# Patent

## Title
Low lift golf ball

## Abstract

A golf ball having a plurality of dimples formed on its outer surface, the outer surface of the golf ball being divided into plural areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, each area of the second group abutting one or more areas of the first group, the first and second groups of areas and dimple shapes and dimensions being configured such that the golf ball is spherically symmetrical as defined by the United States Golf Association (USGA) Symmetry Rules, and such that the golf ball exhibits a lift coefficient (CL) of less than about 0.250 over a range of Reynolds Number (Re) from about 120,000 to about 180,000 and at a spin rate of about 3,500 rpm.

## Background
RELATED APPLICATIONS INFORMATION
This application claims the benefit under 35 U.S.C. §120 of copending U.S. patent application Ser. No. 12/757,964 filed Apr. 9, 2010 and entitled “A Low Lift Golf Ball,” which in turn claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Application Ser. No. 61/168,134 filed Apr. 9, 2009 and entitled “Golf Ball With Improved Flight Characteristics,” all of which are incorporated herein by reference in their entirety as if set forth in full.
BACKGROUND
1. Technical Field
The embodiments described herein are related to the field of golf balls and, more particularly, to a spherically symmetrical golf ball having a dimple pattern that generates low-lift in order to control dispersion of the golf ball during flight.
2. Related Art
The flight path of a golf ball is determined by many factors. Several of the factors can be controlled to some extent by the golfer, such as the ball's velocity, launch angle, spin rate, and spin axis. Other factors are controlled by the design of the ball, including the ball's weight, size, materials of construction, and aerodynamic properties.
The aerodynamic force acting on a golf ball during flight can be broken down into three separate force vectors: Lift, Drag, and Gravity. The lift force vector acts in the direction determined by the cross product of the spin vector and the velocity vector. The drag force vector acts in the direction opposite of the velocity vector. More specifically, the aerodynamic properties of a golf ball are characterized by its lift and drag coefficients as a function of the Reynolds Number (Re) and the Dimensionless Spin Parameter (DSP). The Reynolds Number is a dimensionless quantity that quantifies the ratio of the inertial to viscous forces acting on the golf ball as it flies through the air. The Dimensionless Spin Parameter is the ratio of the golf ball's rotational surface speed to its speed through the air.
Since the 1990's, in order to achieve greater distances, a lot of golf ball development has been directed toward developing golf balls that exhibit improved distance through lower drag under conditions that would apply to, e.g., a driver shot immediately after club impact as well as relatively high lift under conditions that would apply to the latter portion of, e.g., a driver shot as the ball is descending towards the ground. A lot of this development was enabled by new measurement devices that could more accurately and efficiently measure golf ball spin, launch angle, and velocity immediately after club impact.
Today the lift and drag coefficients of a golf ball can be measured using several different methods including an Indoor Test Range such as the one at the USGA Test Center in Far Hills, N.J., or an outdoor system such as the Trackman Net System made by Interactive Sports Group in Denmark. The testing, measurements, and reporting of lift and drag coefficients for conventional golf balls has generally focused on the golf ball spin and velocity conditions for a well hit straight driver shot—approximately 3,000 rpm or less and an initial ball velocity that results from a driver club head velocity of approximately 80-100 mph.
For right-handed golfers, particularly higher handicap golfers, a major problem is the tendency to “slice” the ball. The unintended slice shot penalizes the golfer in two ways: 1) it causes the ball to deviate to the right of the intended flight path and 2) it can reduce the overall shot distance.
A sliced golf ball moves to the right because the ball's spin axis is tilted to the right. The lift force by definition is orthogonal to the spin axis and thus for a sliced golf ball the lift force is pointed to the right.
The spin-axis of a golf ball is the axis about which the ball spins and is usually orthogonal to the direction that the golf ball takes in flight. If a golf ball's spin axis is 0 degrees, i.e., a horizontal spin axis causing pure backspin, the ball will not hook or slice and a higher lift force combined with a 0-degree spin axis will only make the ball fly higher. However, when a ball is hit in such a way as to impart a spin axis that is more than 0 degrees, it hooks, and it slices with a spin axis that is less than 0 degrees. It is the tilt of the spin axis that directs the lift force in the left or right direction, causing the ball to hook or slice. The distance the ball unintentionally flies to the right or left is called Carry Dispersion. A lower flying golf ball, i.e., having a lower lift, is a strong indicator of a ball that will have lower Carry Dispersion.
The amount of lift force directed in the hook or slice direction is equal to: Lift Force * Sine (spin axis angle). The amount of lift force directed towards achieving height is: Lift Force * Cosine (spin axis angle).
A common cause of a sliced shot is the striking of the ball with an open clubface. In this case, the opening of the clubface also increases the effective loft of the club and thus increases the total spin of the ball. With all other factors held constant, a higher ball spin rate will in general produce a higher lift force and this is why a slice shot will often have a higher trajectory than a straight or hook shot.
Table 1 shows the total ball spin rates generated by a golfer with club head speeds ranging from approximately 85-105 mph using a 10.5 degree driver and hitting a variety of prototype golf balls and commercially available golf balls that are considered to be low and normal spin golf balls:











TABLE 1







Spin Axis, degree
Typical Total Spin, rpm
Type Shot




















−30
2,500-5,000
Strong Slice



−15
1,700-5,000
Slice



0
1,400-2,800
Straight



+15
1,200-2,500
Hook



+30
1,000-1,800
Strong Hook










If the club path at the point of impact is “outside-in” and the clubface is square to the target, a slice shot will still result, but the total spin rate will be generally lower than a slice shot hit with the open clubface. In general, the total ball spin will increase as the club head velocity increases.
In order to overcome the drawbacks of a slice, some golf ball manufacturers have modified how they construct a golf ball, mostly in ways that tend to lower the ball's spin rate. Some of these modifications include: 1) using a hard cover material on a two-piece golf ball, 2) constructing multi-piece balls with hard boundary layers and relatively soft thin covers in order to lower driver spin rate and preserve high spin rates on short irons, 3) moving more weight towards the outer layers of the golf ball thereby increasing the moment of inertia of the golf ball, and 4) using a cover that is constructed or treated in such a ways so as to have a more slippery surface.
Others have tried to overcome the drawbacks of a slice shot by creating golf balls where the weight is distributed inside the ball in such a way as to create a preferred axis of rotation.
Still others have resorted to creating asymmetric dimple patterns in order to affect the flight of the golf ball and reduce the drawbacks of a slice shot. One such example was the PolaraTM golf ball with its dimple pattern that was designed with different type dimples in the polar and equatorial regions of the ball.
In reaction to the introduction of the Polara golf ball, which was intentionally manufactured with an asymmetric dimple pattern, the USGA created the “Symmetry Rule”. As a result, all golf balls not conforming to the USGA Symmetry Rule are judged to be non-conforming to the USGA Rules of Golf and are thus not allowed to be used in USGA sanctioned golf competitions.
These golf balls with asymmetric dimples patterns or with manipulated weight distributions may be effective in reducing dispersion caused by a slice shot, but they also have their limitations, most notably the fact that they do not conform with the USGA Rules of Golf and that these balls must be oriented a certain way prior to club impact in order to display their maximum effectiveness.
The method of using a hard cover material or hard boundary layer material or slippery cover will reduce to a small extent the dispersion caused by a slice shot, but often does so at the expense of other desirable properties such as the ball spin rate off of short irons or the higher cost required to produce a multi-piece ball.
SUMMARY
A low lift golf ball is described herein.
According to one aspect, a golf ball having a plurality of dimples formed on its outer surface, the outer surface of the golf ball being divided into plural areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, each area of the second group abutting one or more areas of the first group, the first and second groups of areas and dimple shapes and dimensions being configured such that the golf ball is spherically symmetrical as defined by the United States Golf Association (USGA) Symmetry Rules, and such that the golf ball exhibits a lift coefficient (CL) of less than about 0.250 over a range of Reynolds Number (Re) from about 120,000 to about 180,000 and at a spin rate of about 3,500 rpm.
These and other features, aspects, and embodiments are described below in the section entitled “Detailed Description.”



