Patent Publication Number: US-2023148396-A1

Title: Golf ball

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 17/190,864 filed on Mar. 3, 2021, which is incorporated herein by reference. 
    
    
     FIELD 
     The present invention is a golf ball having a type of dimple and a specific arrangement of the dimples on the surface, which results in controlled flight distance and flight symmetry. 
     BACKGROUND OF THE INVENTION 
     Recent developments in golf ball technology have been focused not only on the development of new golf ball materials and constructions, but also the improvement in their aerodynamic properties. As far back as the 1800&#39;s golfers realized that gutta-percha golf balls with damaged or indented surfaces flew better than smooth new ones. Subsequently, golf balls with brambles (bumps rather than dents), such as the Spalding Agrippa, or with grooves such as the Spalding Silvertown were popular from the late 1800&#39;s to 1908. In 1908, William Taylor, patented a golf ball with indentations (dimples) that flew better than golf balls with brambles or grooves. For the next 60 years most balls looked exactly the same having 336 dimples of the same size distributed in an octahedron or so-called ATTI pattern over the surface. The ATTI pattern, named after its inventor Ralph Atti, was based on an octahedron, split into eight concentric straight-line rows. The only other significant innovation related to the surface of a golf ball during this sixty-year period came from Albert Penfold who invented a mesh-pattern golf ball for Dunlop. This pattern was invented in 1912 and was accepted until the 1930&#39;s. 
     In the 1970&#39;s, additional dimple patterns were introduced which attempted to maximize the surface area coverage of the dimples on the ball. For example, U.S. Pat. No. 4,949,976 to William Gobush discloses a golf ball with 78% dimple area coverage with up to 422 dimples. The 1990&#39;s also saw further increases in dimple surface area coverage up to and above 80%. Dimple patterns have also evolved by incorporating dimple placement in specific geometries based on sectional shapes such as pentagonal, as in U.S. Pat. No. 5,201,522, octahedral, dodecahedral and icosahedral patterns or modified versions of these such as in U.S. Pat. No. 4,880,241, which discloses a golf ball dimple pattern based on a modified icosahedron. 
     In addition to maximizing surface area coverage, further innovations in dimple pattern design have seen not only the number of dimples on a golf ball surface vary but also their diameters and/or depths. These have included dimple patterns with four or five to as many as eleven different dimple diameters. 
     More recently there have been a number of patents which have attempted to not only maximize surface coverage but also impart selected lift and drag properties for the golf ball. For instance, a drag penalty is often incurred when a single row of deep dimples are placed adjacent to the seam and U.S. Pat. No. 6,066,055 (“the &#39;055 patent”) describes how arranging dimple volume differently in (latitudinal) regions is beneficial in producing better ball symmetry, or anisotropy, in flight as compared to a single row of deep dimples near the seam. 
     More specifically the &#39;055 patent teaches a method of arranging the dimples within three separate regions (where the seam line is latitude 0° and both poles are latitude 90°), an equator region defined by latitudes 0 to 17° a shoulder region defined by latitudes from more than 17° to less than 62°, and a pole region defined by latitudes 62° to 90 and when X represents total volume of dimples which belong to the parting line vicinity, Y represents total volume of dimples which belong to the pole vicinity, and Z represents total volume of dimples which belong to the shoulder portion, the ratio X/Z is set to be 0.58 to 0.72, and a ratio Y/Z is set to be 0.22 to 0.30. 
     The &#39;055 patent also teaches that the dimples used should have a circular opening, spherical cross section, and the same diameter and be disposed on the whole surface of the golf ball, and that the depths of the dimples which belong to the parting line vicinity and the pole vicinity are respectively arranged to be deeper than that of the dimples which belong to the shoulder portion by 0.003 mm to 0.06 mm. 
     U.S. Pat. No. 8,047,933 (“the &#39;933 patent”) describes a dimple design with superior performance in carry distance for golfers whose swing profile generates moderate to low ball spin rates. This was achieved by both reducing drag on the overall ball, while increasing lift judiciously. Three separate design features were employed in combination to achieve these results. 
     The first was a method of arranging the dimples within three separate lateral regions (where the seam line is latitude 0° and both poles are latitude 90°), an equator region defined by latitudes 0 to 25° a shoulder region defined by latitudes from more than 25° to less than 65°, and a pole region defined by latitudes 65° to 90°. Thus, for the dimples used which all had a circular opening and spherical cross section, a pattern was used where the dimples near the pole were about 10% more shallow, and the dimples near the equator were about 5% deeper than the same design with no depth progression. 
     The second design feature required that the range of total dimple volume (TDV) should be greater than 370 mm 3  but less than 385 mm 3 . 
     The third design features required that the specific dimple volume ratio, VR (defined by dimple chordal volume divided by the volume of a cylinder with the same diameter and depth as the dimple) should be set to a value of 0.55. 
     Thus, efforts to improve dimple flight performance have focused on placement of dimples not only in different geodimetric shapes but more recently by selective placement of dimples in various latitudinal sections of the golf ball to improve total distance. However, with the ongoing debate on reducing golf ball distance due to the greater distances now being recorded by current PGA professionals and its effect on the playability of golf courses, there is a continuing need for new dimple patterns which incorporate not only variable surface coverage but which can control the dimple effect on the flight profile of the golf ball and thus control its distance. 
     SUMMARY 
     We have found that compared to a golf ball having primarily dimples with a circular opening and spherical cross section, further control of distance and in in seam versus cross seam distance dispersion may be achieved by replacing the spherical dimples with dimples having a dual radius and controlling their placement depths and diameters in selected regions of the golf ball. The dimples are selected such that the dimple depth can be reduced while maintaining dimple volume and by controlling the average dimple depth (h) in the equator, shoulder and pole regions of the golf ball when the golf ball is oriented in the cross seam direction (hex, hsx, hpx respectively) as well as the average dimple depths in the regions from the pole axis to 25° longitude, the region of longitude greater than 25° to less than 65° and the region from longitude 65° to 90° (hei, hsi and hpi respectively). 
     The distance symmetry at increased distance is also maintained by requiring that the ratios hex/hei, hsx/hsi and hpx/hpi all approach unity and that these ratios remain close to unity as the golf ball is initially placed in the cross seam orientation and rotated about its polar axis from 0 to 360°. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS.  1 A and  1 B  are views for explaining the specifics of a dual radius dimple. 
         FIG.  2    is a schematic view showing how to calculate the Volume Ratio, Vr, of a dimple 
         FIG.  3   . shows a golf ball,  30 , in which the ball is oriented in the cross seam direction and has an equator  32 , two poles  34  and  36 , and a primary meridian  42 , which North and South hemispheres  38  and  40  respectively and North East,  48 , North West,  50 , South East,  52  and South West,  54 , quadrants. 
         FIG.  4 A  illustrates a transverse cross section of the golf ball sphere illustrating the position of the latitudinal zones. 
         FIG.  4 B  illustrates a transverse cross section of the golf ball sphere illustrating the position of the longitudinal zones. 
         FIG.  5 A  is a plan view down the pole axis of the golf ball sphere without dimples illustrating the position of the latitudinal and longitudinal and overlap zones in the Northern hemisphere,  38 . 
         FIG.  5 B  is an elevation view of the Northern hemisphere of the golf ball sphere without dimples looking along the axis of the primary meridian,  42 . 
         FIG.  5 C  is an elevation view of the Northern hemisphere of the golf ball sphere without dimples looking along an axis perpendicular to the primary meridian,  42 . 
         FIG.  6 A  is a plan view down the pole axis of the golf ball with dimples illustrating the position of the latitudinal and longitudinal and overlap zones in the Northern hemisphere,  38 . 
         FIG.  6 B  is an elevation view of the Northern hemisphere of the golf ball with dimples looking down the axis of the primary meridian,  42 . 
         FIG.  6 C  is an elevation view of the Northern hemisphere of the golf ball with dimples looking down the axis perpendicular to the primary meridian,  42 . 
         FIG.  6 D  is another elevation view of the Northern hemisphere of the golf ball with dimples. 
         FIG.  7    is a graph showing the observed change in the ratios, hex/hei, hsx/hsi and hpx/hpi, when the golf ball is initially placed in the cross seam orientation and rotated about its polar axis by a value of θ as it rotates 0 to 360°. 
         FIG.  8    illustrates an elevation view of the Northern hemisphere of a golf ball with a grid and a pentagonal pyramid projected on its surface. 
         FIG.  9    illustrates an elevation view of a dimple arrangement according to one embodiment of the invention. 
         FIG.  10    illustrates an elevation view of the Northern hemisphere of a golf ball with a grid and a octagonal pyramid projected on its surface. 
         FIG.  11    illustrates an elevation view of the Northern hemisphere of a golf ball with a grid and a decagonal pyramid projected on its surface. 
         FIG.  12    illustrates a transverse cross section of a 3 piece golf ball  50  comprising a core, an intermediate layer and an outer cover layer. 
         FIG.  13    illustrates a transverse cross section of a 5 piece golf ball comprising a core, an inner intermediate layer, a center intermediate layer, an outer intermediate layer and an outer cover layer. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Having briefly described the present invention, the above and further objects, features and advantages thereof will be recognized by those skilled in the pertinent art from the following detailed description of the invention when taken in conjunction with the accompanying drawings. 
     Any numerical values recited herein include all values from the lower value to the upper value. All possible combinations of numerical values between the lowest value and the highest value enumerated herein are expressly included in this application. 
     The following definitions are provided to aid the reader and are not intended to provide term definitions that would be narrower than would be understood by a person of ordinary skill in the art of golf ball composition and manufacture. 
     The term “bimodal polymer” refers to a polymer comprising two main fractions and more specifically to the form of the polymer&#39;s molecular weight distribution curve, i.e., the appearance of the graph of the polymer weight fraction as a function of its molecular weight. When the molecular weight distribution curves from these fractions are superimposed onto the molecular weight distribution curve for the total resulting polymer product, that curve will show two maxima or at least be distinctly broadened in comparison with the curves for the individual fractions. Such a polymer product is called bimodal. The chemical compositions of the two fractions may be different. 
     The coefficient of restitution (“COR”) of a golf ball is the ratio of the relative velocity after direct impact of the ball with a stationary surface to the relative velocity before impact. One conventional technique for measuring COR uses a golf ball or sphere, an air cannon, and a stationary steel plate. A pair of ballistic light screens, which measure ball velocity, are spaced apart and located between the air cannon and the steel plate. The golf ball is fired from the air cannon toward the steel plate over a range of test velocities from 50 ft/s to 180 ft/s. As the ball travels toward the steel plate, it activates each light screen so that the time at each light screen is measured. This provides an incoming time period proportional to the hail incoming velocity. The ball impacts the steel plate and rebounds though the light screens, which again measure the time period required to transit between the light screens. This provides an outgoing transit time period proportional to the ball outgoing velocity. The COR can be calculated by the ratio of the outgoing transit time period to the incoming transit time period, COR=T out /T in . The golf ball COR&#39;s is often quoted relative to the test velocity of 143 ft/sec in which case the abbreviation COR 143  is used. As used herein, the COR quoted may also be one measured at a test velocity of 125 ft/sec in which case the abbreviation COR 125  is used. 
     The golf ball contact time (CT 143 ) is measured using a similar set up to the measurement of COR, and is defined as the time of contact between the ball and the steel plate in microseconds at an impact speed of 143.8 ft/s (43.83 m/s). Typically, a ball is tested over a range of speeds, such that: a) The impact speeds should not be different from 143.8 ft/s by more than 15 ft/s (4.57 m/s) and b) Sufficient measurements are made at speeds above and below the target speed as to allow for linear interpolation to 143.8 ft/s 
     As used herein, the term “core” is intended to mean the elastic center of a golf ball, which may have a unitary construction. Alternatively, the core itself may have a layered construction, e.g., having a spherical “center” and additional “core layers,” with such layers being made of the same material as the core center. 
     The term “cover” is meant to include any layer of a golf ball that surrounds the core. Thus, a golf ball cover may include both the outermost layer and also any intermediate layers, which are disposed between the golf ball core and outer cover layer. “Cover” may be used interchangeably with the term “cover layer.” 
     As used herein the term “equator’ and “poles” of a golf ball are defined for a spherical golf ball as follows. In this application most drawings and descriptions consider the two-dimensional golf ball sphere. For definiteness we will take the unit sphere of unit radius in three-dimensional space with center the origin, O. This is the set of satisfying the equation: 
         X   2   +y   2   +z   2 =1. 
     where the xy-plane, is called the equatorial plane, which is the horizontal plane and the z-axis as vertical. Any plane passing through the origin cuts the sphere in a circle called a great circle, so the center of a great circle and the center of the sphere coincide. The equatorial plane meets the sphere of the golf ball in a great circle called the equator. 
     The line through the center of the golf ball sphere perpendicular to the plane of equator meets the outer surface of the golf ball sphere in two antipodal points called the poles of the golf ball. The poles of the equator are the North pole N=(0,0,1) and the South pole S=(0, 0, −1). 
     As used herein the term “great circle” is defined circle ole the surface of a sphere which lies in a central plane passing through the sphere&#39;s center. 
     The term “intermediate layer” may be used interchangeably with “mantle layer,” “inner cover layer” or “inner cover” and is intended to mean any layer(s) in a golf ball disposed between the core and the outer cover layer. 
     In the case of a ball with a core, two intermediate layers, and an outer cover layer the term “inner intermediate layer” may be used interchangeably herein with the terms “inner mantle” or “inner mantle layer” and is intended to mean the intermediate layer of the ball positioned nearest to the core, and the term “outer intermediate layer” may be used interchangeably herein with the terms “outer mantle” or “outer mantle layer” and is intended to mean the intermediate layer of the ball which is disposed nearest to the outer cover layer. 
     In the case of a ball with a core, three intermediate layers and an outer cover layer the term “inner intermediate layer” may be used interchangeably herein with the terms “inner mantle” or “inner mantle layer” and is intended to mean the intermediate layer of the ball positioned nearest to the core, the term “outer intermediate layer” may be used interchangeably herein with the terms “outer mantle” or “outer mantle layer” and is intended to mean the intermediate layer of the ball which is disposed nearest to the outer cover layer. The term “center intermediate layer” may be used interchangeably herein with the terms “center mantle” or “center mantle layer” and is intended to mean the intermediate layer of the ball positioned between the inner and outer intermediate layers 
     The term “outer cover layer” is intended to mean the outermost cover layer of the golf ball on which, for example, the dimple pattern, paint and any writing, symbol, etc. is placed. If, in addition to the core, a golf ball comprises two or more cover layers, only the outermost layer is designated the outer cover layer. The remaining layers may be designated intermediate layers. The term outer cover layer is interchangeable with the term “outer cover.” 
     If no intermediate layer is introduced between the core and outer cover layer, a so called “two-piece ball” results, if one additional intermediate layer is introduced between the core and outer cover layer, a so called “three-piece ball” results, if two additional intermediate layers are introduced between the unitary core and outer cover layer, a so called “four-piece ball” results, and if three intermediate layers are introduced between the core and outer cover layer, a so called “five-piece ball” results, and so on. 
     The term “meridian” as used herein refers to a great circle on the surface of a sphere passing through the poles. 
     The term “(meth)acrylate” is intended to mean an ester of methacrylic acid and/or acrylic acid. 
     The term “(meth)acrylic acid copolymers” is intended to mean copolymers of methacrylic acid and/or acrylic acid. 
     The term “polyurea” as used herein refers to materials prepared by reaction of a diisocyanate with a polyamine. 
     The term “polyurethane” as used herein refers to materials prepared by reaction of a diisocyanate with a polyol. 
     The term “reduced equivalent depth dimple” as used herein refers to dimples which have a circular opening and which have a cross sectional profile which results in their exhibiting lower depth than the corresponding spherical single radius dimple of the same diameter and volume. Non-limiting examples of such dimple profiles include dual radius, multiple radius and cylindrical dimple profiles 
     The term “seam” as used herein refers to a line formed on the ball by the coming together of the hemispherical mold halves during the molding process used to make a golf ball. In addition to the term “seam” this line is also referred to as the “parting line” of the golf ball as these terms may be used interchangeably herein. (Given that the mold halves are hemispherical the golf ball seam is often coincident with the golf ball equator). 
     In reference to the golf ball seam, the term “cross seam” as used herein refers to an orientation of the ball such that when placed on the teeing ground the seam is aligned in the horizontal direction parallel to the ground plane and when launched, the ball would spin about the axis described by a line that would pass through the seam (equator) of the ball and that would lie in horizontal plane and be perpendicular to the direction of flight. This is the orientation described as the Pole over Pole (PP) orientation in United States Golf Association and R&amp;A Rules Limited Actual Launch Conditions Overall Distance And Symmetry Test Procedure (Phase II) USGA-TPX3006 Revision 2.0.0 Feb. 28, 2011. 
     Again, in reference to the golf ball seam, the term “in seam” as used herein refers to an orientation of the ball such that when placed on the teeing ground the seam is aligned in the vertical direction perpendicular to the ground plane and when launched, the ball would spin about an axis described by a line that would pass through the poles of the ball and that would lie in horizontal plane and be perpendicular to the direction of flight. This is the orientation described as the Pole Horizontal (PH) orientation in United States Golf Association and R&amp;A Rules Limited Actual Launch Conditions Overall Distance And Symmetry Test Procedure (Phase II) USGA-TPX3006 Revision 2.0.0 Feb. 28, 2011. 
     The term “spherical triangle” as used herein is a figure formed on the surface of a sphere, by three great circular arcs intersecting pairwise in three vertices. The sides of a spherical triangle are thus arcs of great circles. The spherical triangle is the spherical analog of the planar triangle and is sometimes called a Euler triangle (Harris and Stocker 1998). 
     A “thermoplastic” is generally defined as a material that is capable of softening or melting when heated and of hardening again when cooled. Thermoplastic polymer chains often are not cross-linked or are lightly crosslinked using a chain extender, but the term “thermoplastic” as used herein may refer to materials that initially act as thermoplastics, such as during an initial extrusion process or injection molding process, but which also may be crosslinked, such as during a compression molding step to form a final structure. 
     A “thermoset” is generally defined as a material that crosslinks or cures via interaction with as crosslinking or curing agent. The crosslinking may be brought about by energy in the form of heat (generally above 200 degrees Celsius), through a chemical reaction (by reaction with a curing agent), or by irradiation. The resulting composition remains rigid when set and does not soften with heating. Thermosets have this property because the long-chain polymer molecules cross-link with each other to give a rigid structure. A thermoset material cannot be melted and re-molded after it is cured thus thermosets do not lend themselves to recycling unlike thermoplastics, which can be melted and re-molded. 
     The term “unimodal polymer” refers to a polymer comprising one main fraction and more specifically to the form of the polymer&#39;s molecular weight distribution curve, i.e., the molecular weight distribution curve for the total polymer product shows only a single maximum. 
     The term “zone” as used herein is the surface of a spherical segment defined by cutting a sphere with a pair of parallel planes. 
     The above term descriptions are provided solely to aid the reader and should not be construed to have a scope less than that understood by a person of ordinary skill in the art or as limiting the scope of the appended claims. 
     The singular terms “a,” “an,” and “the” include plural referents unless context clearly indicates otherwise. The word “comprises” indicates “includes.” It is further to be understood that all molecular weight or molecular mass values given for compounds are approximate and are provided for description. The materials, methods, and examples are illustrative only and not intended to be limiting. Unless otherwise indicated, description of components in chemical nomenclature refers to the components at the time of addition to any combination specified in the description, but does not necessarily preclude chemical interactions among the components of a mixture once mixed. 
     Any numerical values recited herein include all values from the lower value to the upper value in increments of one unit provided that there is a separation of at least 2 units between any lower value and any higher value. As an example, if it is stated that the amount of a component or a value of a process variable is from 1 to 90, preferably from 20 to 80, more preferably from 30 to 70, it is intended that values such as 15 to 85, 22 to 68, 43 to 51, 30 to 32 etc., are expressly enumerated in this specification. For values, which have less than one unit difference, one unit is considered to be 0.1, 0.01, 0.001, or 0.0001 as appropriate. Thus, all possible combinations of numerical values between the lowest value and the highest value enumerated herein are said to be expressly stated in this application. 
     The present invention can be used to form golf balls of any desired size. “The Rules of Golf” by the USGA dictate that the size of a competition golf ball must be at least 1.680 inches in diameter; however, golf balls of any size can be used for leisure golf play. The preferred diameter of the golf balls is from about 1.670 inches to about 1.800 inches. Oversize golf balls with diameters above about 1.760 inches to as big as 2.75 inches also are within the scope of the invention. 
     Typically, manipulation of dimple volume in a spherical single radius dimple is achieved by varying dimple diameter and/or depth. Dimple diameter and depth is measured generally according to the teachings of U.S. Pat. No. 4,936,587 (the &#39;587 patent), which is included herein by reference thereto. In a regular spherical dimple, a single radius, R, describes the shape of the bottom of the dimple to its open surface. In other words, this radius governs the shape of the dimple toward the bottom of the dimple as well as its depth and volume. 
     In one aspect, the present invention seeks to increase the distance of a golf ball by shallowing the dimples to reduce the drag. Shallow dimples generate high air flow circulation and high lift, but too much lift also can result in loss of distance if the golf ball balloons in flight. This is mediated or offset by selecting the volume of the dimple, so it is sufficient to create the required degree of turbulence to avoid the ball flight ballooning. In a typical spherical profile dimple the depth and volume are directly coupled so that shallowing the dimple also reduces its volume and so reaches a limit into how much they can be shallowed without inducing ballooning. 
     In a typical dual radius dimple, on the other hand, two radii are used to describe the shape of the dimple ( FIGS.  1 A and  1 B ). The major radius (R 1 ) describes the bottom of the dimple, and a minor radius (R 2 ) describes the shape of the dimple about its circumference. As shown by  FIGS.  1 A and  1 B , a feature of the dual radius dimple having a major radius R 1  is that by judicious selection of the minor radius R 2 , it is possible to produce a shallower dimple with no change in total dimple volume or dimple diameter as compared with the corresponding spherical single radius dimple having the same major radius R 1 . 
     This “decoupling” of dimple depth from dimple volume not only allows a shallowing of dimples for a given volume in dual radius dimples but also allows for the same effect in dimples with multiple radii as well as dimples having non curved surfaces. Such examples include but are not limited to multiple radius dimples, cylindrical dimples and, to facilitate the dimple molding process, it is also preferrable if such dimple profiles such as cylindrical are modified such that they are not planar at their base but rather have a spherical bottom cap which facilitates both their molding and subsequent removal from the mold. 
     The cross-sectional profile or dimple shape comprising the dimple patterns of the golf balls of the present invention thus include not only dual radius dimples but also all dimples of spherical opening which have a cross sectional profile which allow dimples having the same opening diameter and dimple volume to exhibit lower depth than the corresponding spherical single radius dimple of the same diameter and volume. These dimples collectively are called “reduced equivalent depth” dimples. 
     More specifically in terms of a reduced equivalent depth dual radius dimple,  FIG.  1 A  shows a cross section of a dual radius dimple,  10  used in the present invention. The dual radius dimple 10 has a surface opening portion of a complete circular shape and is formed into concave shapes which extend from their opening edges and include bottom wall portions  10   a  and peripheral wall portion  10   b.    
     In  FIG.  1 A  the line A-C represents a perpendicular drawn from the deepest portion of the dimple, point C to the boundary of the curvature of R 1  at point A. In the dual radius dimple 10, the curvature (R 1 ) of the bottom wall portion  10   a  and the curvature (R 2 ) of the peripheral wall portion  10   b , which extends from the upper end of the bottom wall portion  10   b  to the opening edge are made different from each other. 
     The dimple diameter (d 2 ) represents the diameter at the open end of the dual radius dimple (sometimes referred to as the opening diameter) or the distance between both contact points F and G of a common tangent connected between both left hand and right hand opening edges of each of the dimple 10, i.e., the distance F-G in  FIG.  1 A . In the dual radius dimple 10, the diameter (d 1 ) is represented by the distance between both left hand and right hand transition points D and E located at the boundary of the curvature R 1  of the bottom wall portion  10   a  and the curvature R 2  of the peripheral wall portion  10   b , i.e., the distance D-E in  FIG.  1 A . 
     For the dual radius dimples used in the present invention the relations between the diameters (d 1 ) and (d 2 ) are set to a relative ratio, a, according to the following equation, 
       α= d   1   /d   2  
 
