Patent Publication Number: US-10758784-B2

Title: Dimple patterns with surface texture for golf balls

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation-in-part of U.S. application Ser. No. 15/811,790, filed, Nov. 14, 2017, currently pending and allowed, which is a continuation-in-part of U.S. application Ser. No. 15/230,811, filed, Aug. 8, 2016, and issued as U.S. Pat. No. 9,844,701, which is a continuation-in-part of U.S. application Ser. No. 15/047,785, filed, Feb. 19, 2016, and issued as U.S. Pat. No. 9,713,746, which is a continuation of U.S. application Ser. No. 14/476,843, filed on Sep. 4, 2014 and issued as U.S. Pat. No. 9,302,155, the disclosures of which are hereby incorporated by reference herein in their entireties. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to golf balls, particularly to golf balls possessing unique dimple patterns including surface texture. More particularly, the invention relates to golf balls having dimples arranged on the outer surface for primary aerodynamic behavior and flight characteristics and surface texture for secondary aerodynamic behavior and/or for creating visually distinct appearance. 
     BACKGROUND OF THE INVENTION 
     Historically, dimple patterns for golf balls have had a variety of geometric shapes, patterns, and configurations. Primarily, patterns are laid out in order to provide desired performance characteristics based on the particular ball construction, material attributes, and player characteristics influencing the ball&#39;s initial launch angle and spin conditions. Therefore, dimple pattern development is a secondary design step that is used to achieve the appropriate aerodynamic behavior, thereby tailoring ball flight characteristics and performance attributes. 
     Aerodynamic forces generated by a ball in flight are a result of its velocity and spin. These forces can be represented by a lift force and a drag force. Lift force is perpendicular to the direction of flight and is a result of air velocity differences above and below the rotating ball. This phenomenon is attributed to Magnus, who described it in 1853 after studying the aerodynamic forces on spinning spheres and cylinders, and is described by Bernoulli&#39;s Equation, a simplification of the first law of thermodynamics. Bernoulli&#39;s equation relates pressure and velocity where pressure is inversely proportional to the square of velocity. The velocity differential, due to faster moving air on top and slower moving air on the bottom created by the ball&#39;s spin, results in lower air pressure on top and an upward directed force on the ball. 
     Drag is opposite to the direction of flight and orthogonal to lift. The overall drag force on a ball is attributed pressure drag and viscous or skin friction drag. A sphere is a bluff body, which is a somewhat inefficient aerodynamic shape. As a result, the accelerating flow field around the ball causes a large pressure differential with high-pressure forward and low-pressure behind the ball. The low pressure area behind the ball is also known as the wake. In order to minimize pressure drag, dimples provide a means to energize the flow field and delay the separation of flow, or reduce the wake region behind the ball. Skin friction is a viscous effect residing close to the surface of the ball within the boundary layer. 
     The industry has seen many efforts to maximize the aerodynamic efficiency of golf balls, through dimple distribution and other methods, though they are closely controlled by golf&#39;s national governing body, the United States Golf Association (U.S.G.A.). One U.S.G.A. requirement is that golf balls have aerodynamic symmetry. Aerodynamic symmetry allows the ball to fly with a very small amount of variation no matter how the golf ball is oriented when tested. Preferably, dimples cover the maximum surface area of the golf ball without detrimentally affecting the aerodynamic symmetry of the golf ball and the ability of the ball to roll smoothly. 
     In attempts to improve aerodynamic symmetry, many dimple patterns have been developed based on geometric shapes. These may include circles, hexagons, triangles, and the like. Other dimple patterns are based in general on the five Platonic Solids including icosahedron, dodecahedron, octahedron, cube, or tetrahedron. Yet other dimple patterns are based on the thirteen Archimedian Solids, such as the small icosidodecahedron, rhomicosidodecahedron, small rhombicuboctahedron, snub cube, snub dodecahedron, or truncated icosahedron. Furthermore, other dimple patterns are based on hexagonal dipyramids. Dimple properties such as number, shape, size, volume, edge angles and arrangement are often manipulated in an attempt to generate a golf ball that has improved aerodynamic properties. 
     Furthermore, secondary surface texture has been suggested to augment the dimples and further refine the aerodynamic properties of the ball. In fact, early golfers found that the feathery golf balls flew better after being played for a while. They then began to purposely roughen the surface to created improved aerodynamic properties. 
     Similarly, U.S. Pat. No. 4,787,638 to Kobayashi discloses a golf ball with a plurality of first dimples arranged substantially uniformly on the outer surface of the ball. The ball also includes a plurality of indentations which are smaller than the dimples and are also arranged substantially uniformly on the outer surface and inside the surfaces of the dimples. The indentations may be formed by grit blasting. Likewise, U.S. Publication No. 2012-0301617 teaches essentially the same micro surface roughness over the surface of the golf ball to affect aerodynamic properties of the ball. 
     U.S. Pat. No. 8,329,081 to Morgan discloses a method of forming a golf ball with secondary surface texture created on the fret areas of a ball. The secondary surface texture is created on the golf ball hob prior to the primary dimples being formed into the hob. When the dimples are formed, they largely obliterate the secondary surface texture except for the fret area and the perimeter of the dimples. 
     U.S. Pat. No. 6,569,038, to Sullivan discloses a ball having dimples with structures therein to energize or agitate the airflow over the dimpled surface to increase the aerodynamic performance of the ball. These structures include sub-dimples and radiating convex or concave arms emanating from the center of the dimple. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a golf ball having an outer surface comprising a plurality of dimples, wherein at least one of the dimples comprises three or more linear channels on the surface thereof having the same channel length L and the same channel width CW; wherein each of the linear channels extends radially outward in a direction from the centroid of the dimple toward the perimeter of the dimple without intersecting the centroid. 
     Thus, each linear channel may extend radially outward from a location on the dimple that is a distance Cd from the dimple&#39;s centroid, wherein Cd≥0. 
     Moreover, the three or more linear channels are spaced by n separation angles θ S , wherein n is the number of linear channels. 
     In one embodiment, all n separation angles θ S  are equal. In another embodiment, at least two of the n separation angles θ S  differ. 
     The linear channels may form a pattern that is axially symmetric about an axis connecting the centroid of the dimple and the center of the golf ball. Alternatively, the linear channels may form a pattern that is not axially symmetric about an axis connecting the centroid of the dimple and the center of the golf ball. 
     In one embodiment, none of the channels intersect each other. In a specific embodiment, at least one linear channel intersects the perimeter of the at least one dimple. In another embodiment, every linear channel intersects the perimeter of the at least one dimple. 
     In one embodiment, at least one dimple has a circular plan shape. In another embodiment, at least one dimple has a non-circular plan shape. 
     In a particular embodiment, channel length L is less than half of dimple diameter and at least two times channel width CW; wherein channel width CW is at least two times channel depth, wherein channel depth is less than or equal to 0.007 inches. 
     At least one dimple may comprise an even number of linear channels; wherein a first half of linear channels intersects a perimeter of the dimple and a second half of linear channels does not intersect the perimeter of the dimple; and wherein the first half of the linear channels and the second half of the linear channels alternate about the dimple&#39;s centroid. 
     At least one dimple may comprise nine linear channels; wherein none of the linear channels intersects the perimeter of the dimple, and wherein the linear channels are spaced by a separation angle θ S  of between 38.0 degrees and 42.0 degrees. 
     At least one dimple may comprise nine linear channels; wherein each linear channel intersects a perimeter of the dimple, and wherein the linear channels are spaced by a separation angle θ S  of between 38.0 degrees and 42.0 degrees. 
     In another embodiment, a golf ball of the invention has an outer surface comprising a plurality of dimples, wherein at least one of the dimples incorporates axially symmetric directional surface texturing comprised of three or more linear channels. At least one of the three or more linear channels has a different channel length L and/or a different channel width CW than at least one other linear channel; and each linear channel extends radially outward without intersecting the dimple&#39;s centroid; and linear channels having the same channel length L and the same channel width CW are spaced by n separation angles θ S , wherein n is the number of linear channels having the same channel length L and the same channel width CW. 
     In a particular such embodiment, the golf ball comprises a first type of linear channel and a second type of linear channel. Each linear channel of the first type has the same channel length L 1  and the same channel width CW 1  and extends radially outward from a location on the dimple that is a distance Cd 1  from the dimple&#39;s centroid, and are spaced about the centroid by a channel separation angle θ S1 . Meanwhile, each linear channel of the second type has the same channel length L 2  and the same channel width CW 2  and extends radially outward from a location on the dimple that is a distance Cd 2  from the dimple&#39;s centroid, and are spaced about the centroid by a channel separation angle θ S2 . The first type of linear channel and the second type of linear channel alternate about the dimple&#39;s centroid. 