BRIEF DESCRIPTION OF THE DRAWINGS
Features, aspects, and embodiments are described in conjunction with the attached drawings, in which:
FIG. 1 is a graph of the total spin rate versus the ball spin axis for various commercial and prototype golf balls hit with a driver at club head speed between 85-105 mph;
FIG. 2 is a picture of golf ball with a dimple pattern in accordance with one embodiment;
FIG. 3 is a top-view schematic diagram of a golf ball with a cuboctahedron pattern in accordance with one embodiment and in the poles-forward-backward (PFB) orientation;
FIG. 4 is a schematic diagram showing the triangular polar region of another embodiment of the golf ball with a cuboctahedron pattern of FIG. 3;
FIG. 5 is a graph of the total spin rate and Reynolds number for the TopFlite XL Straight golf ball and a B2 prototype ball, configured in accordance with one embodiment, hit with a driver club using a Golf Labs robot;
FIG. 6 is a graph or the Lift Coefficient versus Reynolds Number for the golf ball shots shown in FIG. 5;
FIG. 7 is a graph of Lift Coefficient versus flight time for the golf ball shots shown in FIG. 5;
FIG. 8 is a graph of the Drag Coefficient versus Reynolds Number for the golf ball shots shown in FIG. 5;
FIG. 9 is a graph of the Drag Coefficient versus flight time for the golf ball shots shown in FIG. 5;
FIG. 10 is a diagram illustrating the relationship between the chord depth of a truncated and a spherical dimple in accordance with one embodiment;
FIG. 11 is a graph illustrating the max height versus total spin for all of a 172-175 series golf balls, configured in accordance with certain embodiments, and the Pro V1® when hit with a driver imparting a slice on the golf balls;
FIG. 12 is a graph illustrating the carry dispersion for the balls tested and shown in FIG. 11;
FIG. 13 is a graph of the carry dispersion versus initial total spin rate for a golf ball with the 172 dimple pattern and the ProV1® for the same robot test data shown in FIG. 11;
FIG. 14 is a graph of the carry dispersion versus initial total spin rate for a golf ball with the 173 dimple pattern and the ProV1® for the same robot test data shown in FIG. 11;
FIG. 15 is a graph of the carry dispersion versus initial total spin rate for a golf ball with the 174 dimple pattern and the ProV1® for the same robot test data shown in FIG. 11;
FIG. 16 is a graph of the carry dispersion versus initial total spin rate for a golf ball with the 175 dimple pattern and the ProV1® for the same robot test data shown in FIG. 11;
FIG. 17 is a graph of the wind tunnel testing results showing Lift Coefficient (CL) versus DSP for the 173 golf ball against different Reynolds Numbers;
FIG. 18 is a graph of the wind tunnel test results showing the CL versus DSP for the Pro V1 golf ball against different Reynolds Numbers;
FIG. 19 is picture of a golf ball with a dimple pattern in accordance with another embodiment;
FIG. 20 is a graph of the lift coefficient versus Reynolds Number at 3,000 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and a 273 dimple pattern in accordance with certain embodiments;
FIG. 21 is a graph of the lift coefficient versus Reynolds Number at 3,500 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and 273 dimple pattern;
FIG. 22 is a graph of the lift coefficient versus Reynolds Number at 4,000 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and 273 dimple pattern;
FIG. 23 is a graph of the lift coefficient versus Reynolds Number at 4,500 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and 273 dimple pattern;
FIG. 24 is a graph of the lift coefficient versus Reynolds Number at 5,000 rpm spin rate for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern and 273 dimple pattern;
FIG. 25 is a graph of the lift coefficient versus Reynolds Number at 4000 RPM initial spin rate for the 273 dimple pattern and 2-3 dimple pattern balls of Tables 10 and 11;
FIG. 26 is a graph of the lift coefficient versus Reynolds Number at 4500 RPM initial spin rate for the 273 dimple pattern and 2-3 dimple pattern balls of Tables 10 and 11;
FIG. 27 is a graph of the drag coefficient versus Reynolds Number at 4000 RPM initial spin rate for the 273 dimple pattern and 2-3 dimple pattern balls of Tables 10 and 11; and
FIG. 28 is a graph of the drag coefficient versus Reynolds Number at 4500 RPM initial spin rate for the 273 dimple pattern and 2-3 dimple pattern balls of Tables 10 and 11.



DETAILED DESCRIPTION
The embodiments described herein may be understood more readily by reference to the following detailed description. However, the techniques, systems, and operating structures described can be embodied in a wide variety of forms and modes, some of which may be quite different from those in the disclosed embodiments. Consequently, the specific structural and functional details disclosed herein are merely representative. It must be noted that, as used in the specification and the appended claims, the singular forms “a”, “an”, and “the” include plural referents unless the context clearly indicates otherwise.
The embodiments described below are directed to the design of a golf ball that achieves low lift right after impact when the velocity and spin are relatively high. In particular, the embodiments described below achieve relatively low lift even when the spin rate is high, such as that imparted when a golfer slices the golf ball, e.g., 3500 rpm or higher. In the embodiments described below, the lift coefficient after impact can be as low as about 0.18 or less, and even less than 0.15 under such circumstances. In addition, the lift can be significantly lower than conventional golf balls at the end of flight, i.e., when the speed and spin are lower. For example, the lift coefficient can be less than 0.20 when the ball is nearing the end of flight.
As noted above, conventional golf balls have been designed for low initial drag and high lift toward the end of flight in order to increase distance. For example, U.S. Pat. No. 6,224,499 to Ogg teaches and claims a lift coefficient greater than 0.18 at a Reynolds number (Re) of 70,000 and a spin of 2000 rpm, and a drag coefficient less than 0.232 at a Re of 180,000 and a spin of 3000 rpm. One of skill in the art will understand that and Re of 70,000 and spin of 2000 rpm are industry standard parameters for describing the end of flight. Similarly, one of skill in the art will understand that a Re of greater than about 160,000, e.g., about 180,000, and a spin of 3000 rpm are industry standard parameters for describing the beginning of flight for a straight shot with only back spin.
The lift (CL) and drag coefficients (CD) vary by golf ball design and are generally a function of the velocity and spin rate of the golf ball. For a spherically symmetrical golf ball the lift and drag coefficients are for the most part independent of the golf ball orientation. The maximum height a golf ball achieves during flight is directly related to the lift force generated by the spinning golf ball while the direction that the golf ball takes, specifically how straight a golf ball flies, is related to several factors, some of which include spin rate and spin axis orientation of the golf ball in relation to the golf ball's direction of flight. Further, the spin rate and spin axis are important in specifying the direction and magnitude of the lift force vector.
The lift force vector is a major factor in controlling the golf ball flight path in the x, y, and z directions. Additionally, the total lift force a golf ball generates during flight depends on several factors, including spin rate, velocity of the ball relative to the surrounding air and the surface characteristics of the golf ball.
For a straight shot, the spin axis is orthogonal to the direction the ball is traveling and the ball rotates with perfect backspin. In this situation, the spin axis is 0 degrees. But if the ball is not struck perfectly, then the spin axis will be either positive (hook) or negative (slice). FIG. 1 is a graph illustrating the total spin rate versus the spin axis for various commercial and prototype golf balls hit with a driver at club head speed between 85-105 mph. As can be seen, when the spin axis is negative, indicating a slice, the spin rate of the ball increases. Similarly, when the spin axis is positive, the spin rate decreases initially but then remains essentially constant with increasing spin axis.
The increased spin imparted when the ball is sliced, increases the lift coefficient (CL). This increases the lift force in a direction that is orthogonal to the spin axis. In other words, when the ball is sliced, the resulting increased spin produces an increased lift force that acts to “pull” the ball to the right. The more negative the spin axis, the greater the portion of the lift force acting to the right, and the greater the slice.
Thus, in order to reduce this slice effect, the ball must be designed to generate a relatively lower lift force at the greater spin rates generated when the ball is sliced.
Referring to FIG. 2, there is shown golf ball 100, which provides a visual description of one embodiment of a dimple pattern that achieves such low initial lift at high spin rates. FIG. 2 is a computer generated picture of dimple pattern 173. As shown in FIG. 2, golf ball 100 has an outer surface 105, which has a plurality of dissimilar dimple types arranged in a cuboctahedron configuration. In the example of FIG. 2, golf ball 100 has larger truncated dimples within square region 110 and smaller spherical dimples within triangular region 115 on the outer surface 105. The example of FIG. 2 and other embodiments are described in more detail below; however, as will be explained, in operation, dimple patterns configured in accordance with the embodiments described herein disturb the airflow in such a way as to provide a golf ball that exhibits low lift at the spin rates commonly seen with a slice shot as described above.
As can be seen, regions 110 and 115 stand out on the surface of ball 100 unlike conventional golf balls. This is because the dimples in each region are configured such that they have high visual contrast. This is achieved for example by including visually contrasting dimples in each area. For example, in one embodiment, flat, truncated dimples are included in region 110 while deeper, round or spherical dimples are included in region 115. Additionally, the radius of the dimples can also be different adding to the contrast.
But this contrast in dimples does not just produce a visually contrasting appearance; it also contributes to each region having a different aerodynamic effect. Thereby, disturbing air flow in such a manner as to produce low lift as described herein.
While conventional golf balls are often designed to achieve maximum distance by having low drag at high speed and high lift at low speed, when conventional golf balls are tested, including those claimed to be “straighter,” it can be seen that these balls had quite significant increases in lift coefficients (CL) at the spin rates normally associated with slice shots. Whereas balls configured in accordance with the embodiments described herein exhibit lower lift coefficients at the higher spin rates and thus do not slice as much.
A ball configured in accordance with the embodiments described herein and referred to as the B2 Prototype, which is a 2-piece Surlyn-covered golf ball with a polybutadiene rubber based core and dimple pattern “273”, and the TopFlite® XL Straight ball were hit with a Golf Labs robot using the same setup conditions so that the initial spin rates were about 3,400-3,500 rpm at a Reynolds Number of about 170,000. The spin rate and Re conditions near the end of the trajectory were about 2,900 to 3,200 rpm at a Reynolds Number of about 80,000. The spin rates and ball trajectories were obtained using a 3-radar unit Trackman Net System. FIG. 5 illustrates the full trajectory spin rate versus Reynolds Number for the shots and balls described above.
The B2 prototype ball had dimple pattern design 273, shown in FIG. 4. Dimple pattern design 273 is based on a cuboctahedron layout and has a total of 504 dimples. This is the inverse of pattern 173 since it has larger truncated dimples within triangular regions 115 and smaller spherical dimples within square regions or areas 110 on the outer surface of the ball. A spherical truncated dimple is a dimple which has a spherical side wall and a flat inner end, as seen in the triangular regions of FIG. 4. The dimple patterns 173 and 273, and alternatives, are described in more detail below with reference to Tables 5 to 11.
FIG. 6 illustrates the CL versus Re for the same shots shown in FIG. 5; TopFlite® XL Straight and the B2 prototype golf ball which was configured in accordance with the systems and methods described herein. As can be seen, the B2 ball has a lower CL over the range of Re from about 75,000 to 170,000. Specifically, the CL for the B2 prototype never exceeds 0.27, whereas the CL for the TopFlite® XL Straight gets well above 0.27. Further, at a Re of about 165,000, the CL for the B2 prototype is about 0.16, whereas it is about 0.19 or above for the TopFlite® XL Straight.
FIGS. 5 and 6 together illustrate that the B2 ball with dimple pattern 273 exhibits significantly less lift force at spin rates that are associated with slices. As a result, the B2 prototype will be much straighter, i.e., will exhibit a much lower carry dispersion. For example, a ball configured in accordance with the embodiments described herein can have a CL of less than about 0.22 at a spin rate of 3,200-3,500 rpm and over a range of Re from about 120,000 to 180,000. For example, in certain embodiments, the CL can be less than 0.18 at 3500 rpm for Re values above about 155,000.
This is illustrated in the graphs of FIGS. 20-24, which show the lift coefficient versus Reynolds Number at spin rates of 3,000 rpm, 3,500 rpm, 4,000 rpm, 4,500 rpm and 5,000 rpm, respectively, for the TopFlite® XL Straight, Pro V1®, 173 dimple pattern, and 273 dimple pattern. To obtain the regression data shown in FIGS. 23-28, a Trackman Net System consisting of 3 radar units was used to track the trajectory of a golf ball that was struck by a Golf Labs robot equipped with various golf clubs. The robot was setup to hit a straight shot with various combinations of initial spin and velocity. A wind gauge was used to measure the wind speed at approximately 20 ft elevation near the robot location. The Trackman Net System measured trajectory data (x, y, z location vs. time) were then used to calculate the lift coefficients (CL) and drag coefficients (CD) as a function of measured time-dependent quantities including Reynolds Number, Ball Spin Rate, and Dimensionless Spin Parameter. Each golf ball model or design was tested under a range of velocity and spin conditions that included 3,000-5,000 rpm spin rate and 120,000-180,000 Reynolds Number. It will be understood that the Reynolds Number range of 150,000-180,000 covers the initial ball velocities typical for most recreational golfers, who have club head speeds of 85-100 mph. A 5-term multivariable regression model was then created from the data for each ball designed in accordance with the embodiments described herein for the lift and drag coefficients as a function of Reynolds Number (Re) and Dimensionless Spin Parameter (W), i.e., as a function of Re, W, Re^2, W^2, ReW, etc. Typically the predicted CD and CL values within the measured Re and W space (interpolation) were in close agreement with the measured CD and CL values. Correlation coefficients of >96% were typical.
Under typical slice conditions, with spin rates of 3,500 rpm or greater, the 173 and 273 dimple patterns exhibit lower lift coefficients than the other golf balls. Lower lift coefficients translate into lower trajectory for straight shots and less dispersion for slice shots. Balls with dimple patterns 173 and 273 have approximately 10% lower lift coefficients than the other golf balls under Re and spin conditions characteristics of slice shots. Robot tests show the lower lift coefficients result in at least 10% less dispersion for slice shots.
For example, referring again to FIG. 6, it can be seen that while the TopFlite® XL Straight is suppose to be a straighter ball, the data in the graph of FIG. 6 illustrates that the B2 prototype ball should in fact be much straighter based on its lower lift coefficient. The high CL for the TopFlite® XL Straight means that the TopFlite® XL Straight ball will create a larger lift force. When the spin axis is negative, this larger lift force will cause the TopFlite® XL Straight to go farther right increasing the dispersion for the TopFlite® XL Straight. This is illustrated in Table 2:











