Patent Publication Number: US-2020276478-A1

Title: Golf ball having dimples with concentric or non-concentric grooves

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of U.S. patent application Ser. No. 16/207,269, filed Dec. 3, 2018, which is a continuation-in-part of U.S. patent application Ser. No. 15/651,184, filed Jul. 17, 2017, now U.S. Pat. No. 10,195,486, which is a continuation-in-part of U.S. patent application Ser. No. 14/985,792, filed Dec. 31, 2015, now U.S. Pat. No. 9,707,451, the entire disclosures of which are hereby incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to golf ball dimples having concentric grooves or non-concentric grooves on the dimple surface. In particular, the present invention relates to golf ball dimples having circular perimeters and dimple profiles having a concentric or non-concentric groove on the surface of the dimple. When utilized on golf balls, the golf ball dimples of the present invention provide surfaces having unique appearances, while maintaining ideal aerodynamic characteristics. 
     BACKGROUND OF THE INVENTION 
     Golf balls generally include a spherical outer surface with a plurality of dimples formed thereon. The dimples on a golf ball improve the aerodynamic characteristics of a golf ball and, therefore, golf ball manufacturers have researched dimple patterns, shape, volume, and cross-section in order to improve the aerodynamic performance of a golf ball. Determining specific dimple arrangements and dimple shapes that result in an aerodynamic advantage requires an understanding of how a golf ball travels through air. 
     As a threshold matter, a ball without dimples encounters no turbulence in the thin layer of air that flows close to the surface of a golf ball (i.e., the boundary layer). When a ball includes a number of dimples on the surface, the boundary layer becomes turbulent, which moves the separation point, i.e., the point in which the air separates from the surface of the ball, further backward, so that the layer stays attached further along the outer surface of the ball. It is the circumference portion of each dimple, where the dimple wall drops away from the outer surface of the ball, which actually creates the turbulence in the boundary layer. 
     Aerodynamic forces acting on a golf ball are typically resolved into orthogonal components of lift (F L ) and drag (F D ). 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. Lift and drag, among other aerodynamic characteristics of a golf ball, are influenced by the external surface geometry of the ball, which includes the dimples thereon. As such, the dimples on a golf ball play an important role in controlling those parameters. For example, the dimples on a golf ball create a turbulent boundary layer around the ball, i.e., the air in a thin layer adjacent to the ball flows in a turbulent manner. The turbulence energizes the boundary layer and helps it stay attached further around the ball to reduce the area of the wake. This greatly increases the pressure behind the ball and substantially reduces the drag. 
     The design variables associated with the external surface geometry of a golf ball, e.g., surface coverage, dimple pattern layout, and individual dimple geometries, provide golf ball manufacturers the ability to control and optimize ball flight. Recently, golf ball manufacturers have begun to alter the surfaces of the dimple profiles in an attempt to optimize aerodynamic characteristics. However, adjustments and alterations to dimple profiles do not always result in enhanced aerodynamic performance. 
     Accordingly, there remains a need for a dimple profile having an altered surface that provides unique surface appearances, while maintaining desirable aerodynamic characteristics and ideal flight conditions. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a golf ball having a substantially spherical surface, including a plurality of circular dimples on the spherical surface, wherein at least a portion of the plurality of circular dimples include a concentric groove on each dimple surface, wherein each concentric groove has a groove diameter and each dimple has a dimple diameter, wherein a ratio of groove diameter to dimple diameter is about 0.05 to about 0.95, and wherein a ratio of 
     
       
         
           
             
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     is about 0.01 or less, wherein S is the average surface area for all grooves on the ball, N is the number of grooved dimples on the ball, R is the radius of the ball, and P is the surface coverage of a dimple pattern used on the ball. In one embodiment, the groove diameter is about 0.0025 inches to about 0.285 inches. In another embodiment, the dimple diameter is about 0.050 inches to about 0.300 inches. In still another embodiment, each concentric groove has a width of about 0.00250 inches to about 0.0150 inches. In yet another embodiment, each concentric groove has a depth of about 0.0010 inches to about 0.0050 inches. Indeed, the concentric groove may have a half circular, triangular, or half square profile. 
     The present invention is also directed to a golf ball having a substantially spherical surface, including a plurality of dimples on the spherical surface, wherein at least 50 percent of the plurality of dimples include a circular perimeter, a dimple profile defined by a continuous function, and at least one concentric groove on a surface of the dimple profile, wherein the golf ball has a ratio of surface area of the grooves on the golf ball to the total surface area of the golf ball that is replaced by the plurality of dimples of about 0.010 or less, for example, of about 0.008 or less. 
     In one embodiment, the dimple profile is selected from the group consisting of spherical, conical, catenary, elliptical, polynomial, Witch of Agnesi, frequency, Neiles parabola, sine, cosine, hyperbolic sine, and hyperbolic cosine. For example, the dimple profile may be spherical, conical, or catenary. In another embodiment, the concentric groove has a profile that is substantially identical to the dimple profile. In still another embodiment, the concentric groove has a profile defined by the superposition of two or more continuous functions. In yet another embodiment, the concentric groove has a half circular, triangular, or half square profile. In this aspect, the portion of the plurality of circular dimples has a ratio of groove diameter to dimple diameter of about 0.20 to about 0.80. 
     The present invention is further directed to a golf ball dimple having a circular plan shape, including a circular plan shape; a spherical, conical, or catenary dimple profile; and at least one concentric groove on a surface of the dimple profile, wherein the concentric groove has a diameter of about 0.0025 inches to about 0.285 inches, a depth of about 0.0015 inches to about 0.0050 inches, and a width of about 0.0025 inches to about 0.0150 inches. In one embodiment, the concentric groove has a profile selected from the group consisting of half circular, half triangular, half square, half pentagonal, half hexagonal, half heptagonal, or half octagonal. For example, the profile of the concentric groove may be half circular, triangular, or half square. In another embodiment, the golf ball dimple further includes two concentric grooves on the surface of the dimple profile. In still another embodiment, the golf ball dimple further includes a ratio of groove diameter to dimple diameter of about 0.30 to about 0.70. 
     The present invention is also directed to a golf ball having a substantially spherical surface, including a plurality of dimples arranged in a dimple pattern on the spherical surface, wherein: the plurality of dimples includes dimples having a circular plan shape, at least a portion of the plurality of dimples include a non-concentric groove on each dimple surface, and the golf ball has a ratio of surface area of the grooves on the golf ball to total surface area of the golf ball that is replaced by the plurality of dimples of about 0.010 or less. In this aspect, each non-concentric groove has a groove diameter and each dimple has a dimple diameter, and wherein a ratio of groove diameter to dimple diameter is about 0.05 to about 0.95. In another embodiment, at least two dimples in the portion of dimples include non-concentric grooves with a planar preferential direction. In yet another embodiment, at least two dimples in the portion of dimples include non-concentric grooves with an axial preferential direction. In still another embodiment, each non-concentric groove has a groove diameter and a first centroid and each dimple has a dimple diameter and a second centroid, and wherein a distance between the first centroid and the second centroid is at least 5 percent of the dimple diameter. 
     The present invention is further directed to a golf ball having a substantially spherical surface, including a plurality of dimples arranged in a dimple pattern on the spherical surface, wherein: the plurality of dimples includes dimples having a circular plan shape, at least a portion of the plurality of dimples includes (i) at least two dimples having non-concentric grooves with a planar preferential direction, or (ii) at least two dimples having non-concentric grooves with an axial preferential direction, or (iii) a combination of (i) and (ii), and a ratio of 
     
       
         
           
             
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     is about 0.01 or less, wherein S is the average surface area for all grooves on the ball, N is the number of grooved dimples on the ball, R is the radius of the ball, and P is the surface coverage of the dimple pattern. In this aspect, each non-concentric groove has a groove diameter and each dimple has a dimple diameter, and wherein a ratio of groove diameter to dimple diameter is about 0.05 to about 0.95. In another embodiment, the non-concentric grooves with an axial preferential direction are shifted relative to a symmetrical axis of the dimple pattern and the non-concentric grooves with a planar preferential direction are shifted relative to a symmetrical plane of the dimple pattern. In still another embodiment, the dimples having non-concentric grooves with an axial preferential direction are symmetrically arranged about a reference axis and the dimples having non-concentric grooves with a planar preferential direction are symmetrically arranged about a reference plane. In yet another embodiment, the portion of the plurality of dimples includes multiple groups of the at least two dimples having non-concentric grooves with an axial preferential direction. In this aspect, each group may be shifted relative to a different symmetrical axis of the dimple pattern. In another embodiment, each non-concentric groove has a groove diameter and a first centroid and each dimple has a dimple diameter and a second centroid, and wherein a distance between the first centroid and the second centroid is at least 5 percent of the dimple diameter. 
     Moreover, the present invention is directed to a golf ball having a substantially spherical surface, including a plurality of dimples arranged in a dimple pattern on the spherical surface, wherein: the plurality of dimples includes dimples having a circular plan shape, at least a portion of the plurality of dimples include one or more dimples having a concentric groove and two or more dimples having a non-concentric groove, and a ratio of 
     
       
         