     In one embodiment, Cd 1 =Cd 2 . In one such embodiment, either L 1 =L 2 , CW 1 =CW 2 , or L 1 =L 2  and CW 1 =CW 2 . 
     In another embodiment, Cd 2 &gt;Cd 1 . In a specific such embodiment, either L 1 =L 2 , CW 1 =CW 2 , or L 1 =L 2  and CW 1 =CW 2 . 
     In one specific embodiment, linear channels of the first type do not intersect the perimeter of the dimple and linear channels of the second type intersect the perimeter of the dimple. 
     The dimple may comprise ten linear channels comprising five linear channels of the first type and five linear channels of the second type; wherein none of the ten linear channels intersects the perimeter of the dimple; and wherein separation angle θ S1  is between 70 degrees and 74 degrees, and separation angle θ S2  is between 70.0 degrees and 74.0 degrees. 
     The dimple may comprise twelve linear channels comprising six linear channels of the first type and six linear channels of the second type; wherein each of the twelve linear channels intersects the perimeter; and wherein separation angle θ S1  is between 58.0 degrees and 62.0 degrees and separation angle θ S2  is between 58.0 degrees and 62.0 degrees. 
     In one such embodiment, separation angle θ S1  is equal to separation angle θ S2 . In another such embodiment, separation angle θ S1  is greater than separation angle θ S2 . 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the accompanying drawings which form a part of the specification and are to be read in conjunction therewith and in which like reference numerals are used to indicate like parts in the various views: 
         FIG. 1  illustrates a portion of a golf ball with directional surface texturing according to the present invention; 
         FIG. 2  illustrates a cross-sectional view of a dimple incorporating directional surface texturing according to the present invention; 
         FIG. 3  illustrates a first domain and a second domain formed in an icosahedron face projected on a sphere; 
         FIG. 4  illustrates the domains of  FIG. 3  tessellated to cover the surface of a sphere; 
         FIG. 5  illustrates a first portion of a golf ball dimple pattern formed according to the present invention; 
         FIG. 6  illustrates a second portion of a golf ball dimple pattern formed according to the present invention; 
         FIG. 7  illustrates a golf ball formed according to the present invention; 
         FIG. 8  illustrates a first domain and a second domain formed in a cube face projected on a sphere; 
         FIG. 9  illustrates the domains of  FIG. 8  tessellated to cover the surface of a sphere; 
         FIG. 10  illustrates a first portion of a golf ball dimple pattern formed according to the present invention; 
         FIG. 11  illustrates a second portion of a golf ball dimple pattern formed according to the present invention; 
         FIG. 12  illustrates a golf ball formed according to the present invention; 
         FIG. 13  illustrates a dimple having directional surface texturing; 
         FIG. 14  illustrates a dimple having directional surface texturing; 
         FIG. 15  illustrates a dimple having directional surface texturing; 
         FIG. 16  illustrates a cross-section of a dimple having directional surface texturing; 
         FIG. 17  illustrates a cross-section of a dimple having directional surface texturing; 
         FIG. 18  illustrates a cross-section of a dimple having directional surface texturing; 
         FIG. 19  illustrates a dimple having directional surface texturing; 
         FIG. 20  illustrates the surface texturing of the dimple in  FIG. 19 ; 
         FIG. 21  illustrates multiple dimples having directional surface texturing: 
         FIG. 22  illustrates multiple dimples having directional surface texturing: 
         FIG. 23  illustrates a dimple having directional surface texturing; 
         FIG. 24  illustrates the surface texturing of the dimple in  FIG. 23 ; 
         FIG. 25  illustrates a dimple having directional surface texturing; 
         FIG. 26 a    illustrates a dimple having directional surface texturing; 
         FIG. 26 b    illustrates a linear channel having constant channel depth within a dimple; 
         FIG. 27  illustrates a dimple having directional surface texturing; and 
         FIG. 28  illustrates a dimple having directional surface texturing. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is directed to golf ball with improved dimples. The aerodynamic characteristics of a golf ball are largely dependent on the dimples of a golf ball and the way that the dimples are arrange. Golf balls typically include 250 to 450 dimples on the outer surface that range from about 0.08 to 0.2 inches in diameter, if circular. The way that these dimples are arranged over the outer surface, the shapes of the dimples and the edge angles of the dimples are all important to the overall flight performance of the golf ball. 
     In  FIG. 1 , a plurality of dimples having directional surface texturing is disclosed. The dimples  10  through  20 , for example, are adjacent dimples and have different dimple diameters. However, all of the dimples shown include a plurality of linear channels  30  therein. 
     Preferably, a golf ball according to the present invention has an outer surface comprising a plurality of dimples covering greater than 70 percent of the outer surface and at least 20 percent of the dimples incorporate directional surface texturing. Directional surface texturing is defined as a plurality of indentations or protrusions that form aligned arrangements within the dimple. 
     The outer surface of the golf ball preferably comprises less than 400 dimples of different sizes and, more preferably, at least 5 different sizes. In a preferred embodiment, at least 50 percent of the dimples incorporate directional surface texturing such as the linear channels  30  therein. The linear channels  30  are substantially parallel within the dimple. Preferably, there are between 2 and 6 linear channels within the dimples. Although  FIG. 1  shows each of the dimples containing 6 linear channels, it is contemplated that smaller diameter dimples are likely to have less linear channels than larger diameter dimples. For example, in a preferred embodiment, a dimple having a diameter of less than 0.12 inch can have between 2 and 5 linear channels and a dimple having a diameter of 0.12 to 0.2 inch can have between 5 and 8 linear channels. 
     In a preferred embodiment of the invention, the outer surface of the golf ball comprises less than 360 dimples and all of the dimples incorporate directional surface texturing made up of substantially linear arrangements that are aligned. The linear arrangements, like the linear channels  30  disclosed in  FIG. 1 , are preferably substantially parallel to each other and extend across a substantial portion of the dimple. While the linear channels  30  shown in  FIG. 1  are parallel within each dimple, they are at offset angles α with respect to adjacent dimples. The linear channels  30  within a dimple are disposed at angles of between about 10 and 90 degrees with respect to the linear channels  30  of an adjacent dimple. For example, dimple  10  includes linear channels that are disposed at an angle α of between 10 and 90 degrees with respect to each of the adjacent dimples  12 ,  14 ,  18  and  20 . As shown, the linear channel angles α 1  and α 2  are about 60 degrees and α 3  is about 90 degrees. Preferably, the linear channels  30  are arranged at an angle α of between about 30 and 90 degrees with respect to most of the adjacent dimples. In some arrangements, the golf ball can be designed such that no dimple on the ball has an adjacent dimple with parallel linear arrangements. 
     Referring to  FIG. 2 , a cross-section of a dimple is shown. The dimple depth, volume and edge angles of the dimples are measured as set forth in U.S. Pat. No. 7,226,369, as shown in  FIG. 7  and discussed in col. 11, line 64 through, col. 12, line 46, which is incorporated by reference herein. The surface texturing is relatively small in comparison to the dimple and intended as a secondary aerodynamic function as discuss below. For example, preferably, the linear channels  30  have a maximum channel depth d of less than ¼ of a dimple depth. Linear protrusions within a dimple would be the inverse of the linear channels  30  shown. More preferably, the directional surface texturing depth (or protrusion height, if reversed) is less than about 0.002 inches. Also, the directional surface texturing has a width w, such as the channel width shown, that is equal to or greater than the depth and preferably greater than about twice the depth d. Further, the length between the directional surface texturing, shown as l, is preferably equal to or greater than the width w. Preferably, the length l is greater than twice the width w. Where  FIG. 2  discloses a substantially U-shaped cross-section, it is preferred that the cross-section of the channels  30  be V-shaped, U-shaped, rectangular or other partial polygonal shape or any continuous curve defined by superposed curves such as those described in U.S. Publication No. 2012-0165130. 
     Further, the directional surface texturing is substantially elongated. The lengths of the directional surface texturing elements are preferably greater than 5 times the widths and extend substantially across the dimples. For example, the lengths of the linear channels  30  are preferably greater than 5 times the channel widths w and extend substantially across the dimples as shown. If a dimple is about 0.15 inches, the directional surface texturing in the center of the dimple preferably has a length of at least 0.1 inch, and more preferably, about 0.11-0.13 inch. The same directional surface texturing preferably has a width of less than about 0.02. Similarly, smaller dimples having a diameter of about 0.11 inch may have directional surface texturing with a length of about 0.08 to 0.09 inch. Preferably, the width of the directional surface texturing will be approximately the same as the surface texturing in the larger dimples. The table below is an example of a preferred dimple pattern incorporating linear channels as the directional surface texturing. 
     
