Patent Publication Number: US-7582028-B2

Title: Golf ball with lobed dimples

Description:
CROSS REFERENCE TO RELATED APPLICATION 
   This application is a continuation of U.S. application Ser. No. 11/279,478, filed on Apr. 12, 2006, now U.S. Pat. No. 7,367,904 which is a continuation of U.S. application Ser. No. 10/800,448, filed Mar. 15, 2004, now U.S. Pat. No. 7,056,223, which is a continuation of U.S. application Ser. No. 10/153,930, now U.S. Pat. No. 6,749,525, entitled GOLF BALL DIMPLES, and filed on May 23, 2002, the disclosures of which are incorporated herein by reference in their entireties. 

   FIELD OF THE INVENTION 
   The present invention relates to golf balls, and more particularly, to a golf ball having improved dimples. 
   BACKGROUND OF THE INVENTION 
   Golf balls generally include a spherical outer surface with a plurality of dimples formed thereon. Conventional dimples are circular depressions that reduce drag and increase lift. These dimples are formed where a dimple wall slopes away from the outer surface of the ball forming the depression. 
   Drag is the air resistance that opposes the golf ball&#39;s flight direction. As the ball travels through the air, the air that surrounds the ball has different velocities thus, different pressures. The air exerts maximum pressure at a stagnation point on the front of the ball. The air then flows around the surface of the ball with an increased velocity and reduced pressure. At some separation point, the air separates from the surface of the ball and generates a large turbulent flow area behind the ball. This flow area, which is called the wake, has low pressure. The difference between the high pressure in front of the ball and the low pressure behind the ball slows the ball down. This is the primary source of drag for golf balls. 
   The dimples on the golf ball cause a thin boundary layer of air adjacent to the ball&#39;s outer surface to flow in a turbulent manner. Thus, the thin boundary layer is called a turbulent boundary layer. The turbulence energizes the boundary layer and helps move the separation point further backward, so that the layer stays attached further along the ball&#39;s outer surface. As a result, a reduction in the area of the wake, an increase in the pressure behind the ball, and a substantial reduction in drag are realized. It is the circumference of each dimple, where the dimple wall drops away from the outer surface of the ball, which actually creates the turbulence in the boundary layer. 
   Lift is an upward force on the ball that is created by a difference in pressure between the top of the ball and the bottom of the ball. This difference in pressure is created by a warp in the airflow that results from the ball&#39;s backspin. Due to the backspin, the top of the ball moves with the airflow, which delays the air separation point to a location further backward. Conversely, the bottom of the ball moves against the airflow, which moves the separation point forward. This asymmetrical separation creates an arch in the flow pattern that requires the air that flows over the top of the ball to move faster than the air that flows along the bottom of the ball. As a result, the air above the ball is at a lower pressure than the air underneath the ball. This pressure difference results in the overall force, called lift, which is exerted upwardly on the ball. The circumference of each dimple is important in optimizing this flow phenomenon, as well. 
   By using dimples to decrease drag and increase lift, almost every golf ball manufacturer has increased their golf ball flight distances. In order to optimize ball performance, it is desirable to have a large number of dimples, hence a large amount of dimple circumference, which is evenly distributed around the ball. In arranging the dimples, an attempt is made to minimize the space between dimples, because such space does not improve aerodynamic performance of the ball. In practical terms, this usually translates into 300 to 500 circular dimples with a conventional sized dimple having a diameter that typically ranges from about 0.100 inches to about 0.180 inches. 
   When compared to one conventional size dimple, theoretically, an increased number of small dimples may enhance aerodynamic performance by increasing total dimple circumference. However, in reality small dimples are not always very effective in decreasing drag and increasing lift. This results at least in part from the susceptibility of small dimples to paint flooding. Paint flooding occurs when the paint coat on the golf ball partially fills the small dimples, and consequently decreases the dimple&#39;s aerodynamic effectiveness. On the other hand, a smaller number of large dimples also begin to lose effectiveness. This results from the circumference of one large dimple being less than that of a group of smaller dimples. 