TABLE 2







Ball
Dispersion, ft
Distance, yds









TopFlite ® XL Straight
95.4
217.4



Ball 173
78.1
204.4










FIG. 7 shows that for the robot test shots shown in FIG. 5 the B2 ball has a lower CL throughout the flight time as compared to other conventional golf balls, such as the TopFlite® XL Straight. This lower CL throughout the flight of the ball translates in to a lower lift force exerted throughout the flight of the ball and thus a lower dispersion for a slice shot.
As noted above, conventional golf ball design attempts to increase distance, by decreasing drag immediately after impact. FIG. 8 shows the drag coefficient (CD) versus Re for the B2 and TopFlite® XL Straight shots shown in FIG. 5. As can be seen, the CD for the B2 ball is about the same as that for the TopFlite® XL Straight at higher Re. Again, these higher Re numbers would occur near impact. At lower Re, the CD for the B2 ball is significantly less than that of the TopFlite® XL Straight.
In FIG. 9 it can be seen that the CD curve for the B2 ball throughout the flight time actually has a negative inflection in the middle. Thus, the drag for the B2 ball will be less in the middle of the ball's flight as compared to the TopFlite XL Straight. It should also be noted that while the B2 does not carry quite as far as the TopFlite XL Straight, testing reveals that it actually roles farther and therefore the overall distance is comparable under many conditions. This makes sense of course because the lower CL for the B2 ball means that the B2 ball generates less lift and therefore does not fly as high, something that is also verified in testing. Because the B2 ball does not fly as high, it impacts the ground at a shallower angle, which results in increased role.
Returning to FIGS. 2-4, the outer surface 105 of golf ball 100 can include dimple patterns of Archimedean solids or Platonic solids by subdividing the outer surface 105 into patterns based on a truncated tetrahedron, truncated cube, truncated octahedron, truncated dodecahedron, truncated icosahedron, icosidodecahedron, rhombicuboctahedron, rhombicosidodecahedron, rhombitruncated cuboctahedron, rhombitruncated icosidodecahedron, snub cube, snub dodecahedron, cube, dodecahedron, icosahedrons, octahedron, tetrahedron, where each has at least two types of subdivided regions (A and B) and each type of region has its own dimple pattern and types of dimples that are different than those in the other type region or regions.
Furthermore, the different regions and dimple patterns within each region are arranged such that the golf ball 100 is spherically symmetrical as defined by the United States Golf Association (“USGA”) Symmetry Rules. It should be appreciated that golf ball 100 may be formed in any conventional manner such as, in one non-limiting example, to include two pieces having an inner core and an outer cover. In other non-limiting examples, the golf ball 100 may be formed of three, four or more pieces.
Tables 3 and 4 below list some examples of possible spherical polyhedron shapes which may be used for golf ball 100, including the cuboctahedron shape illustrated in FIGS. 2-4. The size and arrangement of dimples in different regions in the other examples in Tables 3 and 4 can be similar or identical to that of FIG. 2 or 4.