       
         
           
               
               
               
               
               
             
               
                 TABLE I 
               
               
                   
               
               
                 Dimple 
                   
                 Number of 
                 Channel 
                 Channel 
               
               
                 Diameter 
                 Number of 
                 Channels/ 
                 Width 
                 Depth 
               
               
                 (in) 
                 Dimples 
                 Dimple 
                 (in) 
                 (in) 
               
               
                   
               
             
            
               
                 0.115 
                 12 
                 4 
                 0.01 
                 0.002 
               
               
                 0.155 
                 20 
                 5 
                 0.01 
                 0.002 
               
               
                 0.160 
                 40 
                 5 
                 0.01 
                 0.002 
               
               
                 0.165 
                 50 
                 5 
                 0.01 
                 0.002 
               
               
                 0.170 
                 60 
                 5 
                 0.01 
                 0.002 
               
               
                 0.175 
                 80 
                 6 
                 0.01 
                 0.002 
               
               
                 0.180 
                 70 
                 6 
                 0.01 
                 0.002 
               
               
                   
               
            
           
         
       
     
     The present invention also provides a method for arranging dimples with directional surface texturing on a golf ball surface. The method includes creating sections on the surface of a golf ball. Preferably, the sections are polyhedrons or portions thereof and then filling the sections with dimples incorporating directional surface texturing. Each of the sections can contain a different arrangement of the directional surface texturing. For example, as discussed with  FIG. 1  above, the dimples  10 - 20  all contain directional surface texturing that is oriented at an angle with respect to an adjacent dimple. This arrangement of the directional surface texturing provides that the ball has a uniform secondary aerodynamic characteristic regardless of the direction the ball is oriented. 
     Referring to  FIGS. 3-12 , a dimple pattern can be formed by choosing control points of a polyhedron, connecting the control points with a non-straight sketch line, patterning the sketch line in a first manner to generate an irregular domain, optionally patterning the sketch line in a second manner to create an additional irregular domain, packing the irregular domain(s) with dimples, and tessellating the irregular domain(s) to cover the surface of the golf ball in a uniform pattern. The control points can include the center of a polyhedral face, a vertex of the polyhedron, a midpoint or other point on an edge of the polyhedron, and others. The method ensures that the symmetry of the underlying polyhedron is preserved while minimizing or eliminating great circles due to parting lines from the molding process. 
     Referring to  FIGS. 3-7 , a golf ball outer surface can be divided into equal sections by the projections of an icosahedron. Each icosahedron can then be divided by a midpoint to midpoint method, for example, to yield two domains that are tessellate to cover the surface of golf ball  100  as shown in  FIGS. 3 and 4 . The two domains are shown as  114   a  and  114   b . The method of forming the different sections and then tessellating them over the surface of a golf ball to create different dimple patterns formed from such sections is set forth in U.S. application Ser. No. 13/675,041, which published as Publication No. 2013-0072325 on Mar. 21, 2013, and which is incorporated by reference in its entirety herein. 
     Referring to  FIGS. 5 and 6 , the sections  114   a  and  114   b  are then filled with directional surface texturing. Elongated, linear protrusions  116  are formed within each dimple such that within the dimple, they are substantially parallel. The protrusions preferably have similar dimensions to the channels discussed above. 
     In a first section, set forth in  FIG. 5 , the directional surface texturing can be formed by selecting a midpoint of the section and then forming the linear elements perpendicular to the radii r 1 -r 3  that emanate from the center. Similarly, in  FIG. 6 , the directional surface texturing is formed by forming protrusions that are perpendicular to the lines l 1  and l 2  emanating from the center dimple  118 . In this manner, as shown in  FIG. 7 , each of the dimples in the sections will have an adjacent dimple with directional surface texturing at an angle between 10 and 90 degrees with respect thereto. This pattern will also form a plurality of great circles GC over the surface of the ball that intersect dimples incorporating directional surface texturing oriented perpendicular thereto. 
     Referring to  FIGS. 8-12 , a golf ball outer surface can be divided into equal sections by the projections of a cube. Each cube can then be divided by a midpoint to midpoint method, for example, to yield two domains that are tessellate to cover the surface of golf ball  100  as shown in  FIGS. 8 and 9 . The two domains are shown as  114   a  and  114   b . Again, the method of forming the different sections and then tessellating them over the surface of a golf ball to create different dimple patterns formed from section is set forth in U.S. application Ser. No. 13/675,041. 
     Referring to  FIGS. 10 and 11 , the sections  114   a  and  114   b  are then filled with directional surface texturing  116 . Elongated, linear protrusions  116  are formed within each dimple such that within the dimple, they are substantially parallel. 
     In a first section, set forth in  FIG. 10 , the directional surface texturing  116  can be formed by forming the linear elements  116  such that they are oriented at about 45 degree angles with respect to the directional surface texturing in an adjacent dimple. Similarly, in  FIG. 11 , the directional surface texturing  116  is formed by forming linear elements that are substantially perpendicular with respect to those in an adjacent dimple. As shown in  FIG. 12 , this type of arrangement results in an overall ball that has no great circles that intersect dimples having directional surface texturing that is perpendicular to the great circle. However, every dimple on the ball  100  still has an adjacent dimple with directional surface texturing at an angle of about 30 to 90 degrees relative thereto. 
