dimple pattern has at least seven different dimple diameters, including a minimum diameter dimple, a maximum diameter dimple, and at least five additional diameter dimples. For example, the quadrilateral dipyramid layouts disclosed herein may include dimple patterns having at least seven different dimple diameters.

As discussed above, in some embodiments, the dimple pattern includes at least one dimple intersecting a side edge of the dimple section. In this embodiment, at least one dimple having the minimum dimple diameter intersects the side edge of the dimple section. In another embodiment, at least one dimple having the maximum dimple diameter intersects the side edge of the dimple section. In still another embodiment, at least one dimple having neither the minimum nor maximum dimple diameter intersects the side edge of the dimple section. Additionally, in some embodiments, the dimple pattern includes at least one dimple lying at a vertex of the dimple section. In one embodiment, at least one dimple having the maximum dimple diameter is located at a vertex of the dimple section. In another embodiment, at least one dimple having the minimum dimple diameter is located at a vertex of the dimple section. In still another embodiment, at least one dimple having neither the minimum nor maximum dimple diameter is located at a vertex of the dimple section.

In one embodiment, the dimple patterns disclosed herein may be symmetric. For example, the dimple patterns within each dimple section may be rotationally symmetric about the central point of each dimple section. That is, the dimple patterns may have three-way rotational symmetry about an axis connecting the center of the golf ball and the central point of the dimple section. In another embodiment, the dimple patterns may have mirror symmetry about a central plane of each dimple section, where the central plane is a plane containing the center of the golf ball, the central point of the corresponding dimple section, and one vertex of the corresponding dimple section.

In still other embodiments, the dimple patterns disclosed herein may be asymmetric. The asymmetric dimple patterns of the present disclosure have no rotational symmetry and/or no mirror symmetry. Without being bound by any particular theory, it is believed asymmetric dimple patterns lacking rotational or mirror symmetry may help reduce the flight distance of the golf ball. The dimple patterns disclosed herein lack at least one or both of rotational symmetry about the center of each dimple section and mirror symmetry about the central plane of each dimple section. In some embodiments, the dimple patterns disclosed herein are not rotationally symmetric about the center of each dimple section and are non-mirror symmetric about the central plane of each dimple section.

In some embodiments, the triangular dipyramid dimple patterns disclosed herein may be asymmetric, i.e., the dimple pattern has no rotational symmetry and/or no mirror symmetry. In other embodiments, the quadrilateral dipyramid dimple patterns disclosed herein may be asymmetric. In still other embodiments, the pentagonal dipyramid dimple patterns disclosed herein may be asymmetric. In yet other embodiments, the hexagonal dipyramid dimple patterns disclosed herein may be asymmetric. In further embodiments, the heptagonal dipyramid dimple patterns disclosed herein may be asymmetric.

In one embodiment, the golf balls of the present disclosure have a quadrilateral dipyramid dimple pattern that is asymmetric. In this embodiment, the dimples are arranged in each dimple section such that the dimple arrangement is not rotationally symmetric about the central point of each dimple section and/or the dimple arrangement has no mirror symmetry. In some embodiments, the asymmetric quadrilateral dipyramid dimple patterns include at least seven different dimple diameters, including a minimum diameter dimple, a maximum diameter dimple, and at least five additional diameter dimples.

In one embodiment, the dimples should be arranged within each dimple section such that the outer surface of the golf ball has dimple free great circles. A golf ball having a “dimple free great circle” refers to a golf ball having an outer surface that contains a great circle which does not intersect any dimples. In mathematical terms, every dimple free great circle follows a path on the surface of a golf ball having a given width, and within the given width, there exists an infinite number of great circles. However, for purposes of the present disclosure, each dimple free great circle traverses a different dimple free path in the dimple pattern than another dimple free great circle.

In one embodiment, the dimples may be arranged within each dimple section such that there are more than three dimple free great circles on the outer surface of the golf ball. For example, the dimples may be arranged within each dimple section such that there are four dimple free great circles on the outer surface of the golf ball. In other embodiments, the dimples may be arranged within each dimple section such that there is one dimple free great circle on the outer surface of the golf ball. In still other embodiments, the dimples may be arranged within each dimple section such that there are no dimple free great circles on the outer surface of the golf ball.

The dimples may be positioned within each dimple section according to any packing method known in the art so long as the dimple sections are substantially identical and meet the symmetry and surface coverage requirements discussed herein. For example, the dimples may be arranged within each dimple section according to the methods described in U.S. Pat. No. 10,183,195, issued on Jan. 22, 2019; U.S. Pat. No. 7,503,856, issued on Mar. 17, 2009; pending U.S. application Ser. No. 16/587,298, filed on Sep. 30, 2019; and pending U.S. application Ser. No. 16/587,321, filed on Sep. 30, 2019, the entire disclosures of which are incorporated herein by reference.