     where 1&gt;α&gt;0; and
 
more preferably 0.95&gt;α&gt;0.35; and
 
even more preferably a=0.70&gt;α&gt;0.40
 
     The two cross-hatched regions in  FIG.  1 A  represent in cross section the total dimple volume, which represents the two different regions of the dimple. The lower dimple region is bordered by lower wall portion  10   a  below the line between the transition points D and E, which corresponds to a volume V1. The upper region of the dimples is that which corresponds to the region above the plane corresponding to the line between the transition points D and E and below the plane corresponding to the line between both contact points F and G of a common tangent connected between both left hand and right hand opening edges of each of the dimple 10. This upper dimple region has a volume V 2 . The total volume of the dimple V t  thus corresponds to the sum V 1 +V 2 . 
     Again, referring to  FIG.  1 B , the dual radius dimple 10, the curvature of the spherical bottom wall portion  10   a  up to transition points D and E has a radius of curvature R 1  and a diameter d 1 , a depth h 1  and a volume V 1 . The volume of this spherical bottom portion of the dimple V 1  is calculated by the expression for a spherical end cap of a sphere such that; 
         V   1   =πh   1   2 /3(3 R   1 - h   1 ) 
     Referring again to  FIG.  1 B , the upper region of the dimple as bordered by the upper wall portion,  10   b  is shown in cross section as the area between the line drawn between points F and G at opening edges of the dimple and the line drawn between the points D and E, which are the transition points between the wall portions  10   a  and  10   b . The radius of curvature of this peripheral wall portion  10   b  has a value R 2 , a diameter d 2  and a depth h 2 . 
     The perpendicular I-L in  FIG.  1 B , represents a perpendicular line drawn downwardly in the direction S from point I (the intersection of the line A-E and the boundary of the curvature of R 2  from point G) to point L, its intersection with the spherical bottom wall portion  10   a.    
     The volume V 2  of the upper dimple region may be expressed by integrating the area function between the limits m 1  and m 2  as follows: 
       ∫ m1   m2 π( b +ω( S )) 2   dS  
 
       where: 
         b =(( R   1   −R   2 )/ R   1 )( d   1 /2); and 
       ω( S )=√{square root over ( R 2 2   −S   2 )}
 
     and solving for m 1  and m 2 : 
         m   1   2   =R   2   2 −( d   1 /2− b ) 2  
 
       and 
         m   2   2   =R   2   2 −( d   2 /2− b ) 2  
 
     Referring now to  FIG.  1 B , the line A-C represents a perpendicular drawn from the deepest portion of the dimple, point C to the boundary of the curvature of R 1  at point A. Along this perpendicular, the depth (h 1 ) of the lower region of the dimple as bordered by the bottom wall portion,  10   a , corresponds to the length of the line B-C where B represents the intersection of the line D-E with the perpendicular. Similarly, the depth (h 2 ) of the upper region of the dimple as bordered by the upper wall portion,  10   b , corresponds to the length of the line B-J where J represents the intersection of the line F-G with the perpendicular. The total depth of the dimple, ht, thus corresponds to the sum h 1 +h 2 . 
     
       
      
       h 
       t 
       =h 
       1 
       +h 
       2  
      
     
     We have now found that the substitution of dual radius dimples for single radius dimples of the same dimple diameter results in a ball with increased distance. While not wishing to be bound by any theory, it is thought that the decoupling of dimple depth from dimple volume in dual radius dimples allows the use of shallower dimples to reduce drag while maintaining sufficient volume to avoid the penalty of loss of distance by increased lift, (which causes “ballooning in golf ball flight). We have also found that although the use of reduced equivalent depth dimples such as dual radius dimples allows for shallowing of the dimples while maintaining their volume, there is a limit to how shallow such dimples can go. 
       FIG.  2    shows how to calculate the dimple volume ratio, Vr, of a dimple 20, which is defined as the amount by which the total volume of a dual radius dimple approaches that of a cylinder having the same opening diameter and depth and is calculated as follows: 
         Vr   i   =V   1 /(π h   i   di   2 /4)
 
     Where Vi is the total volume of dimple i, di is the outer diameter of dimple i and h i  is the total depth of dimple i. 
     Thus, the shallower the dimples go as compared to their volume, the higher the volume ratio becomes. 
     The average dimple volume ratio (AvVr) is given by: 
     
       
         
           
             AvVr 
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 N 
               
               
                 Vri 
                 N 
               
             
           
         
       
     
     Thus, the shallowness of the dimples may be tailored from a manufacturing point of view by requiring all dimples to have the same Vr in which case the individual dimple volume ratio and the average dimple volume ratio become the same. Alternatively, if one seeks to shallow certain dimples by one amount and others by a different amount then the average volume ratio, AvVr is more descriptive. 
     It should also be noted that, at a certain shallowness, the dimples lose their aerodynamic effect. Thus, the dimple volume ratio Vr of each of the dimples used in the present invention or the average volume ratio AvVr of the dual radius dimples used in the present invention should be from about 0.5 to less than about 1, preferably from about 0.525. to about 0.75, even more preferably from about 0.55 to about 0.70. 
     The total number of dimples (Ni) employed on the golf balls of the present invention is from about 250 to about 500, preferably from aboutv275 to about 475, and even more preferably from about 300 to about 450 reduced equivalent depth dimples. Preferably the reduced equivalent depth dimples comprise dual radius dimples. 
     In addition to the total number of dimples (Ni) employed, other parameters to be considered when selecting dimples and the dimple patterns used in the golf balls of the present invention include both the total dimple volume (“TDV”) and the total surface area coverage (COV) of the dimples placed on the surface of the golf balls of the present invention. 
     The total volume of the dimples (TDV) employed on the golf balls of the present invention is calculated using the following formula, 
     
       
      
       TDV=Σ 
       i=1 
       n 
       V 
       i  
      
     
     where TDV is from about 380 to 425 mm 3 , preferably from about 385 to 415 mm 3 , more preferably from about 380 to 405 mm 3 . 
     For golf balls which have reduced distance at high headspeed but maintain distance at lower headspeed the TDV is from about 380 to about 500 mm 3 , preferably from about 380 to about 475 mm 3 , more preferably from about 380 to about 460 mm 3 . 
     The total percentage surface area coverage (COV) of the dimples placed on the surface of the golf balls of the present invention is calculated using the following formula, 
       COV=100*Σ i=1   n π( d   i   2 /4)/ A   o  
 
     Where d i  is the outer diameter of the dimple and A o  is the surface area of a golf ball surface formed by the continuation of the land area surface if the dimples where removed (where the land area is the surface of the ball lying between the dimples). 
     For the golf balls of the present invention A o  has a value of 5720 mm 2  and COV is greater than about 65%, more preferably greater than about 70%, and even more preferably greater than about 75%. 
     As a guide to understanding the layout of the dimples on the surface of the ball, certain terminology which is directly analogous to how the Earth is often described, with respect to points on its surface and with respect to the four points of the compass, will be used herein. Thus, when the golf ball sphere is depicted on a flat sheet it is in the form of a circle which has an upper and lower region which lie towards the top and bottom of the flat surface or sheet respectively and are analogous to the North and South pole regions of the globe. Similarly, the east side of the ball is depicted as being on the right side of the flat surface or sheet as you look at it and the west side of the ball is depicted as being on the left side of the flat surface or sheet as you look at it. Thus, an easterly direction is depicted as moving from the left side of the sheet to the right side and conversely a westerly direction is depicted as moving from the right side of the sheet to the left side as you look at it. 
     As shown in  FIG.  3    the spherical surface of a golf ball,  30 , like the globe, can be defined as having an equator  32  which is a great circle path around the midpoint between the poles (where a great circle path is defined by the intersection between the spherical surface and a plane which passes through the center of the sphere). For golf balls this often corresponds to the parting line or seam formed when the two mold halves used to mold the golf ball are brought together. In some cases, the dimples are separated slightly to make room for the parting line, which results in a perceptible parting line between the halves of the ball, which is coincident with the golf ball equator. In other cases, the mold halves are manufactured such the mating surfaces interlock to varying degrees when coming together such that the parting line or seam is more closely associated with the curvature of the dimples in close proximity the parting line and thus the parting line may in some cases straddle the equator of the golf ball at various points. This renders the parting line or seam less noticeable and thus are often referred to as “seamless” dimple patterns as compared the more convention patterns with a more noticeable seam. Such seamless dimple patterns include that described in U.S. Pat. No. 9,511,524 to R. Stefan and having an issue date of Dec. 6, 2016, the entire contents of which are incorporated by reference herein. The golf balls of the present invention are not limited to the type of parting line configuration selected and include both the conventional type of seam as well any of the so-called seamless dimple parting lines. In either case for the golf balls of the present invention the equatorial path  32  corresponds to the geometric midline of the sphere which is either equivalent or in close correspondence to the golf ball parting line and divides the surface of the sphere into two equal hemispheres. 
     Thus. as shown in  FIG.  3    the golf ball  30  has an equator  32 , and a North pole  34  and a South pole,  36 . The golf ball equator  32  divides the golf ball  30  into a first or North hemisphere  38  and a second or South hemisphere  40 . As also shown in  FIG.  3   , in addition to the two poles and the equator, the spherical surface of a golf ball, like the globe, can also be defined as having a primary meridian  42  which is a great circle path along the pole axis orthogonal to the equator which divides the globe into an East hemisphere  44  and West hemisphere  46 . Thus, the combination of the equator and the primary meridian effectively divide the spherical surface of a golf ball into four equal sized quadrants which can be identified (by analogy with terminology used for the globe) as the North East quadrant, NE,  48 , the North West quadrant, NW,  50 , the South East quadrant, SE,  52 , and the South West quadrant, SW,  54 . 
     Using the traditional latitude and longitude coordinate system, the golf ball has an equator  32  at latitude 0°, and a North pole  34  and a South pole  36  at latitude 90° and longitude 0° in each North hemisphere  38  and a second or South hemisphere  40  respectively. A grid system is placed on the ball in which the North East (NE) quadrant,  48 , has an equator region NEx defined by latitudes 0° to 25° N, and a region NEiE defined by longitudes 0° to 25° E and 155° to 180° E, a shoulder region NSx defined by latitudes from 25° N to 65° N, and a region NSiE defined by longitudes 25° E to 65° E and 115° E to 155° E, a pole region Px defined by latitudes 65° to 90° N, and a region NPiE defined by longitudes 65° to 115° E. 
     Similarly, the North West quadrant  50 , has an equator region NEx defined by latitudes 0° to 25° N, and a region NEiW defined by longitudes 0° to 25° W and 155° to 180° W, a shoulder region NSx defined by latitudes 25° N to less than 65° N, and a region NSiW defined by longitudes from 25° W to 65° W and from 115° E to 155° W, a pole region Px defined by latitudes 65° to 90° N, and a region NPiE defined by longitudes 65° to 115° W. 
     In order to better describe the exact placement of the dimples within the various described zones, as an alternative to the traditional latitude and longitude system, a coordinate system is set up on the surface of the sphere using a latitudinal axis θ and a longitudinal axis ϕ (as shown in  FIG.  3   ). 
     The longitudinal axis ϕ represents a passage of 360 degrees over the surface of the ball along the arc of the primary meridian  42  from the North pole  34  to the South pole  36 , (initially in a southward direction) all points on this line have a coordinate theta (θ) of 0 degrees and a coordinate phi (ϕ) from 0 degrees at the North pole  34  through a coordinate phi (ϕ) of 90 degrees (where the arc of the primary meridian  42  intersects the equator) to a coordinate phi (ϕ) of 180 degrees at the South pole  36  and further around the ball back up to the North pole to complete one full 360 degree passage around the ball. 
     Similarly, the lateral axis θ represents a passage of 360 degrees over the surface of the ball along the arc of the equator, from a coordinate theta (θ) of 0 degrees where the arc of the primary meridian  42  intersects the equator, and so on around the ball initially in an easterly direction to complete one full 360 degree passage around the hall. Thus, phi and theta are the coordinate in degrees of the center of a dimple and where phi measures the displacement longitudinally around the ball from the North pole of the ball (which is set at ϕ=0 degrees) and theta measures the displacement latitudinally eastwards from the arc of the primary meridian  42  and which is set at θ=0 degrees. Thus the North pole has coordinates of ϕ=0° and θ=0° and the South pole has coordinates of ϕ=180° and θ=0°. 
     Using this coordinate system, the golf ball may be further divided both laterally and longitudinally into separate regions using the grid system shown in  FIGS.  4 A and  5 B , in which the surface of a golf ball  30  is oriented in the cross seam direction i.e. with the seam and thus the equator in a horizontal position. 
     Referring now to  FIG.  4 A , the golf ball may be divided laterally into various lateral zones in both the North and South hemispheres (where the letter N indicates the Northern and the letter S the Southern hemisphere of the golf ball). Thus, an equatorial zone, ExN, in the first or Northern hemisphere  38  is defined as the section or zone on the ball surface occurring between the equator  32  and a line formed by a plane parallel to the equator at ϕ=65°. (The corresponding equatorial zone, E×S, in the second or South hemisphere  40  is then defined as the section or zone on the ball surface occurring between the equator  32  and a line formed by a plane parallel to the equator at ϕ=115°). 
     Similarly, a shoulder zone, SxN, in the first or Northern hemisphere  38  is defined as the section or zone on the ball surface occurring between the line formed by a plane parallel to the equator at ϕ=65° and the line formed by a plane parallel to the equator at ϕ=25°. (The corresponding shoulder zone, SxS, in the second or South hemisphere  40  is defined as the section or zone on the ball surface occurring between the line formed by a plane parallel to the equator at ϕ=115° and the line formed by a plane parallel to the equator at ϕ=155°). 
     Finally, a polar zone, PxN in the first or North hemisphere  38  is the section or zone of the spherical end cap on the ball surface formed by a plane parallel to the equator at ϕ=25° in the first or Northern hemisphere  38 . (The corresponding polar zone, PxS, in the second or Southern hemisphere  40  is the section or zone of the spherical end cap on the ball surface formed by a plane parallel to the equator at ϕ=155°. 
     Referring now to  FIGS.  4 B and  4 C , the surface of the golf ball may also be divided into various longitudinal zones (where the letter&#39;s E and W indicate the Eastern and Western hemispheres of the golf ball respectively). Thus, a zone NEiE in the Northern hemisphere  38 , is defined as collectively two regions, the first between the primary meridian arc  42  at θ=0° and the great circle arc at θ=25° and the second between the great circle arc at θ=155° and the great circle arc at θ=180°. (A zone NEiW in the Northern hemisphere  38 , is defined as collectively the two regions, the first between the great circle arc at θ=180° and the great circle arc at θ=205° and the second between the great circle arc at θ=235° and the great circle arc at θ=360° (i.e. the primary meridian  42 )). 
     Similarly, the zone NSiE in the Northern hemisphere  38 , is defined as collectively two regions, the first between the great circle arc at θ=25° and the great circle arc at θ=65° and the second between the great circle arc at θ=115° and the great circle arc at θ=155°. (The zone NSiW in the Northern hemisphere  38 , is defined as collectively two regions, the first between the great circle arc at θ=205° and the great circle arc at θ=245° and the second between the great circle arc at θ=295° and the great circle arc at θ=335°. 
     Finally, a zone NPiE in the Northern hemisphere  38 , is defined as the region between the great circle arc at θ=65° and the great circle arc at theta=115°. (A zone NPiW in the Northern hemisphere  38 , is defined as the region from the great circle arc at theta=245° to the great circle arc at theta=295°). 
     Note that these longitudinal zones are mirrored across the equator in the South hemisphere but with the notations, SEiE, SEiW, SSiE, SSiW, SPiE and SPiW. 
     There are no dimples have centers that lie on the equator. Any dimples whose centers lie on the line that separates the Ex and Sx zones and the Sx and Px in the Northern hemisphere  38  or the second or Southern hemisphere  40  (including any pole dimples if present) are adjudged to be in the Ex and Px zones in each hemisphere respectively. Similarly any dimples whose centers lie on the primary meridian (including any pole dimples if present) are adjudged to be in the Ei zone in the East hemisphere  44 . Any dimples whose centers lie on the line which separates the Ei zones from the Si zone in each of the East hemisphere  46  or West hemisphere,  44  are adjudged to be in the Ei zone in each hemisphere. Any dimples whose centers lie on a line which separates the Si zone from the Pi zone in each of the West hemisphere,  44  or East hemisphere  46  are adjudged to be in the Pi zone in each hemisphere. 
     As there is overlap between the lateral and longitudinal zones, the overlapping areas of the lateral and longitudinal zones, or the so called Overlap Zones are illustrated in  FIGS.  5 A,  5 B and  5 C  in the NE quadrant of the ball with  FIG.  5 A  being an overhead or polar view of the golf ball looking directly down through the polar axis,  FIG.  5 B  being a side view looking directly along the primary meridian axis  42  and  FIG.  5 C  another side view looking directly along an axis perpendicular to the primary meridian axis of the ball,  42 . 
     In each view, Overlap zone A represents the area of overlap between the PxN and NEiE zones, Overlap zone B represents the area of overlap between the PxN and NSiE zones, Overlap zone C represents the area of overlap between the PxN and NPiE zones, Overlap zone D represents the area of overlap between the SxN and NEiE zones, Overlap zone E represents the area of overlap between the SxN and NSiE zones, Overlap zone F represents the area of overlap between the SxN and NPiE zones, Overlap zone G represents the area of overlap between the ExN and NEiE zones, Overlap zone H represents the area of overlap between the ExN and NSiE zones, and Overlap zone I represents the area of overlap between the ExN and NPiE zones, 
     Depending on its placement on the ball, and where the coordinates of the center of dimple fall relative to the default rules of zone prority described earlier, each dimple is thus assigned to both a lateral and longitudinal zone. In one embodiment, the North and South hemispheres of the ball have substantially the same dimple arrangement which is mirrored about the equator. In other embodiments, to minimize dimple crowding problems caused by having deeper dimples in the seam area the pattern in the lower or Southern hemisphere of the ball,  40 , may be rotated about the pole axis using the so-called right-hand rule to indicate the direction of this rotation. In this method, the thumb of the right hand is pointed down the pole axis in a North to South orientation and the curl of the fingers indicates the direction of displacement of the southern hemisphere relative to the north. This would appear as a clockwise direction if viewed above and down the pole axis. In such embodiments, the lower hemisphere is a copy of upper but rotated by greater than or equal to 20 and less than or equal to about 45, preferably greater than or equal to about 25 and less than or equal to about 40, and most preferably greater than or equal to about 30 deg and less than or equal to about 35 degrees. 
     The golf balls of the present invention use dimples having a plurality of different opening diameters, The dimple diameters used in one embodiment are summarized in Table 1. In this embodiment the golf ball has dimples of 12 different diameters. In other embodiments, the golf balls of the present invention have greater than or equal to 2, preferably greater than or equal to 3, more preferably greater than or equal to 4, and most preferably greater than or equal to 5 different opening dimple diameters. For the purposes of this invention, dimples are said to have different diameters when they vary by more than 0.05 mm. 
     Each dimple preferably has an opening diameter from about 1.0 to about 6.5, preferably from about 2.0 mm to about 6.0, and more preferably from about 3.0 mm to about 5.0 mm. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Dimple Diameter Notation 
               