     Furthermore, the present invention also contemplates an improvement in the aerodynamic characteristics of the golf ball. In particular, it is an object of the invention to improve the aerodynamics at low Reynolds Numbers and low Spin Ratios with the directional surface texturing. The aerodynamic properties of a golf ball and improvements in those properties are specifically discussed in detail in U.S. Pat. No. 7,226,369, and particularly in col. 4-col. 10 and col. 12-col. 17, which is incorporated by reference herein in its entirety. More particularly, the golf ball dimple pattern preferably comprises less than 370 dimples and more preferably less than 360 dimples covering over 75% of the outer surface of the ball and containing directional surface texturing within each dimple. More particularly, the golf ball preferably has a coefficient of lift at a Reynolds No. of 70,000 and Spin ration of 0.188 of greater than 0.24 and more preferably greater than 0.25. Moreover, the golf ball preferably has a coefficient of drag at a Reynolds No. of 70,000 and Spin Ratio of 0.188 of less than 0.27. 
     Referring to  FIGS. 13-16 , dimples  40 ,  50  and  60  all have 3 or more substantially parallel linear channels (or protrusions)  41 - 43 ,  51 - 53  and  61 - 62 , respectively. Preferably, the linear channels have a U-shaped cross-section with a depth of less than 0.005 inch and a radius of at least 0.001 inch. The channels are preferably formed by laser etching or machining the surface of the mold cavities that form the golf ball or by forming surface texturing on the hob that forms the mold cavities. In  FIG. 13 , the linear channels  41 - 43  do not extend across the dimple. Preferably, the channels have a length L that is greater than 50% of the chord length CL. For example, the linear channel  42 , at the center of the dimple, extends greater than 50% of the dimple diameter. In  FIG. 14 , the linear channels  51 - 53  extend entirely across the width of the dimple and intersect the dimple perimeter  55 . Preferably, the linear channels have a length that is less than about 110% of the chord length of the dimple. Thus, for all linear channels, it is preferred that they extend between 50% and 110% of the chord length of the dimple. More preferably, the linear channels have a length of between 80% and 105% of the dimple chord length extending through the length of the channel. Referring to  FIG. 15 , the dimple includes linear channels  61 - 63 . The channel(s)  62  at the center of the dimple preferably does not extend across the width of the dimple such that it does not intersect an adjacent dimple. Thus the center channels, in this embodiment, can extend between about 50% and 95% of the dimple chord length (diameter). However, the perimeter channels,  61  and  63 , extend greater than 100% of the chord length such that they would extend into fret area. Center linear channels are defined as those linear channels that are closer to the center of the dimple than the side perimeter, whereas perimeter linear channels are those channels that are closer to the side perimeter than the center. Preferably, the dimples and the linear channels cover at least 70% of the dimple outer surface, and more preferably, between 82% and 95%. 
     Referring to  FIG. 16 , the dimples on the ball have a dimple radius Rd of at least 0.2 inch, and more preferably between about 0.2 inch and 1.4 inch. The linear channels have a channel radius Rc of between 0.001 inch and 0.08 inch. Furthermore, the linear channels have a channel depth Dc of between 0.0003 inch and 0.005 inch. More preferably, the linear channel depth Dc is between 0.0003 inch and 0.003 inch, and most preferably, between 0.0005 inch and 0.003 inch. In one embodiment, the linear channel depth Dc can be greater in the center linear channels than in the perimeter linear channels. 
     The dimples are preferably circular and have a dimple diameter DD of 0.11 inch to 0.22 inch, but the dimples could also be hexagons or other geometric shapes. The linear channels are relatively shallow compared to the depth of the dimple they are in, and preferably, have a channel depth Dc that is less than 1/10 of the dimple depth DD as measured from the phantom curved surface of the ball&#39;s outer surface. 
     Each of the dimples on the ball can contain between 3 and 200 linear channels, and more preferably, between 3 and 50 linear channels. Most preferably, the dimples contain between 3 and 25 linear channels. As shown in  FIG. 17 , the dimple can contain 9 linear channels. In this case, the channel width CW is greater than the length between channels, whereas in  FIG. 16 , when there are only 3 linear channels, the length between channels is greater than the channel width CW.  FIG. 18  illustrates an embodiment where there are 19 linear channels and the linear channels essentially abut one another through the bottom surface of the dimple. 
     Table II below describes several embodiments of golf balls according to the present invention wherein every dimple has directional surface texturing as described: 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE II 
               
               
                   
               
               
                   
                   
                   
                 Channel 
                 Channel 
                 % 
               
               
                   
                   
                 # Channels/ 
                 Radius 
                 Depth 
                 Chord 
               
               
                 Embodiment 
                 # Dimples 
                 Dimple 
                 (in) 
                 (in) 
                 Length 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1 
                 352 
                 3 
                 0.02 
                 0.002 
                 70 
               
               
                 2 
                 352 
                 3 
                 0.02 
                 0.002 
                 70 
               
               
                   
                   
                   
                 (center) 
                   
                   
               
               
                   
                   
                   
                 0.02 
                 0.001 
                 105 
               
               
                   
                   
                   
                 (perimeter) 
                   
                   
               
               
                 3 
                 352 
                 9 
                 0.02 
                 0.002 
                 105 
               
               
                 4 
                 328 
                 11 
                 0.02 
                 0.002 
                 85 
               
               
                 5 
                 328 
                 19 
                 0.02 
                 0.0008 
                 95 
               
               
                   
               
            
           
         
       
     