TABLE 3





13 Archimedean Solids and 5 Platonic solids - relative


surface areas for the polygonal patches

























% surface


% surface



Name of
# of

area for
# of

area for
# of


Archimedean
Region
Region A
all of the
Region
Region B
all of the
Region


solid
A
shape
Region A's
B
shape
Region B's
C





truncated
30
triangles
17%
20
Hexagons
30%
12


icosidodeca-









hedron









Rhombicos
20
triangles
15%
30
squares
51%
12


idodeca-









hedron









snub
80
triangles
63%
12
Pentagons
37%



dodeca-









hedron









truncated
12
pentagons
28%
20
Hexagons
72%



icosahedron









truncated
12
squares
19%
8
Hexagons
34%
6


cubocta-









hedron









Rhombicub-
8
triangles
16%
18
squares
84%



octahedron









snub cube
32
triangles
70%
6
squares
30%



Icosado-
20
triangles
30%
12
Pentagons
70%



decahedron









truncated
20
triangles
 9%
12
Decagons
91%



dodeca-









hedron









truncated
6
squares
22%
8
Hexagons
78%



octahedron









Cubocta-
8
triangles
37%
6
squares
63%



hedron









truncated
8
triangles
11%
6
Octagons
89%



cube









truncated
4
triangles
14%
4
Hexagons
86%



tetrahedron


















% surface
Total
% surface
% surface
% surface


Name of

area for
number
area per
area per
area per


Archimedean
Region C
all of the
of
single A
single B
single C


solid
shape
Region C's
Regions
Region
Region
Region





truncated
decagons
53%
62
0.6%
1.5%
4.4%


icosidodeca-








hedron








Rhombicos
pentagons
35%
62
0.7%
1.7%
2.9%


idodeca-








hedron








snub


92
0.8%
3.1%



dodeca-








hedron








truncated


32
2.4%
3.6%



icosahedron








truncated
octagons
47%
26
1.6%
4.2%
7.8%


cubocta-








hedron








Rhombicub-


26
2.0%
4.7%



octahedron








snub cube


38
2.2%
5.0%



Icosado-


32
1.5%
5.9%



decahedron








truncated


32
0.4%
7.6%



dodeca-








hedron








truncated


14
3.7%
9.7%



octahedron








Cubocta-


14
4.6%
10.6%



hedron








truncated


14
1.3%
14.9%



cube








truncated


8
3.6%
21.4%



tetrahedron




















TABLE 4







Shape of

Surface area


Name of Platonic Solid
# of Regions
Regions

per Region



















Tetrahedral Sphere
4
triangle
100%
25%


Octahedral Sphere
8
triangle
100%
13%


Hexahedral Sphere
6
squares
100%
17%


Icosahedral Sphere
20
triangles
100%
 5%


Dodecahadral Sphere
12
pentagons
100%
 8%









FIG. 3 is a top-view schematic diagram of a golf ball with a cuboctahedron pattern illustrating a golf ball, which may be ball 100 of FIG. 2 or ball 273 of FIG. 4, in the poles-forward-backward (PFB) orientation with the equator 130 (also called seam) oriented in a vertical plane 220 that points to the right/left and up/down, with pole 205 pointing straight forward and orthogonal to equator 130, and pole 210 pointing straight backward, i.e., approximately located at the point of club impact. In this view, the tee upon which the golf ball 100 would be resting would be located in the center of the golf ball 100 directly below the golf ball 100 (which is out of view in this figure). In addition, outer surface 105 of golf ball 100 has two types of regions of dissimilar dimple types arranged in a cuboctahedron configuration. In the cuboctahedral dimple pattern 173, outer surface 105 has larger dimples arranged in a plurality of three square regions 110 while smaller dimples are arranged in the plurality of four triangular regions 115 in the front hemisphere 120 and back hemisphere 125 respectively for a total of six square regions and eight triangular regions arranged on the outer surface 105 of the golf ball 100. In the inverse cuboctahedral dimple pattern 273, outer surface 105 has larger dimples arranged in the eight triangular regions and smaller dimples arranged in the total of six square regions. In either case, the golf ball 100 contains 504 dimples. In golf ball 173, each of the triangular regions and the square regions containing thirty-six dimples. In golf ball 273, each triangular region contains fifteen dimples while each square region contains sixty four dimples. Further, the top hemisphere 120 and the bottom hemisphere 125 of golf ball 100 are identical and are rotated 60 degrees from each other so that on the equator 130 (also called seam) of the golf ball 100, each square region 110 of the front hemisphere 120 borders each triangular region 115 of the back hemisphere 125. Also shown in FIG. 4, the back pole 210 and front pole (not shown) pass through the triangular region 115 on the outer surface 105 of golf ball 100.
Accordingly, a golf ball 100 designed in accordance with the embodiments described herein will have at least two different regions A and B comprising different dimple patterns and types. Depending on the embodiment, each region A and B, and C where applicable, can have a single type of dimple, or multiple types of dimples. For example, region A can have large dimples, while region B has small dimples, or vice versa; region A can have spherical dimples, while region B has truncated dimples, or vice versa; region A can have various sized spherical dimples, while region B has various sized truncated dimples, or vice versa, or some combination or variation of the above. Some specific example embodiments are described in more detail below.
It will be understood that there is a wide variety of types and construction of dimples, including non-circular dimples, such as those described in U.S. Pat. No. 6,409,615, hexagonal dimples, dimples formed of a tubular lattice structure, such as those described in U.S. Pat. No. 6,290,615, as well as more conventional dimple types. It will also be understood that any of these types of dimples can be used in conjunction with the embodiments described herein. As such, the term “dimple” as used in this description and the claims that follow is intended to refer to and include any type of dimple or dimple construction, unless otherwise specifically indicated.
But first, FIG. 10 is a diagram illustrating the relationship between the chord depth of a truncated and a spherical dimple. The golf ball having a preferred diameter of about 1.68 inches contains 504 dimples to form the cuboctahedral pattern, which was shown in FIGS. 2-4. As an example of just one type of dimple, FIG. 12 shows truncated dimple 400 compared to a spherical dimple having a generally spherical chord depth of 0.012 inches and a radius of 0.075 inches. The truncated dimple 400 may be formed by cutting a spherical indent with a flat inner end, i.e. corresponding to spherical dimple 400 cut along plane A-A to make the dimple 400 more shallow with a flat inner end, and having a truncated chord depth smaller than the corresponding spherical chord depth of 0.012 inches.
The dimples can be aligned along geodesic lines with six dimples on each edge of the square regions, such as square region 110, and eight dimples on each edge of the triangular region 115. The dimples can be arranged according to the three-dimensional Cartesian coordinate system with the X-Y plane being the equator of the ball and the Z direction passing through the pole of the golf ball 100. The angle φ is the circumferential angle while the angle θ is the co-latitude with 0 degrees at the pole and 90 degrees at the equator. The dimples in the North hemisphere can be offset by 60 degrees from the South hemisphere with the dimple pattern repeating every 120 degrees. Golf ball 100, in the example of FIG. 2, has a total of nine dimple types, with four of the dimple types in each of the triangular regions and five of the dimple types in each of the square regions. As shown in Table 5 below, the various dimple depths and profiles are given for various implementations of golf ball 100, indicated as prototype codes 173-175. The actual location of each dimple on the surface of the ball for dimple patterns 172-175 is given in Tables 6-9. Tables 10 and 11 provide the various dimple depths and profiles for dimple pattern 273 of FIG. 4 and an alternative dimple pattern 2-3, respectively, as well as the location of each dimple on the ball for each of these dimple patterns. Dimple pattern 2-3 is similar to dimple pattern 273 but has dimples of slightly larger chord depth than the ball with dimple pattern 273, as shown in Table 11.
















TABLE 5





Dimple ID#
1
2
3
4
5
6
7
8
9















Ball 175
















Type Dimple Region
Triangle
Triangle
Triangle
Triangle
Square
Square
Square
Square
Square


Type Dimple
spherical
spherical
spherical
spherical
truncated
truncated
truncated
truncated
truncated


Dimple Radius, in
0.05
0.0525
0.055
0.0575
0.075
0.0775
0.0825
0.0875
0.095


Spherical Chord
0.008
0.008
0.008
0.008
0.012
0.0122
0.0128
0.0133
0.014


Depth, in











Truncated Chord
n/a
n/a
n/a
n/a
0.0035
0.0035
0.0035
0.0035
0.0035


Depth, in











# of dimples in
9
18
6
3
12
8
8
4
4


region
















Ball 174
















Type Dimple Region
Triangle
Triangle
Triangle
Triangle
Square
Square
Square
Square
Square


Type Dimple
truncated
truncated
truncated
truncated
spherical
spherical
spherical
spherical
spherical


Dimple Radius, in
0.05
0.0525
0.055
0.0575
0.075
0.0775
0.0825
0.0875
0.095


Spherical Chord
0.0087
0.0091
0.0094
0.0098
0.008
0.008
0.008
0.008
0.008


Depth, in











Truncated Chord
0.0035
0.0035
0.0035
0.0035
n/a
n/a
n/a
n/a
n/a


Depth, in











# of dimples in
9
18
6
3
12
8
8
4
4


region
















Ball 173
















Type Dimple Region
Triangle
Triangle
Triangle
Triangle
Square
Square
Square
Square
Square


Type Dimple
spherical
spherical
spherical
spherical
truncated
truncated
truncated
truncated
truncated


Dimple Radius, in
0.05
0.0525
0.055
0.0575
0.075
0.0775
0.0825
0.0875
0.095


Spherical Chord
0.0075
0.0075
0.0075
0.0075
0.012
0.0122
0.0128
0.0133
0.014


Depth, in











Truncated Chord
n/a
n/a
n/a
n/a
0.005
0.005
0.005
0.005
0.005


Depth, in











# of dimples in
9
18
6
3
12
8
8
4
4


region
















Ball 172
















Type Dimple Region
Triangle
Triangle
Triangle
Triangle
Square
Square
Square
Square
Square