           
             
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     is about 0.01 or less, wherein S is the average surface area for all grooves on the ball, N is the number of grooved dimples on the ball, R is the radius of the ball, and P is the surface coverage of the dimple pattern. In this aspect, each concentric groove and each non-concentric groove has a groove diameter and each dimple has a dimple diameter, wherein a ratio of groove diameter to dimple diameter is about 0.05 to about 0.95. In still another embodiment, the one or more dimples having a concentric groove are centered along a reference axis or a reference plane. In yet another embodiment, the two or more dimples having a non-concentric groove are arranged adjacent to the centered dimples having a concentric groove. In another embodiment, the non-concentric grooves include an axial preferential direction or a planar preferential direction. In this aspect, each non-concentric groove has a groove diameter and a first centroid and each dimple has a dimple diameter and a second centroid, and wherein a distance between the first centroid and the second centroid is at least 10 percent of the dimple diameter. 
     The present invention is further directed to a golf ball having a generally spherical surface and comprising a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples have a circular plan shape, a spherical profile shape, an edge angle of from 10.0° to 20.0° , a dimple depth of from 0.004 inches to 0.020 inches, and comprise at least three concentric grooves on each dimple surface, and optionally a center indentation. Each circular groove has an arcuate cross-sectional profile. The center indentation, if present, has a circular plan shape and an arcuate cross-sectional profile. The radii of all of the arcuate cross-sectional profiles of the circular grooves, and the radius of the arcuate cross-sectional profile of the center indentation, if present, are substantially equal and have a value of from 0.015 inches to 0.125 inches. Each pair of adjacent concentric grooves has a horizontal separation distance of from 0.007 inches to 0.060 inches. The distance between the spherical profile of the dimple and a spherical profile containing the deepest point of each of the grooves is from 0.0005 inches to 0.007 inches. 
     The present invention is further directed to a golf ball having a generally spherical surface and comprising a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples have a circular plan shape, a spherical profile shape, an edge angle of from 10.0° to 20.0° , a dimple depth of from 0.004 inches to 0.020 inches, and comprise at least three concentric grooves on each dimple surface, and optionally a center indentation. Each circular groove has a half-square cross-sectional profile. The center indentation, if present, has a circular plan shape and a half-square cross-sectional profile. Each pair of adjacent concentric grooves has a horizontal separation distance of from 0.007 inches to 0.060 inches. The distance between the spherical profile of the dimple and a spherical profile containing the deepest point of each of the grooves is from 0.0005 inches to 0.007 inches. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Further features and advantages of the invention can be ascertained from the following detailed description that is provided in connection with the drawings described below: 
         FIG. 1  illustrates a golf ball according to one embodiment of the present invention; 
         FIGS. 2A-2C  illustrate various dimple profile shapes contemplated by the present invention; 
         FIG. 3A  illustrates an enlarged top plan view of a dimple according to an embodiment of the present invention; 
         FIGS. 3B and 3C  illustrate cross-sectional views (I-I) of the dimple depicted in  FIG. 3A ; 
         FIG. 4A-4B  illustrate various groove profile shapes contemplated by the present invention; 
         FIG. 5  is a graphical representation of groove surface areas; 
         FIG. 6  illustrates a dimple pattern of a golf ball created in accordance with one embodiment of the present invention; 
         FIG. 7  illustrates a dimple pattern of a golf ball created in accordance with another embodiment of the present invention; 
         FIG. 8  illustrates a dimple pattern of a golf ball created in accordance with still another embodiment of the present invention; 
         FIG. 9  illustrates an enlarged top plan view of a dimple according to another embodiment of the present invention; 
         FIG. 10A-10B  illustrate an arrangement of non-concentric grooved dimples according to one embodiment of the present invention; 
         FIGS. 11A-11B  illustrate an arrangement of non-concentric grooved dimples according to another embodiment of the present invention; 
         FIG. 12  illustrates a dimple pattern of a golf ball created in accordance with one embodiment of the present invention; 
         FIG. 13  illustrates a dimple pattern of a golf ball created in accordance with another embodiment of the present invention; 
         FIG. 14  illustrates a dimple pattern of a golf ball created in accordance with still another embodiment of the present invention; 
         FIG. 15  illustrates an example of a group of non-concentric grooved dimples according to one embodiment of the present invention; 
         FIG. 16  illustrates an example of a group of non-concentric grooved dimples according to another embodiment of the present invention; 
         FIG. 17  illustrates an example of a group of non-concentric and concentric grooved dimples according to one embodiment of the present invention; 
         FIG. 18A  illustrates an enlarged top plan view of a dimple according to an embodiment of the present invention; 
         FIGS. 18B and 18C  illustrate cross-sectional views (A-A) of the dimple depicted in  FIG. 18A ; 
         FIG. 19A  illustrates an enlarged top plan view of a dimple according to an embodiment of the present invention; and 
         FIGS. 19B and 19C  illustrate cross-sectional views (A-A) of the dimple depicted in  FIG. 19A . 
     
    
    