   One attempt to improve the aerodynamics of a golf ball is to create a ridge-like polygon inside a non-circular dimple and near the center of the dimple, where the edges of the polygon are positioned below the un-dimpled surface of the ball. This approach is described in U.S. Pat. No. 6,315,686 B1 and U.S. Patent Application Publication No. 2002/0025864 A1. The &#39;686B1 and &#39;864A1 references theorize that the polygonal ridges generate the turbulent boundary layer during low and intermediate ball velocities, and the non-circular dimples with the polygonal centers are used in conjunction with the conventional circular dimples on a golf ball. U.S. Pat. No. 4,869,512 also discloses the use of non-circular dimples with conventional circular dimples to improve aerodynamic performance of a golf ball. These non-circular dimples have shapes that include triangular, petal, oblong, and partially overlapping circles, among others. Additionally, U.S. Pat. No. 5,377,989 discloses non-circular isodiametrical dimples, wherein the dimples have an odd number of curved sides. 
   Another approach for improving the aerodynamics of a golf ball is suggested in U.S. Pat. No. 6,162,136, wherein a preferred solution is to minimize the land surface or undimpled surface of the ball to maximize dimple coverage. One way of maximizing the dimple coverage of the ball is to pack closely together circular dimples having various sizes, as disclosed in U.S. Pat. Nos. 5,957,786 and 6,358,161. In practice, the circular dimple coverage is limited to about 85% or less when non-overlapping dimples are used. Another attempt to maximize dimple coverage is to use polygonal dimples with polyhedron dimple surfaces, i.e., dimple surfaces constructed from planar surfaces, as suggested in a number of patent references including U.S. Pat. Nos. 6,290,615B1, 5,338,039, 5,174,578, 4,090,716, and 4,830,378, among others. Theoretically, higher dimple coverage is attainable with these polygonal dimples. However, it has been demonstrated that polygonal dimples with polyhedron dimple surfaces do not achieve performance improvements commensurate with their coverage improvements. It is believed that the linear edges of the polygonal dimples and the connecting sharp apices generate more drag than the curved edges of the circular dimples. 
   Hence, there remains a need in the art for a golf ball that has a high dimple coverage and superior aerodynamic performance. 
   SUMMARY OF THE INVENTION 
   The present invention is directed to a golf ball with improved dimples. 
   The present invention is also directed to a golf ball with improved aerodynamic characteristics. 
   The present invention is also directed to an arrangement of the improved dimples on a golf ball. 
   The present invention is directed to a dimple comprising a plurality of lobes positioned radially around the center of the dimple, wherein each lobe is defined by a circumferential segment and the circumferential segments define at least a part of the perimeter of the dimple. Each lobe comprises a first curved profile extending from the circumferential segment to the center of the dimple and the first curved profile of each lobe abuts each other in an uninterrupted manner. The lobes may be further defined by spoke-like ridges positioned between adjacent lobes. These spoke-like ridges may extend from the perimeter toward the center of the dimple or to the center of the dimple. Each lobe further comprises a second curved profile extending across the width of the lobe. Alternatively, the portions of the perimeter where the circumferential segments abut can be rounded. Additionally, the size, shape and/or angular spacing of the lobes on a single dimple may vary. 
   The curvature or prominence of the lobes can be defined by a ratio of an inside radius (Ri) to an outside radius (Ro). The inside radius extends from the center to a trough or a location on the lobe radially closest to the center. The outside radius extends from the center to an apex point of the lobe. In accordance to one aspect of the present invention, the inventive dimple includes uniform multi-lobed dimples. The inside radius and outside radius are constant for all these lobes, and the prominence of each lobe is the same as that for the other lobes in the same dimple. The prominence ratio for uniform lobes is less than 1.0. Preferably, this ratio is between about 0.70 and about 0.95; more preferably the ratio is between about 0.75 and about 0.90; and most preferably the ratio is between about 0.80 and about 0.90. 