Type Dimple
spherical
spherical
spherical
spherical
spherical
spherical
spherical
spherical
spherical


Dimple Radius, in
0.05
0.0525
0.055
0.0575
0.075
0.0775
0.0825
0.0875
0.095


Spherical Chord
0.0075
0.0075
0.0075
0.0075
0.005
0.005
0.005
0.005
0.005


Depth, in











Truncated Chord
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a
n/a


Depth, in











# of dimples in
9
18
6
3
12
8
8
4
4


region
















TABLE 6





(Dimple Pattern 172)


















Dimple #
1



Type
spherical



Radius
0.05



SCD
0.0075



TCD
n/a


#
Phi
Theta





1
0
28.81007


2
0
41.7187


3
5.308533
47.46948


4
9.848338
23.49139


5
17.85912
86.27884


6
22.3436
79.34939


7
24.72264
86.27886


8
95.27736
86.27886


9
97.6564
79.84939


10
102.1409
86.27884


11
110.1517
23.49139


12
114.6915
47.46948


13
120
28.81007


14
120
41.7187


15
125.3085
47.46948


16
129.8483
23.49139


17
137.8591
86.27884


18
142.3436
79.84939


19
144.7226
86.27886


20
215.2774
86.27886


21
217.6564
79.84939


22
222.1409
86.27884


23
230.1517
23.49139


24
234.6915
47.46948


25
240
23.81007


26
240
41.7187


27
245.3085
47.46948


28
249.8483
23.49139


29
257.8591
86.27884


30
262.3436
79.84939


31
264.7226
86.27886


32
335.2774
86.27886


33
337.6564
79.84939


34
342.1409
86.27884


35
350.1517
23.49139


36
354.6915
47.46948






Dimple #
2



Type
spherical



Radius
0.0525



SCD
0.0075



TCD
n/a


#
Phi
Theta





1
3.606874
86.10963


2
4.773603
59.66486


3
7.485123
79.72027


4
9.566953
53.68971


5
10.81146
86.10963


6
12.08533
72.79786


7
13.37932
60.13101


8
16.66723
66.70139


9
19.58024
73.34845


10
20.76038
11.6909


11
24.53367
18.8166


12
46.81607
15.97349


13
73.18393
15.97349


14
95.46633
18.8166


15
99.23962
11.6909


16
100.4198
73.34845


17
103.3328
66.70139


18
106.6207
60.13101


19
107.9147
72.79786


20
109.1885
86.10963


21
110.433
53.68971


22
112.5149
79.72027


23
115.2264
59.66486


24
116.3931
86.10963


25
123.6069
86.10963


26
124.7736
59.66486


27
127.4851
79.72027


28
129.567
53.68971


29
130.8115
86.10963


30
132.0853
72.79786


31
133.3793
60.13101


32
136.6672
66.70139


33
139.5802
73.34845


34
140.7604
11.6909


35
144.5337
18.8166


36
166.8161
15.97349


37
193.1839
15.97349


38
215.4663
18.8166


39
219.2396
11.6909


40
220.4198
73.34845


41
223.3323
66.70139


42
226.6207
60.13101


43
227.9147
72.79786


44
229.1885
86.10963


45
230.433
53.68971


46
232.5149
79.72027


47
235.2264
59.66486


48
236.3931
86.10963


49
243.6069
85.10963


50
244.7736
59.66486


51
247.4851
79.72027


52
249.567
53.68971


53
250.8115
86.10963


54
252.0853
72.79786


55
253.3793
60.13101


56
256.6672
66.70139


57
259.5802
73.34845


58
260.7604
11.6909


59
264.5337
18.8166


60
286.8161
15.97349


61
313.1839
15.97349


62
335.4663
18.8166


63
339.2396
11.6909


64
340.4198
73.34845


65
343.3328
66.70139


66
346.6207
60.13101


67
347.9147
72.79786


68
349.1885
86.10963


69
350.433
53.68971


70
352.5149
79.72027


71
355.2264
59.66486


72
356.3931
86.10963






Dimple #
3



Type
spherical



Radius
0.055



SCD
0.0075



TCD
n/a


#
Phi
Theta





1
0
17.13539


2
0
79.62325


3
0
53.39339


4
8.604739
66.19316


5
15.03312
79.65081


6
60
9.094473


7
104.9669
79.65081


8
111.3953
66.19316


9
120
17.13539


10
120
53.39339


11
120
79.62325


12
128.6047
66.19316


13
135.0331
79.65081


14
180
9.094473


15
224.9669
79.65081


16
231.3953
66.19316


17
240
17.13539


18
240
53.39339


19
240
79.62325


20
248.6047
66.19316


21
255.0331
79.65081


22
300
9.094473


23
344.9669
79.65081


24
351.3953
66.19316






Dimple #
4



Type
spherical



Radius
0.0575



SCD
0.0075



TCD
n/a


#
Phi
Theta





1
0
4.637001


2
0
65.89178


3
4.200798
72.89446


4
115.7992
72.89446


5
120
4.637001


6
120
65.89178


7
124.2008
72.89446


8
235.7992
72.89446


9
240
4.637001


10
240
65.89178


11
244.2008
72.89446


12
355.7992
72.89446






Dimple #
5



Type
spherical



Radius
0.075



SCD
0.005



TCD
n/a


#
Phi
Theta





1
11.39176
35.80355


2
17.86771
45.18952


3
26.35389
29.36327


4
30.46014
74.86406


5
33.84232
84.58637


6
44.16317
84.53634


7
75.83683
84.53634


8
86.15768
84.58637


9
89.53986
74.86406


10
93.64611
29.36327


11
102.1323
45.18952


12
108.6082
35.80355


13
131.3918
35.80355


14
137.3677
45.18952


15
146.3539
29.36327


16
150.4601
74.86406


17
153.3423
84.58637


18
164.1632
84.58634


19
195.8368
84.58634


20
206.1577
84.58637


21
209.5399
74.86406


22
213.6461
29.36327


23
222.1323
45.18952


24
228.6082
35.80355


25
251.3918
35.80355


26
257.8677
45.18952


27
266.3539
29.36327


28
270.4601
74.86406


29
273.8423
84.58637


30
234.1632
84.58634


31
315.8368
84.58634


32
326.1577
84.58637


33
329.5399
74.86406


34
333.6461
29.36327


35
342.1323
45.18952


36
348.6082
35.80355






Dimple #
6



Type
spherical



Radius
0.0775



SCD
0.005



TCD
n/a


#
Phi
Theta





1
22.97427
54.90551


2
27.03771
64.89835


3
47.66575
25.59568


4
54.6796
84.41703


5
65.3204
84.41703


6
72.33425
25.59568


7
92.96229
64.89835


8
97.02573
54.90551


9
142.9743
54.90551


10
147.0377
64.89835


11
167.6657
25.59568


12
174.6796
84.41703


13
185.3204
84.41703


14
192.3343
25.59568


15
212.9623
64.89835


16
217.0257
54.90551


17
262.9743
54.90551


18
267.0377
64.89835


19
237.6657
25.59568


20
294.6796
84.41703


21
305.3204
84.41703


22
312.3343
25.59568


23
332.9623
64.89835


24
337.0257
54.90551






Dimple #
7



Type
spherical



Radius
0.0825



SCD
0.005



TCD
n/a


#
Phi
Theta





1
35.91413
51.35559


2
38.90934
62.34835


3
50.48062
36.43373


4
54.12044
73.49879


5
65.87956
73.49879


6
69.51938
36.43373


7
31.09066
62.34835


8
84.08587
51.35559


9
155.9141
51.35559


10
158.9093
62.34835


11
170.4806
36.43373


12
174.1204
73.49879


13
185.8796
73.49879


14
189.5194
36.43373


15
201.0907
62.34835


16
204.0859
51.35559


17
275.9141
51.35559


18
278.9093
62.34835


19
290.4806
36.43373


20
294.1204
73.49879


21
305.8796
73.49879


22
309.5194
36.43373


23
321.0907
62.34835


24
324.0859
51.35559






Dimple #
8



Type
spherical



Radius
0.0875



SCD
0.005



TCD
n/a


#
Phi
Theta





1
32.46033
39.96433


2
41.97126
73.6516


3
78.02874
73.6516


4
87.53967
39.96433


5
152.4603
39.96433


6
161.9713
73.6516


7
198.0287
73.6516


8
207.5397
39.96433


9
272.4603
39.96433


10
281.9713
73.6516


11
318.0287
73.6516


12
327.5397
39.96433






Dimple #
9



Type
spherical



Radius
0.095



SCD
0.005



TCD
n/a


#
Phi
Theta





1
51.33861
48.53996


2
52.61871
61.45814


3
67.38129
61.45814


4
68.66139
48.53996


5
171.3386
48.53996


6
172.6187
61.45814


7
187.3813
61.45814


8
188.6614
48.53996


9
291.3386
48.53996


10
292.6187
61.45814


11
307.3813
61.45814


12
308.6614
48.53996
















TABLE 7





(Dimple Pattern 173)


