     The dimples on a golf ball according to the present invention are preferably circular in plan shape and have a diameters of 0.11 inch to 0.22 inch, but could also be n-sided polygons, where n is between 3 and 10, or other geometric shapes such as those that are defined by periodic functions along a simple path. Preferably, the golf ball has 4 or more diameters of dimples that have multiple dimple depths ranging from 0.005 to 0.03 and edge angles ranging from 10 degrees to 20 degrees. 
     In a preferred embodiment, each of the dimples on the golf ball has the same number of linear channels. For example, the golf ball can have about 300 to 360 dimples having dimple diameters from 0.11 inch to 0.22 inch. Each of the dimples can contain the same number of linear channels as set forth in Table II above. Preferably, in one embodiment, the width of the channels can vary with dimple diameter such that a dimple having a first diameter that is less than a second diameter of a second dimple has a first channel width that is less than a second channel width. For example, a dimple having a diameter of 0.11 inch can have channel widths of 0.011 inch and a dimple having a diameter of 0.18 inch can have channel widths of 0.018. Thus, the channel widths progressively increase with dimple diameter. 
     In another embodiment, each dimple on the golf ball has the number of linear channels therein based on the dimple diameter such that a dimple having a first diameter that is less than a second diameter of a second dimple has a first number of channels that is less than a second number of channels in the second dimple. For example, a golf ball can have all of the linear channels having a channel width of 0.02 inch and the number of channels in each dimple is dependent on the dimple diameter. In one example, a dimple having a diameter of 0.11 inch can have 5 linear channels and a dimple having a diameter of 0.18 inch can have 9 linear channels. 
     Still further, in another embodiment of the present invention, the depth of the linear channels can vary depending on the depth of the dimple. For example, the depths of the linear channels can be a function of dimple depth. In one embodiment, the channel depth can be about 1/10 of the dimple depth such that a dimple having a depth of 0.01 inch has a channel depth of 0.001 inch and a dimple having a depth of 0.02 has a channel depth of 0.002. In another embodiment, the depth of the channels is inversely proportional to the number of channels in a dimple. Thus a dimple can have 3 channels having a first depth and a second dimple can have 11 channels having a second depth that is less than the first depth. 
     In another preferred embodiment of the present invention the golf ball comprises at least one dimple having a circular plan shape and non-linear directional surface texturing that is comprised of a plurality of channels or protrusions that are non-linear and parallel when viewing the dimple perpendicular to the dimple edge plane as shown in  FIGS. 19-24 . Preferably, the channels or protrusions are arcuate, meaning they have an arc radius but the arc spans less than 180 degrees. For example, the arcs of non-linear channels  200 ,  201  and  202  in  FIG. 19  span about 135 degrees. Thus, the present invention excludes channels that create a closed loop within the dimple (such as circles which are 360 degrees, squares, triangles, or other closed paths). As shown in  FIGS. 19-24 , dimples incorporating non-linear directional surface texturing are specifically directed to parallel line segments such as circular arcs of less than 180 degrees, splines, staggered line segments, etc. 
     Referring to  FIGS. 19 and 20 , the non-linear channels  200 ,  201  and  202  are determined to be parallel by defining the channel center line,  200 C,  201 C and  202 C, defined by the midpoint between the edges of the channels. Once the center lines  200 C,  201 C and  202 C are defined for two channels, the channels are parallel if the distance between the two channel center lines (the parallel distance D p ) is the same for every point along at least one of the channels. For example, the distance D p1  shown in  FIG. 20  is the same for every point in the channels. Thus, if the channels are the same shape and length the distance between the center lines D p  will be the same for every point along each center line. 
     As shown in  FIGS. 19 and 20 , every measurement of the parallel distance D p1  and D p2  between two channels is substantially equal for the adjacent channels. If the largest parallel distance D p  and the smallest parallel distance D p  between two adjacent channels are substantially equal then the channels are parallel. As shown in  FIG. 19 , it is preferable that the dimples incorporating non-linear directional surface texturing have a circular plan shape and there are two or more parallel arc-shaped channels. In the dimple shown in  FIG. 19 , there are three non-linear parallel channels positioned within the perimeter of the dimple  220 . All three channels  200 ,  201  and  202  are circular arcs that span approximately 135 degrees and are the same length. In  FIG. 19 , first channel  200  has a first channel centerline  200 C, second channel  201  has a second channel centerline  201 C, and third channel  202  has a third channel centerline  202 C. The dimple diameter, D, in this particular example is about 0.15 inches. The channel centerlines are arcs having an arc radii, ar, equal to about 0.067 such that ar=0.45D The channel lengths, channel widths and channel depths for all channels incorporated herein should be as set forth above in reference to  FIGS. 2, 16, 17 and 18 , including the proportionality to the dimple diameters. More preferably, the channel width for the non-linear channels  200 ,  201  and  202  are all about 0.012 inches. However, while it is preferred that channel widths and channel depths remain constant within a dimple, it is contemplated that the channel widths and depths can differ by at least 0.002. For example, the channel width for channel  201  could be greater than the channel width for channels  200  and  202 . The parallel distance D p1  between the first channel  200  and the second channel  201  is approximately 0.03 inches and the parallel distance D p2  between the second channel  201  and the third channel  202  is approximately 0.03 inches. However, D p1  and D p2  do not have to be equal. 
       FIG. 20  shows a close-up view of channels  200  and  201 . There are four separate measurement of the parallel distance D p1  at four different points along the channel centerlines  200 C and  201 C. All four measures of D p1  are equal, and therefore, the channels  200  and  201  are parallel. 
     In one particular embodiment of the invention, the dimples incorporating non-linear directional surface texturing having non-linear parallel channels do not have any adjacent dimples having non-linear directional surface texturing. In a further preferred embodiment as shown in  FIG. 21 , at least two dimples  220  and  230  having non-linear directional surface texturing have mirror symmetry about a centerline  210 . In yet a further preferred embodiment as shown in  FIG. 22 , at least three dimples  220 ,  240  and  250  having non-linear directional surface texturing are rotationally symmetric about a centroid  212  of the dimples. 
     In another preferred embodiment, the dimples can incorporate non-linear directional surface texturing where the non-linear channels are parallel but one of the lengths is less than the other length. Referring to  FIGS. 23 and 24 , dimple  310  incorporates parallel, non-linear channels  300 ,  301  and  302 . As set forth above, the distance between the center lines  300 C,  301 C and  302 C will be the same for every point along the shorter channel. Thus, in this case, a portion of the longest channel  301  will not have an equivalent point of measure in channels  300  and  302  and the channels are still considered parallel. In this particular example, the dimple diameter of dimple  310  is about 0.175 inches. The channel centerlines  300 C,  301 C and  302 C are splines (piecewise polynomial parametric curves with all arcs spanning less than 180 degrees) of varying lengths. The channel width for all three channels is approximately 0.014 inches. The parallel distance D p1  between the first channel  300  and the second channel  301  is equal to about 0.049 inches and the parallel distance D p2  between the second channel  301  and the third channel  302  is equal to 0.049 inches. Again, D p1  and D p2  do not have to be equal, but are preferably the same. 
       FIG. 24  is a close-up view of channels  300  and  301 . This figure shows four separate measurements of the parallel distance D p1  at four different points along the channel centerlines  300 C and  301 C. All four measures are substantially equal showing that the channels  300  and  301  are parallel. In this example, every point of the centerline  300 C has a corresponding point on centerline  301 C at a parallel distance of D p1 , but not every point of  301 C will have a corresponding point on  300 C due to the centerlines having different lengths. 
     In a different embodiment, a golf ball of the invention has an outer surface comprising a plurality of dimples, wherein at least one of the dimples comprises three or more linear channels on the surface thereof. Each linear channel has the same channel length L and the same channel width CW; and each of the linear channels extends radially outward in a direction from a centroid of the dimple toward the perimeter of the dimple without intersecting the dimple&#39;s centroid. Moreover, the three or more linear channels are spaced by n separation angles θ S , wherein n is the number of linear channels. 
     As used herein, the term “centroid” refers to the dimple&#39;s center. The term perimeter refers to the outermost edge of a dimple that is adjacent to a land area of the outer surface of the golf ball. Furthermore, a linear channel is considered to extend radially outward within a given dimple if the linear channel&#39;s centerline (as depicted, for example, in  FIGS. 25, 26   a ,  26   b ,  27  and  28 ) intersects the dimple&#39;s centroid. 
     The linear channels may form a pattern that is axially symmetric about an axis connecting the centroid of the dimple and the center of the golf ball. Alternatively, the linear channels may form a pattern that is not axially symmetric about an axis connecting the centroid of the dimple and the center of the golf ball. 