   In accordance to another aspect of the present invention, the inventive dimple also includes non-uniform multi-lobed dimples. These non-uniform multi-lobed dimples can be either concentric or eccentric. Concentric non-uniform multi-lobed dimples include dimples with the center of Ri coincides with the center of Ro, and eccentric non-uniform multi-lobed dimples include dimples with the center of Ri being spaced apart from the center of Ro. 
   Concentric non-uniform multi-lobed dimples may have a constant Ri and a constant Ro. Additionally, concentric non-uniform multi-lobed dimples may include those with a constant Ri and varying Ro, those with varying Ri and constant Ro, and those with varying Ri and varying Ro. Although, the prominence of each lobe may be different than other lobes in the same dimple, the prominence ratio for the concentric non-uniform multi-lobed dimple is the ratio of Ri (or average Ri) to Ro (or average Ro). The prominence ratio is preferably less than 1.0. Preferably, this ratio is between about 0.70 and about 0.95; more preferably the ratio is between about 0.75 and about 0.90; and most preferably the ratio is between about 0.80 and about 0.90. 
   Eccentric non-uniform multi-lobed dimples may also have constant Ri and Ro. They may also have either varying Ri or varying Ro, or both. The prominence ratio for eccentric non-uniform multi-lobed dimples is defined similarly to the prominence ratio for concentric non-uniform multi-lobed dimples. 
   The dimple may comprise any number of lobes. For illustrative purposes, the dimple of the present invention is depicted to have between three and seven lobes. 
   The present invention is also directed to a golf ball having the multi-lobed dimples incorporated on its outer surface. In accordance to one aspect of the present invention, the multi-lobed dimples are arranged in a hexagonal array, wherein one multi-lobed dimple is surrounded by six multi-lobed dimples. The multi-lobed dimples are preferably arranged in an icosahedron pattern. The icosahedron pattern further comprises twelve vertex dimples, wherein each vertex dimple is surrounded by five multi-lobed dimples. 
   In accordance to another aspect of the present invention, the golf ball comprises uniform multi-lobed dimples and non-uniform multi-lobed dimples arranged in an icosahedron pattern. Preferably, the uniform lobed dimples occupy a substantial portion of the outer surface on the golf ball and the non-uniform multi-lobed dimples surround the vertex dimples to improve dimple coverage. 
   In accordance to another aspect of the present invention, the number of lobes of each multi-lobed dimple is the same as the number of dimples surrounding said multi-lobed dimple. Hence, each multi-lobed dimple in the hexagonal array comprises six lobes, and each vertex dimple comprises five lobes. 
   In accordance to another aspect of the present invention, the apex points of adjacent lobes straddle a line connecting the centers of adjacent dimples to maximize dimple coverage. 
   The multi-lobed dimples of the present invention improve the aerodynamic performance of a golf ball, because they provide greater dimple circumference on the golf ball than non-overlapping conventional circular dimples. They also provide higher dimple coverage, i.e., as much as about 93%, than dimensionally similar non-overlapping conventional circular dimples. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings which form a part of the specification and are to be read in conjunction therewith and in which like reference numerals are used to indicate like parts in the various views: 
       FIGS. 1(A)-1(E)  are plan views of preferred embodiments of the uniform multi-lobed dimple of the present invention; 
       FIGS. 2(A)-2(D)  are sectional views along lines  2 A- 2 A,  2 B- 2 B,  2 C- 2 C and  2 D- 2 D, respectively, in  FIGS. 1(A)-1(C) ;  FIG. 2(E)  is an alternative embodiment of  FIG. 2(A) ; 
       FIG. 3  is a plan view of another embodiment of the dimple of the present invention; 
       FIG. 4  is a plan view of another embodiment of the dimple of the present invention; 
       FIG. 5  is a plan view of a hexagonal packing of a preferred embodiment of the present invention; 
       FIG. 6  is a plan view of a packing array for a vertex dimple of a preferred embodiment of the present invention; 
       FIG. 7  is a plan view of a hexagonal packing of conventional circular dimples; 
       FIGS. 8(A)-8(D)  are plan views of an exemplary uniform multi-lobed dimple with various prominence ratios; 
       FIGS. 9(A)-9(D)  are plan views of preferred embodiments of the non-uniform multi-lobed dimples of the present invention; and 
       FIG. 10  is a plan view of another preferred embodiment of the non-uniform multi-lobed dimple of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   As illustrated in  FIGS. 1(A) to 1(E) , where like numbers designate like parts, reference number  10  generally designates the inventive multi-lobed dimple of the present invention and reference numbers  12 ,  14 ,  16 ,  18  and  20  specifically designate some of the preferred embodiments of the multi-lobed dimple  10  in accordance to the present invention. Preferably, the multi-lobed dimple  10 , as shown in  FIGS. 1-6 , comprises uniform lobes, i.e., uniform size, shape and angular spacing. 