            
           
           
               
               
            
               
                 Dimple Diameter (mm) 
                 Notation 
               
               
                   
               
            
           
           
               
               
            
               
                 3.2 
                 d i   
               
               
                 3.3 
                 d ii   
               
               
                 3.7 
                 d iii   
               
               
                 3.8 
                 d iv   
               
               
                 4.1 
                 d v   
               
               
                 4.2 
                 d vi   
               
               
                 4.3 
                 d vii   
               
               
                 4.4 
                 d viii   
               
               
                 4.5 
                 d ix   
               
               
                 4.6 
                 d x   
               
               
                 4.7 
                 d xi   
               
               
                 4.8 
                 d xii   
               
               
                   
               
            
           
         
       
     
     Table 2 lists the coordinates of the dimples and their diameters in one embodiment of the golf balls of the present invention, 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Dimple Placement in the NE Quadrant of the Golf Ball (theta (θ) = 0-180 degs and phi (ϕ) = 0 to 90 degrees). 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Phi 
                 Theta 
                 Diameter 
                   
                 Phi 
                 Theta 
                 Diameter 
                   
                 Phi 
                 Theta 
                 Diameter 
               
               
                 Dimple # 
                 (deg) 
                 (deg) 
                 (mm) 
                 Dimple # 
                 (deg) 
                 (deg) 
                 (mm) 
                 Dimple # 
                 (deg) 
                 (deg) 
                 (mm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 0.000 
                 0.000 
                 3.20 
                 23 
                 62.504 
                 21.424 
                 4.70 
                 45 
                 40.933 
                 88.442 
                 4.55 
               
               
                 2 
                 9.486 
                 0.000 
                 3.75 
                 24 
                 62.504 
                 165.424 
                 4.70 
                 46 
                 28.776 
                 94.926 
                 4.55 
               
               
                 3 
                 17.493 
                 180.000 
                 4.45 
                 25 
                 61.706 
                 180.000 
                 4.75 
                 47 
                 33.192 
                 72.000 
                 4.65 
               
               
                 4 
                 20.818 
                 0.000 
                 4.40 
                 26 
                 40.933 
                 55.558 
                 4.55 
                 48 
                 45.502 
                 72.000 
                 4.35 
               
               
                 5 
                 9.486 
                 144.000 
                 3.75 
                 27 
                 40.933 
                 127.558 
                 4.55 
                 49 
                 50.742 
                 99.644 
                 4.75 
               
               
                 6 
                 17.493 
                 36.000 
                 4.45 
                 28 
                 28.776 
                 49.074 
                 4.55 
                 50 
                 39.196 
                 108.000 
                 4.75 
               
               
                 7 
                 20.818 
                 144.000 
                 4.40 
                 29 
                 28.776 
                 121.074 
                 4.55 
                 51 
                 52.922 
                 84.178 
                 4.30 
               
               
                 8 
                 9.486 
                 72.000 
                 3.75 
                 30 
                 33.192 
                 144.000 
                 4.65 
                 52 
                 55.872 
                 72.000 
                 3.25 
               
               
                 9 
                 17.493 
                 108.000 
                 4.45 
                 31 
                 45.502 
                 144.000 
                 4.35 
                 53 
                 64.699 
                 79.288 
                 4.70 
               
               
                 10 
                 20.818 
                 72.000 
                 4.40 
                 32 
                 50.742 
                 27.644 
                 4.75 
                 54 
                 62.504 
                 93.424 
                 4.70 
               
               
                 11 
                 40.933 
                 16.442 
                 4.55 
                 33 
                 50.742 
                 44.356 
                 4.75 
                 55 
                 61.706 
                 108.000 
                 4.75 
               
               
                 12 
                 40.933 
                 160.442 
                 4.55 
                 34 
                 50.742 
                 116.356 
                 4.75 
                 56 
                 72.932 
                 173.410 
                 4.60 
               
               
                 13 
                 28.776 
                 22.926 
                 4.55 
                 35 
                 39.196 
                 36.000 
                 4.75 
                 57 
                 76.015 
                 5.256 
                 3.65 
               
               
                 14 
                 28.776 
                 166.926 
                 4.55 
                 36 
                 52.922 
                 59.822 
                 4.30 
                 58 
                 83.979 
                 23.695 
                 4.50 
               
               
                 15 
                 33.192 
                 0.000 
                 4.65 
                 37 
                 52.922 
                 131.822 
                 4.30 
                 59 
                 83.979 
                 167.695 
                 4.50 
               
               
                 16 
                 45.502 
                 0.000 
                 4.35 
                 38 
                 55.872 
                 144.000 
                 3.25 
                 60 
                 85.355 
                 0.000 
                 4.10 
               
               
                 17 
                 50.742 
                 171.644 
                 4.75 
                 39 
                 64.699 
                 64.712 
                 4.70 
                 61 
                 84.899 
                 11.758 
                 4.20 
               
               
                 18 
                 39.196 
                 180.000 
                 4.75 
                 40 
                 64.699 
                 136.712 
                 4.70 
                 62 
                 84.899 
                 155.758 
                 4.20 
               
               
                 19 
                 52.922 
                 12.178 
                 4.30 
                 41 
                 64.699 
                 151.288 
                 4.70 
                 63 
                 83.787 
                 180.000 
                 4.50 
               
               
                 20 
                 52.922 
                 156.178 
                 4.30 
                 42 
                 62.504 
                 50.576 
                 4.70 
                 64 
                 74.003 
                 16.478 
                 4.40 
               
               
                 21 
                 55.872 
                 0.000 
                 3.25 
                 43 
                 62.504 
                 122.576 
                 4.70 
                 65 
                 74.003 
                 160.478 
                 4.4 
               
               
                 22 
                 64.699 
                 7.288 
                 4.70 
                 44 
                 61.706 
                 36.000 
                 4.75 
                 66 
                 72.932 
                 29.410 
                 4.6 
               
               
                 67 
                 72.932 
                 42.590 
                 4.6 
                 77 
                 74.003 
                 127.522 
                 4.4 
               
               
                 68 
                 76.015 
                 138.744 
                 3.65 
                 78 
                 72.932 
                 101.410 
                 4.6 
               
               
                 69 
                 76.015 
                 149.256 
                 3.65 
                 79 
                 72.932 
                 114.590 
                 4.6 
               
               
                 70 
                 83.979 
                 48.305 
                 4.50 
                 80 
                 76.015 
                 66.744 
                 3.65 
               
               
                 71 
                 83.979 
                 120.305 
                 4.50 
                 81 
                 76.015 
                 77.256 
                 3.65 
               
               
                 72 
                 85.355 
                 144.000 
                 4.10 
                 82 
                 83.979 
                 95.695 
                 4.5 
               
               
                 73 
                 84.899 
                 60.242 
                 4.2 
                 83 
                 85.355 
                 72.000 
                 4.1 
               
               
                 74 
                 84.899 
                 132.242 
                 4.2 
                 84 
                 84.899 
                 83.758 
                 4.2 
               
               
                 75 
                 83.787 
                 36.000 
                 4.5 
                 85 
                 83.787 
                 108.000 
                 4.5 
               
               
                 76 
                 74.003 
                 55.522 
                 4.4 
                 86 
                 74.003 
                 88.478 
                 4.4 
               
               
                   
               
            
           
         
       
     
     In this embodiment the pattern in the Northern hemisphere is repeated in the Southern hemisphere by mirroring across the equator and the pattern in the North Eastern and South Eastern quadrants is repeated in the North Western and South Western quadrants respectively by mirroring across the primary meridian. 
     Thus, in this embodiment, as there are no dimples on the equator, the total of 322 dimples on the ball are distributed with 161 dimples in each of the Northern and Southern hemispheres and the pattern in the Northern hemisphere is duplicated in the Southern hemisphere. 
     As shown in Table 3, in analyzing each quadrant of the golf ball in the Northern hemisphere, the golf ball in this embodiment (having a total of 322 dual radius dimples, with 161 dimples in the Northern hemisphere) had 29 dimples in the EiE zone in the NE quadrant (or about 9% of the total no. of dimples), 34 dimples in the SiE zone in the NE quadrant (or about 11% of the total no, of dimples) and 23 dimples in the PiE zone in the NE quadrant (or about 7% of the total no. of dimples). 
     The golf ball also had 18 dimples in the EiW zone in the NW quadrant (or about 6% of the total no. of dimples), 34 dimples in the SiW zone in the NW quadrant (or about 11% of the total no. of dimples) and 23 dimples in the NW zone in the NW quadrant (or about 7% of the total no. of dimples). 
     Further, in this embodiment, as shown in Table 3, of the total of 322 dimples on the ball there are 86 dimples in the North Eastern quadrant  48  including a pole dimple (Dimple #1). This layout is duplicated in the North Western  50  quadrant by mirroring about the primary meridian  42 . The shared dimples include the pole dimple (Dimple #1) and the 10 shared dimples (dimple #&#39;s 2, 3, 4, 15, 16, 18, 21, 25, 60 and 63) which lie on the primary meridian  42 . There are a total of 11 shared dimples which are assigned to the zones in the Northeast quadrant but not the Northwest quadrant. 
     More specifically, within the two quadrants in each of the North and South hemispheres these 11 shared dimples are distributed all in the EiE zone in the longitudinal sections in each of the North and South hemispheres and are distributed in the lateral sections in each of the North and South hemispheres as follows; four shared dimples assigned to the PxE zone (dimple #&#39;s 1, 2 3 and 4); five shared dimples assigned to the SxE zone (dimple #&#39;s 15, 16, 18, 21 and 25); and two shared dimples assigned to the ExE zone (dimple #&#39;s 60 and 63). 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Number of Dimples Assigned to Each Lateral and Longitudinal 
               
               
                 Zone in the Northern hemisphere by Quadrant 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                   
                   
                 % of Total No. of 
               
               
                   
                 Quadrant 
                 Zone 
                 No. of Dimples 
                 Dimples 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 NE 
                 ExN 
                 31 
                 9.6 
               
               
                   
                 NE 
                 SxN 
                 45 
                 14.0 
               
               
                   
                 NE 
                 PxN 
                 10 
                 3.1 
               
               
                   
                 Total 
                   
                 86 
                 27 
               
               
                   
                 NE 
                 NEiE 
                 29 
                 9.0 
               
               
                   
                 NE 
                 NSiE 
                 34 
                 10.6 
               
               
                   
                 NE 
                 NPiE 
                 23 
                 7.1 
               
               
                   
                 Total 
                   
                 86 
                 27 
               
               
                   
                 NW 
                 ExN 
                 29 
                 9.0 
               
               
                   
                 NW 
                 SxN 
                 40 
                 12.4 
               
               
                   
                 NW 
                 PxN 
                 6 
                 1.9 
               
               
                   
                 Total 
                   
                 75 
                 23 
               
               
                   
                 NW 
                 NEiW 
                 18 
                 5.6 
               
               
                   
                 NW 
                 NSiW 
                 34 
                 10.6 
               
               
                   
                 NW 
                 NPiW 
                 23 
                 7.1 
               
               
                   
                 Total 
                   
                 75 
                 23 
               
               
                   
                   
               
               
                   
                 *For this embodiment the total no. of dimples was 322 
               
            
           
         
       
     
     Thus, the Northeast quadrant has a total of 86 and the Northwest quadrant a total of 75 dimples to give a total of 161 dimples in the Northern hemisphere. This layout is mirrored in the Southern hemisphere about the equator to account for all 322 dimples. In other embodiments, the occurrence of pole dimples centered at the apex of the North and South hemispheres is optional. 
     As a result of division of the ball surface both longitudinally and laterally the surface is now divided into overlapping zones of the golf ball as shown in the various views in  FIGS.  5 A- 5 C and  6 A- 6 D , Table 4 shows the coordinate ranges for the dimples in each Overlap zone. No dimples have centers that lie on the equator. As summarized in Table 4, in this embodiment having a total of 322 dual radius dimples, there were 4 dimples in overlap zone A in the NE quadrant (or about 1% of the total no. of dimples), 3 dimples in overlap zone B in the NE quadrant (or about 1% of the total no. of dimples), 3 dimples in overlap zone C in the NE quadrant (or about 1% of the total no. of dimples), 15 dimples in overlap zone in the NE quadrant (or about 5% of the total no. of dimples), 19 dimples in overlap zone E in the NE quadrant (or about 6% of the total no. of dimples), 11 dimples in overlap zone F in the NE quadrant (or about 3% of the total no. of dimples) 10 dimples in overlap zone Ci in the NE quadrant (or about 3% of the total no. of dimples), 12 dimples in overlap zone H in the NE quadrant (or about 4% of the total no. of dimples) and 9 dimples in overlap zone I in the NE quadrant (or about 3% of the total no. of dimples). 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Dimple Coordinates and Total Number of Dimples Assigned to Each 
               