     Separation angles, channel lengths and channel widths of channels of a given dimple are measured in a plane that is normal to an axis connecting the center of the golf ball and the dimple&#39;s centroid. 
     In some embodiments, linear channel origination distance Cd may be closer to the centroid than to the dimple&#39;s perimeter. In other embodiments, linear channel origination distance Cd may be closer to the perimeter than to the dimple&#39;s centroid. 
     Herein, two given linear channels are considered to be the same if their channel lengths L vary by 0.002 inches or less and their channel widths CW vary by 0.002 inches or less. 
     Likewise, two given linear channels are considered to differ if their channel lengths L vary by more than 0.002 inches and/or their channel widths CW vary by more than 0.002 inches. 
     Dimples preferably have a circular plan shape but may alternatively have a non-circular plan shape. The diameter of a dimple having a circular plan shape is twice the radial distance of a straight line segment that passes through the centroid (the center of the dimple) and whose endpoints lie on the perimeter of the dimple (the circle). 
     For purposes of the present disclosure, dimples with a non-circular plan shape have an effective dimple diameter defined as twice the average radial distance of the set of points defining the plan shape from the plan shape centroid. It is to be understood that a dimple having a circular plan shape has a circular perimeter, and a dimple having a non-circular plan shape has a non-circular perimeter. 
     In one embodiment, all n separation angles θ S  are equal. In another embodiment, at least two of the n separation angles θ S  differ. 
     Herein, two given separation angles θ S  which vary by less than 4.0 degrees when measured on the finished golf ball are considered to be “equal”. In turn, two given separation angles θ S  which vary by 4.0 degrees or greater when measured on the finished golf ball are considered to differ. 
     In a specific embodiment, none of the channels intersect each other. In one embodiment, at least one linear channel intersects a perimeter of the at least one dimple. In another embodiment, every linear channel intersects a perimeter of the at least one dimple. 
     In one embodiment, at least one dimple has a perimeter that is circular. In another embodiment, at least one dimple has a perimeter that is non-circular. 
     In a particular embodiment, channel length L is less than half of dimple diameter and at least two times channel width CW; wherein channel width CW is at least two times channel depth, wherein channel depth is less than or equal to 0.007 inches. 
     Each of the at least three linear channels extend radially outward from a location on the dimple that is a distance Cd from the dimple&#39;s centroid; that is, Cd&gt;0. 
     At least one dimple may comprise an even number of linear channels; wherein a first half of the linear channels intersect a perimeter of the dimple and a second half of the linear channels does not intersect the perimeter of the dimple; and wherein the first half of the linear channels and the second half of the linear channels alternate about the dimple&#39;s centroid. 
     At least one dimple may comprise nine linear channels; wherein none of the linear channels intersects a perimeter of the dimple, and the wherein linear channels are spaced by a separation angle θ S  of between 38.0 degrees and 42.0 degrees. 
     At least one dimple may comprise nine linear channels; wherein each linear channel intersects a perimeter of the dimple, and wherein the linear channels are spaced by a separation angle θ S  of between 38.0 degrees and 42.0 degrees. 
     In another embodiment, a golf ball of the invention has an outer surface comprising a plurality of dimples, wherein at least one of the dimples incorporates axially symmetric directional surface texturing comprised of three or more linear channels. At least one of the three or more linear channels has a different channel length L and/or a different channel width CW than at least one other linear channel; and all linear channels extend radially outward without intersecting the dimple&#39;s centroid; and linear channels having the same channel length L and the same channel width CW are spaced by n separation angles θ S , wherein n is the number of linear channels having the same channel length L and the same channel width CW. 
     In a particular such embodiment, the golf ball comprises a first type of linear channel and a second type of linear channel. Each linear channel of the first type has the same channel length L 1  and the same channel width CW 1  and extends outward from a location on the dimple that is a distance Cd 1  from the dimple&#39;s centroid and are spaced by a channel separation angle θ S1 . 
     Meanwhile, each linear channel of the second type has the same channel length L 2  and the same channel width CW 2  and extends radially outward from a location on the dimple that is a distance Cd 2  from the dimple&#39;s centroid and are spaced by a channel separation angle θ S2 . The first type of linear channel and the second type of linear channel alternate about the dimple&#39;s centroid. 
     In one embodiment, Cd 1 =Cd 2 . In one such embodiment, at least one of L 1 =L 2  or CW 1 =CW 2 . 
     In another embodiment, Cd 2 &gt;Cd 1 . In one possible linear channel arrangement, at least one of L 1 =L 2  or CW 1 =CW 2 . In one specific such embodiment, Cd 2  is closer to the perimeter than to the centroid. In another such specific embodiment, Cd 2  is closer to the centroid than to the perimeter. 
     In one embodiment, linear channels of the first type do not intersect a perimeter of the dimple and linear channels of the second type intersect the perimeter of the dimple. 
     Alternatively, the dimple may comprise ten linear channels comprising five linear channels of the first type and five linear channels of the second type; wherein none of the ten linear channels intersects the perimeter of the dimple; and wherein separation angle θ S1  is between 70 degrees and 74 degrees, and separation angle θ S2  is between 70.0 degrees and 74.0 degrees. 
     The dimple may comprise twelve linear channels comprising six linear channels of the first type and six linear channels of the second type; wherein each of the twelve linear channels intersects the perimeter; and wherein separation angle θ S1  is between 58.0 degrees and 62.0 degrees and separation angle θ S2  is between 58.0 degrees and 62.0 degrees. 
     In one such embodiment, separation angle θ S1  is equal to separation angle θ S2 . In another such embodiment, separation angle θ S1  is greater than separation angle θ S2 . 
     A given linear channel may be positioned partially or entirely closer to the perimeter than to the dimple&#39;s centroid. Alternatively, the given linear channel may be positioned partially or entirely closer to the dimple&#39;s centroid than to the dimple&#39;s perimeter. Of course, embodiments are envisioned wherein the length of the given linear channel is equally spaced between the centroid and the perimeter. Thus, in one embodiment, a dimple may include three types of linear channels, wherein a first type is positioned on the dimple partially or entirely closer to the perimeter than to the dimple&#39;s centroid; a second type is positioned on the dimple partially or entirely closer to the dimple&#39;s centroid than to the dimple&#39;s perimeter; and a third type is positioned on the dimple such that the length of the dimple is equally spaced between the dimple&#39;s centroid and perimeter. 
     The length, width and depth of each channel are as measured on an unpainted dimple surface. In one embodiment, at least one channel has a paint layer thereon having a thickness that is sufficient to create a channel visual appearance that differs from an adjacent dimple surface visual appearance without changing the golf ball&#39;s aerodynamic drag. In an alternative embodiment, at least one channel has a paint layer thereon having a thickness that is sufficient to change the golf ball&#39;s aerodynamic drag. 
     Preferably, the dimples on the ball have a dimple radius of at least 0.2 inch and the linear channels have a channel radius between 0.001 and 0.08 inch, and more preferably 0.007 inch to 0.07 inch. The linear channels are relatively shallow compared to the depth of the dimple they are in, and preferably, have a channel depth of 0.0003 inch to 0.003 inch. 
     The dimples are preferably circular in plan shape and have a diameters of 0.11 inch to 0.22 inch, but could also be polygonal or other geometric shapes. The dimples can also be spherically shaped in cross section or have a cross section defined by a number of functions. Preferably, the golf ball has four or more diameters of dimples that have multiple dimple depths and edge angles. 
     In one embodiment, each of the dimples has the same number of linear channels. In another embodiment, each dimple has the same number of linear channels and the channel widths vary according to dimple diameters. In yet another embodiment, the number of linear channels varies based on the dimple diameter. Still further, in another embodiment, the depth of the linear channels can vary depending on the depth of the dimple. 
     In another preferred embodiment of the present invention the golf ball comprises at least one dimple having a circular plan shape and linear directional surface texturing that is comprised of a plurality of channels that are linear and extending radially outward when viewing the dimple perpendicular to the dimple edge plane. 
     The length, width and depth of each channel are as measured on an unpainted dimple surface. In one embodiment, at least one channel has a paint layer thereon having a thickness that is sufficient to create a channel visual appearance that differs from an adjacent dimple surface visual appearance without changing the golf ball&#39;s drag. In an alternative embodiment, at least one channel has a paint layer thereon having a thickness that is sufficient to change the golf ball&#39;s drag. 
     Several examples of possible radially extending linear channels arrangements for dimples of golf balls of the invention are included in TABLE III below wherein for each linear channel arrangement the number of dimples as well as their respective measurements (widths, lengths and depths) and separation angles are provided as follows: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE III 
               