     DETAILED DESCRIPTION 
     The present invention is directed to golf ball dimples having concentric or non-concentric grooves on the dimple surface. In particular, in one embodiment, the present invention is directed to a golf ball dimple having a circular plan shape, a profile defined by a continuous function, and a concentric groove on the surface of the dimple. In another embodiment, the present invention is directed to a golf ball dimple having a circular plan shape, a profile defined by a continuous function, and a non-concentric groove on the surface of the dimple. While the present invention described herein demonstrates the use of either a concentric groove or a non-concentric groove on a single dimple, the present invention may also contemplate a single dimple having both a concentric groove and a non-concentric groove. The present invention is also directed to the use of one or more of the dimples of the present invention in a dimple pattern applied to a golf ball. 
     Advantageously, in one embodiment, golf balls including dimples produced in accordance with the present invention have visually distinct surface textures. Indeed, the dimples of the present invention possess a unique visual appearance. Additionally, in another embodiment, the dimples of the present invention result in enhanced aerodynamic performance. In particular, the concentric groove lowers the air resistance immediately after the ball is hit because the boundary layer is thin, but has little to no effect on the thicker boundary layer once the ball is at the highest point of its trajectory and, thus, ultimately maintains lift. As a result, golf balls including the dimples of the present invention have visually distinct appearances that maintain ideal flight conditions. 
     Referring to  FIG. 1 , a golf ball  10  has a spherical core (not shown) and a cover  4 . Numerous dimples  6  are formed on the cover  4  of the golf ball. The upper flattened portion of the cover  4  extending from dimple to dimple is the land surface  8 . Each dimple  6  has a plan shape. A dimple 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. The present invention contemplates dimples having a circular plan shape. However, non-circular plan shapes may also be suitable for use with the present invention. 
     According to the present invention, each circular dimple has a dimple profile. A dimple profile, as used herein, refers to the cross section of the dimple as seen from a side view of the dimple. The present invention contemplates dimples having profiles created from a continuous function. For example, the dimples of the present invention have circular plan shapes and corresponding dimple profiles that begin as a continuous function. 
     The profile of dimples according to the present invention may be defined by any known continuous function. For example, a continuous function is a function for which small changes in the input result in small changes in the output. In one embodiment, the present invention contemplates the use of continuous functions that lead to smooth transitions of the dimple profile to the golf ball surface. 
     In this aspect, the dimple profiles of the present invention may be defined by any continuous function including, but not limited to, 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 invention include those that can be defined by the following functions: spherical, conical, catenary, elliptical, polynomial, Witch of Agnesi, frequency, Neiles parabola, sine, cosine, hyperbolic sine, and hyperbolic cosine profiles. 
       FIGS. 2A-2C  illustrate various dimple profile shapes contemplated by the present invention. As shown in  FIGS. 2A-2C , the dotted line represents the phantom spherical face of the dimple (i.e., the region of the surface of the golf ball that was cut away to form the dimple). In one embodiment, the dimple profile of the present invention is defined by a spherical profile. For example,  FIG. 2A  shows a cross-sectional view of a dimple  6  having a spherical profile  12 . In another embodiment, the dimple profile of the present invention is defined by a catenary curve. As shown in  FIG. 2B , a dimple  6  according to the present invention may have a catenary profile  12 . In yet another embodiment, the dimple profile of the present invention is defined by a conical profile. Indeed,  FIG. 2C  shows a cross-sectional view of a dimple  6  having a conical profile  12 . 
     According to one embodiment of the present invention, the circular golf ball dimples of the present invention include at least one groove on the dimple surface. In this aspect, the dimple includes a groove along the dimple profile surface such that no part of the groove is in contact with the land surface of the golf ball. 
     Concentric Grooves 
     In one embodiment, the groove is concentric with the dimple perimeter so that the groove maintains a circular plan shape. In this aspect, the circular groove and the circular dimple share a common center or centroid.  FIG. 3A  illustrates an enlarged top plan view of a dimple according to one embodiment the present invention. As shown in  FIG. 3A , the dimple  6  includes a dimple profile  12  and a concentric groove  14  on the surface of the dimple profile  12 . The double dashed line located within the groove  14  represents the region of the surface that was cut away to form the groove  14 .  FIG. 3B  is a cross-sectional view (I-I) of the dimple depicted in  FIG. 3A . As shown in  FIG. 3B , the dimple profile  12  begins as a continuous sloping profile and includes a groove  14  that forms a recess in the sloping profile. The dotted line shown in  FIG. 3B  represents the phantom spherical face of the dimple (i.e., the region of the surface of the golf ball that was cut away to form the dimple). 
     As shown in  FIG. 3A , the dimple  6  has a diameter. For example, the dimple diameter D 1  represents the distance between contact points when common tangent lines are depicted at both sides of the dimple  6 . In one embodiment, the dimple diameter D 1  is about 0.050 inches to about 0.300 inches. In another embodiment, the dimple diameter D 1  is about 0.075 inches to about 0.275 inches. In yet another embodiment, the dimple diameter D 1  is about 0.100 inches to about 0.250 inches. In still another embodiment, the dimple diameter D 1  is about 0.125 inches to about 0.225 inches. 
     The dimple  6  also has a depth. As shown in  FIG. 3B , the dimple depth is depicted by the double sided arrow Z. Indeed, the dimple depth Z represents the distance between the deepest part of the dimple  6  and the phantom spherical face of the dimple. In one embodiment, the dimple depth Z is within a range of about 0.003 inches to about 0.025 inches. In another embodiment, the dimple depth Z is about 0.005 inches to about 0.020 inches. In still another embodiment, the dimple depth Z is about 0.006 inches to about 0.017 inches. 
     When the dimple profile is spherical, the dimple  6  also has an edge angle. Edge angle is often used in place of depth when describing spherical dimple profiles. The edge angle (θ E ) is defined as the angle between a first tangent line at the conical edge of the dimple profile and a second tangent line at the phantom ball surface. For example, as shown in  FIG. 3C , the edge angle θ E  is defined as the angle between the first tangent line T 1  and the second tangent line T 2 . In one embodiment, the edge angle is about 10 degrees to about 15 degrees. In another embodiment, the edge angle may be about 13 degrees to about 15 degrees. For example, the edge angle may be about 14 degrees. 
     The concentric groove  14  has a diameter. As shown in  FIG. 3A , the groove diameter D 2  represents the distance between contact points when common tangent lines are depicted at both sides of the concentric groove  14 . In one embodiment, the groove diameter D 2  is about 0.0025 inches to about 0.285 inches. In another embodiment, the groove diameter D 2  is about 0.0075 inches to about 0.250 inches. In yet another embodiment, the groove diameter D 2  is about 0.010 inches to about 0.200 inches. In still another embodiment, the groove diameter D 2  is about 0.050 inches to about 0.175 inches. Indeed, the groove diameter D 2  may be about 0.100 inches to about 0.150 inches. 
     The location of the groove  14  on the dimple surface  12  may vary. In this aspect, the ratio of the groove diameter D 2  to the dimple diameter D 1  determines the location of the groove  14  along the dimple profile  12 . For example, as will be apparent to one of ordinary skill in the art, a ratio approaching 1.00 will result in a groove located closer to the outer edge of the dimple, while a ratio approaching zero will result in a groove located closer to the center of the dimple. 
     The concentric groove diameter D 2  maintains a given ratio to the corresponding dimple diameter D 1 . In one embodiment, the ratio of the groove diameter D 2  to the dimple diameter D 1  is about 0.05 to about 0.95. In another embodiment, the ratio of the groove diameter D 2  to the dimple diameter D 1  is about 0.10 to about 0.90. In still another embodiment, the ratio of the groove diameter D 2  to the dimple diameter D 1  is about 0.20 to about 0.80. In yet another embodiment, the ratio of the groove diameter D 2  to the dimple diameter D 1  is about 0.30 to about 0.70. In still another embodiment, the ratio of the groove diameter D 2  to the dimple diameter D 1  is about 0.40 to about 0.60. 
     The groove  14  also has a width. As shown in  FIG. 3A , the width W of the groove  14  represents the distance between the outer and the inner edges of the groove  14 . In one embodiment, the width W of the groove  14  is about 0.0150 inches or less. In another embodiment, the width W of the groove  14  is about 0.0100 inches or less. In still another embodiment, the width W of the groove  14  is about 0.0075 inches or less. In still another embodiment, the width W of the groove  14  is about 0.0050 inches or less. In yet another embodiment, the width W of the groove  14  is about 0.0025 inches or less. 
     The width W of the groove  14  may also be expressed as a ratio with the dimple diameter D 1 . In one embodiment, the width W of the groove is selected such that the ratio between the width W and the dimple diameter D 1  is less than or equal to 0.05. In another embodiment, the ratio of the width W to the dimple diameter D 1  is less than or equal to 0.04. In still another embodiment, the ratio of the width W to the dimple diameter D 1  is less than or equal to 0.03. In yet another embodiment, the ratio of the width W to the dimple diameter D 1  is less than or equal to 0.02. 
     In addition, the width W of the groove  14  may also be expressed as a ratio with the groove diameter D 2 . In one embodiment, the width W of the groove is selected such that the ratio between the width W and the groove diameter D 2  ranges from about 0.018 to about 0.100. In another embodiment, the ratio of the width W to the groove diameter D 2  ranges from about 0.018 to about 0.070. In still another embodiment, the ratio of the width W to the groove diameter D 2  ranges from about 0.018 to about 0.053. 
     Further, the groove  14  has a depth. As shown in the cross-sectional view of  FIG. 3B , the depth Y represents the distance from the phantom surface of the dimple profile  12  to the deepest portion of the groove  14 . In one embodiment, the depth Y is about 0.0050 inches or less. In another embodiment, the depth Y is about 0.0025 inches or less. In still another embodiment, the depth Y is about 0.0015 inches or less. In yet another embodiment, the depth Y is about 0.0010 inches or less. 
     The cross-sectional shape of the groove  14  may also vary. As would be understood by one of ordinary skill in the art, the cross-sectional shape of the groove refers to the shape of the groove profile. In one embodiment, the cross-sectional shape of the groove  14  is half circular. For example, as shown in  FIG. 3B , the cross-sectional shape of the groove  14  may be half round. In another embodiment, the cross-sectional shape of the groove  14  is half polygonal. Indeed, in this aspect of the invention, suitable polygons include, but are not limited to, triangles, squares, pentagons, hexagons, heptagons, and octagons. For instance, as shown in  FIG. 4A , the cross-sectional shape of the groove  14  may be triangular such that the top phantom surface of the groove is the third leg of the triangle. Further, the cross-sectional shape of the groove  14  may be half of a square as shown in  FIG. 4B . In yet another embodiment, the cross-sectional shape of the groove  14  may be half pentagonal, half hexagonal, half heptagonal, or half octagonal. 
     In another embodiment, the cross-sectional shape of the groove  14  is identical to the shape of the dimple profile  12 . Indeed, any of the dimple profile shapes discussed above may be utilized as the profile of the groove. In still another embodiment, the cross-sectional shape of the groove  14  is defined by the superposition of two or more continuous and differentiable functions. For example, the cross-sectional shape of the groove  14  may 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 Nos. 2015/0119171 and 2012/0165130, the entire disclosures of which are incorporated by reference herein. 
     In yet another embodiment, the profile of the groove  14  can be a weighted function. In this regard, the weighted function can be used to selectively control or modify the profile of the groove  14 . For example, one or more continuous weighting functions can be applied as multiplicative constructs to the profile defined by any of the continuous functions discussed above to result in a continuous, differentiable weighted profile, as disclosed in U.S. Patent Publication No. 2013/0172123, which is incorporated in its entirety by reference herein. 
     In a particular embodiment, as illustrated in  FIGS. 18A-18C and 19A-19C , the present invention provides dimples having a circular plan shape, a spherical profile shape, and including at least three concentric grooves on the dimple surface. The concentric grooves have a circular plan shape and a spherical (i.e., arcuate) cross-sectional profile. The dimple optionally includes a center indentation. The center indentation, if present, preferably has a circular plan shape, a spherical (i.e., arcuate) cross-sectional profile, and shares a common center or centroid with the dimple. The dimples preferably have a scallop height H S  of from 0.0005 inches and 0.007 inches. Scallop height H S  is the distance between the spherical dimple profile into which the grooves are formed, referred to herein as A 1 , and the spherical profile shape which includes the deepest point of each of the grooves and the deepest point of the center indentation if a center indentation is present, referred to herein as A 2 . Preferably, A 1  and A 2  are concentric arcs. As discussed further below, A 1  and A 2  are used to determine the edge angle θ E  of the dimples of the present invention. Preferably, dimples of the present invention have an edge angle θ E  of from 10.0° to 20.0°. Each of the grooves preferably has a profile arc radius of from 0.015 inches and 0.125 inches. In a particular embodiment, the radii of all of the arcuate cross-sectional profiles of the circular grooves are substantially equal. Preferably, all pairs of adjacent grooves have a horizontal separation distance of from 0.007 inches to 0.060 inches. Preferably, the center indentation, if present, has a diameter equal to the width of at least one groove, and a profile arc radius equal to the radius of at least one of the arcuate cross-sectional profiles of the circular grooves. 
       FIG. 18A  illustrates an enlarged top plan view of a dimple according to a particular embodiment of the present invention. As shown in  FIG. 18A , dimple  40  has a dimple diameter D 1  and includes three concentric grooves  42 ,  43 , and  44 , and a center indentation  41 , on the dimple surface. Grooves  42 ,  43 , and  44  each have a circular plan shape and an arcuate cross-sectional profile. Center indentation  41  has a circular plan shape and an arcuate cross-sectional profile. Center indentation  41  has a diameter DC. Groove  42  has a width W 1 , groove  43  has a width W 2 , and groove  44  has a width W 3 . 
       FIG. 18B  is a cross-sectional view (A-A) of the dimple depicted in  FIG. 18A , and  FIG. 18C  is an enlarged view of the cross-sectional view depicted in  FIG. 18B . The profile arcs of center indentation  41  and grooves  42 ,  43 , and  44  each have a radius R 1 , R 2 , R 3 , and R 4 , respectively. The center of center indentation  41  lies on center dimple axis  5 . The horizontal separation distance DS between the center of the profile arc of the center indentation and the center  42 -C of the profile arc of groove  42  is the same as the horizontal separation distance DS between the center  42 -C of the profile arc of groove  42  and the center  43 -C of the profile arc of groove  43 , and also the same as the horizontal separation distance DS between the center  43 -C of the profile arc of groove  43  and the center  44 -C of the profile arc of groove  44 . For purposes of the present invention, horizontal separation distances are the same if they differ by no more 0.003 inches. Scallop height H S  is the distance between spherical profile shape A 1 , i.e., the spherical dimple profile into which the grooves are formed, and spherical profile shape A 2 , i.e., the spherical profile shape which includes the deepest point of each of center indentation  41  and grooves  42 ,  43 , and  44 . The dimple surface centroid  7  corresponds to the deepest point of the center indentation and lies on center dimple axis  5 . Phantom surface  2  is a continuation of land surface  4  and shows the portion of the surface of the golf ball that was cut away to form the dimple. In this particular embodiment, dimple depth Z, which represents the distance between the deepest part of the dimple and the phantom spherical face of the dimple, corresponds to the distance between phantom surface  2  and dimple surface centroid  7 . First tangent line T 1  is the line that is tangent to spherical profile shape A 1  at the point of intersection P 1  between spherical profile shape A 1  and phantom surface  2 . Second tangent line T 2  is the line that is tangent to phantom surface  2  at the point of intersection P 1  between spherical profile shape A 1  and phantom surface  2 . Edge angle θ E  is the angle between T 1  and T 2 . The dimple diameter is the distance between P 1  and its equivalent point at the opposite end of the dimple profile. 
     In a particular aspect of the embodiment shown in  FIGS. 18A-18C , dimples of the present invention have a dimple diameter D 1  of 0.176 inches, a scallop height H S  of 0.003 inches, an edge angle θ E  of 18.8°, a dimple depth Z of 0.016 inches, and the following additional properties:
         a) center indentation  41  has a diameter DC of 0.027 inches and a profile arc radius, R 1 , of 0.031 inches;   b) groove  42  has a groove width W 1  of 0.027 inches and a profile arc radius R 2  of 0.031 inches;   c) groove  43  has a groove width W 2  of 0.027 inches and a profile arc radius R 3  of 0.031 inches;   d) groove  44  has a groove width W 3  of 0.020 inches and a profile arc radius R 4  of 0.031 inches; and   e) horizontal separation distances DS are equal to about 0.025 inches.       