               
                 Overlap Zone in North Eastern Quadrant of the Golf Ball*. 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                 Overlap 
                   
                 No. of 
                   
               
               
                 Quadrant 
                 Zones 
                 Zone 
                 Dimple Coordinates 
                 Dimples 
                 % 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 NE 
                 PxN, 
                 A 
                 ϕ = 0°-25° 
                 4 
                 1.2 
               
               
                   
                 NEiE 
                   
                 θ = 0°-25° and 155°-180° 
               
               
                 NE 
                 PxN, 
                 B 
                 ϕ = 0°-25° 
                 3 
                 0.9 
               
               
                   
                 NSiE 
                   
                 θ = &gt;25°-&lt;65° and &gt;115°-&lt;155° 
               
               
                 NE 
                 PxN, 
                 C 
                 ϕ = 0°-25° 
                 3 
                 0.9 
               
               
                   
                 NPiE 
                   
                 θ = 65°-115° 
               
               
                 NE 
                 SxN, 
                 D 
                 ϕ = &gt;25°-&lt;65° 
                 15 
                 4.7 
               
               
                   
                 NEiE 
                   
                 θ = 0°-25° and 155°-180° 
               
               
                 NE 
                 SxN, 
                 E 
                 ϕ = &gt;25°-&lt;65° 
                 19 
                 5.9 
               
               
                   
                 NSiE 
                   
                 θ = &gt;25°-&lt;65° and &gt;115°-&lt;155° 
               
               
                 NE 
                 SxN, 
                 F 
                 ϕ = &gt;25°-&lt;65° 
                 11 
                 3.4 
               
               
                   
                 NPiE 
                   
                 θ = 65°-115° 
               
               
                 NE 
                 ExN, 
                 G 
                 ϕ = 65°-90° 
                 10 
                 3.1 
               
               
                   
                 NEiE 
                   
                 θ = 0°-25° and 155°-180° 
               
               
                 NE 
                 ExN, 
                 H 
                 ϕ = 65°-90° 
                 12 
                 3.7 
               
               
                   
                 NSiE 
                   
                 θ = &gt;25°-&lt;65° and &gt;115°-&lt;155° 
               
               
                 NE 
                 ExN, 
                 I 
                 ϕ = 65°-90° 
                 9 
                 2.8 
               
               
                   
                 NPiE 
                   
                 θ = 65°-115° 
                   
                   
               
               
                 Total 
                   
                   
                   
                 86 
                 27 
               
               
                   
               
            
           
         
       
     
     Each of these numbers were duplicated in the South East quadrant, which pattern is the mirrored about the equator and primary meridian to complete the dimple pattern over the whole ball. The reason for the occurrence of inequalities in some of the dimple coordinate definitions arises from the assignment of shared dimples to a default region, when the center of its circular opening resides on a boundary line between different zones. 
     In addition to location, diameters and numbers in each zone, the depths and volumes of the dimples on the ball are selected such that the aerodynamic force experienced by the spinning ball in flight is closely balanced in both the cross seam and inseam orientations. Without wishing to be bound by any theory, it can be appreciated that if the depth of dimples in the lateral sections of the ball approximate those in the longitudinal sections of the ball a more symmetrical balance of the aerodynamic forces experienced by a spinning ball may be achieved. 
     The flight performance (including the ability to control the distance of the golf ball and at the same time improve the inseam/cross seam dispersion) of golf balls with dual radius dimples may be achieved by selecting a Volume ratio for the dimples while and maintaining each dimples diameter and alpha (a) value at 0.555 and 0.5 respectively and setting a total depth and for dual radius dimples the magnitude of the inner and outer radii of curvature (R1 and R2). 
     In general, for the golf balls of the present invention, the depth of the reduced equivalent depth dual radius dimples are from about 0.060 to about 0.200 mm, preferably from about 0.065 to about 0.180 mm, and more preferably from about 0.070 to about 0.160 mm. More specifically, for the golf balls of the present invention, the depth of the reduced equivalent depth dual radius dimples in the Ex zone closest to the parting line of the golf hall are constrained to be greater than about 0.145 mm. preferably greater than about 0.150 mm, even more preferably greater than about 0.155 mm and most preferably greater than about 0.160 mm. 
     The average total volumes of the dimples in in the regions Ex, Sx, Px, Ei, Si, and Pi, ( V   ex    V   sx    V   px    V   ei    V   si  and  V   pi  respectively) is obtained by summing the dimple volumes (V) of all the dimples in a given region and dividing it by the number of dimples (N) in that region. Note that a dimple is said to be in a given region when the center of its circular opening resides within the latitudinal or longitudinal limits of that region as defined above. Thus, for example the average dimple volume in the Ex region,  V ex, is determined by the following summation: 
     
       
         
           
             
               
                 V 
                 _ 
               
               ⁢ 
               ex 
             
             = 
             
               
                 
                   ∑ 
                   x 
                 
                 
                   N 
                   = 
                   1 
                 
               
               
                 V 
                 Nex 
               
             
           
         
       
     
     For the golf balls of the present invention, the ratios 
     
       
         
           
             
               
                 
                   V 
                   _ 
                 
                 ⁢ 
                 ex 
               
               
                 
                   V 
                   _ 
                 
                 ⁢ 
                 ei 
               
             
             , 
             
               
                 
                   
                     V 
                     _ 
                   
                   ⁢ 
                   sx 
                 
                 
                   
                     V 
                     _ 
                   
                   ⁢ 
                   si 
                 
               
               ⁢ 
                   
               and 
               ⁢ 
               
                   
                   
                      
                   
               
               ⁢ 
               
                 
                   
                     V 
                     _ 
                   
                   ⁢ 
                   px 
                 
                 
                   
                     V 
                     _ 
                   
                   ⁢ 
                   pi 
                 
               
             
           
         
       
     
     are each all greater than or equal to 0.60 and less than or equal to 1.25, preferably each all greater than or equal to 0.65 and less than or equal to 1.20, and even more preferably each all greater than or equal to 0.7 and less than or equal to 1.15. 
     We have also surprisingly found that improvement in inseam versus cross seam distance symmetry for golf balls having dual radius dimples may be obtained by controlling the relative ratios of the average dimple depth ( h ) in the regions Ex, Sx, Px, Ei, Si, and Pi ( h ex,  h sx,  h px,  h ei,  h si and  h pi respectively). 
     The average dimple depth in a given region is obtained by summing the dimple depths (h) of all golf balls in a given region and dividing it by the number of dimples (N) in that region. Note that a dimple is said to be in a given region when the center of its circular opening resides within the latitudinal and/or longitudinal limits of that region as defined above. Thus, for example the average dimple depth in the ExN region,  h ex, is determined by the following summation where Nex is the no. of dimples in the specified region Ex zone and h is the total depth of these dimples in the specified regions Ex zone: 
     
       
         
           
             
               
                 h 
                 ¯ 
               
               ⁢ 
               e 
               ⁢ 
               x 
             
             = 
             
               
                 ∑ 
                 
                   N 
                   = 
                   1 
                 
                 x 
               
               
                 h 
                 Nex 
               
             
           
         
       
     
     Similarly, if the specified region of interest is the NE quadrant,  h ex would be the average depth of the dimples in the ExN region of that zone. Similarly the value of  h ei in that quadrant would be the average depth of the dimples in the NEiE zone and so on. If the specified region of interest is Overlap Zone N then the value of hex in that region would be the average depth of the dimples in the SxN region of that overlap zone and the value of hei in that quadrant would be the average depth of the dimples in the NSiW zone.q 
     For the golf balls of the present invention, the average depth of the dimples namely ( h ex,  h sx,  h px,  h ei,  h si and  h pi) in either the North East or North West quadrant of the golf ball, are each of from about 0.060 to about 0.200 mm, preferably of from about 0.065 to about 0.180 mm, more preferably of from about 0.070 to about 0.160 mm. 
     For the golf balls of the present invention, the ratios  h ex/ h ei,  h sx/ h si, and  h px/ h pi in either the North East or North West quadrant of the golf ball are each all greater than or equal to 0.75 and less than or equal to 1.20, preferably each all greater than or equal to 0.78 and less than or equal to 1.15, and even more preferably each all greater than or equal to 0.80 and less than or equal to 1.10. 
     In addition to prescribing the above-described ratios of  h ex/ h ei,  h sx/ h si, and  h px/ h pi in a given region, we have also found that the improvements in the in seam versus cross seam distance dispersion symmetry for such golf balls having dual radius dimples results from the balancing of the dimple effect on the aerodynamic load on the ball as the ball rotates through the air. Applicants have found that this can be accomplished by selecting the dimple depths such that changes in the ratios of  h ex/ h ei,  h sx/ h si and  h px/ h pi in the Northern hemisphere are maintained within a certain range. 
     More specifically, the golf ball is placed in the cross seam orientation and an original or initial reference region grid or window placement established around the pole to pole axis with the equator separating the North and South hemispheres and the primary meridian separating the East and West hemispheres. In the original reference region window placement:
         a) the equatorial reference zone ExN, the shoulder reference zone SxN and the pole reference zone PxN were each located as previously defined in the North East quadrant of the golf ball; and   b) the reference zone NEiE the reference zone NSiE and the reference zone NPiE were each located as previously defined in in the North East quadrant of the golf ball.       

     The ball initially in the reference placement is then rotated around the polar axis by three degrees while maintaining the grid in its original orientation and spatial coordinates. The grid in the original reference region position is then applied to the partially rotated golf ball and the new average dimple depths in the rotated regions  h ex r    h ei r ,  h sx r ,  h si r ,  h pi r  and  h pi r  and their relative ratios  h ex r / h ei r ,  h sx r / h si r , and  h px r / h pi r  determined. Note that a dimple is said to be in a given region when the center of its circular opening resides within the latitudinal or longitudinal limits of that reference region as defined above. 
       FIG.  7    shows the observed change in each of the depth ratios of these ratios in the North East quadrant of the golf ball in original reference region window where θ represents the degrees of rotation about its polar axis for one embodiment of the golf ball of the present invention. For clarity, the determination of the minima and maxima of each of these ratios of Δe, Δs and Δp was only shown for the Δp and Δp mid  determination in  FIG.  7    but the same analysis method is used for the determination of Δe and Δe mid  and Δs and Δs mid . 
     This magnitude of the variation in the ratios of  h ex r / h ei r ,  h sx r / h si r  and  h px r / h pi r  measured when the ball is rotated from 0 to 360 degrees is then expressed as a percentage of the midline value or a percent symmetry variation i.e. % Δe, % Δs and % Δp respectively, which are calculated as follows, 
       %Δ e =(Δ e/Δe   mid )×100;
 
       %Δ s =(Δ s/Δs   mid )×100; and
 
       %Δ p =(Δ p/Δp   mid )×100
 
     For the golf balls of the present invention, % Δe, % Δs and % Δp are each preferably greater than 0 but less than about 7%, more preferably each greater than about 0.5% but less than about 6.5%, and even more preferably each greater than about 1% but less than about 6%. 
     In other embodiments of the golf balls of the present invention, the golf ball dimple patterns may also be laid out by initially projecting regular polyhedra including but not limited to triangular bipyramids, quadrilateral bipyramids, pentagonal bipyramids, hexagonal bipyramids, heptagonal bipyramids, decahedral bipyramids and dodecahedral bipyramids onto the surface of the hall and placing the reduced equivalent depth dimples within the faces of the projected polyhedron. The grid system as described herein may then be overlaid on the projected polyhedron to enable the previously prescribed average depths, ( h ex,  h sx,  h px,  h ei,  h si and  h pi), average depth ratios ( h ex/ h ei,  h sx/ h si and  h px/ h pi) and the values of % Δe, % Δs and % Δp associated with the golf balls rotational symmetry. The grid system is overlaid such that the primary meridian coincides with one of the sides of the repeating triangles in the regular polyhedra. In some embodiments, to minimize dimple crowding problems caused by having deeper dimples in the seam area the pattern in the lower or Southern hemisphere of the ball,  40 , may be rotated about the pole axis using the so-called right-hand rule to indicate the direction of this rotation. In this method, the thumb of the right hand is pointed down the pole axis in a North to South orientation and the curl of the fingers indicates the direction of displacement of the southern hemisphere relative to the north. This would appear as a clockwise direction if viewed above and down the pole axis. In such embodiments, the lower hemisphere is a copy of upper but rotated by greater than or equal to 20 and less than or equal to about 45, preferably greater than or equal to about 25 and less than or equal to about 40, and most preferably greater than or equal to about 30 deg and less than or equal to about 35 degrees 
     In one embodiment, the golf ball dimple pattern is laid out from the projection of a regular pentagonal bipyramid on the golf ball surface and overlay of the previously defined grid zones. As shown in the side elevation view of the Northern hemisphere in  FIG.  8   , each of the five spherical repeating spherical triangle of the pentagonal pyramid has a vertex at the North pole  34  with one of the sides of the five spherical repeating spherical triangle of the pentagonal pyramid defining the primary meridian  42  (θ=0 degrees) and the other side corresponds to the arc at θ=72 degrees,  66 , with the base of the triangle defined by the portion of the equator  32  between the intersection of these arcs. The projection of the grid on this surface is shown as described previously with the arcs of the primary meridian at θ=72 degrees  42 . and the arcs at θ=25 degrees, 56, and θ=65 degrees,  62  and at θ=90 degrees,  60 , which serve to define the visible portion of the NEE, NSiE and NPiE zones respectively and by the arcs at ϕ=25 degrees, and ϕ=65 degrees which in combination with the equator portion  32  ϕ=90 degrees serve to define to define the visible portions of the PxN, SxN and ExN zones respectively. The pentagonal pyramid is projected on each of the northern and southern hemispheres of the ball, when viewed in a cross seam orientation, with each hemisphere connected by their bases. 
     As shown in  FIG.  9    the dimples are placed into each of the five repeating spherical triangles of the pentagonal pyramid such that the pattern within each is symmetrical about a mirror plane  68  passing through the pole  34  and the geometric center of the spherical triangle to the midpoint of the base (dashed line  68  in  FIG.  9   ). The pattern of the dimples which lie on or within the edges of spherical triangle formed by the primary meridian,  42 , the mirror plane  68 , and the portion of the equator  32  between the intersection of these arcs thus represent the minimum repeating pattern. Thus, the pattern within the five spherical triangles is copied every 72 degrees within each hemisphere, given the pentagonal bipyramid projection upon which it as based and the pattern within the minimum repeating pattern is copied every 36 degrees.  FIG.  9    shows the placement of the dimples within the minimum repeating pattern with the dimple numbers and their coordinates and diameters corresponding to the dimples summarized in Table 2. The dimple depths were selected such that that in the various section of the grid pattern superimposed on the pentagonal bipyramid they exhibit the previously described values of depths, h, average depths,  h ex  h sx,  h px, and  h ei,  h si and  h pi, the depth ratios  h ex/ h ei,  h sx/ h si, and  h px/ h pi and the values of % Δe, % Δs and % Δp in the North eastern quadrant for dimples laid out using the grid system and without a polygonal projection. 
       FIG.  10    illustrates a golf ball with one of the eight spherical triangles in the Northern hemisphere resulting from the projection of a regular octagonal bipyramid on the golf balls surface, and overlay of the previously defined grid zones. The repeating spherical triangle of the octahedron has a vertex at the North pole  34  and the sides of the triangle correspond to the arcs at the primary meridian  42  (θ=0 degrees) and θ=45 degrees,  68 , and the portion of the equator  32  between the intersection of these arcs. The projection of the grid on this surface is shown as described previously with the arcs of the primary meridian at (θ=0 degrees  42 , and the arcs at (θ=25 degrees,  56 , and (θ=65 degrees,  62  and at θ=90 degrees,  60 , which serve to define the visible portion of the NEiE, NSiE and NPiE zones respectively and by the arcs at ϕ=25 degrees, and θ=65 degrees which in combination with the equator portion  32  ϕ=90 degrees serve to define the visible portions of the PxN, SxN and ExN zones respectively. 
       FIG.  11    illustrates an embodiment where the golf ball pattern is laid out from the projection of a regular decahedral bipyramid on the golf ball surface golf ball and the overlay of the previously defined grid zones. The only difference with that of the layout pattern described for  FIG.  10    is that the sides of the spherical triangle correspond to the arcs at the primary meridian  42  (θ=0 degrees and θ=36 degrees,  70 , and the portion of the equator  32  between the intersection of these arcs form one of the ten spherical triangles in the Northern hemisphere. 
     Thus in summary, the total number of reduced equivalent depth dimples (Ni) employed in the dimple patterns used on the golf balls of the present invention have from about 250 to about 500, preferably from about 275 to about 475, and even more preferably from about 300 to about 450 reduced equivalent depth dimples. Preferably the reduced equivalent depth dimples comprise dual radius dimples. 
     The total volume of the reduced equivalent depth dimples (TDV) employed on the golf balls of the present invention is from about 380 to about 530 mm 3 , preferably from about 380 to about 475 mm 3 , more preferably from about 380 to about 460 mm 3 , or from about 380 to 425 mm 3 , preferably from about 385 to 415 mm 3 , more preferably from about 380 to 405 mm 3 . 
     The total percentage surface area coverage (COV) of the reduced equivalent depth dimples placed on the surface of the golf balls of the present invention is greater than about 65%, more preferably greater than about 70%, and even more preferably greater than about 75%. 
     The volume ratios, Vr, of the individual reduced equivalent depth dual radius dimples or the average volume ratio (AvVr) of the reduced equivalent depth dual radius dimples used in the present invention should each be from about 0.5 to less than about 1, preferably from about 0.525. to about 0.75, even more preferably from about 0.55 to about 0.70. 
     The reduced equivalent depth dimples used in the present invention have a dimple diameter from about 1.0 to about 6.5, preferably from about 2.0 mm to about 6.0, and more preferably from about 3.0 mm to about 5.0 mm. 
     For the golf balls of the present invention, the depth of the dimples are from about 0.060 to about 0.200 mm, preferably from about 0.065 to about 0.180 mm, more preferably from about 0.070 to about 0.160 mm. 
     For the golf balls of the present invention, the depth of the reduced equivalent depth dual radius dimples in the Ex region and closest to the parting line of the golf ball are constrained to be greater than about 0.145 mm, preferably greater than about 0.150 mm, even more preferably greater than about 0.155 mm. 
     The dual radius dimples used in the present invention have a radius of curvature (R 1 ) of the bottom wall portion from about 10 to about 30, preferably from about 13 mm to about 27 mm and a radius of curvature (R 2 ) of the upper wall portion from about 10 to about 28 and preferably from about 6 mm to about 11 mm. 
     For the reduced equivalent depth dual radius dimples used in the present invention the relative ratio of the diameters, d 1 /d 2  of the dimples, or a, is greater than 0 and less than about 1, preferably is greater than or equal to 0.35 and less than or equal to 0.95 and more preferably is greater than or equal to 0.40 and less than or equal to 0.70. 
     For the golf balls of the present invention, the ratios of the average volumes of the reduced equivalent depth dual radius dimples in each region, 
     