Dimple #
1



Type
spherical



Radius
0.05



SCD
0.0075



TCD
n/a


#
Phi
Theta





1
0
28.81007


2
0
41.7187


3
5.30853345
47.46948


4
9.848337904
23.49139


5
17.85912075
86.27884


6
22.34360082
79.84939


7
24.72264341
86.27886


8
95.27735659
86.27886


9
97.65639918
79.84939


10
102.1408793
86.27884


11
110.1516621
23.49139


12
114.6914665
47.46948


13
120
28.81007


14
120
41.7187


15
125.3085335
47.46948


16
129.8483379
23.49139


17
137.8591207
86.27884


18
142.3436008
79.84939


19
144.7226434
86.27386


20
215.2773566
86.27886


21
217.6563992
79.84939


22
222.1408793
86.27884


23
230.1516621
23.49139


24
234.6914665
47.46948


25
240
23.81007


26
240
41.7187


27
245.3085395
47.46948


28
249.8483379
23.49139


29
257.8591207
86.27884


30
262.3436008
79.84939


31
264.7226434
86.27886


32
335.2773566
86.27886


33
337.6563992
79.84939


34
342.1408793
86.27884


35
350.1516621
23.49139


36
354.6914665
47.46948






Dimple #
2



Type
spherical



Radius
0.0525



SCD
0.0075



TCD
n/a


#
Phi
Theta





1
3.606873831
86.10963


2
4.773603104
59.66486


3
7.485123389
79.72027


4
9.566952638
53.68971


5
10.81146128
86.10963


6
12.08533241
72.79786


7
13.37931975
60.13101


8
16.66723032
66.70139


9
19.58024114
73.34845


10
20.76038062
11.6909


11
24.53367306
13.8166


12
46.81607116
15.97349


13
73.18392884
15.97349


14
95.46632694
18.8166


15
99.23961938
11.6909


16
100.4197589
73.34845


17
103.3327697
66.70139


18
106.6206802
60.13101


19
107.9146676
72.79786


20
109.1885387
86.10963


21
110.4330474
53.68971


22
112.5148766
79.72027


23
115.2263969
59.66486


24
116.3931262
86.10963


25
123.6068738
86.10963


26
124.7736031
59.66486


27
127.4851234
79.72027


28
129.5669526
53.68971


29
130.8114613
86.10963


30
132.0853324
72.79786


31
133.3793198
60.13101


32
136.6672303
66.70139


33
139.5802411
73.34845


34
140.7603806
11.6909


35
144.5336731
18.8166


36
166.8160712
15.97349


37
193.1839288
15.97349


38
215.4663269
18.8166


39
219.2396194
11.6909


40
220.4197589
73.34845


41
223.3327697
66.70139


42
226.6206802
60.13101


43
227.9146676
72.79786


44
229.1885307
86.10963


45
230.4330474
53.68971


46
232.5148766
79.72027


47
235.2263969
59.66486


48
236.3931262
86.10963


49
243.6068738
85.10963


50
244.7736031
59.66486


51
247.4851234
79.72027


52
249.5669526
53.68971


53
250.8114613
88.10963


54
252.0853324
72.79786


55
253.3793198
60.13101


56
256.6672303
66.70139


57
259.5802411
73.34845


58
260.7603806
11.6909


59
264.5336731
18.8166


60
286.8160712
15.97349


61
313.1839288
15.97349


62
335.4663269
18.8166


63
339.2396194
11.6909


64
340.4197589
73.34845


65
343.3327697
66.70139


66
346.6206802
60.13101


67
347.9146676
72.79786


68
349.1885387
86.10963


69
350.4330474
53.68971


70
352.5148766
79.72027


71
355.2263969
59.66486


72
356.3931262
86.10963






Dimple #
3



Type
spherical



Radius
0.055



SCD
0.0075



TCD
n/a


#
Phi
Theta





1
0
17.13539


2
0
79.62325


3
0
53.39339


4
8.604738835
66.19316


5
15.03312161
79.65081


6
60
9.094473


7
104.9668784
79.65081


8
111.3952612
66.19316


9
120
17.13539


10
120
53.39339


11
120
79.62325


12
128.6047388
66.19316


13
135.0331216
79.65081


14
180
9.094473


15
224.9668784
79.65081


16
231.3952612
66.19316


17
240
17.13539


18
240
53.39339


19
240
79.62325


20
248.6047388
66.19316


21
255.0331216
79.65081


22
300
9.094473


23
344.9668784
79.65081


24
351.3952612
66.19316






Dimple #
4



Type
spherical



Radius
0.0575



SCD
0.0075



TCD
n/a


#
Phi
Theta





1
0
4.637001


2
0
65.89178


3
4.200798314
72.89446


4
115.7992017
72.89446


5
120
4.637001


6
120
65.89178


7
124.2007983
72.89446


8
235.7902017
72.89446


9
240
4.637001


10
240
65.89178


11
244.2007983
72.89446


12
355.7992017
72.89446






Dimple #
5



Type
truncated



Radius
0.075



SCD
0.0119



TCD
0.005


#
Phi
Theta





1
11.39176224
35.80355


2
17.86771474
45.18952


3
26.35389345
29.36327


4
30.46014274
74.86406


5
33.84232422
84.58637


6
44.16316959
84.53634


7
75.83683042
84.53634


8
86.15767578
84.58637


9
89.53985726
74.86406


10
93.64610555
29.36327


11
102.1322853
45.18952


12
108.6082378
35.80355


13
131.3917622
35.80355


14
137.8677147
45.13952


15
146.3538935
29.36327


16
150.4601427
74.86406


17
153.3423242
84.58637


18
164.1631696
84.58634


19
195.8368304
84.58634


20
206.1576758
84.58637


21
209.5398573
74.86406


22
213.6461065
29.36327


23
222.1322853
45.18952


24
228.6082378
35.80355


25
251.3917622
35.80355


26
257.8677147
45.18952


27
266.3538935
29.36327


28
270.4601427
74.86406


29
273.8423242
84.58637


30
234.1631696
84.58634


31
315.8368304
84.58634


32
326.1576758
84.58637


33
329.5398573
74.86406


34
333.6461065
29.36327


35
342.1322853
45.18952


36
348.6082378
35.80355






Dimple #
6



Type
truncated



Radius
0.0775



SCD
0.0122



TCD
0.005


#
Phi
Theta





1
22.97426943
54.90551


2
27.03771469
64.89835


3
47.6657487
25.59568


4
54.67960187
84.41703


5
65.32039813
84.41703


6
72.3342513
25.59568


7
92.96228531
64.89835


8
97.02573057
54.90551


9
142.9742694
54.90551


10
147.0377147
64.89835


11
167.6657487
25.59568


12
174.6796019
84.41703


13
185.3203981
84.41703


14
192.3342513
25.59568


15
212.9622853
64.89835


16
217.0257306
54.90551


17
262.9742694
54.90551


18
267.0377147
64.89835


19
237.6657487
25.59568


20
294.6796019
84.41703


21
305.3203981
84.41703


22
312.3342513
25.59568


23
332.9622853
64.89835


24
337.0257306
54.90551






Dimple #
7



Type
truncated



Radius
0.0825



SCD
0.0128



TCD
0.005


#
Phi
Theta





1
35.91413117
51.35559


2
38.90934195
62.34835


3
50.48062345
36.43373


4
54.12044072
73.49879


5
65.87955928
73.49879


6
69.51937655
36.43373


7
81.09065805
62.34835


8
84.08586893
51.35559


9
155.9141312
51.35559


10
158.909342
62.34835


11
170.4806234
36.43373


12
174.1204407
73.49879


13
185.8795593
73.49879


14
189.5193766
36.43373


15
201.090656
62.34835


16
204.0858688
51.35559


17
275.9141312
51.35559


18
278.909342
62.34835


19
290.4806234
36.43373


20
294.1204407
73.49879


21
305.8795593
73.49879


22
309.5193766
36.43373


23
321.090658
62.34835


24
324.0858698
51.35559






Dimple #
8



Type
truncated



Radius
0.0875



SCD
0.0133



TCD
0.005


#
Phi
Theta





1
32.46032855
39.96433


2
41.97126436
73.6516


3
78.02873584
73.6516


4
37.53967145
39.96433


5
152.4603285
39.96433


6
161.9712644
73.6516


7
198.0287356
73.6516


8
207.5396715
39.96433


9
272.4603285
39.96433


10
281.9712644
73.6516


11
318.0287356
73.6516


12
327.5396715
39.96433






Dimple #
9



Type
truncated



Radius
0.095



SCD
0.014



TCD
0.005


#
Phi
Theta





1
51.33861068
48.53996


2
52.61871427
61.45814


3
67.38128573
61.45814


4
68.66138932
48.53996


5
171.3386107
48.53996


6
172.6187143
61.45814


7
187.3812857
61.45814


8
188.6613893
48.53996


9
291.3386107
48.53996


10
292.6187143
61.45814


11
307.3812857
61.45814


12
308.6613893
48.53996
















TABLE 8





(Dimple Pattern 174)


