   In accordance to one aspect of the invention, the dimple  10  comprises a plurality of lobes  22 , arranged radially around the center C of the dimple. Each lobe  22  is preferably separated from adjacent lobes by radial lines or spoke-like ridges  24 . Preferably, dimple  10  has at least three lobes.  FIGS. 1(A)-1(E)  illustrate dimple  10  having three lobes to seven lobes, respectively. Dimple  10  may have any number of lobes and the present invention is not limited to any specific embodiment illustrated herein. 
   Circumferential segments  26  of lobe  22 , which are positioned between two adjacent spoke-like ridges  24 , are preferably curved. Suitable curved shapes include, but are not limited to, elliptical, parabolic, conic, hyperbolic, sinusoidal, or any combination of these curves, e.g., part of circumferential segment  26  may be elliptical while the other portions may be parabolic or hyperbolic. They may include arbitrary curved shapes that can be defined by spline curves. While a circumferential segment  26  may incorporate localized concavities, it is preferred that each segment be wholly convex. Also, the apex of each lobe may or may not be positioned at the midpoint between adjacent troughs of each lobe. 
   The surfaces of multi-lobed dimple  10  are preferably curved and preferably comprise a plurality of curved profiles, as shown in cross-sectional views  FIGS. 2(A)-2(E) . Preferably, each lobe  22  has a curved profile  30  along the radial direction, i.e., a curved profile extending from the apex point of the lobe radially to the center C of the dimple. Each lobe  22  also has a curved profile  32  extending across the width of the lobe, e.g., a curved profile extending from one spoke-like ridge  24  to the adjacent spoke-like ridge  24 . These two curved profiles  30 ,  32  may have the same or different curvatures. 
     FIG. 2(A)  is a representative cross-sectional view along line  2 A- 2 A in  FIG. 1(A)  of a dimple with an odd number of lobes, such as dimples  12 ,  16  and  20 , and  FIG. 2(B)  is a representative cross-sectional view along line  2 B- 2 B in  FIG. 1(B)  of a dimple with an even number of lobes, such as dimples  14  and  18 .  FIG. 2(B)  is also a representative sectional view along line  2 B- 2 B of an odd-number lobe dimple, such as  FIG. 1(C) .  FIGS. 2(C) and 2(D)  are representative cross-sectional views along lines  2 C- 2 C and  2 D- 2 D in  FIG. 1(B) , respectively, of a single lobe  22 .  FIG. 2(E)  is an alternative embodiment of  FIG. 2(A) . 
   As shown in  FIG. 2(A) , spoke-like ridge  24  tapers in elevation from the edge of the dimple toward the center C of the dimple. Spoke-like ridge  24  may have a curved profile as shown, or alternatively it may have a linear profile as illustrated in  FIG. 2(E) . Spoke-like ridge  24  may extend to the center C of the dimple or may extend only partly toward the center. Preferably, the width of each lobe  22  comprises curved profile  32 , as shown in  FIG. 2(C) , wherein curved profile  32  terminates at spoke-like ridge  24  and abuts curved profiles  32  of adjacent lobes, as shown in  FIG. 2(D) . 