       
         
           
             
               
                 
                   V 
                   _ 
                 
                 ⁢ 
                 ex 
               
               
                 
                   V 
                   _ 
                 
                 ⁢ 
                 ei 
               
             
             , 
             
               
                 
                   
                     V 
                     _ 
                   
                   ⁢ 
                   sx 
                 
                 
                   
                     V 
                     _ 
                   
                   ⁢ 
                   si 
                 
               
               ⁢ 
                   
               and 
               ⁢ 
               
                   
                   
                      
                   
               
               ⁢ 
               
                 
                   
                     V 
                     _ 
                   
                   ⁢ 
                   px 
                 
                 
                   
                     V 
                     _ 
                   
                   ⁢ 
                   pi 
                 
               
             
           
         
       
     
     are each all greater than or equal to 0.60 and less than or equal to 1.25, preferably each all greater than or equal to 0.65 and less than or equal to 1.20, and even more preferably each all greater than or equal to 0.7 and less than or equal to 1.15. 
     For the golf balls of the present invention, the average depth of the dimples in each region, namely,  h ex  h sx,  h px, and  h ei,  h si and  h pi are each from about 0.060 to about 0.200 mm, preferably from about 0.065 to about 0.180 mm, more preferably from about 0.070 to about 0.17 mm, even more preferably from about 0.070 to about 0.160 mm. 
     For the golf balls of the present invention, the depth ratios of the reduced equivalent depth dual radius dimples in the North Eastern quadrant,  h ex/ h ei,  h sx/ h si, and  h px/ h pi are each all greater than or equal to 0.75 and less than or equal to 1.20, preferably each all greater than or equal to 0.78 and less than or equal to 1.15, and even more preferably each all greater than or equal to 0.80 and less than or equal to 1.10. 
     This magnitude of the variation in the ratios of  h ex r / h ei r ,  h sx r / h si r  and  h px r / h pi r  in the North Eastern quadrant measured when the ball is rotated from 0 to 360 degrees about its polar or axis, expressed as the percentages % Δe, % Δs and % Δp respectively. are each preferably greater than 3 but less than about 7%, more preferably each greater than about 0.5% but less than about 6.5%, and even more preferably each greater than about 1% but less than about 6%. 
     Each quadrant of the golf ball includes dual radius dimples having greater than or equal to 2, preferably greater than or equal to 3, more preferably greater than or equal to 4, and most preferably greater than or equal to 5 different opening dimple diameters. For the purposes of this invention, dimples are said to have different diameters when they vary by more than 0.05 mm. 
     For the golf balls of the present invention, the percentage of the total number of dimples in the ExN zone in the North Eastern quadrant is from about 15 to about 25%, preferably from about 10% to about 20% and most preferably from about 5% to about 15% of the total number of dimples (Ni) on the golf ball. 
     The percentage of the total number of dimples in the SxN zone in the in the North Eastern quadrant is from about 20% to about 30%, preferably from about 15% to about 25% and most preferably from about 10% to about 20% of the total number of dimples (Ni) on the golf ball. 
     The percentage of the total number of dimples in the PxN zone in the North Eastern quadrant is from about 1% to about 15%, preferably from about 2% to about 10% and most preferably from about 3% to about 7% of the total number of dimples (Ni) on the golf ball. 
     For the golf balls of the present invention, the percentage of the total number of dimples in the North Eastern quadrant in the NEiE zone is from about 15 to about 25%, preferably from about 10% to about 20% and most preferably from about 5% to about 15% of the total number of dimples (Ni) on the golf ball. 
     The percentage of the total number of dimples in the NSiE zone in the North Eastern quadrant is from about 15 to about 25%, preferably from about 10% to about 20% and most preferably from about 5% to about 15% of the total number of dimples (Ni) on the golf ball. 
     The percentage of the total number of dimples in the NPiE zone in the North Eastern quadrant is from about 15 to about 25%, preferably from about 10% to about 20% and most preferably from about 5% to about 15% of the total number of dimples (Ni) on the golf ball. 
     The percentage of the total number of dimples in Overlap zones A, B and C are from 0 to about 4, preferably from 0 to about 3 and more preferably from 0 to about 2% of the total number of dimples on the ball. These dimples have a total depth from about 0.30 to about 0.70, preferably from about 0.35 to about 0.65 and more preferably from about 0.40 to about 0.60 mm, and an average depth ( h   A ,  h   B  and  h   C  respectively) from about 0.02 to about 0.40, preferably from about 0.05 to about 0.30 and more preferably from about 0.10 to about 0.20 mm. 
     The percentage of the total number of dimples in Overlap zones D, E and F is from about 1.0 to about 7.0, preferably from about 2.0 to about 6.5 and more preferably from about 3.0 to about 6.0% of the total number of dimples on the ball. These dimples have a total depth from about 0.75 to about 4.5, preferably from about 1.0 to about 4.0 and more preferably from about 1.50 to about 3.50 mm, and an average depth ( h   D ,  h E and  h   F  respectively) from about 0.05 to about 0.30, preferably from about 0.05 to about 0.25 and more preferably from about 0.10 to about 0.20 mm. 
     The percentage of the total number of dimples in Overlap zones G, H and I is from about 1.0 to about 7.0, preferably from about 2.0 to about 6.5 and more preferably from about 2.5 to about 6.0% of the total number of dimples on the ball. These dimples have a total depth from about 0.75 to about 3.0, preferably from about 1.0 to about 2.5 and more preferably from about 1.5 to about 2.0 mm, and an average depth ( h   G ,  h   H  and  h   I  respectively) from about 0.05 to about 0.3, preferably from about 0.10 to about 0.20 and more preferably from about 0.150 to about 0.17 mm. 
     Given the ubiquity of synthetic polymers and their wide range of properties it is not surprising that a large number of polymers along with their attendant stabilizing additive and filler packages are generally considered useful for making the components of the golf balls of the present invention including their core, intermediate layer(s) and outer cover layer. These include, without limitation the materials and attendant manufacturing methods described in U.S. Pat. No. 8,047,933, column 7 line 14 to column 22, line 6, the contents of which are herein incorporated by reference. 
     More specific examples of particular polymeric materials useful for making golf ball cores, optional intermediate layer(s) and outer covers, again without limitation, are provided below. 
     A most preferred polymeric material for the outer cover layer of the golf ball of the present invention is a polyurea or polyurethane, prepared by combining a diisocyanate with either a polyamine or polyol respectively, and one or more chain extenders (in the case of a thermoplastic polyurea or polyurethane) or curing agents (in the case of a thermoset polyurea or polyurethane) The final composition may advantageously be employed as an intermediate layer in a golf ball and even more advantageously as an outer cover layer. 
     The diisocyante and polyol or polyamine components may be previously combined to form a prepolymer prior to reaction with the chain extender or curing agent. Any such prepolymer combination is suitable for use in the present invention. Commercially available prepolymers include LFH580, LFH120, LFH710, LFH1570, LF930A, LF950A, LF601D, LF751D, LFG963A, LFG640D. 
     In the case of a thermoset polyurethane or polyurea, most preferred prepolymers are the polytetramethylene ether glycol terminated toluene diisocyanate prepolymers including those available from Uniroyal Chemical Company of Middlebury, Conn., under the trade name ADIPRENE® LF930A, LF950A, LF601D, and LF751D. 
     Preferably the curative may comprise a slow-reacting diamine or a fast-reacting diamine or any and all mixtures thereof. Such diamines include dimethylthio-2,4-toluenediamine sold under the trade name Ethacure® 300 and diethyl-2,4-toluenediamine sold under the trade name Ethacure® 100 both by Albermarle Corporation, Other curatives or additional additives may be added to control the cure rate of the thermoset mixture including diols polyols and polymeric diols and polyols. On such diol is butane 1,4-diol, 
     Because the polyureas or polyurethanes used to make the covers of such golf balls generally contain an aromatic component, e.g., aromatic diisocyanate, polyol, or polyamine, they are susceptible to discoloration upon exposure to light, particularly ultraviolet (UV) light. To slow down the discoloration, light and UV stabilizers, e.g., TINUVIN® 770, 765, 571 and 328, are added to these aromatic polymeric materials. In addition, non-aromatic components may be used to minimize this discoloration, one example of which is described in U.S. Pat. No. 7,879,968, filed on May 31, 2007, the entire contents of which are hereby incorporated by reference. 
     The formulations and methods of making the thermoset polyurethane and polyurea used to form the outer cover layers of the golf balls of the present invention are more fully disclosed in U.S. Pat. No. 6,793,864 issuing on Sep. 21, 2004, the entire contents of which are incorporated herein by reference. 
     The outer cover and/or one or intermediate layers of the golf ball may also comprise one or more ionomer resins. One family of such resins was developed in the mid-1960&#39;s, by E.I. DuPont de Nemours and Co., and sold under the trademark SURLYN®. Preparation of such ionomers is well known, for example see U.S. Pat. No. 3,264,272. Generally speaking, most commercial ionomers are unimodal and consist of a polymer of a mono-olefin, e.g., an alkene, with an unsaturated mono- or dicarboxylic acids having 3 to 12 carbon atoms. An additional monomer in the form of a mono- or dicarboxylic acid ester may also be incorporated in the formulation as a so-called “softening comonomer.” The incorporated carboxylic acid groups are then neutralized by a basic metal ion salt, to form the ionomer. The metal cations of the basic metal ion salt used for neutralization include Li + , Na + , K + , Zn 2+ , Ca 2+ , Co 2+ , Ni 2+ , Cu 2+ , Pb 2+ , and Mg 2+ , with the Li + , Na + , Ca 2+ , Zn 2+ , and Mg 2+  being preferred. The basic metal ion salts include those of for example formic acid, acetic acid, nitric acid, and carbonic acid, hydrogen carbonate salts, oxides, hydroxides, and alkoxides. 
     The first commercially available ionomer resins contained up to 16 weight percent acrylic or methacrylic acid, although it was also well known at that time that, as a general rule, the hardness of these cover materials could be increased with increasing acid content. Hence, in Research Disclosure 29703, published in January 1989, DuPont disclosed ionomers based on ethylene/acrylic acid or ethylene/methacrylic acid containing acid contents of greater than 15 weight percent. In this same disclosure, DuPont also taught that such so called “high acid ionomers” had significantly improved stiffness and hardness and thus could be advantageously used in golf ball construction, when used either singly or in a blend with other ionomers. 
     More recently, high acid ionomers can be ionomer resins with acrylic or methacrylic acid units present from 16 wt. % to about 35 wt. % in the polymer. Generally, such a high acid ionomer will have a flexural modulus from about 50,000 psi to about 125,000 psi. 
     Ionomer resins further comprising a softening comonomer, present from about 10 wt. % to about 50 wt. % in the polymer, have a flexural modulus from about 2,000 psi to about 10,000 psi, and are sometimes referred to as “soft” or “very low modulus” ionomers. Typical softening comonomers include n-butyl acrylate, iso-butyl acrylate, n-butyl methacrylate, methyl acrylate and methyl methacrylate. 
     Today, there are a wide variety of commercially available ionomer resins based both on copolymers of ethylene and (meth)acrylic acid or terpolymers of ethylene and (meth)acrylic acid and (meth)acrylate, all of which many of which are be used as a golf ball component. The properties of these ionomer resins can vary widely due to variations in acid content, softening comonomer content, the degree of neutralization, and the type of metal ion used in the neutralization. The full range commercially available typically includes ionomers of polymers of general formula, E/X/Y polymer, wherein E is ethylene, X is a C 3  to C 8  α,β-ethylenically unsaturated carboxylic acid, such as acrylic or methacrylic acid, and is present in an amount from about 2 to about 30 weight % of the E/X/Y copolymer, and Y is a softening comonomer selected from the group consisting of alkyl acrylate and alkyl methacrylate, such as methyl acrylate or methyl methacrylate, and wherein the alkyl groups have from 1-8 carbon atoms, Y is in the range of 0 to about 50 weight % of the E/X/Y copolymer, and wherein the acid groups present in said ionomeric polymer are partially neutralized with a metal selected from the group consisting of lithium, sodium, potassium, magnesium, calcium, barium, lead, tin, zinc or aluminum, and combinations thereof. 
     The ionomer may also be a so-called bimodal ionomer as described in U.S. Pat. No. 6,562,906 (the entire contents of which are herein incorporated by reference). These ionomers are bimodal as they are prepared from blends comprising polymers of different molecular weights. Specifically they include bimodal polymer blend compositions comprising: a) a high molecular weight component having molecular weight of about 80,000 to about 500,000 and comprising one or more ethylene/α,β-ethylenically unsaturated C 3-8  carboxylic acid copolymers and/or one or more ethylene, alkyl(meth)acrylate, (meth)acrylic acid terpolymers; said high molecular weight component being partially neutralized with metal ions selected from the group consisting of lithium, sodium, zinc, calcium, magnesium, and a mixture of any these; and b) a low molecular weight component having a molecular weight of about from about 2,000 to about 30,000 and comprising one or more ethylene/α,β-ethylenically unsaturated C 3-8  carboxylic acid copolymers and/or one or more ethylene, alkyl(meth)acrylate, (meth)acrylic acid terpolymers; said low molecular weight component being partially neutralized with metal ions selected from the group consisting of lithium, sodium, potassium, magnesium, calcium, barium, lead, tin, zinc or aluminum, and a mixture of any these. 
     In addition to the unimodal and bimodal ionomers, also included are the so-called “modified ionomers” examples of which are described in U.S. Pat. Nos. 6,100,321, 6,329,458 and 6,616,552, the entire contents of all of which are herein incorporated by reference. 
     The modified unimodal ionomers may be prepared by mixing: a) an ionomeric polymer comprising ethylene, from 5 to 25 weight percent (meth)acrylic acid, and from 0 to 40 weight percent of a (meth)acrylate monomer, said ionomeric polymer neutralized with metal ions selected from the group consisting of lithium, sodium, potassium, magnesium, calcium, barium, lead, tin, zinc or aluminum, and any and all mixtures thereof; and b) from about 5 to about 40 weight percent (based on the total weight of said modified ionomeric polymer) of one or more fatty acids or metal salts of said fatty acid, the metal selected from the group consisting of lithium, sodium, potassium, magnesium, calcium, barium, lead, tin, zinc or aluminum, and any and all mixtures thereof; and the fatty acid preferably being stearic acid. 
     The modified bimodal ionomers, which are ionomers derived from the earlier described bimodal ethylene/carboxylic acid polymers (as described in U.S. Pat. No. 6,562,906, the entire contents of which are herein incorporated by reference), are prepared by mixing; a) a high molecular weight component having molecular weight of about 80,000 to about 500,000 and comprising one or more ethylene/α,β-ethylenically unsaturated C 3-8  carboxylic acid copolymers and/or one or more ethylene, alkyl (meth)acrylate, (meth)acrylic acid terpolymers; said high molecular weight component being partially neutralized with metal ions selected from the group consisting of lithium, sodium, potassium, magnesium, calcium, barium, lead, tin, zinc or aluminum, and any and all mixtures thereof; and b) a low molecular weight component having a molecular weight of about from about 2,000 to about 30,000 and comprising one or more ethylene/α,β-ethylenically unsaturated C 3-8  carboxylic acid copolymers and/or one or more ethylene, alkyl(meth)acrylate, (meth)acrylic acid terpolymers; said low molecular weight component being partially neutralized with metal ions selected from the group consisting of lithium, sodium, potassium, magnesium, calcium, barium, lead, tin, zinc or aluminum, and any and all mixtures thereof; and c) from about 5 to about 40 weight percent (based on the total weight of said modified ionomeric polymer) of one or more fatty acids or metal salts of said fatty acid, the metal selected from the group consisting of lithium, sodium, potassium, magnesium, calcium, barium, lead, tin, zinc or aluminum, and any and all mixtures thereof; and the fatty acid preferably being stearic acid. 
     More specifically, the fatty or waxy acid salts utilized in the various modified ionomers are composed of a chain of alkyl groups containing from about 4 to 75 carbon atoms (usually even numbered) and characterized by a —COOH terminal group. The generic formula for all fatty and waxy acids above acetic acid is CH 3 (CH 2 ) x COOH, wherein the carbon atom count includes the carboxyl group (i.e. x=2-73). The fatty or waxy acids utilized to produce the fatty or waxy acid salts modifiers may be saturated or unsaturated, and they may be present in solid, semi-solid or liquid form. 
     Examples of suitable saturated fatty acids, i.e., fatty acids in which the carbon atoms of the alkyl chain are connected by single bonds, include but are not limited to stearic acid (CH 3 (CH 2 ) 16 COOH), palmitic acid (CH 3 (CH 2 ) 14 COOH), pelargonic acid (CH 3 (CH 2 ) 7 COOH) and lauric acid (CH 3 (CH 2 ) 10 COOH). Examples of suitable unsaturated fatty acids, i.e., a fatty acid in which there are one or more double bonds between the carbon atoms in the alkyl chain, include but are not limited to oleic acid (CH 3 (CH 2 ) 7 CH:CH(CH 2 ) 7 COOH). 
     The source of the metal ions used to produce the metal salts of the fatty or waxy acid salts used in the various modified ionomers are generally various metal salts which provide the metal ions capable of neutralizing, to various extents, the carboxylic acid groups of the fatty acids. These include the sulfate, carbonate, acetate and hydroxylate salts of zinc, barium, calcium and magnesium. 
     Since the fatty acid salts modifiers comprise various combinations of fatty acids neutralized with a large number of different metal ions, several different types of fatty acid salts may be utilized in the invention, including metal stearates, laureates, oleates, and palmitates, with calcium, zinc, sodium, lithium, potassium and magnesium stearate being preferred, and calcium and sodium stearate being most preferred. 
     The fatty or waxy acid or metal salt of said fatty or waxy acid is present in the modified ionomeric polymers in an amount of from about 5 to about 40, preferably from about 7 to about 35, more preferably from about 8 to about 20 weight percent (based on the total weight of said modified ionomeric polymer). 
     As a result of the addition of the one or more metal salts of a fatty or waxy acid, from about 40 to 100, preferably from about 50 to 100, more preferably from about 70 to 100 percent of the acidic groups in the final modified ionomeric polymer composition are neutralized by a metal ion. Suitable modified ionomer polymers contemplated for use with the present invention include, hut are not limited to, the ENTIRA® family of polymers including ENTIRA 8218 commercially available from Dow Chemical and Dupont® HPF 1000, Dupont® HPF 1000, Dupont® HPF 1035, Dupont® HPF AD 1072, Dupont® HPF 2000, Dupont® HPC AD 1043, and Dupont® HPC AD 1022, all commercially available from E.I. du Pont de Nemours and Company. 
     A preferred ionomer composition may be prepared by blending one or more of the unimodal ionomers, bimodal ionomers, or modified unimodal or bimodal ionomeric polymers as described herein, and further blended with a zinc neutralized ionomer of a polymer of general formula E/X/Y where E is ethylene, X is a softening comonomer such as acrylate or methacrylate and is present in an amount of from 0 to about 50, preferably 0 to about 25, most preferably 0, and Y is acrylic or methacrylic acid and is present in an amount from about 5 wt. % to about 25, preferably from about 10 to about 25, and most preferably about 10 to about 20 wt % of the total composition. 
     Golf ball materials within the scope of the present invention also can include, in suitable amounts, one or more additional ingredients generally employed in plastics formulation or the preparation of golf ball compositions. Conventional additives such as plasticizers, pigments, antioxidants, U.V. absorbers, optical brighteners, or any other additives may generally employed. Agents provided to achieve specific functions, such as additives and stabilizers, can be present. Exemplary suitable ingredients include colorants, antioxidants, colorants, dispersants, mold releasing agents, processing aids, fillers, and any and all combinations thereof. Although not required, UV stabilizers, or photo stabilizers such as substituted hydroxyphenyl benzotriazoles may be utilized in the present invention to enhance the UV stability of the final compositions. An example of a commercially available UV stabilizer is the stabilizer sold by Ciba Geigy Corporation under the tradename TINUVIN®. 
     Typically, the various golf ball intermediate layer and/or cover formulations compositions are made by mixing together the various components and other additives with or without melting them. Dry blending equipment, such as a tumble mixer, V-blender, ribbon blender, or two-roll mill, can be used to mix the compositions. The golf ball compositions can also be mixed using a mill, internal mixer such as a Banbury or Farrel continuous mixer, extruder or combinations of these, with or without application of thermal energy to produce melting. 