       FIG. 19A  illustrates an enlarged top plan view of a dimple according to another particular embodiment of the present invention. As shown in  FIG. 19A , dimple  50  has a dimple diameter D 1  and includes six concentric grooves  51 ,  52 ,  53 ,  54 ,  55 , and  56 , on the dimple surface. Dimple  50  does not have a center indentation. Grooves  51 ,  52 ,  53 ,  54 ,  55 , and  56  each have a circular plan shape and an arcuate cross-sectional profile. Grooves  51 ,  52 ,  53 ,  54 ,  55 , and  56  have widths W 1 , W 2 , W 3 , W 4 , W 5 , and W 6 , respectively. 
       FIG. 19B  is a cross-sectional view (A-A) of the dimple depicted in  FIG. 19A , and  FIG. 19C  is an enlarged view of the cross-sectional view depicted in  FIG. 19B . The profile arcs of grooves  51 ,  52 ,  53 ,  54 ,  55 , and  56  each have a radius R 1 , R 2 , R 3 , R 4 , R 5 , and R 6 , respectively. The horizontal separation distance DS between the center  51 -C of the profile arc of groove  51  and the center  52 -C of the profile arc of groove  52  is the same as the horizontal separation distance DS between the center  52 -C of the profile arc of groove  52  and the center  53 -C of the profile arc of groove  53 , and also the same as the horizontal separation distance DS between the center  53 -C of the profile arc of groove  53  and the center  54 -C of the profile arc of groove  54 , and also the same as the horizontal separation distance DS between the center  54 -C of the profile arc of groove  54  and the center  55 -C of the profile arc of groove  55 , and also the same as the horizontal separation distance DS between the center  55 -C of the profile arc of groove  55  and the center  56 -C of the profile arc of groove  56 . Scallop height Hs is the distance between spherical profile shape A 1 , i.e., the spherical dimple profile into which the grooves are formed, and spherical profile shape A 2 , i.e., the spherical profile shape which includes the deepest point of each of grooves  51 ,  52 ,  53 ,  54 ,  55 , and  56 . The dimple surface centroid  7  lies on center dimple axis  5 . Phantom surface  2  is a continuation of land surface  4  and shows the portion of the surface of the golf ball that was cut away to form the dimple. The distance between phantom surface  2  and dimple surface centroid  7  is less than the dimple depth Z, which represents the distance between the deepest part of the dimple and the phantom spherical face of the dimple. First tangent line T 1  is the line that is tangent to spherical profile shape A 1  at the point of intersection P 1  between spherical profile shape A 1  and phantom surface  2 . Second tangent line T 2  is the line that is tangent to phantom surface  2  at the point of intersection P 1  between spherical profile shape A 1  and phantom surface  2 . Edge angle θ E  is the angle between T 1  and T 2 . The dimple diameter is the distance between P 1  and its equivalent point at the opposite end of the dimple profile. 
     In a particular aspect of the embodiment shown in  FIGS. 19A-19C , dimples of the present invention have a dimple diameter D 1  of 0.178 inches, a scallop height H S  of 0.002 inches, an edge angle θ E  of 15.3°, a dimple depth Z of 0.013 inches, and the following additional properties:
         a) groove  51  has a groove width W 1  of 0.015 inches and a profile arc radius R 1  of 0.020 inches;   b) groove  52  has a groove width W 2  of 0.015 inches and a profile arc radius R 2  of 0.020 inches;   c) groove  53  has a groove width W 3  of 0.015 inches and a profile arc radius R 3  of 0.020 inches;   d) groove  54  has a groove width W 4  of 0.015 inches and a profile arc radius R 4  of 0.020 inches;   e) groove  55  has a groove width W 5  of 0.015 inches and a profile arc radius R 5  of 0.020 inches;   f) groove  56  has a groove width W 6  of 0.014 inches and a profile arc radius R 5  of 0.020 inches;   g) horizontal separation distances DS are equal to about 0.014 inches; and   h) the distance between phantom surface  2  and dimple surface centroid  7  is about 0.011 inches.       