The present disclosure contemplates dimples having a circular plan shape. A “plan shape,” as used herein, refers to the perimeter of the dimple as seen from a top view of the dimple, or the demarcation between the dimple and the outer surface of the golf ball or fret surface. However, non-circular plan shapes may also be suitable for use with the present disclosure. For example, the plan shape may be any one of a circle, square, triangle, rectangle, oval, or other geometric or non-geometric shape. In another embodiment, the dimples may have a plan shape defined by low frequency periodic functions or high frequency periodic functions.

In one embodiment, the dimples contemplated for use in the dimple patterns are spherical dimples (i.e., dimples having a circular plan shape and a dimple profile based on a spherical function). A “dimple profile,” as used herein, refers to the cross section of the dimple as seen from a side view of the dimple. However, other dimple profile shapes may also be suitable for use with the present disclosure. For example, the dimples may be defined by the revolution of a catenary curve about an axis, such as that disclosed in U.S. Pat. Nos. 6,796,912 and 6,729,976, the entire disclosures of which are incorporated by reference herein. In another embodiment, the dimple profiles may correspond to ellipses, saucer-shapes, truncated cones, and flattened trapezoids.

In still another embodiment, the dimples may have profiles defined by a continuous function, such as a polynomial function, an exponential function, a trigonometric function, and a hyperbolic function. Specific non-limiting examples of suitable dimple profiles contemplated by the present disclosure include those that can be defined by the following functions: conical, catenary, polynomial, Witch of Agnesi, frequency, Neiles parabola, sine, cosine, hyperbolic sine, and hyperbolic cosine profiles.

The dimple profile may also be defined by combining a spherical curve and a different curve, such as a cosine curve, a frequency curve or a catenary curve, as disclosed in U.S. Patent Publication No. 2012/0165130, which is incorporated in its entirety by reference herein. Similarly, the dimple profile may be defined by a combination of two or more curves. For example, in one embodiment, the dimple profile is defined by combining a spherical curve and a different curve. In another embodiment, the dimple profile is defined by combining a cosine curve and a different curve. In still another embodiment, the dimple profile is defined by combining a frequency curve and a different curve. In yet another embodiment, the dimple profile is defined by combining a catenary curve and a different curve. In still another embodiment, the dimple profile may be defined by combining three or more different curves. In yet another embodiment, one or more of the curves may be a functionally weighted curve, as disclosed in U.S. Patent Publication No. 2013/0172123, which is incorporated in its entirety by reference herein.

Dimple patterns generated by the present disclosure can achieve a low percentage of surface coverage. As used herein, “surface coverage” refers to the percentage of the ball surface that has been removed by the formation of dimples. In other words, the surface coverage is the surface area of a sphere having the diameter of the golf (D) minus the surface area of the fret area of the golf ball. By reducing the surface coverage, the flight and distance of the golf ball can be reduced.

Surface coverage may be calculated using equation (I):

where n is the number of dimples on the ball, r is the dimple plan shape radius (equal to the dimple diameter/2), and h is the cap height as shown in.

In one embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 75 percent or less. In another embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 70 percent or less. In another embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 65 percent or less. In another embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 60 percent or less. In still another embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 50 percent or less. In yet another embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 40 percent or less. In another embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 30 percent or less. In still another embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 20 percent or less. In yet another embodiment, the dimple patterns generated by the present disclosure have a surface coverage of about 15 percent.

As discussed above, the dimple patterns within each dimple section, for example, within each spherical triangle, include dimples having at least two different dimple diameters, including a minimum dimple diameter and a maximum dimple diameter. In one embodiment, each dimple has a dimple diameter of about 0.030 inches to about 0.200 inches. In another embodiment, each dimple has a dimple diameter of about 0.050 inches to about 0.180 inches. In still another embodiment, each dimple has a dimple diameter of about 0.070 inches to about 0.160 inches. In yet another embodiment, each dimple has a dimple diameter of about 0.090 inches to about 0.140 inches. In still another embodiment, each dimple has a dimple diameter of about 0.100 inches to about 0.200 inches. In another embodiment, each dimple has a dimple diameter of about 0.100 inches to about 0.180 inches. In yet another embodiment, each dimple has a dimple diameter of about 0.100 inches to about 0.160 inches. In still another embodiment, each dimple has a dimple diameter of about 0.100 inches to about 0.150 inches.

In some embodiments, the minimum dimple diameter is less than 0.100 inches. For instance, the minimum dimple diameter may be about 0.030 inches to about 0.100 inches. In another embodiment, the minimum dimple diameter may be about 0.050 inches to about 0.090 inches. In further embodiments, the minimum dimple diameter is about 0.100 inches. In still further embodiments, the minimum dimple diameter may be more than 0.100 inches. For example, the minimum dimple diameter may be about 0.100 inches to about 0.150 inches. In another embodiment, the minimum dimple diameter may be about 0.100 inches to about 0.125 inches.