     The cores of the golf balls of the present invention may include the traditional rubber components used in golf ball applications including, both natural and synthetic rubbers, such as cis-1,4-polybutadiene, trans-1,4-polybutadiene, 1,2-polybutadiene, cis-polyisoprene, trans-polyisoprene, polyalkenamers, polychloroprene, polybutylene, styrene-butadiene rubber, styrene-butadiene-styrene block copolymer and partially and fully hydrogenated equivalents, styrene-isoprene-styrene block copolymer and partially and fully hydrogenated equivalents, nitrile rubber, silicone rubber, and polyurethane, as well as mixtures of these. Polybutadiene rubbers, especially 1,4-polybutadiene rubbers containing at least 40 mol %, and more preferably 80 to 100 mol % of cis-1,4 bonds, are preferred because of their high rebound resilience, moldability, and high strength after vulcanization. The polybutadiene component may be synthesized by using rare earth-based catalysts, nickel-based catalysts, or cobalt-based catalysts, conventionally used in this field. Polybutadiene obtained by using lanthanum rare earth-based catalysts usually employ a combination of a lanthanum rare earth (atomic number of 57 to 71)-compound, but particularly preferred is a neodymium compound. 
     When synthetic rubbers such as the aforementioned polybutadienes and/or its blends are used in the golf balls of the present invention they may contain further materials typically often used in rubber formulations including crosslinking agents, co-crosslinking agents, peptizers and accelerators. 
     Suitable cross-linking agents for use in the golf balls of the present invention include peroxides, sulfur compounds, or other known chemical cross-linking agents, as well as mixtures of these. Non-limiting examples of suitable cross-linking agents include primary, secondary, or tertiary aliphatic or aromatic organic peroxides such as Trigonox® 145-45B, marketed by Akrochem Corp. of Akron, Ohio; 1,1-bis(t-butylperoxy)-3,3,5 tri-methylcyclohexane, such as Varox® 231-XL, marketed by R. T. Vanderbilt Co., Inc. of Norwalk, Conn.; and di-(2,4-dichlorobenzoyl)peroxide. 
     Besides the use of chemical cross-linking agents, exposure of the composition to radiation also can serve as a cross-linking agent. Radiation can be applied to the unsaturated polymer mixture by any known method, including using microwave or gamma radiation, or an electron beam device. Additives may also be used to improve radiation curing of the diene polymer. 
     The rubber and cross-linking agent may be blended with a co-cross-linking agent, which may be a metal salt of an unsaturated carboxylic acid. Examples of these include zinc and magnesium salts of unsaturated fatty acids having 3 to 8 carbon atoms, such as acrylic acid, methacrylic acid, maleic acid, and fumaric acid, palmitic acid with the zinc salts of acrylic and methacrylic acid being most preferred. The core compositions used in the present invention may also incorporate one or more of the so-called “peptizers”. 
     The peptizer preferably comprises an organic sulfur compound and/or its metal or non-metal salt. Examples of such organic sulfur compounds include thiophenols, such as pentachlorothiophenol, 4-butyl-o-thiocresol, 4 t-butyl-p-thiocresol, and 2-benzamidothiophenol; thiocarboxylic acids, such as thiobenzoic acid; 4,4′ dithio dimorpholine; and, sulfides, such as dixylyl disulfide, dibenzoyl disulfide; dibenzothiazyl disulfide; di(pentachlorophenyl)disulfide; dibenzamido diphenyldisulfide (DBDD), and alkylated phenol sulfides, such as VULTAC® marketed by Atofina Chemicals, Inc. of Philadelphia, Pa. Preferred organic sulfur compounds include pentachlorothiophenol, and dibenzamido diphenyldisulfide. 
     Examples of the metal salt of an organic sulfur compound include sodium, potassium, lithium, magnesium calcium, barium, cesium and zinc salts of the above-mentioned thiophenols and thiocarboxylic acids, with the zinc salt of pentachlorothiophenol being most preferred. 
     Examples of the non-metal salt of an organic sulfur compound include ammonium salts of the above-mentioned thiophenols and thiocarboxylic acids wherein the ammonium cation has the general formula [NR 1 R 2 R 3 R 4 ] +  where R 1  R 2  R 3  and R 4  are selected from the group consisting of hydrogen, a C 1 -C 20  aliphatic, cycloaliphatic or aromatic moiety, and any and all combinations thereof, with the most preferred being the NH 4   + -salt of pentachlorothiophenol. 
     Additional peptizers include aromatic or conjugated peptizers comprising one or more heteroatoms, such as nitrogen, oxygen and/or sulfur. More typically, such peptizers are heteroaryl or heterocyclic compounds having at least one heteroatom, and potentially plural heteroatoms, where the plural heteroatoms may be the same or different. Such peptizers include peptizers such as an indole peptizer, a quinoline peptizer, an isoquinoline peptizer, a pyridine peptizer, purine peptizer, a pyrimidine peptizer, a diazine peptizer, a pyrazine peptizer, a triazine peptizer, a carbazole peptizer, or combinations of such peptizers. A most preferred such peptizer is a tetrachloro-pyridinethiol and most preferably 2,3,5,6-tetrachloro-4-pyridinethiol. 
     Such peptizers are more fully disclosed in U.S. Pat. No. 8,912,286 issuing on Dec. 16, 2014, the entire contents of which are herein incorporated by reference. 
     The core component polymer(s), crosslinking agent(s), filler(s) and the like can be mixed together with or without melting them. In one method of manufacture the cross-linking agents and other components can be added to the unsaturated polymer as part of a concentrate using dry blending, roll milling, or melt mixing. The various core components can be mixed together with the cross-linking agents, or each additive can be added in an appropriate sequence to the milled unsaturated polymer. The resulting mixture can be subjected to, for example, a compression or injection molding process, to obtain solid spheres for the core. The polymer mixture is subjected to a molding cycle in which heat, and pressure are applied while the mixture is confined within a mold. The cavity shape depends on the portion of the golf ball being formed. The compression and heat liberate free radicals by decomposing one or more peroxides, which initiate cross-linking. The temperature and duration of the molding cycle are selected based upon the type of peroxide and peptizer selected. The molding cycle may have a single step of molding the mixture at a single temperature for fixed time duration. 
     After core formation, the golf ball cover and any mantle layers are typically positioned over the core using one of three methods: casting, injection molding, or compression molding. 
     Injection molding generally involves using a mold having one or more sets of two hemispherical mold sections that mate to form a spherical cavity during the molding process. The pairs of mold sections are configured to define a spherical cavity in their interior when mated. When used to mold an outer cover layer for a golf ball, the mold sections can be configured so that the inner surfaces that mate to form the spherical cavity include protrusions configured to form dimples on the outer surface of the molded cover layer. When used to mold an intermediate layer(s) onto an existing structure, such as a ball core, the mold includes a number of support pins disposed throughout the mold sections. The support pins are configured to be retractable, moving into and out of the cavity perpendicular to the spherical cavity surface. The support pins maintain the position of the core while the molten material flows through the gates into the cavity between the core and the mold sections. The mold itself may be a cold mold or a heated mold 
     Compression molding of a ball outer cover or intermediate layer(s) may also utilize the initial step of making half shells by injection molding the layer material into an injection mold. The half shells then are positioned in a compression mold around a ball core, whereupon heat and pressure are used to mold the half shells into a complete layer over the core, with or without a chemical reaction such as crosslinking Compression molding also can be used as a curing step after injection molding. In such a process, an outer layer of thermally curable material is injection molded around a core in a cold mold. After the material solidifies, the ball is removed and placed into a mold, in which heat, and pressure are applied to the ball to induce curing in the outer layer. 
     Covers may also be formed around the cores using compression molding. Cover materials for compression molding may also be extruded or blended resins or castable resins. 
     In the case of outer cover layers made from a thermoset polyurethane or polyurea composition for golf balls of the present invention a most preferred method is that of casting. Casting (also called “cast-molding”) is performed in a ball cavity formed by bringing together two mold halves that define respective hemispherical cavities. Casting is especially suitable when forming the outer cover layer of a thermoset material, including the thermoset polyurethane or polyurea formulations used in the golf balls of the present invention. In the casting process, a precise amount of liquid thermoset resin is introduced into a first mold cavity of a given pair of mold half shells and allowed to partially cure (“gel”). The core or preformed core with any intermediate layers is placed in the hemispherical cavity of one mold half and supported by the partially cured resin. 
     Once the castable composition is at least partially cured (e.g., to a point where the core will not substantially move), additional castable composition is introduced into a second mold cavity of each pair, and the mold is closed. As the mold halves are brought together, the resin flows around the core and forms the cover. The closed mold is then subjected to heat and pressure to cure the composition, thereby forming the outer layer about the core. The mold is then cooled for removal of the ball from the mold body. The mold cavities include a negative of the dimple pattern of the present invention to impart the dimples onto the outer cover layer. A more complete description of cast molding a thermoset polyurethane or polyurea outer cover on a preformed golf ball core having one or more intermediate layers is disclosed in U.S. Pat. No. 5,885,172 issuing on Mar. 23, 1999, the entire contents of which are incorporated by reference herein. 
     The golf balls of the present invention may comprise from 0 to at least 5 intermediate layer(s), preferably from 0 to 3 intermediate layer(s), more preferably from 1 to 3 intermediate layer(s), and most preferably 1 to 2 intermediate layer(s).  FIGS.  4  and  5    illustrate a three piece and five piece golf ball construction respectively, 
     More generally, the intermediate layers of the golf balls of the present invention have a thickness of about 0.01 to about 0.50, preferably from about 0.02 to about 0.30 or more preferably from about 0.03 to about 0.20 or most preferably from about 0.02 to about 0.10 in. 
     More generally, the intermediate layers of the golf balls of the present invention also have a hardness greater than about 25 and less than about 85, preferably greater than about 30 and less than about 80, more preferably greater than about 35 and less than about 75, and most preferably greater than about 35 and less than about 70 Shore D units as measured on the ball. 
     More generally, the intermediate layers of the golf balls of the present invention also have a flexural modulus from about 5 to about 500, preferably from about 15 to about 400, more preferably from about 20 to about 300, still more preferably from about 25 to about 200, and most preferably from about 30 to about 150 kpsi. 
     More generally, the outer cover layer of the golf balls of the present invention have a thickness of about 0.010 to about 0.08, preferably from about 0.015 to about 0.06, and more preferably from about 0.020 to about 0.040 in. 
     More generally, the outer cover layer of the golf balls of the present invention also has a hardness from about 40 to about 70, preferably from about 45 to about 70 or about 50 to about 70, more preferably from 47 to about 68 or about 45 to about 70, and most preferably from about 50 to about 65 Shore D as measured on the ball. 
     More generally, the COR 125  of the golf balls of the present invention is greater than about 0.760, preferably greater than about 0.780, more preferably greater than 0.790, most preferably greater than 0.795, and especially greater than 0.800 at 125 ft/sec inbound velocity. 
     More generally, the COR 143  of the golf balls of the present invention is also greater than about 0.760, preferably greater than about 0.780, more preferably greater than 0.790, most preferably greater than 0.795, and especially greater than 0.800 when measured at 143 ft/sec inbound velocity. 
     The Contact Time, CT 143  of the golf balls of the present invention is greater than or equal to about 400 microsecs, preferably greater than or equal to about 550 microsecs, more preferably greater than or equal to about 650 microsecs when measured at 143 ft/sec velocity. 
     More generally, the core of the golf balls of the present invention is a unitary core with little or no difference between the hardness of the core measured at its center and the hardness as measured at its outer surface ie no such appreciable core hardness gradient. 
     However, the core of the golf balls of the present invention may also comprise a center and one or more core layers disposed around the center. These core layers comprise the same rubber as used in the center portion. The various core layers (including the center) may each exhibit a different hardness. The difference between the center hardness and that of the next adjacent layer, as well as the difference in hardness between the various core layers is greater than 2, preferably greater than 5, most preferably greater than 10 units of Shore D. 
     In one preferred embodiment, the hardness of the center and each sequential layer increases progressively outwards from the center to outer core layer. 
     In another preferred embodiment, the hardness of the center and each sequential layer decreases progressively inwards from the outer core layer to the center. 
     Referring to the drawing in  FIG.  12   , there is illustrated a transverse cross section of a 3 piece golf ball  50  comprising a core  52 , an intermediate layer  54  and an outer cover layer  56 . Golf ball  50  also typically includes plural dimples 58 formed in the outer cover layer  56  and arranged in various desired patterns (dimples 58 are not to scale, and  FIG.  4    does not illustrate the presently disclosed dimple pattern). 
     More specifically, the intermediate layer of the three piece golf balls of the present invention has a thickness of from about 0.01 to about 0.20 inch, preferably from about 0.02 to about 0.15 inch, more preferably from about 0.03 to about 0.10 inch and most preferably from about 0.03 to about 0.07 inches. 
     The intermediate layer of the three piece golf balls of the present invention also has a hardness of from about 25 to about 80, more preferably of from about 30 to about 70, even more preferably of from about 40 to about 60 Shore D. 
     The outer cover layer of the three piece golf balls of the present invention has a thickness of from about 0.01 to about 0.20 inch, preferably from about 0.02 to about 0.15 inch, more preferably from about 0.03 to about 0.10 inch and most preferably from about 0.03 to about 0.07 inches. 
     The outer cover layer of the three piece golf balls of the present invention also has a hardness of from about 25 to about 80, more preferably from about 30 to about 70, even more preferably from about 40 to about 60 Shore D. 
     The core of the three piece golf balls of the present invention has a diameter of from about 0.5 to about 1.62, preferably from about 0.7 to about 1.60, more preferably from about 1 to about 1.58 inches. 
     The core of the three piece golf balls of the present invention has a PGA compression of from about 10 to about 100, preferably from about 35 to about 90, more preferably from about 40 to about 80. 
     The three-piece golf balls of the present invention has a PGA ball compression greater than about 30, preferably greater than 40, more preferably greater than about 50, most preferably greater than about 60. 
     Referring to the drawing in  FIG.  13    there is illustrated a transverse cross section of a 5 piece golf ball  70  comprising a core  72 , an inner intermediate layer  74 , a center intermediate layer  76 , an outer intermediate layer  78  and an outer cover layer  80 . Golf ball  70  also typically includes plural dimples 82 formed in the outer cover layer  80  and arranged in various desired patterns (dimples 82 are not to scale, and  FIG.  5    does not illustrate the presently disclosed dimple pattern). 
     More specifically, the inner intermediate layer of the five piece golf balls of the present invention has a thickness of from about 0.01 to about 0.20 inch, preferably from about 0.02 to about 0.15 inch, more preferably from about 0.03 to about 0.10 inch and most preferably from about 0.03 to about 0.07 inches. 
     The inner intermediate layer of the five piece golf balls of the present invention has a hardness of from about 25 to about 80, more preferably from about 30 to about 70, even more preferably from about 35 to about 60 Shore D. 
     The center intermediate layer of the five piece golf balls of the present invention has a thickness of from about 0.01 to about 0.20 inch, preferably from about 0.02 to about 0.15 inch, more preferably from about 0.03 to about 0.10 inch and most preferably from about 0.03 to about 0.07 inches. 
     The center intermediate layer of the five piece golf balls of the present invention also has a hardness of from about 25 to about 80, more preferably from about 30 to about 70, even more preferably from about 40 to about 60 Shore D. 
     The outer intermediate layer of the five piece golf balls of the present invention has a thickness of from about 0.01 to about 0.20 inch, preferably from about 0.02 to about 0.15 inch, more preferably from about 0.03 to about 0.10 inch and most preferably from about 0.03 to about 0.07 inches. 
     The outer intermediate layer of the five piece golf balls of the present invention also has a hardness of from about 25 to about 85, more preferably from about 30 to about 80, even more preferably from about 40 to about 75 Shore D. 
     The outer cover layer of the five piece golf balls of the present invention has a thickness of from about 0.01 to about 0.20 inch, preferably from about 0.02 to about 0.15 inch, more preferably from about 0.015 to about 0.10 inch and most preferably from about 0.02 to about 0.07 inches. 
     The outer cover layer of the five piece golf balls of the present invention also has a hardness of from about 25 to about 80, more preferably from about 30 to about 70, even more preferably from about 40 to about 60 Shore D. 
     The core of the five piece golf balls of the present invention has a diameter of from about 0.5 to about 1.62, preferably from about 0.7 to about 1.60, more preferably from about 1 to about 1.58 inches. 
     The core of the five piece golf balls of the present invention has a PGA compression of from about 10 to about 100, preferably from about 20 to about 90, more preferably from about 30 to about 80. 
     The five-piece golf balls of the present invention have a PGA ball compression greater than about 30, preferably greater than 40, more preferably greater than about 50, most preferably greater than about 65. 
     EXAMPLES 
     The following examples are provided to illustrate certain features of working embodiments of the disclosed invention. A person of ordinary skill in the art will appreciate that the invention is not limited to those features exemplified by these working embodiments. 
     Shore D hardness can be measured in accordance with ASTM D2240. Hardness of a layer can be measured on the ball, perpendicular to a land area between the dimples (referred to as “on-the-ball” hardness). The Shore D hardness of a material prior to fabrication into a ball layer can also be measured (referred to as “material” hardness). Unless otherwise specified the Shore D measurements quoted for the layers of the golf balls of the present invention are measured on the ball. 
     Core or ball diameter may be determined using standard linear calipers or a standard size gauge. 
     Compression may be measured by applying a spring-loaded force to the sphere to be examined, with a manual instrument (an “Atti gauge”) manufactured by the Atti Engineering Company of Union City, N.J. This machine, equipped with a Federal Dial Gauge, Model D81-C, employs a calibrated spring under a known load. The sphere to be tested is forced a distance of 0.2 inch (5 mm) against this spring. If the spring, in turn, compresses 0.2 inch, the compression is rated at 100; if the spring compresses 0.1 inch, the compression value is rated as 0. Thus, more compressible, softer materials will have lower Atti gauge values than harder, less compressible materials. The value is taken shortly after applying the force and within at least 5 secs if possible. Compression measured with this instrument is also referred to as PGA compression. 
     The approximate relationship that exists between Atti or PGA compression and Riehle compression can be expressed as: (Atti or PGA compression)=(160-Riehle Compression). Thus, a Riehle compression of 100 would be the same as an Atti compression of 60. 
     The ball performance was determined using a Robot Driver Test, which utilized a commercial swing robot in conjunction with a radar measuring system. The test consists of launching the ball using a robotic arm to which was attached a titanium driver at a fixed tee location, club lie angle, swing speed and power profile. A radar system was used to determine the speed, launch angle, backspin, and carry distance of the ball. The data was then processed for multiple shots on different days at an outdoor test facility. 
     A commercially available TaylorMade Tour Preferred X golf ball was used as a control ball in the setup for the purpose of test validity. A second control ball having the same dimple pattern as the Tour Preferred X was manufactured at the same time and with the same materials and ball construction as the experimental balls in order to remove any variability due to manufacturing conditions such that any measured gain or loss was solely due to the effect of the dimple pattern on the aerodynamics of the experimental balls. 
     Example 1 
     A five piece golf ball was used having a ball construction consisting of a unitary polybutadiene core, core, three intermediate layers made from ionomer formulations and a polyurethane outer cover layer which was cast molded around the combined core and intermediate layers. 
     A total of 322 reduced equivalent depth dual radius dimples having a dimple diameter relative ratio, α, of 0.5. were molded on the golf ball with placement in the various regions of the golf ball. The dimple coordinates, diameters, depths and volume ratios average dimple depths in each section, the various depth ratios and the % Δe, % Δs and % Δp values are summarized in are summarized in Table 6. 
     Thus, of the total of 322 dimples on the ball there are 86 dimples in the North Eastern quadrant include a pole dimple (Dimple #1). This layout is mirrored about the primary meridian in the Northwest quadrant other than shared pole dimple and the 10 shared dimples, Dimple #&#39;s 2, 4, 6, 7, 10 and 15, which lie on the primary meridian (Theta=0 degrees) and Dimples 3, 18, 25 and 63 which also lie on the primary meridian (Theta=180 degrees). Thus, there are a total of 11 shared dimples which are included in the Northeast quadrant but not the Northwest quadrant. Thus the Northeast quadrant has a total of 86 and the Northwest quadrant a total of 75 dimples to give a total of 161 dimples in the Northern hemisphere. This layout is mirrored in the Southern hemisphere about the equator to account for all 322 dimples. The % Dimple Surface Area Coverage (COV) was 85%. 
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Dimple Placement for Dimples in the NE Quadrant of the Golf Ball 
               