   An important aspect of multi-lobed dimple  10  is that the center region of the dimple is substantially uninterrupted, as illustrated in  FIG. 2(B) . In other words, the curved profile  30  extending along the length of lobe  22  is substantially smooth, and the curved profile  30  of one lobe continuously and smoothly extends to and abuts with the curved profile  30  of the opposite lobe or near-opposite lobe, as shown in  FIG. 2(B) . Some discontinuity at the abutment of curved profiles  30  or at the abutment of curved profile  30  and spoke-like ridge  24  is acceptable, so long as the center region of dimple  10 , where these structures abut, remains substantially smooth. The center region may also be substantially smooth and flat, particularly when spoke-like ridges  24  do not extend to the center of the dimple. Hence, the dimple  10  of the present invention has overcome the poor aerodynamic performance of sharp connecting apices and linear edges of the polygonal structures disclosed in the prior art. 
   In accordance to another aspect of the present invention, circumferential segment  26  of lobe  22  may have a lesser amount of curvature or prominence as illustrated in  FIG. 1(A)-1(E) , or a higher amount of curvature or prominence as shown in  FIG. 3 . The prominence of circumferential segment  26  is defined as the ratio of an inside radius, Ri, to an outside radius, Ro. Ri extends from the center C of the dimple to trough point  34 , where two adjacent lobes  22  abut. Ro extends from the center C of dimple to the apex point  36  of lobe  22 . When the ratio, Ri/Ro, is close to 1.0, the prominence of circumferential segment  26  is low, such as those shown in  FIGS. 1(A)-1(E) . When the ratio, Ri/Ro, is significantly less than 1.0, the prominence of circumferential segment  26  is high, such as those shown in  FIG. 3 . When the ratio, Ri/Ro, equals 1.0, the dimple is substantially circular. Preferred Ri/Ro ratio in accordance to the present invention is between about 0.70 and about 0.95, more preferably between about 0.75 and about 0.90 and most preferably between about 0.80 and about 0.90. For uniform lobes  22  illustrated in  FIGS. 1-6 , the prominence of the lobes in a single dimple  10  in is also uniform, and the prominence of each lobe is the same as the prominence of the dimple  10 .  FIGS. 8(A)-8(D)  illustrate exemplary dimple  18  with prominence ratios of 0.70, 0.80, 0.90 and 0.95, respectively. 
   Alternatively, spoke-like ridge  24  may be optionally omitted from dimple  10 , as shown in  FIG. 4 . The perimeter of dimple  10  may also be rounded at points  34 ′, where two adjacent lobes abut, to increase the smoothness of the circumference of the dimple. 
   Dimples  10  advantageously improve the aerodynamic performance of the golf ball. First, dimples  10  comprise spoke-like ridges  24 , which improve the airflow over the dimples, while the perimeter remains substantially round and smooth to take advantage of the superior aerodynamic performance of round dimples. Without being limited to any particular theory, as disclosed in co-pending patent application Ser. No. 09/847,764, filed on May 2, 2001, entitled “Golf Ball Dimples,” and assigned to the same assignee as the present invention, structures formed on the dimple surfaces agitate or energize the air flow over the dimple surfaces and thereby reducing the thickness of the boundary layer above dimple surfaces. The disclosure of this co-pending patent application is incorporated herein by reference in its entirety. 
   Another advantage realized from multi-lobed dimples  10  of the present invention is that due to the shape of the perimeter of dimples  10 , the dimple coverage on a golf ball can be increased to more than about 90%, and more preferably to at least about 93%. In order to achieve the highest possible dimple coverage, each multi-lobed dimple is preferably surrounded by six other multi-lobed dimples that are touching or nearly touching it or each other in a hexagonal packing as illustrated in  FIG. 5 . It has been shown that hexagonal packing provides the highest percentage of dimple coverage. Among the commonly used dimple patterns, those based on the geometry of an icosahedron, i.e., a polyhedron having twenty triangular faces, usually provide the closest approximation to full hexagonal packing. Icosahedron patterns typically have twelve vertex dimples, and in accordance to the present invention each vertex multi-lobed dimple is preferably surrounded by five multi-lobed dimples, as illustrated in  FIG. 6 . Preferably, the vertex dimples are smaller in size than the surrounding dimples to maximize the dimple coverage. 