     For embodiments of the present invention such as those shown in  FIGS. 18A-18C and 19A-19C , dimple properties should be determined on molded, unfinished golf balls (i.e., before paint and/or coating layers are applied). 
     Non-Concentric Grooves 
     In another embodiment, the groove is non-concentric with the dimple perimeter. In this aspect, the circular groove is positioned on the surface of a dimple with a circular plan shape such that the groove and the dimple perimeter are non-concentric. That is, the non-concentric groove and the circular dimple perimeter are off-center (i.e., the groove and the dimple do not share a common center or centroid).  FIG. 9  illustrates an enlarged top plan view of a dimple according to one embodiment the present invention. As shown in  FIG. 9 , the dimple  6  includes a dimple profile  12  and a non-concentric groove  20  on the surface of the dimple profile  12 . The space located within the non-concentric groove  20  represents the region of the surface that was cut away to form the groove  20 .  FIG. 9  also shows the centroid of each of the non-concentric groove  20  and the dimple  6 . The center or centroid of the non-concentric groove  20  is represented by C 1 , while the center or centroid of the dimple  6  is represented by C 2 . As can be seen, the non-concentric groove  20  is off-center from dimple  6  and does not share a common centroid with dimple  6 . 
     As discussed above with respect to concentric grooves, the dimple  6  has a diameter D 1  (also shown in  FIG. 9 ). Any of the values for dimple diameter D 1  discussed above are suitable for use with dimples having non-concentric grooves  20 . Similarly, any of the values for dimple depth Z discussed above are suitable for use with dimples having non-concentric grooves  20 . Moreover, when the dimple having a non-concentric groove is spherical in nature, any of the values for the dimple edge angle θ E  discussed above are suitable for use with spherical dimples having non-concentric grooves  20 . 
     Like the dimple  6 , the non-concentric groove  20  also has a diameter. As shown in  FIG. 9 , the non-concentric groove  20  has a diameter D 2 . The groove diameter D 2  represents the distance between contact points when common tangent lines are depicted at both sides of the non-concentric groove  20 . The groove diameter D 2  determines the size of the groove in relation to the dimple. Any of the values for groove diameters D 2  discussed above with respect to the concentric grooves are suitable for use with the non-concentric grooves  20 . For instance, in one embodiment, the groove diameter D 2  may be equal to about one half of the dimple diameter D 1 . In another embodiment, the groove diameter D 2  may be equal to about one quarter of the dimple diameter D 1 . Similarly, any of the values for groove width W and groove depth Y discussed above are suitable for use with the non-concentric grooves  20 . 
     In this aspect, because the aforementioned dimensions for dimple diameter D 1 , dimple depth Z, dimple edge angle θ E , groove diameter D 2 , and groove width W are applicable to the non-concentric grooves as well as the dimples having the concentric grooves, any of the values for the ratio of the groove diameter D 2  to the dimple diameter D 1 , the ratio of the groove width W to the dimple diameter D 1 , and the ratio of the groove width W to the groove diameter D 2  discussed above are also applicable to the non-concentric grooves as well as the dimples having the concentric grooves. 
     The cross-sectional shape of the non-concentric groove  20  may also vary. The non-concentric groove  20  may have any cross-sectional shape discussed above with respect to the concentric grooves. For example, the non-concentric groove  20  may have any of the following cross-sectional shapes: half circular, half polygonal, triangular, half of a square, half pentagonal, half hexagonal, half heptagonal, or half octagonal. In another embodiment, the cross-sectional shape of the groove  20  may be identical to the shape of the dimple profile  12  utilized on the dimple  6 . Indeed, any of the dimple profile shapes discussed above may be utilized as the profile of the non-concentric groove. 
     According to the present invention, the groove is considered to be non-concentric when the location of the centroid of the dimple plan shape is substantially different from the location of the centroid of the circular groove. More particularly, the groove is considered to be non-concentric when the distance between the centroid of the dimple plan shape and the centroid of the circular groove is greater than or equal to 5 percent of the dimple diameter D 1  (i.e., 0.05×D 1 ). In another embodiment, the groove may be considered non-concentric when the distance between the centroid of the dimple plan shape and the centroid of the circular groove is greater than or equal to 10 percent of dimple diameter D 1  (i.e., 0.10×D 1 ). In still another embodiment, the groove may be considered non-concentric when the distance between the centroid of the dimple plan shape and the centroid of the circular groove is greater than or equal to 20 percent of dimple diameter D 1  (i.e., 0.20×D 1 ). In yet another embodiment, the groove may be considered non-concentric when the distance between the centroid of the dimple plan shape and the centroid of the circular groove is greater than or equal to 25 percent of dimple diameter D 1  (i.e., 0.25×D 1 ). In another embodiment, the groove may be considered non-concentric when the distance between the centroid of the dimple plan shape and the centroid of the circular groove is greater than or equal to 30 percent of dimple diameter D 1  (i.e., 0.30×D 1 ). In still another embodiment, the groove may be considered non-concentric when the distance between the centroid of the dimple plan shape and the centroid of the circular groove is greater than or equal to 40 percent of dimple diameter D 1  (i.e., 0.40×D 1 ). 
     For example, as shown in  FIG. 9 , the centroid of the non-concentric groove  20  (C 1 ) is located distance D c  from the centroid of the dimple  6  (C 2 ). In this non-limiting example, the non-concentric groove  20  has a groove diameter D 2  of about one half of the dimple diameter D 1 . The distance between non-concentric groove centroid C 1  and dimple centroid C 2  (represented by D c ) is equal to about 10 percent of the dimple diameter D 1 . Thus, the groove depicted in  FIG. 9  is considered to be non-concentric. 
     Unlike the concentric grooves which maintain the same centroid as the dimple, the location of the centroid of non-concentric groove  20  may vary across the dimple surface  12 . That is, the non-concentric groove  20  may be located at any point on the surface of the dimple  6  so long as no part of the groove is in contact with the land surface of the golf ball. In another embodiment, the non-concentric grooves  20  of the present invention may be shifted within the dimple  6  in a preferred or preferential direction. As used herein, “preferential direction” refers to the shift of the non-concentric groove  20  on the dimple surface relative to a particular reference point. Examples of preferential direction may include planar preferential, meaning dimples are shifted toward or away from a given reference plane, and axial preferential, meaning dimples are shifted toward or away from a given reference axis. 
     In one embodiment, the non-concentric grooves  20  of the present invention may be shifted in an axial preferential direction. In this aspect, when the shift is axial preferential, the non-concentric grooves  20  are shifted relative to a reference axis. The reference axis may be any axis on the golf ball. That is, the non-concentric grooves  20  may be shifted relative to any axis of the dimple pattern on the golf ball. In one embodiment, the reference axis is an axis of symmetry, i.e., the non-concentric grooves  20  are shifted relative to an axis of symmetry of the dimple pattern. For example, the reference axis may be a polar axis. In another embodiment, the dimple pattern may include more than one reference axis. For instance, the dimple pattern may include multiple symmetrical axes such that multiple groups of non-concentric grooves are shifted relative to the different symmetrical axes. In this aspect, a single golf ball may include up to  20  different axes. 
     In this aspect, for a group of dimples to be defined as axial preferential, there must be at least two dimples having non-concentric grooves shifted relative to the same reference axis. In another embodiment, when there is an axial preferential shift, there may be at least three dimples having non-concentric grooves  20  shifted relative to the same reference axis. In another embodiment, when there is an axial preferential shift, there may be at least five dimples having non-concentric grooves  20  shifted relative to the same reference axis. In another embodiment, when there is an axial preferential shift, there may be at least six dimples having non-concentric grooves  20  shifted relative to the same reference axis. In still another embodiment, when there is an axial preferential shift, there may be at least eight dimples having non-concentric grooves  20  shifted relative to the same reference axis. In yet another embodiment, when there is an axial preferential shift, there may be at least ten dimples having non-concentric grooves  20  shifted relative to the same reference axis. For instance, when there is an axial preferential shift, there may be at least 12 dimples having non-concentric grooves  20  shifted relative to the same reference axis. In still other embodiments, every dimple on the golf ball may have non-concentric grooves  20  shifted relative to the same reference axis, for example, the polar axis. 
     When the preferential direction is axial preferential, the direction of the shift may vary. In one embodiment, the direction of the shift is toward the reference axis. That is, the non-concentric grooves  20  are shifted toward the edge of the dimple  6  that is closest to the reference axis. The distance of the shift will depend on the placement of the groove centroid. For example, as placement of the groove centroid approaches the edge of the dimple that is closest to the reference axis, the greater the shift toward the reference axis. In other words, if the groove centroid is closer to the reference axis than the centroid of the dimple plan shape, then the non-concentric groove  20  is shifted toward the reference axis. In another embodiment, the direction of the shift is away from the reference axis. For instance, the non-concentric grooves  20  are shifted away from the edge of the dimple  6  that is closest to the reference axis. Here, as placement of the groove centroid approaches the edge of the dimple that is farthest from the reference axis, the greater the shift away from the reference axis. In other words, if the groove centroid is farther away from the reference axis than the centroid of the dimple plan shape, then the non-concentric groove  20  is shifted away from the reference axis. 
     In this aspect, in a group of dimples defined as axial preferential, all of the non-concentric grooves  20  in the dimple group may he shifted in the same direction. For example, all of the non-concentric grooves  20  on the dimples may be shifted toward the reference axis. Alternatively, all of the non-concentric grooves  20  on the dimples may be shifted away from the reference axis. In another embodiment, in a group of dimples defined as axial preferential, some of the non-concentric grooves  20  in the dimple group may be shifted toward the reference axis, while other non-concentric grooves  20  in the dimple group may be shifted away from the reference axis (and vice versa). For instance, in a group of five dimples defined as axial preferential, three of the dimples may have non-concentric grooves  20  that are shifted toward the reference axis, while the other two dimples may have non-concentric grooves  20  shifted away from the reference axis. 