Dimple #
1



Type
truncated



Radius
0.05



SCD
0.0087



TCD
0.0035


#
Phi
Theta





1
0
28.81007


2
0
41.7187


3
5.308533
47.46948


4
9.846338
23.49139


5
17.85912
86.27884


6
22.3436
79.34939


7
24.72264
86.27886


8
95.27736
86.27886


9
97.6564
79.84939


10
102.1409
86.27884


11
110.1517
23.49139


12
114.6915
47.46948


13
120
28.81007


14
120
41.7187


15
125.3085
47.46948


16
129.8483
23.49139


17
137.8591
86.27884


18
142.3436
79.84939


19
144.7226
86.27886


20
215.2774
86.27886


21
217.6564
79.84939


22
222.1409
86.27884


23
230.1517
23.49139


24
234.6915
47.46948


25
240
23.81007


26
240
41.7187


27
245.3085
47.46948


28
249.8483
23.49139


29
257.8591
86.27884


30
262.3436
79.84939


31
264.7226
86.27886


32
335.2774
86.27886


33
337.6564
79.84939


34
342.1409
86.27884


35
350.1517
23.49139


36
354.6915
47.46948






Dimple #
2



Type
truncated



Radius
0.0525



SCD
0.0091



TCD
0.0035


#
Phi
Theta





1
3.606874
86.10963


2
4.773603
59.66486


3
7.485123
79.72027


4
9.566953
53.68971


5
10.81146
86.10963


6
12.08533
72.79786


7
13.37932
60.13101


8
16.66723
66.70139


9
19.58024
73.34845


10
20.76038
11.6909


11
24.53367
18.8166


12
46.81607
15.97349


13
73.18393
15.97349


14
95.46633
18.8166


15
99.23962
11.6909


16
100.4198
73.34845


17
103.3328
66.70139


18
106.6207
60.13101


19
107.9147
72.79786


20
109.1385
86.10963


21
110.433
53.68971


22
112.5149
79.72027


23
115.2264
59.66486


24
116.3931
86.10963


25
123.6069
86.10963


26
124.7736
59.66486


27
127.4851
79.72027


28
129.567
53.68971


29
130.8115
86.10963


30
132.0853
72.79786


31
133.3793
60.13101


32
136.6672
66.70139


33
139.5802
73.34845


34
140.7604
11.6909


35
144.5337
18.8166


36
166.8161
15.97349


37
193.1839
15.97349


38
215.4663
18.8166


39
219.2396
11.6909


40
220.4198
73.34845


41
223.3323
66.70139


42
226.6207
60.13101


43
227.9147
72.79786


44
229.1885
86.10963


45
230.433
53.68971


46
232.5149
79.72027


47
235.2264
59.66486


48
236.3931
86.10963


49
243.6069
85.10963


50
244.7736
59.66486


51
247.4851
79.72027


52
249.567
53.68971


53
250.8115
86.10963


54
252.0853
72.79786


55
253.3793
60.13101


56
256.6672
66.70139


57
259.5802
73.34845


58
260.7604
11.6909


59
264.5337
18.8166


60
286.8161
15.97349


61
313.1839
15.97349


62
335.4663
18.8166


63
339.2396
11.6909


64
340.4198
73.34845


65
343.3328
66.70139


66
346.6207
60.13101


67
347.9147
72.79786


68
349.1885
86.10963


69
350.433
53.68971


70
352.5149
79.72027


71
355.2264
59.66486


72
356.3931
86.10963






Dimple #
3



Type
truncated



Radius
0.055



SCD
0.0094



TCD
0.0035


#
Phi
Theta





1
0
17.13539


2
0
79.62325


3
0
53.39339


4
8.604739
66.19316


5
15.03312
79.65081


6
60
9.094473


7
104.9669
79.65081


8
111.3953
66.19316


9
120
17.13539


10
120
53.39339


11
120
79.62325


12
128.6047
66.19316


13
135.0331
79.65081


14
180
9.094473


15
224.9669
79.65081


16
231.3953
66.19316


17
240
17.13539


18
240
53.39339


19
240
79.62325


20
248.6047
66.19316


21
255.0331
79.65081


22
300
9.094473


23
344.9669
79.65081


24
351.3953
66.19316






Dimple #
4



Type
truncated



Radius
0.0575



SCD
0.0098



TCD
0.0035


#
Phi
Theta





1
0
4.637001


2
0
65.89178


3
4.200798
72.89446


4
115.7992
72.89446


5
120
4.637001


6
120
65.89178


7
124.2008
72.89446


8
235.7992
72.89446


9
240
4.637001


10
240
65.89178


11
244.2008
72.89446


12
355.7992
72.89446






Dimple #
5



Type
spherical



Radius
0.075



SCD
0.008



TCD
n/a


#
Phi
Theta





1
11.39176
35.80355


2
17.86771
45.18952


3
26.35389
29.36327


4
30.46014
74.86406


5
33.84232
84.58637


6
44.16317
84.53634


7
75.83683
84.53634


8
86.15768
84.58637


9
89.53986
74.86406


10
93.64611
29.36327


11
102.1323
45.18952


12
108.6082
35.80355


13
131.3918
35.80355


14
137.8677
45.18952


15
146.3539
29.36327


16
150.4601
74.86406


17
153.8423
84.58637


18
164.1632
84.58634


19
195.8368
84.58634


20
206.1577
84.58637


21
209.5399
74.86406


22
213.6461
29.36327


23
222.1323
45.18952


24
228.6082
35.80355


25
251.3913
35.80355


26
257.3677
45.18952


27
266.3539
29.36327


28
270.4601
74.86406


29
273.3423
84.58637


30
234.1632
84.58634


31
315.8368
84.58634


32
326.1577
84.58637


33
329.5399
74.86406


34
333.6461
29.36327


35
342.1323
45.18952


36
348.6082
35.80355






Dimple #
6



Type
spherical



Radius
0.0775



SCD
0.008



TCD
n/a


#
Phi
Theta





1
22.97427
54.90551


2
27.03771
64.89835


3
47.66575
25.59568


4
54.6796
84.41703


5
65.3204
84.41703


6
72.33425
25.59568


7
92.96229
64.89835


8
97.02573
54.90551


9
142.9743
54.90551


10
147.0377
64.89835


11
167.6657
25.59568


12
174.6796
84.41703


13
185.3204
84.41703


14
192.3343
25.59568


15
212.9623
64.89835


16
217.0257
54.90551


17
262.9743
54.90551


18
267.0377
64.89835


19
237.6657
25.59563


20
294.6796
84.41703


21
305.3204
84.41703


22
312.3343
25.59563


23
332.9623
64.89835


24
337.0257
54.90551






Dimple #
7



Type
spherical



Radius
0.0825



SCD
0.008



TCD
n/a


#
Phi
Theta





1
35.91413
51.35559


2
38.90934
62.34835


3
50.48062
36.43373


4
54.12044
73.49879


5
65.87956
73.49879


6
69.51938
36.43373


7
31.09066
62.34835


8
84.08587
51.35559


9
155.9141
51.35559


10
158.9093
62.34835


11
170.4806
36.43373


12
174.1204
73.49879


13
185.8796
73.49879


14
189.5194
36.43373


15
201.0907
62.34835


16
204.0859
51.35559


17
275.9141
51.35559


18
278.9093
62.34835


19
290.4806
36.43373


20
294.1204
73.49879


21
305.8796
73.49879


22
309.5194
36.43373


23
321.0907
62.34835


24
324.0859
51.35559






Dimple #
8



Type
spherical



Radius
0.0875



SCD
0.008



TCD
n/a


#
Phi
Theta





1
32.46033
39.96433


2
41.97126
73.6516


3
78.02874
73.6516


4
37.53967
39.96433


5
152.4603
39.96433


6
161.9713
73.6516


7
198.0287
73.6516


8
207.5397
39.96433


9
272.4603
39.96433


10
281.9713
73.6516


11
318.0287
73.6516


12
327.5397
39.96433






Dimple #
9



Type
spherical



Radius
0.095



SCD
0.008



TCD
n/a


#
Phi
Theta





1
51.33861
48.53996


2
52.61871
61.45814


3
67.38129
61.45814


4
68.66139
48.53996


5
171.3386
48.53996


6
172.6187
61.45814


7
187.3813
61.45814


8
188.6614
48.53996


9
291.3386
48.53996


10
292.6137
61.45814


11
307.3813
61.45814


12
308.6614
48.53996
















TABLE 9





(Dimple Pattern 175)


