               
                   
               
               
                   
                   
                 Channel 
                 Channel 
                 Channel 
                 Channel 
                 Separation 
               
               
                   
                 # Channels/ 
                 Width 
                 Length 
                 Depth 
                 Radius 
                 Angle 
               
               
                 Ex. No. 
                 Dimple 
                 (in.) 
                 (in.) 
                 (in.) 
                 (in.) 
                 θ S1 ; θ S2   
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 1 
                 9 
                 0.014 
                 0.067 
                 0.002 
                 0.016 
                 40 
               
               
                 2 
                 10 
                 0.014 
                 0.067 
                 0.002 
                 0.016 
                 72 
               
               
                   
                   
                 0.011 
                 0.031 
                 0.001 
                 0.016 
                 72 
               
               
                 3 
                 12 
                 0.014 
                 0.076 
                 0.002 
                 0.016 
                 60 
               
               
                   
                   
                 0.015 
                 0.056 
                 0.002 
                 0.016 
                 60 
               
               
                 4 
                 9 
                 0.014 
                 0.076 
                 0.002 
                 0.016 
                 40 
               
               
                   
               
            
           
         
       
     
     Referring to dimple channel arrangement example Ex.1 of TABLE III in connection with  FIG. 25 , dimple  368  has a perimeter  370 , a dimple diameter DD of about 0.180 inches, and a dimple surface  372 . Dimple surface  372  is spherical, has an edge angle of about 14.25 degrees, and contains nine linear channels  374 , each having the dimensions set forth in TABLE I. None of nine linear channels  374  intersect dimple perimeter  370 , and each has a center line  374 -C between which there is a channel separation angle θ S  such that all of the channels are rotationally symmetric about an axis connecting a center of the golf ball to dimple centroid  371 . Also, none of the nine linear channels  374  intersects centroid  371  but rather, are each extends radially outward from a location on the dimple that is a distance Cd from the dimple&#39;s centroid  371 . 
     Meanwhile, referring to dimple channel arrangement example Ex. 2 of TABLE III in connection with  FIGS. 26 a  and 26 b   , dimple  378  has a perimeter  380 , a dimple diameter DD of about 0.180 inches, and a dimple surface  382 . Dimple surface  382  is spherical, has an edge angle of about 14.25 degrees, and contains ten linear channels including a first type of five linear channels  384  and a second type of five linear channels  386 . Linear channels  384  and linear channels  386  are all contained within the entirety of the dimple perimeter (that is, none of the ten channels intersect dimple perimeter  380 ). Consecutive center lines  84 -C of the first type of linear channels  384  are separated by a channel separation angle θ S1  such that all of the channels are rotationally symmetric about an axis connecting the center of the ball to the dimple centroid  381 . In turn, consecutive center lines  86 -C of the second type of linear channels  386  are separated by a channel separation angle θ S2  such that all of the channels are rotationally symmetric about an axis connecting the center of the ball to the dimple centroid  381 . The first channel type and second channel type have different dimensions as shown in TABLE III. 
     Moreover, none of the ten linear channels  384  and  386  intersects centroid  381 . Instead, each of linear channels  384  extends radially outward from a location on the dimple that is a distance Cd 1  from the dimple&#39;s centroid  381 , while each of linear channels  386  extends radially outward from a location on the dimple that is a distance Cd 2  from the dimple&#39;s centroid  381 . In this embodiment, Cd 1  is closer to centroid  381  than to perimeter  380 . In some such embodiments, Cd 2  may also be closer to centroid  381  than to perimeter  380 . Alternatively, Cd 2  may be closer to perimeter  380  than to centroid  381 . Of course, embodiments are also envisioned wherein Cd 2  is equidistant from centroid  381  and perimeter  380 . And embodiments are indeed also possible wherein both Cd 1  and Cd 2  are closer to perimeter  380  than to centroid  381 ; or both Cd 1  and Cd 2  are equidistant from centroid  381  and perimeter  380 . 
     Furthermore, it is evident from  FIG. 26 b    that both types of linear channels  384  and  386  have constant channel depths Dc 1  and Dc 2 , respectively, extending below extrapolated surface  382   e  which continues between surfaces  382  of dimple  378 . 
     Referring next to dimple channel arrangement example Ex.3 of TABLE III in connection with  FIG. 27 , dimple  388  has a perimeter  390 , a dimple diameter DD of about 0.180 inches, and a dimple surface  392 . Dimple surface  392  is spherical, has an edge angle of about 14.25 degrees, and contains twelve linear channels including a first type of six linear channels  394  and a second type of six linear channels  396 . Linear channels  394  and linear channels  396  all intersect dimple perimeter  390 . Consecutive center lines  394 -C of the first type of linear channels  394  are separated by a channel separation angle θ S1  such that all of the channels are rotationally symmetric about an axis connecting the center of the ball to the dimple centroid  391 . In turn, consecutive center lines  396 -C of the second type of linear channels  396  are separated by a channel separation angle θ S2  such that all of the channels are rotationally symmetric about an axis connecting the center of the ball to the dimple centroid  391 . The first channel type and second channel type have different dimensions as shown in TABLE III. 
     Moreover, none of the ten linear channels  394  and  396  intersects centroid  391 . Instead, each of linear channels  394  extends radially outward from a location on the dimple that is a distance Cd 1  from the dimple&#39;s centroid  391 , while each of linear channels  396  extends radially outward from a location on the dimple that is a distance Cd 2  from the dimple&#39;s centroid  391 . 
     Finally, referring to dimple channel arrangement example Ex.4 of TABLE III in connection with  FIG. 28 , dimple  418  has a perimeter  420 , a dimple diameter DD of about 0.180 inches, and a dimple surface  422 . Dimple surface  422  is spherical, has an edge angle of about 14.25 degrees, and contains nine linear channels  424 , each having the dimensions set forth in TABLE I. Each of nine linear channels  424  intersect dimple perimeter  420 , and each has a center line  424 -C between which there is a channel separation angle θ S  such that all of the channels are rotationally symmetric about an axis connecting a center of the golf ball to dimple centroid  421 . Additionally, none of the nine linear channels  424  intersects centroid  421  but rather, each extends radially outward from a location on the dimple that is a distance Cd from the dimple&#39;s centroid  421 . 
       FIGS. 25-28  also demonstrate that width (CW 1 ) of each linear channel is constant with respect to center lines  374 -C,  384 -C,  394 -C and  424 -C, respectively. 
     Thus, at least one dimple of golf balls of the invention incorporates axially symmetric directional surface texturing comprised of three or more linear channels which extend radially outward from the dimple&#39;s centroid without intersecting it; and wherein meanwhile, consecutive same-type linear channels are separated by a channel separation angle θ Sn , wherein n is a designation distinguishing different channel types. For example where a given dimple includes first and second different channel types, channel separation angle θ S1  can be used to represent the separation angles between consecutive channels of the first channel type, and separation angle θ S2  can be used to represent the separation angles between consecutive channels of the second channel type. 
     In this regard, the channels of a given dimple may have the same or different measurements; intersect or not intersect each other and/or a perimeter of the dimple. Dimple perimeter may be circular or non-circular. All channel separation angles θ S  may be the same, or, alternating channel separation angles θ S  may be the same. For example, a dimple may have a first type of linear channels and a second type of linear channels, wherein the two types have different channel widths and channel lengths; and wherein channel separation angles θ S1  between consecutive first type channels differs from channel separation angle θ S2  between consecutive second type channels. 