       FIGS. 10A and 10B  are non-limiting examples of groups of dimples having non-concentric grooves  20  that are defined as axial preferential. As shown in both  FIGS. 10A and 10B , a group of three dimples have non-concentric grooves  20 . The non-concentric grooves  20  are shifted relative to a reference axis (the axis is normal to the given view). An axial preferential shift, such as that shown in  FIGS. 10A and 10B , may be done by identifying the dimple centroid and drawing a reference line that passes through the dimple centroid and the reference axis. As shown in  FIGS. 10A and 10B , each of the dimple centroids is identified (represented by C 2 ) and reference lines  603  are drawn for each of the dimples. Reference line  603  passes through each dimple centroid C 2  and the reference axis  601 . After the dimple centroids are determined, the non-concentric grooves and the groove centroids are identified. To achieve a shift that is defined as axial preferential, the centroids of the non-concentric grooves should lie on the reference lines. For example, as shown in  FIGS. 10A and 10B , each of the centroids C 1  of the non-concentric grooves  20  is located on reference lines  603 . In other words, because the groove centroids C 1  are located on a reference line that passes through the reference axis, the shift of the non-concentric grooves  20  on the dimples depicted in  FIGS. 10A and 10B  is axial preferential. However, as can be seen from  FIG. 10A , the non-concentric grooves  20  are shifted toward the reference axis, while the non-concentric grooves  20  of  FIG. 10B  are shifted away from the reference axis. 
     The arrangement of the non-concentric grooves  20  on the dimples in each axial preferential group may vary. In one embodiment, the non-concentric grooves  20  may be symmetric about the reference axis. In another embodiment, the non-concentric grooves  20  may be arranged randomly about the reference axis. 
     In another embodiment, the non-concentric grooves  20  of the present invention may be shifted in a planar preferential direction. In this aspect, when the shift is planar preferential, the non-concentric grooves  20  are shifted relative to a reference plane on a dimple pattern. The reference plane may be any plane on the golf ball. That is, the non-concentric grooves  20  may be shifted relative to any plane on the golf ball. In one embodiment, the reference plane is a plane of symmetry, i.e., the non-concentric grooves  20  are shifted relative to a plane of symmetry. For example, the reference plane may be a center plane. In another embodiment, the dimple pattern may include more than one reference plane. For instance, the dimple pattern may include multiple planes of symmetry such that multiple groups of non-concentric grooves are shifted relative to the different symmetrical planes. 
     In this aspect, for a group of dimples to be defined as planar preferential, there must be at least two dimples having non-concentric grooves  20  that share the same reference plane. In another embodiment, when there is a planar preferential shift, there may be at least three dimples having non-concentric grooves  20  shifted relative to the same reference plane. In still another embodiment, when there is a planar preferential shift, there may be at least six dimples having non-concentric grooves  20  shifted relative to the same reference plane. In yet another embodiment, when there is a planar preferential shift, there may be at least 12 dimples having non-concentric grooves  20  shifted relative to the same reference plane. For instance, when there is a planar preferential shift, there may be at least  20  dimples having non-concentric grooves  20  shifted relative to the same reference plane. In still other embodiments, every dimple on the golf ball may have non-concentric grooves  20  shifted relative to the same reference plane, for example, the center plane. 
     When the preferential shift is planar preferential, the direction of the shift may vary. In one embodiment, the direction of the shift is toward the reference plane. That is, the non-concentric grooves  20  are shifted toward the edge of the dimple  6  that is closest to the reference plane. The distance of the shift will depend on the placement of the groove centroid. For example, as placement of the groove centroid approaches the edge of the dimple that is closest to the reference plane, the greater the shift toward the reference plane. In other words, if the groove centroid is closer to the reference plane than the centroid of the dimple plan shape, then the non-concentric groove  20  is shifted toward the reference plane. In another embodiment, the direction of the shift is away from the reference plane. For instance, the non-concentric grooves  20  are shifted away from the edge of the dimple  6  that is closest to the reference plane. Here, as placement of the groove centroid approaches the edge of the dimple that is farthest from the reference plane, the greater the shift away from the reference plane. In other words, if the groove centroid is farther away from the reference plane than the centroid of the dimple plan shape, then the non-concentric groove  20  is shifted away from the reference plane. 
     In this aspect, in a group of dimples defined as planar preferential, all of the non-concentric grooves  20  in the dimple group may be shifted in the same direction. For example, all of the non-concentric grooves  20  on the dimples may be shifted toward the reference plane. Alternatively, all of the non-concentric grooves  20  on the dimples may be shifted away from the reference plane. In another embodiment, in a group of dimples defined as planar preferential, some of the non-concentric grooves  20  in the dimple group may be shifted toward the reference plane, while other non-concentric grooves  20  in the dimple group may be shifted away from the reference plane (and vice versa). For instance, in a group of twelve dimples defined as planar preferential, seven of the dimples may have non-concentric grooves  20  that are shifted toward the reference plane, while the other five dimples may have non-concentric grooves  20  shifted away from the reference plane. In still another embodiment, the shift may be parallel to the reference plane. 
       FIGS. 11A and 11B  are non-limiting examples of groups of dimples having non-concentric grooves  20  that are defined as planar preferential. As shown in both  FIGS. 11A and 11B , a group of two dimples have non-concentric grooves  20 . The dimples having non-concentric grooves  20  share the same reference plane  701 . A planar preferential shift, such as that shown in  FIGS. 11A and 11B , may be done by identifying the dimple centroid and drawing a reference line that passes through the dimple centroid and that is normal to the reference plane. As shown in  FIGS. 11A and 11B , each of the dimple centroids is identified (represented by C 2 ) and reference lines  703  are drawn for each of the dimples. Reference line  703  passes through each dimple centroid C 2  and is normal to reference plane  701 . After the dimple centroids are determined, the non-concentric groove and the groove centroid are identified. To achieve a shift that is defined as planar preferential, the centroid of the non-concentric groove should lie on the reference line. For example, as shown in  FIGS. 11A and 11B , each of the centroids C 1  of the non-concentric grooves  20  is located on the reference lines  703 . In other words, because the groove centroids C 1  are located on a reference line that is normal to the reference plane, the shift of the non-concentric grooves  20  on the dimples depicted in  FIGS. 11A and 11B  is planar preferential. However, as can be seen from  FIG. 11A , the non-concentric grooves  20  are shifted toward the reference plane, while the non-concentric grooves  20  of  FIG. 11B  are shifted away from the reference plane. 
     The arrangement of the non-concentric grooves  20  on the dimples in each planar preferential group may vary. In one embodiment, the non-concentric grooves  20  may be symmetric about the reference plane. In another embodiment, the non-concentric grooves  20  may be arranged randomly about the reference plane. 
     In another embodiment of the present invention, dimples having non-concentric grooves  20  shifted in an axial preferential direction may be used in combination with dimples having non-concentric grooves  20  shifted in a planar preferential direction. In this aspect, any of the axial preferential and planar preferential non-concentric grooves may be shifted toward the respective reference axis or plane or away from the respective reference axis or plane. 
     In still another embodiment, dimple groups contemplated by the present invention may include dimples having concentric grooves  14  and dimples having non-concentric grooves  20 . In one embodiment, dimples having concentric grooves  14  may be used in combination with dimples having non-concentric grooves  20  shifted in an axial preferential direction. In this aspect, the dimples having concentric grooves  14  may be centered at the reference axis, while the dimples having non-concentric grooves  20  may be arranged around the concentric grooved dimples in an axial preferential direction. In another embodiment, dimples having concentric grooves  14  may be used in combination with dimples having non-concentric grooves  20  shifted in a planar preferential direction. In this aspect, the dimples having concentric grooves  14  may be centered at the reference plane, while the dimples having non-concentric grooves  20  may be arranged around the concentric grooved dimples in a planar preferential direction. In still another embodiment, dimples having concentric grooves  14  may be used in combination with dimples having non-concentric grooves  20  shifted in an axial preferential direction and dimples having non-concentric grooves  20  shifted in a planar preferential direction. In any of the above-described embodiments, when the axial preferential and planar preferential non-concentric grooves  20  are used in combination with concentric grooves  14 , the axial preferential and planar preferential non-concentric grooves  20  may be shifted toward the respective reference axis/plane, away from the respective reference axis/plane, or combinations thereof. Furthermore, any of the above-described arrangements may include dimples having no grooves. 
     Surface Area 
     Regardless of whether the groove is concentric or non-concentric, the surface area of the groove may vary based on the width W, depth Y, and shape of the groove. However, in one embodiment, the surface area of the concentric and non-concentric grooves contemplated by the present invention is about 0.00010 square inches to about 0.010 square inches. In another embodiment, the surface area of the concentric and non-concentric grooves is about 0.00020 square inches to about 0.0050 square inches. In still another embodiment, the surface area of the concentric and non-concentric grooves is about 0.00025 square inches to about 0.0010 square inches. 
     In this aspect of the invention, the surface area of the dimple  6  is increased by the addition of the concentric groove  14  or the non-concentric groove  20 . In one embodiment, the surface area of the dimple  6  having the concentric groove  14  or the non-concentric groove  20  is increased by about 1.0 percent when compared to the surface area of a dimple without a groove. In another embodiment, the surface area of the dimple  6  having the concentric groove  14  or the non-concentric groove  20  is increased by about 2.0 percent when compared to the surface area of a dimple without a groove. In still another embodiment, the surface area of the dimple  6  having the concentric groove  14  or the non-concentric groove  20  is increased by about 3.0 percent when compared to the surface area of a dimple without a groove. 
     In another embodiment, the relationship between the surface area of the grooves on the ball and the surface area of the parts of the ball that are replaced by dimples can be expressed as the following ratio: 
     