               
                 Theta = 0-180 degs and Phi = 0 to 90 degrees) for Example 1. 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Phi 
                 Theta 
                 Diameter 
                 Depth 
                 Radius Inner 
                 Radius Outer 
                 Zone 
                 Zone 
                 Overlap 
               
               
                 Dimple # 
                 (deg) 
                 (deg) 
                 (mm) 
                 (mm) 
                 (R1, mm) 
                 (R2, mm) 
                 (X) 
                 (I) 
                 Zone 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 0.000 
                 0.000 
                 3.2 
                 0.0963 
                 18.074 
                 7.505 
                 PxN 
                 EiE 
                 A 
               
               
                 2 
                 9.486 
                 0.000 
                 3.75 
                 0.1128 
                 21.188 
                 8.795 
                 PxN 
                 EiE 
                 A 
               
               
                 3 
                 17.493 
                 180.000 
                 4.45 
                 0.1340 
                 25.148 
                 10.411 
                 PxN 
                 EiE 
                 A 
               
               
                 4 
                 20.818 
                 0.000 
                 4.4 
                 0.1323 
                 24.854 
                 10.322 
                 PxN 
                 EiE 
                 A 
               
               
                 5 
                 9.486 
                 144.000 
                 3.75 
                 0.1128 
                 21.188 
                 8.795 
                 PxN 
                 SiE 
                 B 
               
               
                 6 
                 17.493 
                 36.000 
                 4.45 
                 0.1340 
                 25.148 
                 10.411 
                 PxN 
                 SiE 
                 B 
               
               
                 7 
                 20.818 
                 144.000 
                 4.4 
                 0.1323 
                 24.854 
                 10.322 
                 PxN 
                 SiE 
                 B 
               
               
                 8 
                 9.486 
                 72.000 
                 3.75 
                 0.1128 
                 21.188 
                 8.795 
                 PxN 
                 PiE 
                 C 
               
               
                 9 
                 17.493 
                 108.000 
                 4.45 
                 0.1340 
                 25.148 
                 10.411 
                 PxN 
                 PiE 
                 C 
               
               
                 10 
                 20.818 
                 72.000 
                 4.4 
                 0.1323 
                 24.854 
                 10.322 
                 PxN 
                 PiE 
                 C 
               
               
                 11 
                 40.933 
                 16.442 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 EiE 
                 D 
               
               
                 12 
                 40.933 
                 160.442 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 EiE 
                 D 
               
               
                 13 
                 28.776 
                 22.926 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 EiE 
                 D 
               
               
                 14 
                 28.776 
                 166.926 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 EiE 
                 D 
               
               
                 15 
                 33.192 
                 0.000 
                 4.65 
                 0.1623 
                 22.671 
                 9.419 
                 SxN 
                 EiE 
                 D 
               
               
                 16 
                 45.502 
                 0.000 
                 4.35 
                 0.1518 
                 21.207 
                 8.808 
                 SxN 
                 EiE 
                 D 
               
               
                 17 
                 50.742 
                 171.644 
                 4.75 
                 0.1658 
                 23.167 
                 9.614 
                 SxN 
                 EiE 
                 D 
               
               
                 18 
                 39.196 
                 180.000 
                 4.75 
                 0.1658 
                 23.167 
                 9.614 
                 SxN 
                 EiE 
                 D 
               
               
                 19 
                 52.922 
                 12.178 
                 4.3 
                 0.1500 
                 20.972 
                 8.716 
                 SxN 
                 EiE 
                 D 
               
               
                 20 
                 52.922 
                 156.178 
                 4.3 
                 0.1500 
                 20.972 
                 8.716 
                 SxN 
                 EiE 
                 D 
               
               
                 21 
                 55.872 
                 0.000 
                 3.25 
                 0.1135 
                 15.850 
                 6.576 
                 SxN 
                 EiE 
                 D 
               
               
                 22 
                 64.699 
                 7.288 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 EiE 
                 D 
               
               
                 23 
                 62.504 
                 21.424 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 EiE 
                 D 
               
               
                 24 
                 62.504 
                 165.424 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 EiE 
                 D 
               
               
                 25 
                 61.706 
                 180.000 
                 4.75 
                 0.1568 
                 24.457 
                 10.162 
                 SxN 
                 EiE 
                 D 
               
               
                 26 
                 40.933 
                 55.558 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 SiE 
                 E 
               
               
                 27 
                 40.933 
                 127.558 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 SiE 
                 E 
               
               
                 28 
                 28.776 
                 49.074 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 SiE 
                 E 
               
               
                 29 
                 28.776 
                 121.074 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 SiE 
                 E 
               
               
                 30 
                 33.192 
                 144.000 
                 4.65 
                 0.1623 
                 22.671 
                 9.419 
                 SxN 
                 SiE 
                 E 
               
               
                 31 
                 45.502 
                 144.000 
                 4.35 
                 0.1518 
                 21.207 
                 8.808 
                 SxN 
                 SiE 
                 E 
               
               
                 32 
                 50.742 
                 27.644 
                 4.75 
                 0.1658 
                 23.167 
                 9.614 
                 SxN 
                 SiE 
                 E 
               
               
                 33 
                 50.742 
                 44.356 
                 4.75 
                 0.1658 
                 23.167 
                 9.614 
                 SxN 
                 SiE 
                 E 
               
               
                 34 
                 50.742 
                 116.356 
                 4.75 
                 0.1658 
                 23.167 
                 9.614 
                 SxN 
                 SiE 
                 E 
               
               
                 35 
                 39.196 
                 36.000 
                 4.75 
                 0.1658 
                 23.167 
                 9.614 
                 SxN 
                 SiE 
                 E 
               
               
                 36 
                 52.922 
                 59.822 
                 4.3 
                 0.1500 
                 20.972 
                 8.716 
                 SxN 
                 SiE 
                 E 
               
               
                 37 
                 52.922 
                 131.822 
                 4.3 
                 0.1500 
                 20.972 
                 8.716 
                 SxN 
                 SiE 
                 E 
               
               
                 38 
                 55.872 
                 144.000 
                 3.25 
                 0.1135 
                 15.850 
                 6.576 
                 SxN 
                 SiE 
                 E 
               
               
                 39 
                 64.699 
                 64.712 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 SiE 
                 E 
               
               
                 40 
                 64.699 
                 136.712 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 SiE 
                 E 
               
               
                 41 
                 64.699 
                 151.288 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 SiE 
                 E 
               
               
                 42 
                 62.504 
                 50.576 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 SiE 
                 E 
               
               
                 43 
                 62.504 
                 122.576 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 SiE 
                 E 
               
               
                 44 
                 61.706 
                 36.000 
                 4.75 
                 0.1568 
                 24.457 
                 10.162 
                 SxN 
                 SiE 
                 E 
               
               
                 45 
                 40.933 
                 88.442 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 PiE 
                 F 
               
               
                 46 
                 28.776 
                 94.926 
                 4.55 
                 0.1589 
                 22.187 
                 9.197 
                 SxN 
                 PiE 
                 F 
               
               
                 47 
                 33.192 
                 72.000 
                 4.65 
                 0.1623 
                 22.671 
                 9.419 
                 SxN 
                 PiE 
                 F 
               
               
                 48 
                 45.502 
                 72.000 
                 4.35 
                 0.1518 
                 21.207 
                 8.808 
                 SxN 
                 PiE 
                 F 
               
               
                 49 
                 50.742 
                 99.644 
                 4.75 
                 0.1658 
                 23.167 
                 9.614 
                 SxN 
                 PiE 
                 F 
               
               
                 50 
                 39.196 
                 108.000 
                 4.75 
                 0.1658 
                 23.167 
                 9.614 
                 SxN 
                 PiE 
                 F 
               
               
                 51 
                 52.922 
                 84.178 
                 4.3 
                 0.1500 
                 20.972 
                 8.716 
                 SxN 
                 PiE 
                 F 
               
               
                 52 
                 55.872 
                 72.000 
                 3.25 
                 0.1135 
                 15.850 
                 6.576 
                 SxN 
                 PiE 
                 F 
               
               
                 53 
                 64.699 
                 79.288 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 PiE 
                 F 
               
               
                 54 
                 62.504 
                 93.424 
                 4.7 
                 0.1554 
                 24.196 
                 10.023 
                 SxN 
                 PiE 
                 F 
               
               
                 55 
                 61.706 
                 108.000 
                 4.75 
                 0.1568 
                 24.457 
                 10.162 
                 SxN 
                 PiE 
                 F 
               
               
                 56 
                 72.932 
                 173.410 
                 4.6 
                 0.1702 
                 21.178 
                 8.789 
                 ExN 
                 EiE 
                 G 
               
               
                 57 
                 76.015 
                 5.256 
                 3.65 
                 0.1349 
                 16.810 
                 6.987 
                 ExN 
                 EiE 
                 G 
               
               
                 58 
                 83.979 
                 23.695 
                 4.5 
                 0.1730 
                 19.971 
                 8.273 
                 ExN 
                 EiE 
                 G 
               
               
                 59 
                 83.979 
                 167.695 
                 4.5 
                 0.1730 
                 19.971 
                 8.273 
                 ExN 
                 EiE 
                 G 
               
               
                 60 
                 85.355 
                 0.000 
                 4.1 
                 0.1575 
                 18.193 
                 7.553 
                 ExN 
                 EiE 
                 G 
               
               
                 61 
                 84.899 
                 11.758 
                 4.2 
                 0.1614 
                 18.643 
                 7.731 
                 ExN 
                 EiE 
                 G 
               
               
                 62 
                 84.899 
                 155.758 
                 4.2 
                 0.1614 
                 18.643 
                 7.731 
                 ExN 
                 EiE 
                 G 
               
               
                 63 
                 83.787 
                 180.000 
                 4.5 
                 0.1730 
                 19.971 
                 8.273 
                 ExN 
                 EiE 
                 G 
               
               
                 64 
                 74.003 
                 16.478 
                 4.4 
                 0.1629 
                 20.257 
                 8.401 
                 ExN 
                 EiE 
                 G 
               
               
                 65 
                 74.003 
                 160.478 
                 4.4 
                 0.1629 
                 20.257 
                 8.401 
                 ExN 
                 EiE 
                 G 
               
               
                 66 
                 72.932 
                 29.410 
                 4.6 
                 0.1702 
                 21.178 
                 8.789 
                 ExN 
                 SiE 
                 H 
               
               
                 67 
                 72.932 
                 42.590 
                 4.6 
                 0.1702 
                 21.178 
                 8.789 
                 ExN 
                 SiE 
                 H 
               
               
                 68 
                 76.015 
                 138.744 
                 3.65 
                 0.1349 
                 16.810 
                 6.987 
                 ExN 
                 SiE 
                 H 
               
               
                 69 
                 76.015 
                 149.256 
                 3.65 
                 0.1349 
                 16.810 
                 6.987 
                 ExN 
                 SiE 
                 H 
               
               
                 70 
                 83.979 
                 48.305 
                 4.5 
                 0.1730 
                 19.971 
                 8.273 
                 ExN 
                 SiE 
                 H 
               
               
                 71 
                 83.979 
                 120.305 
                 4.5 
                 0.1730 
                 19.971 
                 8.273 
                 ExN 
                 SiE 
                 H 
               
               
                 72 
                 85.355 
                 144.000 
                 4.1 
                 0.1575 
                 18.193 
                 7.553 
                 ExN 
                 SiE 
                 H 
               
               
                 73 
                 84.899 
                 60.242 
                 4.2 
                 0.1614 
                 18.643 
                 7.731 
                 ExN 
                 SiE 
                 H 
               
               
                 74 
                 84.899 
                 132.242 
                 4.2 
                 0.1614 
                 18.643 
                 7.731 
                 ExN 
                 SiE 
                 H 
               
               
                 75 
                 83.787 
                 36.000 
                 4.5 
                 0.1730 
                 19.971 
                 8.273 
                 ExN 
                 SiE 
                 H 
               
               
                 76 
                 74.003 
                 55.522 
                 4.4 
                 0.1629 
                 20.257 
                 8.401 
                 ExN 
                 SiE 
                 H 
               
               
                 77 
                 74.003 
                 127.522 
                 4.4 
                 0.1629 
                 20.257 
                 8.401 
                 ExN 
                 SiE 
                 H 
               
               
                 78 
                 72.932 
                 101.410 
                 4.6 
                 0.1702 
                 21.178 
                 8.789 
                 ExN 
                 PiE 
                 I 
               
               
                 79 
                 72.932 
                 114.590 
                 4.6 
                 0.1702 
                 21.178 
                 8.789 
                 ExN 
                 PiE 
                 I 
               
               
                 80 
                 76.015 
                 66.744 
                 3.65 
                 0.1349 
                 16.810 
                 6.987 
                 ExN 
                 PiE 
                 I 
               
               
                 81 
                 76.015 
                 77.256 
                 3.65 
                 0.1349 
                 16.810 
                 6.987 
                 ExN 
                 PiE 
                 I 
               
               
                 82 
                 83.979 
                 95.695 
                 4.5 
                 0.1730 
                 19.971 
                 8.273 
                 ExN 
                 PiE 
                 I 
               
               
                 83 
                 85.355 
                 72.000 
                 4.1 
                 0.1575 
                 18.193 
                 7.553 
                 ExN 
                 PiE 
                 I 
               
               
                 84 
                 84.899 
                 83.758 
                 4.2 
                 0.1614 
                 18.643 
                 7.731 
                 ExN 
                 PiE 
                 I 
               
               
                 85 
                 83.787 
                 108.000 
                 4.5 
                 0.1730 
                 19.971 
                 8.273 
                 ExN 
                 PiE 
                 I 
               
               
                 86 
                 74.003 
                 88.478 
                 4.4 
                 0.1629 
                 20.257 
                 8.401 
                 ExN 
                 PiE 
                 I 
               
               
                   
               
               
                 *for all dimples VR = 0.555 and α = 0.500 
               
            
           
         
       
     
     As shown in Table 7, in the NE quadrant the golf ball had 31 dimples in the NEx zone having an average depth ( h ex) of 0.161 mm, 45 dimples in the NSx zone having an average depth ( h sx) of 0.155 mm, and 10 dimples in the Px zone (NPx) having an average depth ( h px) of 0.123 mm. 
     The golf ball also had 29 dimples in the NEiE zone having average depth (hei) of 0.153 mm, 34 dimples in the NSiE zone having an average depth (hsi) of 0.155 mm, and 23 dimples in the NNE zone having an average depth (hpi) of 0.153 mm. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Total and Average Depths in Zones of North East Quadrant for Example 1 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 ExN 
                 SxN 
                 PxN 
                 NEiE 
                 NSiE 
                 NPiE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Total Depth (mm) 
                 5.004 
                 6.973 
                 1.233 
                 4.423 
                 5.275 
                 3.512 
               
               
                 No. of Dimples 
                 31 
                 45 
                 10 
                 29 
                 34 
                 23 
               
               
                 Av Depth (h mm) 
                 0.161 
                 0.155 
                 0.123 
                 0.153 
                 0.155 
                 0.153 
               
               
                   
               
            
           
         
       
     