   In accordance to another aspect of the invention, preferably the number of lobes in each multi-lobed dimple  10  matches the number of neighboring dimples. For example, center dimple  18  in  FIG. 5  preferably has six lobes  22  and is surrounded by six dimples. Center dimple  16  in  FIG. 6  has five lobes  22  and is surrounded by five dimples. In the preferred icosahedron pattern, the twelve vertex dimples are the five-lobed dimples  16  surrounded by five six-lobed dimples  18 . The remaining dimples, including the ones surrounding the vertex dimples  16 , are the six-lobed dimples  18  and are surrounded by six neighboring dimples. 
   In accordance to another aspect of the invention, optimal dimple coverage can be realized by a preferred orientation of the dimples. As shown in  FIGS. 5 and 6 , preferably the apex points  36  of two adjacent lobes  22  straddle an imaginary line  40  (shown in phantom) that connects the centers of any two neighboring dimples. In other words, any two adjacent apex points  36  are separated by a line  40 . For example, in the hexagonal packing shown in  FIG. 5 , any two adjacent apex points  36  are divided by a line  40 , and are located equal distances or substantially equal distances from line  40 . In the vertex dimple packing shown in  FIG. 6 , any two apex points  36  are divided by a line  40 . 
   Arrangement of multi-lobed dimples  10  in accordance to the present invention produces significantly higher dimple coverage than arrangement with conventional circular dimples. A region of a golf ball with the six-lobed dimples  18  arranged in a hexagonal array, as shown in  FIG. 5 , has about 93% dimple coverage. In comparison, the dimple coverage of a dimensionally similar hexagonal array of conventional circular dimples as shown in  FIG. 7  is only about 88%. As used herein, “dimensionally similar” means that the centers C of the multi-lobed dimples  18  arranged in hexagonal array shown in  FIG. 5  are located at the same corresponding positions as the centers C of the conventional dimples shown in  FIG. 7 . On commercial golf balls with at least one seam line, the dimple coverage would be a few percentage points less. However, the dimple coverage with the inventive multi-lobed dimples remains significantly higher than the dimple coverage with conventional circular dimples. Hence it can be readily seen that the dimples  10  of the present invention provide much higher dimple coverage to produce golf balls with superior aerodynamic performance. 
   Another advantage of the dimples  10  is that for dimensionally similar dimple arrangements, such as the hexagonal arrays shown in  FIGS. 5 and 7 , dimples  10  provide more dimple circumference than non-overlapping conventional circular dimples. This is one of the results of having higher percentage of dimple coverage on the golf ball. As discussed above, since dimple circumference creates turbulence in the boundary layer, the greater dimple circumference length of multi-lobed dimples  10  improves the aerodynamics of golf balls. 
   In accordance to another aspect of the present invention, the multi-lobed dimples also include non-uniform lobes. As illustrated in  FIGS. 9(A)-9(D)  and  FIG. 10 , the size, shape and angular spacing of the lobes of dimple  42  are not uniform. As used herein, reference number  42  generally designates the inventive non-uniform multi-lobed dimple of the present invention, and reference numbers  44 ,  46 ,  48 ,  50  and  52  specifically designate some of the preferred embodiments of the non-uniform multi-lobed dimple in accordance to the present invention. Non-uniform multi-lobed dimples include concentric dimples and eccentric dimples. Concentric non-uniform multi-lobed dimples are dimples wherein the center of the inside radius, Ri, coincides with the center of the outside radius, Ro. Eccentric non-uniform multi-lobed dimples are dimples wherein Ri is spaced apart from Ro. 
   An example of concentric non-uniform multi-lobed dimple  44  is illustrated in  FIG. 9(A) . The lobes of dimple  44  vary in width, i.e., the distance between adjacent troughs  34 , and in prominence, i.e., the curvature of the circumferential segments. However, the inside radius, Ri, is the same for all the lobes, and the outside radius is also the same for all the lobes. Concentric non-uniform multi-lobed dimples also include dimples that have constant Ri for all the lobes but varying Ro, dimples that have constant Ro but varying Ri and dimples that have varying Ro and varying Ri. 