       
         
           
             
               S 
               · 
               N 
             
             
               4 
                
               
                 πR 
                 2 
               
                
               P 
             
           
         
       
     
     where:
         S is the average surface area for all grooves on the ball;   N is the number of grooved dimples on the ball;   R is the radius of the ball; and   P is the surface coverage of the dimple pattern used on the ball.       

     In this aspect of the present invention, the number of dimples on the ball may range from about 200 dimples to about 500 dimples. In another embodiment, the number of dimples may range from about 250 dimples to about 450 dimples. In still another embodiment, the number of dimples may range from about 300 dimples to 400 dimples. In yet another embodiment, the number of dimples may range from 300 to 350 dimples. 
     While the concentric and non-concentric grooved dimples of the present invention may be used for one or more dimples on a golf ball, it is not necessary that the grooved dimples be used on every dimple of a golf ball. In general, it is preferred that a sufficient number of dimples on the ball are constructed in accordance with the present invention so that the aerodynamic characteristics of the ball may be altered. In this aspect of the present invention, the number of grooved dimples on the ball N may range from at least about 15 percent of the dimples to about 100 percent of the dimples. For example, at least about 25 percent of the dimples on the golf ball include at least one concentric groove or at least one non-concentric groove according to the present invention. In another embodiment, at least about 50 percent of the dimples on the golf ball include at least one concentric groove or at least one non-concentric groove according to the present invention. In still another embodiment, at least about 70 percent of the dimples on the golf ball include at least one concentric groove or at least one non-concentric groove according to the present invention. In yet another embodiment, at least about 90 percent of the dimples on the golf ball include at least one concentric groove or at least one non-concentric groove. Indeed, 100 percent of the dimples on the golf ball may include the concentric grooved or non-concentric grooved dimples of the present invention. 
     In one embodiment, the total surface area for all grooves (including both concentric grooves and non-concentric grooves) on the ball (represented by S·N) may range from about 0.010 square inches to about 0.080 square inches. In another embodiment, the total surface area for all grooves on the ball may range from about 0.020 square inches to about 0.070 square inches. In still another embodiment, the total surface area for all grooves on the ball may range from about 0.030 square inches to about 0.060 square inches. For example, the average surface area for all grooves on the ball may be about 0.050 square inches. 
     In this aspect, the diameter of the golf ball may range from about 1.680 inches to about 1.800 inches, more preferably from about 1.680 inches to about 1.760 inches. A diameter of from about 1.680 inches (43 mm) to about 1.740 inches (44 mm) is most preferred. Thus, in one embodiment, the radius of the ball R may range from about 0.840 inches to about 0.880 inches. In another embodiment, the radius of the ball R may range from about 0.840 inches to about 0.870 inches. 
     Further, in this aspect of the invention, the surface coverage of all dimples on the ball P may range from about 65 percent to about 90 percent. In another embodiment, the surface coverage of all dimples P may range from about 70 percent to 88 percent. In still another embodiment, the surface coverage of all dimples P may range from about 72 percent to 85 percent. In yet another embodiment, the surface coverage of all dimples P may range from about 75 percent to 83 percent. 
     The surface coverage of a dimple pattern P is related to the total surface area of the golf ball that is replaced by dimples. In this aspect, the total surface area of the ball that is replaced by a dimple pattern may range from about 5.70 square inches to about 8.00 square inches. In another embodiment, the total surface area of the ball that is replaced by a dimple pattern may range from about 6.20 square inches to about 7.80 square inches. In still another embodiment, the total surface area of the ball that is replaced by a dimple pattern may range from about 6.40 square inches to about 7.50 square inches. For example the total surface area of the ball that is replaced by a dimple pattern may be about 7.35 square inches. 
     Overall, according to the present invention, the ratio of the surface area of all grooves on the ball to the total surface area of the ball that is replaced by dimples (as described above) is about 0.010 or less. In another embodiment, the ratio of the surface area of the grooves on the ball to the total surface area of the ball that is replaced by dimples is about 0.008 or less. In still another embodiment, the ratio of the surface area of the grooves on the ball to the total surface area of the ball that is replaced by dimples is about 0.006 or less. In yet another embodiment, the ratio of the surface area of the grooves on the ball to the total surface area of the ball that is replaced by dimples is about 0.005 or less. 
       FIG. 5  shows the relationship between the ratio of the surface area of the grooves on the ball to the surface area of a spherical ball that is replaced by dimples. For example, at a total groove surface area of 0.06 square inches, the ratio value (e.g., the ratio of the surface area of the grooves on the ball to the total surface area of the ball that is replaced by a dimple pattern) decreases from about 0.009 to about 0.008 as the surface coverage increases over a range of 0.76 to 0.85. Similarly, at a total groove surface area of 0.03 square inches, the ratio value (e.g., the ratio of the surface area of the grooves on the ball to the total surface area of the ball that is replaced by a dimple pattern) decreases from about 0.0045 to about 0.004 as the surface coverage increases over a range of 0.76 to 0.85. 
     While the dimples of the present invention have been described herein as having one groove, it should be understood that the dimples of the present invention may include one or more concentric or non-concentric grooves. In one embodiment, the dimples of the present invention include at least two concentric grooves  14  or at least two non-concentric grooves  20 . In another embodiment, the dimples of the present invention include at least three concentric grooves  14  or at least three non-concentric grooves  20 . In this aspect, the concentric grooves  14  and non-concentric grooves  20  may be located at any point along the dimple profile surface so long as the dimensions of the grooves are within the parameters discussed above. 
     Dimple Patterns &amp; Packing 
     The grooved dimples produced in accordance with the present invention can be used in constructing a visually distinct dimple pattern that improves the aerodynamic performance of the golf ball.  FIGS. 6-8  demonstrate various dimple patterns created in accordance with the present invention. For example,  FIG. 6  shows a dimple pattern  16  having concentric grooved dimples produced in accordance with the present invention. As shown in  FIG. 6 , all of the dimples  6  on the golf ball  10  include a concentric groove  14  having a ratio of the groove diameter D 2  to the dimple diameter D 1  of 0.90. In this aspect, due to the higher ratio of D 2 :D 1 , the concentric groove is located closer to the outer edge of the dimple.  FIG. 7  shows a dimple pattern  16  having concentric grooved dimples produced in accordance with another embodiment of the present invention. As shown in  FIG. 7 , all of the dimples  6  on the golf ball  10  include a concentric groove  14  having a ratio of the groove diameter D 2  to the dimple diameter D 1  of 0.70. In still another embodiment,  FIG. 8  shows a dimple pattern  16  having concentric grooved dimples produced in accordance with the present invention. As shown in  FIG. 8 , all of the dimples  6  on the golf ball  10  include a concentric groove  14  having a ratio of the groove diameter D 2  to the dimple diameter D 1  of 0.20. In this aspect, due to the lower ratio of D 2 :D 1 , the concentric groove is located closer to the center of the dimple. 
     In one embodiment, a dimple pattern may include a random arrangement of concentric and/or non-concentric grooved dimples. In another embodiment, a dimple pattern may include various groups of non-concentric and/or concentric grooved dimples arranged around the golf ball. In this aspect, the non-concentric grooved dimples utilized in dimple patterns contemplated by the present invention may be shifted in a preferential direction or may not be shifted in a preferential direction. In another embodiment, the dimple patterns may include a combination of non-concentric grooved dimples that are shifted in a preferential direction and are not shifted in a preferential direction. 
       FIGS. 12-14  also demonstrate various dimple patterns created in accordance with the present invention.  FIG. 12  shows a dimple pattern  16  having multiple groups of non-concentric grooved dimples shifted in an axial preferential direction. As shown in  FIG. 12 , each dimple group  30  includes numerous dimples  6  having non-concentric grooves  20  shifted towards a center axis. In this aspect, the pattern of non-concentric grooved dimples in each group  30  is repeated several times around the golf ball  10  such that there are several groups of dimples, each group having non-concentric groove dimples shifted toward multiple symmetrical axes corresponding to the dimple pattern. 
       FIG. 13  shows a dimple pattern  16  having a group of non-concentric grooved dimples shifted in a planar preferential direction. As shown in  FIG. 13 , the dimple group  30  includes numerous dimples  6  having non-concentric grooves  20  shifted towards a center plane. In this aspect, the pattern of non-concentric grooved dimples in the group  30  appears once on the golf ball  10 ; however, the pattern may be repeated around the golf ball  10 . 
       FIG. 14  shows a dimple pattern  16  having a group of concentric grooved dimples and non-concentric grooved dimples shifted in a planar preferential direction. As shown in  FIG. 14 , the dimple group  30  includes numerous dimples  6  having concentric grooves  14 , non-concentric grooves  20  shifted towards a center plane, and non-concentric grooves  20  shifted away from a center plane. The pattern of concentric grooved dimples and non-concentric grooved dimples in the group  30  appears once on the golf ball  10 ; however, the pattern may be repeated around the golf ball  10 . 
     While the present invention is not limited by any particular dimple pattern, dimples having at least one concentric groove or at least one non-concentric groove according to the present invention may be arranged along parting lines or equatorial lines, in proximity to the poles, or along the outlines of a geodesic or polyhedron pattern. Conventional dimples, or those dimples that do not include the concentric or non-concentric groove, may occupy the remaining spaces. The reverse arrangement is also suitable. Suitable dimple patterns include, but are not limited to, polyhedron-based patterns (e.g., tetrahedron, icosahedron, octahedron, dodecahedron, icosidodecahedron, cuboctahedron, and triangular dipyramid), phyllotaxis-based patterns, spherical tiling patterns, and random arrangements. 
     The dimple patterns of the present invention may be of any count. In one embodiment, the dimple count ranges from about 300 to about 500. In another embodiment, the dimple count is about 302. In still another embodiment, the dimple count is about 328. In yet another embodiment, the dimple count is about 352. In still another embodiment, the dimple count is about 376. In addition, the dimple pattern may include any number of dimple sizes. In one embodiment, the number of dimple sizes range from about 1 to about 30. In another embodiment, the number of dimple sizes range from about 5 to about 20. 
     In this aspect, the dimple pattern may include about 302 dimples in five sizes. In another embodiment, the dimple pattern may include about 312 dimples in five sizes. In still another embodiment, the dimple pattern may include about 328 dimples in seven sizes. In yet another embodiment, the dimple pattern may include about 352 dimples in five sizes. In still another embodiment, the dimple pattern may include about 376 dimples in eight sizes. 
     Golf Ball Construction 
     The grooves of the present invention may be added to the dimples at any point during the construction of the golf ball. In one embodiment, the groove may be added at the tooling stage by milling or burning the groove into the dimples of a dimple pattern. In this aspect, the resulting dimple pattern forms the interior surface of the cavity of a golf ball mold, which can then be used in an injection molding or compression molding process to form a cover layer comprising the golf ball dimple pattern. In another embodiment, the groove may be added after the molding process. In this aspect, the grooves may be added to the dimples by creating indentations in a molded or finished golf ball. 
     The dimples of the present invention may be used with practically any type of ball construction. For instance, the golf ball may have a two-piece design, a double cover, or two-component dual core construction depending on the type of performance desired of the ball. Other suitable golf ball constructions include solid, wound, liquid-filled, and/or dual cores, and multiple intermediate layers. 
     Different materials may be used in the construction of the golf balls made with the present invention. For example, the cover of the ball may be made of a thermoset or thermoplastic, a castable or non-castable polyurethane and polyurea, an ionomer resin, balata, or any other suitable cover material known to those skilled in the art. Conventional and non-conventional materials may be used for forming core and intermediate layers of the ball including polybutadiene and other rubber-based core formulations, ionomer resins, highly neutralized polymers, and the like. 
     The golf balls of the invention may be formed using a variety of application techniques. For example, the golf ball layers may be formed using compression molding, flip molding, injection molding, retractable pin injection molding, reaction injection molding (RIM), liquid injection molding (LIM), casting, vacuum forming, powder coating, flow coating, spin coating, dipping, spraying, and the like. Conventionally, compression molding and injection molding are applied to thermoplastic materials, whereas RIM, liquid injection molding, and casting are employed on thermoset materials. 
     EXAMPLES 
     The following non-limiting examples demonstrate golf ball dimples made in accordance with the present invention. The examples are merely illustrative of the preferred embodiments of the present invention, and are not to be construed as limiting the invention, the scope of which is defined by the appended claims. 
     Example 1 
     The following example illustrates various grooved dimples contemplated by the present invention. In particular, Table 1 provides spherical grooved dimples with varying edge angles and surface coverage (S) where the ratio of 
     