     As shown in Table 12, the golf ball dimples also had a depth ratio  h ex/ h ei of 1.052, a depth ratio  h sx/ h si of 1.000 and depth ratio  h px/ h pi of 0.804. 
     The % Δe, % Δs and % Δp values for the golf ball of Example 1 were 6.137%, 3.253% and 4.504%, respectively. 
     In terms of the Overlap zones in the North East Quadrant, the total and average dimple depths in each zone are summarized in Table 8, 
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Total and Average Depths of Dimples in Overlap Zones of North East Quadrant for Example 1 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
               
               
                   
                 Zone A 
                 Zone B 
                 Zone C 
                 Zone D 
                 Zone E 
                 Zone F 
                 Zone G 
                 Zone H 
                 Zone I 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Total Depth (mm) 
                 0.4753 
                 0.3791 
                 0.3791 
                 2.3180 
                 2.9604 
                 1.6947 
                 1.6302 
                 1.9353 
                 1.4381 
               
               
                 No. of Dimples 
                 4 
                 3 
                 3 
                 15 
                 19 
                 11 
                 10 
                 12 
                 9 
               
               
                 Av Depth (h mm) 
                 0.119 
                 0.126 
                 0.126 
                 0.155 
                 0.156 
                 0.154 
                 0.163 
                 0.161 
                 0.160 
               
               
                   
               
            
           
         
       
     
     Example 2 
     A golf ball was prepared having the same ball construction and repeating dimple pattern with the same number and type of dimples in each section and the same outer dimple diameters as for Example 1. The depths and radii of curvature of the dimples were varied while maintaining each dimples volume ratio at 0.555 as shown in Table 9. The % Dimple Surface Area Coverage (COV) was 85%. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 Dimple Placement for Dimples in the NE Quadrant of the Golf Ball 
               
               
                 Theta = 0-180 degs and Phi = 0 to 90 degrees) for Example 2. 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Phi 
                 Theta 
                 Diameter 
                 Depth 
                 Radius Inner 
                 Radius Outer 
                 Zone 
                 Zone 
                 Overlap 
               
               
                 Dimple # 
                 (deg) 
                 (deg) 
                 (mm) 
                 (mm) 
                 (R1, mm) 
                 (R2, ; mm) 
                 (X) 
                 (I) 
                 Zone 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 0.000 
                 0.000 
                 3.2000 
                 0.100 
                 17.5022 
                 7.2428 
                 PxN 
                 EiE 
                 A 
               
               
                 2 
                 9.486 
                 0.000 
                 3.7500 
                 0.117 
                 20.5167 
                 8.5097 
                 PxN 
                 EiE 
                 A 
               
               
                 3 
                 17.493 
                 180.000 
                 4.4500 
                 0.138 
                 24.3519 
                 10.0921 
                 PxN 
                 EiE 
                 A 
               
               
                 4 
                 20.818 
                 0.000 
                 4.4000 
                 0.137 
                 24.0676 
                 9.9724 
                 PxN 
                 EiE 
                 A 
               
               
                 5 
                 9.486 
                 144.000 
                 3.7500 
                 0.117 
                 20.5167 
                 8.5097 
                 PxN 
                 SiE 
                 B 
               
               
                 6 
                 17.493 
                 36.000 
                 4.4500 
                 0.138 
                 24.3519 
                 10.0921 
                 PxN 
                 SiE 
                 B 
               
               
                 7 
                 20.818 
                 144.000 
                 4.4000 
                 0.137 
                 24.0676 
                 9.9724 
                 PxN 
                 SiE 
                 B 
               
               
                 8 
                 9.486 
                 72.000 
                 3.7500 
                 0.117 
                 20.5167 
                 8.5097 
                 PxN 
                 PiE 
                 C 
               
               
                 9 
                 17.493 
                 108.000 
                 4.4500 
                 0.138 
                 24.3519 
                 10.0921 
                 PxN 
                 PiE 
                 C 
               
               
                 10 
                 20.818 
                 72.000 
                 4.4000 
                 0.137 
                 24.0676 
                 9.9724 
                 PxN 
                 PiE 
                 C 
               
               
                 11 
                 40.933 
                 16.442 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 EiE 
                 D 
               
               
                 12 
                 40.933 
                 160.442 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 EiE 
                 D 
               
               
                 13 
                 28.776 
                 22.926 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 EiE 
                 D 
               
               
                 14 
                 28.776 
                 166.926 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 EiE 
                 D 
               
               
                 15 
                 33.192 
                 0.000 
                 4.6500 
                 0.168 
                 21.9554 
                 9.1091 
                 SxN 
                 EiE 
                 D 
               
               
                 16 
                 45.502 
                 0.000 
                 4.3500 
                 0.157 
                 20.5382 
                 8.5240 
                 SxN 
                 EiE 
                 D 
               
               
                 17 
                 50.742 
                 171.644 
                 4.7500 
                 0.171 
                 22.4359 
                 9.2956 
                 SxN 
                 EiE 
                 D 
               
               
                 18 
                 39.196 
                 180.000 
                 4.7500 
                 0.171 
                 22.4359 
                 9.2956 
                 SxN 
                 EiE 
                 D 
               
               
                 19 
                 52.922 
                 12.178 
                 4.3000 
                 0.155 
                 20.3100 
                 8.4360 
                 SxN 
                 EiE 
                 D 
               
               
                 20 
                 52.922 
                 156.178 
                 4.3000 
                 0.155 
                 20.3100 
                 8.4360 
                 SxN 
                 EiE 
                 D 
               
               
                 21 
                 55.872 
                 0.000 
                 3.2500 
                 0.117 
                 15.3496 
                 6.3550 
                 SxN 
                 EiE 
                 D 
               
               
                 22 
                 64.699 
                 7.288 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 EiE 
                 D 
               
               
                 23 
                 62.504 
                 21.424 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 EiE 
                 D 
               
               
                 24 
                 62.504 
                 165.424 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 EiE 
                 D 
               
               
                 25 
                 61.706 
                 180.000 
                 4.7500 
                 0.162 
                 23.6846 
                 9.8212 
                 SxN 
                 EiE 
                 D 
               
               
                 26 
                 40.933 
                 55.558 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 SiE 
                 E 
               
               
                 27 
                 40.933 
                 127.558 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 SiE 
                 E 
               
               
                 28 
                 28.776 
                 49.074 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 SiE 
                 E 
               
               
                 29 
                 28.776 
                 121.074 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 SiE 
                 E 
               
               
                 30 
                 33.192 
                 144.000 
                 4.6500 
                 0.168 
                 21.9554 
                 9.1091 
                 SxN 
                 SiE 
                 E 
               
               
                 31 
                 45.502 
                 144.000 
                 4.3500 
                 0.157 
                 20.5382 
                 8.5240 
                 SxN 
                 SiE 
                 E 
               
               
                 32 
                 50.742 
                 27.644 
                 4.7500 
                 0.171 
                 22.4359 
                 9.2956 
                 SxN 
                 SiE 
                 E 
               
               
                 33 
                 50.742 
                 44.356 
                 4.7500 
                 0.171 
                 22.4359 
                 9.2956 
                 SxN 
                 SiE 
                 E 
               
               
                 34 
                 50.742 
                 116.356 
                 4.7500 
                 0.171 
                 22.4359 
                 9.2956 
                 SxN 
                 SiE 
                 E 
               
               
                 35 
                 39.196 
                 36.000 
                 4.7500 
                 0.171 
                 22.4359 
                 9.2956 
                 SxN 
                 SiE 
                 E 
               
               
                 36 
                 52.922 
                 59.822 
                 4.3000 
                 0.155 
                 20.3100 
                 8.4360 
                 SxN 
                 SiE 
                 E 
               
               
                 37 
                 52.922 
                 131.822 
                 4.3000 
                 0.155 
                 20.3100 
                 8.4360 
                 SxN 
                 SiE 
                 E 
               
               
                 38 
                 55.872 
                 144.000 
                 3.2500 
                 0.117 
                 15.3496 
                 6.3550 
                 SxN 
                 SiE 
                 E 
               
               
                 39 
                 64.699 
                 64.712 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 SiE 
                 E 
               
               
                 40 
                 64.699 
                 136.712 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 SiE 
                 E 
               
               
                 41 
                 64.699 
                 151.288 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 SiE 
                 E 
               
               
                 42 
                 62.504 
                 50.576 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 SiE 
                 E 
               
               
                 43 
                 62.504 
                 122.576 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 SiE 
                 E 
               
               
                 44 
                 61.706 
                 36.000 
                 4.7500 
                 0.162 
                 23.6846 
                 9.8212 
                 SxN 
                 SiE 
                 E 
               
               
                 45 
                 40.933 
                 88.442 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 PiE 
                 F 
               
               
                 46 
                 28.776 
                 94.926 
                 4.5500 
                 0.164 
                 21.4870 
                 8.9291 
                 SxN 
                 PiE 
                 F 
               
               
                 47 
                 33.192 
                 72.000 
                 4.6500 
                 0.168 
                 21.9554 
                 9.1091 
                 SxN 
                 PiE 
                 F 
               
               
                 48 
                 45.502 
                 72.000 
                 4.3500 
                 0.157 
                 20.5382 
                 8.5240 
                 SxN 
                 PiE 
                 F 
               
               
                 49 
                 50.742 
                 99.644 
                 4.7500 
                 0.171 
                 22.4359 
                 9.2956 
                 SxN 
                 PiE 
                 F 
               
               
                 50 
                 39.196 
                 108.000 
                 4.7500 
                 0.171 
                 22.4359 
                 9.2956 
                 SxN 
                 PiE 
                 F 
               
               
                 51 
                 52.922 
                 84.178 
                 4.3000 
                 0.155 
                 20.3100 
                 8.4360 
                 SxN 
                 PiE 
                 F 
               
               
                 52 
                 55.872 
                 72.000 
                 3.2500 
                 0.117 
                 15.3496 
                 6.3550 
                 SxN 
                 PiE 
                 F 
               
               
                 53 
                 64.699 
                 79.288 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 PiE 
                 F 
               
               
                 54 
                 62.504 
                 93.424 
                 4.7000 
                 0.160 
                 23.4312 
                 9.7212 
                 SxN 
                 PiE 
                 F 
               
               
                 55 
                 61.706 
                 108.000 
                 4.7500 
                 0.162 
                 23.6846 
                 9.8212 
                 SxN 
                 PiE 
                 F 
               
               
                 56 
                 72.932 
                 173.410 
                 4.6000 
                 0.176 
                 20.5107 
                 8.5057 
                 ExN 
                 EiE 
                 G 
               
               
                 57 
                 76.015 
                 5.256 
                 3.6500 
                 0.140 
                 16.2801 
                 6.7493 
                 ExN 
                 EiE 
                 G 
               
               
                 58 
                 83.979 
                 23.695 
                 4.5000 
                 0.178 
                 19.3420 
                 8.0431 
                 ExN 
                 EiE 
                 G 
               
               
                 59 
                 83.979 
                 167.695 
                 4.5000 
                 0.178 
                 19.3420 
                 8.0431 
                 ExN 
                 EiE 
                 G 
               
               
                 60 
                 85.355 
                 0.000 
                 4.1000 
                 0.155 
                 20.3100 
                 8.4360 
                 ExN 
                 EiE 
                 G 
               
               
                 61 
                 84.899 
                 11.758 
                 4.2000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 EiE 
                 G 
               
               
                 62 
                 84.899 
                 155.758 
                 4.2000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 EiE 
                 G 
               
               
                 63 
                 83.787 
                 180.000 
                 4.5000 
                 0.178 
                 19.3420 
                 8.0431 
                 ExN 
                 EiE 
                 G 
               
               
                 64 
                 74.003 
                 16.478 
                 4.4000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 EiE 
                 G 
               
               
                 65 
                 74.003 
                 160.478 
                 4.4000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 EiE 
                 G 
               
               
                 66 
                 72.932 
                 29.410 
                 4.6000 
                 0.176 
                 20.5107 
                 8.5057 
                 ExN 
                 SiE 
                 H 
               
               
                 67 
                 72.932 
                 42.590 
                 4.6000 
                 0.176 
                 20.5107 
                 8.5057 
                 ExN 
                 SiE 
                 H 
               
               
                 68 
                 76.015 
                 138.744 
                 3.6500 
                 0.140 
                 16.2801 
                 6.7493 
                 ExN 
                 SiE 
                 H 
               
               
                 69 
                 76.015 
                 149.256 
                 3.6500 
                 0.140 
                 16.2801 
                 6.7493 
                 ExN 
                 SiE 
                 H 
               
               
                 70 
                 83.979 
                 48.305 
                 4.5000 
                 0.178 
                 19.3420 
                 8.0431 
                 ExN 
                 SiE 
                 H 
               
               
                 71 
                 83.979 
                 120.305 
                 4.5000 
                 0.178 
                 19.3420 
                 8.0431 
                 ExN 
                 SiE 
                 H 
               
               
                 72 
                 85.355 
                 144.000 
                 4.1000 
                 0.155 
                 20.3100 
                 8.4360 
                 ExN 
                 SiE 
                 H 
               
               
                 73 
                 84.899 
                 60.242 
                 4.2000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 SiE 
                 H 
               
               
                 74 
                 84.899 
                 132.242 
                 4.2000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 SiE 
                 H 
               
               
                 75 
                 83.787 
                 36.000 
                 4.5000 
                 0.178 
                 19.3420 
                 8.0431 
                 ExN 
                 SiE 
                 H 
               
               
                 76 
                 74.003 
                 55.522 
                 4.4000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 SiE 
                 H 
               
               
                 77 
                 74.003 
                 127.522 
                 4.4000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 SiE 
                 H 
               
               
                 78 
                 72.932 
                 101.410 
                 4.6000 
                 0.176 
                 20.5107 
                 8.5057 
                 ExN 
                 PiE 
                 I 
               
               
                 79 
                 72.932 
                 114.590 
                 4.6000 
                 0.176 
                 20.5107 
                 8.5057 
                 ExN 
                 PiE 
                 I 
               
               
                 80 
                 76.015 
                 66.744 
                 3.6500 
                 0.140 
                 16.2801 
                 6.7493 
                 ExN 
                 PiE 
                 I 
               
               
                 81 
                 76.015 
                 77.256 
                 3.6500 
                 0.140 
                 16.2801 
                 6.7493 
                 ExN 
                 PiE 
                 I 
               
               
                 82 
                 83.979 
                 95.695 
                 4.5000 
                 0.178 
                 19.3420 
                 8.0431 
                 ExN 
                 PiE 
                 I 
               
               
                 83 
                 85.355 
                 72.000 
                 4.1000 
                 0.155 
                 20.3100 
                 8.4360 
                 ExN 
                 PiE 
                 I 
               
               
                 84 
                 84.899 
                 83.758 
                 4.2000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 PiE 
                 I 
               
               
                 85 
                 83.787 
                 108.000 
                 4.5000 
                 0.178 
                 19.3420 
                 8.0431 
                 ExN 
                 PiE 
                 I 
               
               
                 86 
                 74.003 
                 88.478 
                 4.4000 
                 0.168 
                 19.6189 
                 8.1338 
                 ExN 
                 PiE 
                 I 
               
               
                   
               
               
                 *for all dimples VR = 0.555 and α = 0.500 
               
            
           
         
       
     
     As shown in Table 10, in the North Eastern quadrant, the golf ball had 31 dimples in the Ex zone (ExN) having an average depth ( h ex) of 0.166 mm, 45 dimples in the SxN zone having an average depth ( h sx) of 0.160 mm, and 10 dimples in the PxN zone having an average depth ( h px) of 0.127 mm. 
     The golf ball also had 29 dimples in the NEiE zone having an average depth ( h ei) of 0.157 mm, 34 dimples in the NSiE zone having an average depth ( h si) of 0.160 mm, and 23 dimples in the NPiE zone having an average depth ( h pi) of 0.157 mm. 
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 Total and Average Depths of Dimples in 
               
               
                 North East Quadrant Zones for Example 2 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 ExN 
                 SxN 
                 PxN 
                 NEiE 
                 NSiE 
                 NPiE 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Total Depth (mm) 
                 5.153 
                 7.203 
                 1.275 
                 4.565 
                 5.444 
                 3.622 
               
               
                 No. of Dimples 
                 31 
                 45 
                 10 
                 29 
                 34 
                 23 
               
               
                 Av Depth (mm) 
                 0.166 
                 0.160 
                 0.127 
                 0.157 
                 0.160 
                 0.157 
               
               
                   
               
            
           
         
       
     
     As summarized in Table 12, the golf ball dimples in the North Eastern quadrant also had a depth ratio  h ex/ h ei of 1.057, a depth ratio  h sx/ h si of 1.000 and depth ratio hpx/hpi of 0.809. 
     The % Δe, % Δs and % Δp values for the golf ball of Example 2 were 6.102%, 3.240% and 4.483%, respectively. 
     In terms of the Overlap zones in the North East Quadrant, the total and average dimple depths in each zone are summarized in Table 10. 
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 Total and Average Depths of Dimples in Overlap Zones in the North East Quadrant for Example 2 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
                 Overlap 
               
               
                   
                 Zone A 
                 Zone B 
                 Zone C 
                 Zone D 
                 Zone E 
                 Zone F 
                 Zone G 
                 Zone H 
                 Zone I 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Total Depth (mm) 
                 0.491 
                 0.392 
                 0.392 
                 2.394 
                 3.058 
                 1.751 
                 1.679 
                 1.994 
                 1.479 
               
               
                 No. of Dimples 
                 4 
                 3 
                 3 
                 15 
                 19 
                 11 
                 10 
                 12 
                 9 
               
               
                 Av Depth (h mm) 
                 0.123 
                 0.131 
                 0.131 
                 0.160 
                 0.161 
                 0.159 
                 0.168 
                 0.166 
                 0.164 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 Dimple Properties for Examples 1 and 2. 
               
            
           
           
               
               
               
            
               
                   
                 Ex 1 
                 Ex 2 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Ratio  h ex/ h ei 
                 1.052 
                 1.057 
               
               
                   
                 Ratio  h sx/ h si 
                 1.000 
                 1.000 
               
               
                   
                 Ratio  h px/ h pi 
                 0.804 
                 0.809 
               
               
                   
                 % Δe 
                 6.137 
                 6.102 
               
               
                   
                 % Δs 
                 3.253 
                 3.240 
               
               
                   
                 % Δp 
                 4.504 
                 4.483 
               
               
                   
                 % Dimple Surface Area Coverage (COV) 
                 85 
                 85 
               
               
                   
                 Av Dimple Volume Ratio (AvVR) 
                 0.555 
                 0.555 
               
               
                   
                 Total Dimple Volume mm 3  (TDV) 
                 427 
                 441 
               
               
                   
                   
               
            
           
         
       
     
     In view of the many possible embodiments to which the principles of the disclosed invention may be applied, it should be recognized that the illustrated embodiments are only preferred examples of the invention and should not be taken as limiting the scope of the invention.