     While in preferred embodiments a given dimple incorporates one channel type or two differing channel types, it is envisioned that a dimple may contain any number of differing channel types possible for a given dimple surface area and perimeter measurement. 
     And preferably, a dimple incorporates at least three linear channels. 
     The length of a given linear channel is preferably less than one half of the dimple&#39;s diameter DD and does not intersect the dimple&#39;s centroid. Meanwhile, the linear channel&#39;s length is preferably twice channel width, which in turn, is preferably twice channel depth, where the channel&#39;s depth is preferably equal to or less than 0.007 inches. 
     Thus, in one non-limiting example, a linear channel may have a depth of 0.007 inches, a width of 0.014 inches or greater, and a length of 0.028 inches or greater. In another non-limiting example, a linear channel may have a depth of 0.006 inches, a width of 0.012 inches or greater, and a length of 0.024 inches or greater. In yet another non-limiting example, a linear channel may have a depth of 0.005 inches, a width of 0.010 or greater, and a length of 0.020 inches or greater. In still another non-limiting example, a linear channel may have a depth of 0.004 inches, a width of 0.008 inches or greater, and a length of 0.016 inches or greater. In an alternative embodiment, a linear channel may have a depth of 0.003 inches, a width of 0.006 inches or greater, and a length of 0.012 inches or greater. In a different embodiment, a linear channel may have a depth of 0.002 inches, a width of 0.004 inches or greater, and a length of 0.008 inches or greater. Or, a linear channel may have a depth of 0.001 inches, a width of 0.002 inches or greater, and a length of 0.004 inches or greater. 
     Golf balls of the invention may include dimples having many different radially outward extending linear channel arrangements consistent with the disclosure herein. For example, a dimple may include two different channel types, a first type having a separation angle θ S1  and a second type having a separation angle θ S2  which alternate about the centroid in predetermined pattern. Channels of the second type may for example have a channel separation angle θ S2  that is greater than channel separation angle θ S1  of the first type. In a specific such embodiment, the dimple may include six linear channels of the first type and three linear channels of the second type, wherein two of the six linear channels of the first type are located/positioned between consecutive linear channels of the second type. In this embodiment, separation angle θ S2  between the second type of linear channels is 120°. And two given linear channels of the first type that are positioned between consecutive linear channels of the second type are separated by a separation angle θ S1  of 40° when measured between center lines of consecutive channels of the same type. In this embodiment, not all linear channels of the first type have the same separation angle of 40°. Any two given linear channels of the first type having a linear channel of the second type positioned there between have a separation angle of 80° in this embodiment. 
     If instead, a dimple contains nine linear channels of the first type and three linear channels of the second type, then three of the nine linear channels of the first type may be located between consecutive linear channels of the second type. In this embodiment, separation angle θ S2  between the second type of linear channels is still 120°, whereas θ S1  between the first type of linear channels is 30°, and any two given linear channels of the first type having a linear channel of the second type positioned there between have a separation angle of 60° in this embodiment. 
     Accordingly, golf balls of the invention can produce a wide range of unique primary aerodynamic behavior and flight characteristics, unique secondary aerodynamic behaviors, and visually distinct appearances, by preselecting any and all of i) the total number of such dimples included on/within the golf ball&#39;s outer surface; ii) the total number of linear channels included on such a dimple (≥3); iii) the sizing (e.g. length/width) of each linear channel on/in such a dimple; and iv) the locations of the linear channels on such a dimple and the spacing (separation angle θ S ) there between. 
     Generally, a dimple may include either of an odd total number of linear channels or an even total number of linear channels. In embodiments wherein a given dimple comprises two or more types of linear channels, the dimple may include an odd number of each type of linear channel, an even number of each type of linear channel, or an odd number of one or more types of linear channels and an even number of one or more types of linear channels. 
     And all linear channels can be equally spaced (separation angle θ S ) on/within the dimple (about the centroid); or be unequally spaced on/within the dimple (that is, at least two separation angles θ S  differ); or a combination thereof. 
     The at least three linear channels always extend radially outward from the dimple&#39;s centroid without intersecting it. The at least three linear channels may all have the same linear channel lengths and/or linear channel widths, and/or distances from the centroid. Alternatively, at least one linear channel may differ from at least one other linear channel with respect to any or each of linear channel length and/or linear channel width, and/or distance from the centroid. 
     Furthermore, two given linear channels may extend radially outward from locations on the dimple&#39;s surface that are the same radial distance from the centroid and also closer to the centroid than to the perimeter. Alternatively, two given linear channels may extend radially outward from locations on the dimple&#39;s surface that are different radial distances from the centroid but still both be closer to the centroid than to the perimeter. It is also contemplated that in some embodiments, two given linear channels may extend radially outward from locations on the dimple&#39;s surface that are both closer to the perimeter than to the centroid; and in such embodiments, it is envisioned that their respective radial distances from the centroid may be the same or differ. 
     In any of these embodiments, one or more linear channel may intersect the perimeter. Alternatively, in any of these embodiments, it is possible to construct the dimple such that none of the linear channels intersect the perimeter. 
     None of the linear channels on a given dimple intersect since each extends radially outward in relation to the dimple&#39;s centroid but does not intersect the centroid. Furthermore, a given linear channel is located on/within a single dimple and does not extend beyond that dimple into the land area of the outer surface of the golf ball nor into/onto another dimple and therefore does not intersect any linear channel of another dimple. 
     This being said, a golf ball of the invention may additionally contain one or more dimples having profiles and channel arrangements as also disclosed herein and/or in any parent application(s) referred to in the Cross-Reference and each of which is hereby incorporated herein by reference in its entirety. 
     When numerical lower limits and numerical upper limits are set forth herein, it is contemplated that any combination of these values may be used. All numerical values and ranges set forth herein are approximate. 
     All patents, publications, test procedures, and other references cited herein, including priority documents, are fully incorporated by reference to the extent such disclosure is not inconsistent with this invention and for all jurisdictions in which such incorporation is permitted. 
     While the illustrative embodiments of the invention have been described with particularity, it will be understood that various other modifications will be apparent to and can be readily made by those of ordinary skill in the art without departing from the spirit and scope of the invention. For example, the dimples discussed herein are shown as circular dimples. However, it is understood that the present invention is intended to cover polygonal shaped dimples such as, for example, those disclosed in U.S. Pat. Nos. 7,722,484 and 7,867,109, which are incorporated by reference herein in their entirety. Further embodiments above are described with respect to including linear channels. However, it is easily appreciated that the channels can be formed as protrusions as well. Accordingly, it is not intended that the scope of the claims appended hereto be limited to the examples and descriptions set forth herein, but rather that the claims be construed as encompassing all of the features of patentable novelty which reside in the present invention, including all features which would be treated as equivalents thereof by those of ordinary skill in the art to which the invention pertains.