       
         
           
             
               S 
               · 
               N 
             
             
               4 
                
               π 
                
               
                   
               
                
               
                 R 
                 2 
               
                
               P 
             
           
         
       
     
     is 0.01. The measurements in Table 1 apply to both concentric and non-concentric grooved dimples. N represents the number of grooved dimples on the golf ball, S is equal to the average surface area for all grooves on the ball, P is the surface coverage of the dimple pattern used on the ball, and R is the radius of the ball. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Spherical Dimples Having Ratio of 0.010 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Surface 
                   
                   
                 Total Groove 
               
               
                 Edge Angle 
                 Coverage 
                   
                 Ball Radius 
                 Surface Area 
               
               
                 (°) 
                 (P) 
                 4πR 2 P 
                 (R) 
                 (S × N) 
               
               
                   
               
               
                 13 
                 0.847 
                 7.5102 
                 0.84 
                 0.075102 
               
               
                 13 
                 0.827 
                 7.3329 
                 0.84 
                 0.073329 
               
               
                 13 
                 0.804 
                 7.1289 
                 0.84 
                 0.071289 
               
               
                 14 
                 0.847 
                 7.5102 
                 0.84 
                 0.075102 
               
               
                 14 
                 0.827 
                 7.3329 
                 0.84 
                 0.073329 
               
               
                 14 
                 0.804 
                 7.1289 
                 0.84 
                 0.071289 
               
               
                 15 
                 0.847 
                 7.5102 
                 0.84 
                 0.075102 
               
               
                 15 
                 0.827 
                 7.3329 
                 0.84 
                 0.073329 
               
               
                 15 
                 0.804 
                 7.1289 
                 0.84 
                 0.071289 
               
               
                   
               
            
           
         
       
     
     Example 2 
       FIG. 15  presents one example of a group of non-concentric grooved dimples according to one embodiment of the present invention. More specifically,  FIG. 15  shows an enlarged view of a group of dimples having non-concentric grooves that may be used on a golf ball, for example, in a golf ball dimple pattern exemplified in  FIG. 12 . As shown in  FIG. 15 , the group  30  is composed of 12 dimples, each of the dimples  6  have non-concentric grooves  20  shifted in an axial preferential direction. All of the non-concentric grooves  20  are shifted toward a center axis A c . 
     In this non-limiting example, the non-concentric grooves  20  have a groove diameter D 2  equal to about one half of the dimple diameter D 1  and a groove width W of about 0.005 inches. For each of the dimples, the distance between the centroid of the dimple C 2  and the centroid of the groove C 1  is about 10 percent of the dimple diameter D 1 , which qualifies each of the grooves as non-concentric. 
     Example 3 
       FIG. 16  presents another example of a group of non-concentric grooved dimples according to one embodiment of the present invention. More specifically,  FIG. 16  shows an enlarged view of a group of dimples having non-concentric grooves that may be used on a golf ball, for example, in a golf ball dimple pattern exemplified in  FIG. 13 . As shown in  FIG. 16 , the group  30  is composed of 22 dimples, each of the dimples  6  have non-concentric grooves  20  shifted in a planar preferential direction. All of the non-concentric grooves  20  are shifted toward a center plane P. 
     In this non-limiting example, the non-concentric grooves  20  have a groove diameter D 2  equal to about one half of the dimple diameter D 1  and a groove width W of about 0.005 inches. For each of the dimples, the distance between the centroid of the dimple C 2  and the centroid of the groove C 1  is about 10 percent of the dimple diameter D 1 , which qualifies each of the grooves as non-concentric. 
     Example 4 
       FIG. 17  presents yet another example of a group of non-concentric grooved dimples according to one embodiment of the present invention. More specifically,  FIG. 17  shows an enlarged view of a group of dimples having both concentric grooves and non-concentric grooves that may be used on a golf ball, for example, in a golf ball dimple pattern exemplified in  FIG. 14 . As shown in  FIG. 17 , the group  30  is composed of 25 dimples, three of the dimples have concentric grooves  14  and 22 of the dimples have non-concentric grooves  20  shifted in a planar preferential direction. The concentric grooves  14  are centered on a center plane P c . The non-concentric grooves  20  are a combination of grooves shifted toward the center plane P c  and away from the center plane P c . 
     In this non-limiting example, the concentric grooves  14  have a groove diameter D 2  equal to about one half of the dimple diameter D 2  and a groove width W of about 0.005 inches. The non-concentric groves  20  shifted toward the center plane P c  have a groove diameter D 2  equal to about one half of the dimple diameter D 1  and a groove width W of about 0.005 inches. For each of the dimples having non-concentric grooves  20  shifted toward the center plane P c , the distance between the centroid of the dimple C 2  and the centroid of the groove C 1  is about 10 percent of the dimple diameter D 1 , which qualifies each of the grooves as non-concentric. The non-concentric grooves  20  shifted away from the center plane P c  have a groove diameter D 2  equal to about one quarter of the dimple diameter D 1  and a groove width W of about 0.0025 inches. For each of the dimples having non-concentric grooves  20  shifted away from the center plane P c , the distance between the centroid of the dimple C 2  and the centroid of the groove C 1  is about 30 percent of the dimple diameter D 1 , which qualifies each of the grooves as non-concentric. 
     Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements. Furthermore, when numerical ranges of varying scope are set forth herein, it is contemplated that any combination of these values inclusive of the recited values may be used. 
     The invention described and claimed herein is not to be limited in scope by the specific embodiments herein disclosed, since these embodiments are intended as illustrations of several aspects of the invention. Any equivalent embodiments are intended to be within the scope of this invention. Indeed, various modifications of the invention in addition to those shown and described herein will become apparent to those skilled in the art from the foregoing description. Such modifications are also intended to fall within the scope of the appended claims. All patents and patent applications cited in the foregoing text are expressly incorporated herein by reference in their entirety.