The minimum and maximum differences between any two dimple diameters within a dimple section may vary. In one embodiment, the minimum difference between any two dimple diameters within a dimple section is about 0.010 inches or more. In another embodiment, the minimum difference between any two dimple diameters within a dimple section is about 0.020 inches or more. In another embodiment, the minimum difference between any two dimple diameters within a dimple section is about 0.030 inches or more. In another embodiment, the minimum difference between any two dimple diameters within a dimple section is about 0.040 inches or more. In further embodiments, the maximum difference between any two dimple diameters within a dimple section is about 0.100 inches or less. In other embodiments, the maximum difference between any two dimple diameters within a dimple section is about 0.080 inches or less. In another embodiment, the maximum difference between any two dimple diameters within a dimple section is about 0.065 inches or less. In still another embodiment, the maximum difference between any two dimple diameters within a dimple section is about 0.055 inches or less. In another embodiment, the maximum difference between any two dimple diameters within a dimple section is about 0.045 inches or less. For instance, the difference between any two dimple diameters within each dimple section is about 0.030 inches to about 0.080 inches. In other embodiments, the difference between any two dimple diameters within each dimple section is about 0.010 inches to about 0.100 inches.

In one embodiment, the dimples contemplated for use in the dimple patterns of the present disclosure have a circular plan shape. However, as noted above, the dimples may also have a variety of other plan shapes. The diameter of a dimple having a non-circular plan shape is defined by its equivalent diameter, de, which may be calculated according to equation (II):

where dis the equivalent dimple diameter and A is the plan shape area of the dimple. By the term, “plan shape area,” it is meant the area 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 golf ball to the point of the calculated surface depth. In one embodiment, the equivalent diameters of dimples having non-circular plan shapes are the same as the ranges of dimple diameters discussed above for the circular plan shaped dimples.

Diameter measurements are determined on finished golf balls according to. Generally, it may be difficult to measure a dimple's diameter due to the indistinct nature of the boundary dividing the dimple from the ball's undisturbed land surface. Due to the effect of paint and/or the dimple design itself, the junction between the land surface and dimple may not be a sharp corner and is therefore indistinct. This can make the measurement of a dimple's diameter somewhat ambiguous.

To resolve this problem, dimple diameter on a finished golf ball is measured according to the method shown in.shows a dimple half-profile, extending from a dimple centerlineto the land surface outside of the dimple. A ball phantom surfaceis constructed above the dimple as a continuation of the land surface. A first tangent line Tis then constructed at a point on the dimple sidewall that is spaced 0.003 inches radially inward from the phantom surface. The first tangent line Tintersects the phantom surfaceat a point P, which defines a nominal dimple edge position. A second tangent line Tis then constructed, tangent to the phantom surfaceat P. The edge angle is the angle between the first tangent line Tand the second tangent line T. The dimple diameter is the distance between Pand its equivalent point diametrically opposite along the dimple perimeter. Alternatively, it is twice the distance between Pand the dimple centerline, measured in a direction perpendicular to the dimple centerline. The dimple depth is the distance measured along a ball radius from the phantom surfaceof the ball to the deepest point on the dimple. The chord plane runs through the point Pand is normal to the dimple centerline. The chord depth is the distance from the chord plane to the deepest part of the dimple. The cap height is the distance from the chord plane to the phantom surfacealong the dimple centerline. The dimple volume is the space enclosed between the phantom surfaceand the dimple surface(extended along the first tangent line Tuntil it intersects the phantom surface).

The dimple patterns of the present disclosure may have varying edge angles depending on the desired surface coverage. Optimization of the edge angles using the equations provided herein can help reduce the flight of the ball while maintaining ideal trajectories. For spherical dimples, the edge angle is defined as the angle between the first tangent line Tand the second tangent line T, as shown in. In one embodiment, the average edge angle (θ) of all the dimple edge angles on the golf ball is related to the surface coverage based on the range displayed in equation (III) below:

where SC is the surface coverage and the format for SC is the decimal form of percentage (for example, 50 percent coverage is 0.50).is a graphical representation of the relationship between edge angle and surface coverage of spherical dimples according to an embodiment of the present disclosure. In one embodiment, the dimples of the present disclosure may have any edge angle falling within the range of values shown in. For instance, with a desired surface coverage of about 70 percent, the average edge angle of all the dimple edge angles on the golf ball may range from about 9.38 degrees to about 20.15 degrees. In another embodiment, with a desired surface coverage of about 50 percent, the average edge angle of all the dimple edge angles on the golf ball may range from about 11.45 degrees to about 27.85 degrees. In still another embodiment, with a desired surface coverage of about 30 percent, the average edge angle of all the dimple edge angles on the golf ball may range from about 20.62 degrees to about 49.15 degrees. In yet another embodiment, with a desired surface coverage of about 15 percent, the average edge angle of all the dimple edge angles on the golf ball may range from about 32.16 degrees to about 74.05 degrees. Accordingly, in some embodiments, as the surface coverage of the dimple patterns generated by the present disclosure decreases, the average edge angles may increase.