   Dimple  46  is an example of a concentric non-uniform multi-lobed dimple with constant Ri and varying Ro. As shown in  FIG. 9(B) , the inside radius of the lobes is the same, since the troughs  34  are located at a same radial distance from the center, and the apex points of the lobes are located at varying radial distances from this center. Dimple  48 , as shown in  FIG. 9(C) , represents an example of a concentric non-uniform multi-lobed dimple with constant Ro and varying Ri. Dimple  50 , as illustrated in  FIG. 9(D) , is an example of a concentric non-uniform multi-lobed dimple with varying Ro and varying Ri. 
   The prominence ratio of the concentric non-uniform multi-lobed dimples, including dimples  44 ,  46 ,  48  and  50 , is the ratio of Ri (or the average Ri, if Ri is varying) to Ro (or the average Ro, if Ro is varying). The average radius, Ro or Ri, is the average of the radii of all the lobes or the average between the maximum radius and the minimum radius. 
   Dimple  52 , as shown in  FIG. 10 , illustrates an example of the eccentric non-uniform multi-lobed dimple. As shown, the center Ci of the inside radius Ri is spaced apart from the center Co of the outside radius Ro. Also as shown, Ri and Ro are constant in dimple  52 . Similar to the concentric dimples discussed above, either Ri or Ro may vary, or both Ro and Ri may vary. The prominence ratio for the eccentric non-uniform multi-lobed dimples is also defined as the ratio of Ri (or average Ri) to Ro (or average Ro). 
   An advantage of non-uniform multi-lobed dimples  42  is that these dimples can be used to more efficiently fill spaces that are somewhat irregular in shape. For example, they can be used instead of uniform multi-lobed dimples  10  around the vertex dimples to fill-in gaps  54 , as shown in  FIG. 6 . Lobes from non-uniform dimples  42  may be selectively enlarged to fill-in as much of gaps  54  as possible. The availability of concentric or eccentric multi-lobed dimples with constant or varying Ri and/or Ro provides golf ball designers with the tools to reduce further the land areas in various types of dimple patterns. 
   The prominence ratios described above have been expressed as ratios of Ri to Ro, or averages thereof. Other ratios may also be used to express the curvature/prominence of the circumferential segments, or the prominence of the dimple. For example, the prominence ratio may alternatively be expressed as a ratio of the difference between Ri and Ro to the width of each lobe, i.e., the linear distance between the troughs, i.e., (Ro-Ri)/(W). The present invention is, therefore, not limited to any particular definition of prominence or curvature. 
   Alternatively, a golf ball may include inventive dimples  10 , as well as conventional dimples. For example, a golf ball with an icosahedron dimple pattern may have dimples  10  arranged along the edges of the icosahedron triangles, and conventional dimples located within the triangles. Furthermore, dimples  10  may have different sizes in order to further improve dimple coverage, similar to the dimple arrangements disclosed in U.S. Pat. Nos. 5,957,786 and 6,358,161B1. The disclosures of the &#39;786 and &#39;161B1 patents are hereby incorporated herein by reference, in their entireties. As disclosed by these references, a golf ball may have circular dimples of many different sizes arranged in an icosahedron pattern to maximize dimple coverage. Multi-lobed dimples  10  in a plurality of sizes may be arranged on a golf ball in a similar pattern. 
   Alternatively, multi-lobed dimples  10  of the present invention may be arranged in an octahedron or dodecahedron pattern or other patterns. The present invention is not limited to any particular dimple pattern. Additionally, a multi-lobed dimple in accordance to the present invention may comprise at least two lobes and the remaining portion of the dimple is either circular or polygonal. 
   While various descriptions of the present invention are described above, it is understood that the various features of the embodiments of the present invention shown herein can be used singly or in combination thereof. The multi-lobed dimples of the present invention can be incorporated into other types of objects in flight. Additionally, a plurality of multi-lobed dimples having different Ri/Ro ratios, different number of lobes and different sizes can be incorporated on a single golf ball. This invention is also not to be limited to the specifically preferred embodiments depicted therein.