Dimple #
1



Type
spherical



Radius
0.05



SCD
0.008



TCD
n/a


#
Phi
Theta





1
0
28.81007


2
0
41.7187


3
5.308533
47.46948


4
9.846338
23.49139


5
17.85912
86.27884


6
22.3436
79.34939


7
24.72264
86.27886


8
95.27736
86.27886


9
97.6564
79.84939


10
102.1409
86.27884


11
110.1517
23.49139


12
114.6915
47.46948


13
120
28.81007


14
120
41.7187


15
125.3085
47.46948


16
129.8483
23.49139


17
137.8591
86.27884


18
142.3436
79.84939


19
144.7226
86.27886


20
215.2774
86.27886


21
217.6564
79.84939


22
222.1409
86.27884


23
230.1517
23.49139


24
234.6915
47.46948


25
240
23.81007


26
240
41.7187


27
245.3085
47.46948


28
249.8483
23.49139


29
257.8591
86.27884


30
262.3436
79.34939


31
264.7226
86.27886


32
335.2774
86.27886


33
337.6564
79.84939


34
342.1409
86.27884


35
350.1517
23.49139


36
354.6915
47.46948






Dimple #
2



Type
spherical



Radius
0.0525



SCD
0.008



TCD
n/a


#
Phi
Theta





1
3.606874
86.10963


2
4.773603
59.66486


3
7.485123
79.72027


4
9.566953
53.68971


5
10.81146
86.10963


6
12.08533
72.79786


7
13.37932
60.13101


8
16.66723
66.70139


9
19.58024
73.34845


10
20.76038
11.6909


11
24.53367
18.8166


12
46.81607
15.97349


13
73.18393
15.97349


14
95.46633
18.8166


15
99.23962
11.6909


16
100.4198
73.34845


17
103.3328
66.70139


18
106.6207
60.13101


19
107.9147
72.79786


20
109.1885
86.10963


21
110.433
53.68971


22
112.5149
79.72027


23
115.2264
59.66486


24
116.3931
86.10963


25
123.6069
86.10963


26
124.7736
59.66486


27
127.4851
79.72027


28
129.567
53.68971


29
130.8115
86.10963


30
132.0853
72.79786


31
133.3793
60.13101


32
136.6672
66.70139


33
139.5802
73.34845


34
140.7604
11.6909


35
144.5337
18.8166


36
166.8161
15.97349


37
193.1839
15.97349


38
215.4663
18.8166


39
219.2396
11.6909


40
220.4198
73.34845


41
223.3323
66.70139


42
226.6207
60.13101


43
227.9147
72.79786


44
229.1885
86.10963


45
230.433
53.68971


46
232.5149
79.72027


47
235.2264
59.66486


48
236.3931
86.10963


49
243.6069
85.10963


50
244.7736
59.66486


51
247.4851
79.72027


52
249.567
53.68971


53
250.8115
86.10963


54
252.0853
72.79786


55
253.3793
60.13101


56
256.6672
66.70139


57
259.5802
73.34845


58
260.7604
11.6909


59
264.5337
18.8166


60
286.8161
15.97349


61
313.1839
15.97349


62
335.4663
18.8166


63
339.2396
11.6909


64
340.4198
73.34845


65
343.3328
66.70139


66
346.6207
60.13101


67
347.9147
72.79786


68
349.1885
86.10963


69
350.433
53.68971


70
352.5149
79.72027


71
355.2264
59.66486


72
356.3931
86.10963






Dimple #
3



Type
spherical



Radius
0.055



SCD
0.008



TCD
n/a


#
Phi
Theta





1
0
17.13539


2
0
79.62325


3
0
53.39339


4
8.604739
66.19316


5
15.03312
79.65081


6
60
9.094473


7
104.9669
79.65081


8
111.3953
66.19316


9
120
17.13539


10
120
53.39339


11
120
79.62325


12
128.6047
66.19316


13
135.0331
79.65081


14
180
9.094473


15
224.9669
79.65081


16
231.3953
66.19316


17
240
17.13539


18
240
53.39339


19
240
79.62325


20
248.6047
66.19316


21
255.0331
79.65081


22
300
9.094473


23
344.9669
79.65081


24
351.3953
66.19316






Dimple #
4



Type
spherical



Radius
0.0575



SCD
0.008



TCD
n/a


#
Phi
Theta





1
0
4.637001


2
0
65.89178


3
4.200798
72.89446


4
115.7992
72.89446


5
120
4.637001


6
120
65.89178


7
124.2008
72.89446


8
235.7992
72.89446


9
240
4.637001


10
240
65.89178


11
244.2008
72.89446


12
355.7992
72.89446






Dimple #
5



Type
truncated



Radius
0.075



SCD
0.012



TCD
0.0035


#
Phi
Theta





1
11.39176
35.80355


2
17.86771
45.18952


3
26.35389
29.36327


4
30.46014
74.86406


5
33.84232
84.58637


6
44.16317
84.53634


7
75.83683
84.53634


8
86.15768
84.58637


9
89.53986
74.86406


10
93.64611
29.36327


11
102.1323
45.18952


12
108.6082
35.80355


13
131.3918
35.80355


14
137.3677
45.18952


15
146.3539
29.36327


16
150.4601
74.86406


17
153.3423
84.58637


18
164.1632
84.58634


19
195.8368
84.58634


20
206.1577
84.58637


21
209.5399
74.86406


22
213.6461
29.36327


23
222.1323
45.18952


24
228.6082
35.80355


25
251.3918
35.80355


26
257.8677
45.18952


27
266.3539
29.36327


28
270.4601
74.86406


29
273.8423
84.58637


30
234.1632
84.58634


31
315.8368
84.58634


32
326.1577
84.58637


33
329.5399
74.86406


34
333.6461
29.36327


35
342.1323
45.18952


36
348.6082
35.80355






Dimple #
6



Type
truncated



Radius
0.0775



SCD
0.0122



TCD
0.0035


#
Phi
Theta





1
22.97427
54.90551


2
27.03771
64.89835


3
47.66575
25.59568


4
54.6796
84.41703


5
65.3204
84.41703


6
72.33425
25.59568


7
92.96229
64.89835


8
97.02573
54.90551


9
142.9743
54.90551


10
147.0377
64.89835


11
167.6657
25.59568


12
174.6796
84.41703


13
185.3204
84.41703


14
192.3343
25.59568


15
212.9623
64.89835


16
217.0257
54.90551


17
262.9743
54.90551


18
267.0377
64.89835


19
287.6657
25.59568


20
294.6796
84.41703


21
305.3204
84.41703


22
312.3343
25.59563


23
332.9623
64.89835


24
337.0257
54.90551






Dimple #
7



Type
truncated



Radius
0.0825



SCD
0.0128



TCD
0.0035


#
Phi
Theta





1
35.91413
51.35559


2
38.90934
62.34835


3
50.48062
36.43373


4
54.12044
73.49879


5
65.87956
73.49879


6
69.51938
36.43373


7
81.09066
62.34835


8
84.08587
51.35559


9
155.9141
51.35559


10
158.9093
62.34835


11
170.4806
36.43373


12
174.1204
73.49879


13
185.8796
73.49879


14
189.5194
36.43373


15
201.0907
62.34835


16
204.0859
51.35559


17
275.9141
51.35559


18
278.9093
62.34835


19
290.4806
36.43373


20
294.1204
73.49879


21
305.8796
73.49879


22
309.5194
36.43373


23
321.0907
62.34835


24
324.0859
51.35559






Dimple #
8



Type
truncated



Radius
0.0875



SCD
0.0133



TCD
0.0035


#
Phi
Theta





1
32.46033
39.96433


2
41.97126
73.6516


3
78.02874
73.6516


4
87.53967
39.96433


5
152.4603
39.96433


6
161.9713
73.6516


7
198.0287
73.6516


8
207.5397
39.96433


9
272.4603
39.96433


10
281.9713
73.6516


11
318.0287
73.6516


12
327.5397
39.96433






Dimple #
9



Type
truncated



Radius
0.095



SCD
0.014



TCD
0.0035


#
Phi
Theta





1
51.33861
48.53996


2
52.61871
61.45814


3
67.38129
61.45814


4
68.66139
48.53996


5
171.3386
48.53996


6
172.6187
61.45814


7
187.3813
61.45814


8
188.6614
48.53996


9
291.3386
48.53996


10
292.6187
61.45814


11
307.3813
61.45814


12
308.6614
48.53996
















TABLE 10





(Dimple Pattern 273)


















Dimple #
1



Type
truncated



Radius
0.0750



SCD
0.0132



TCD
0.0050


#
Phi
Theta





1
0
25.85946


2
120
25.85946


3
240
25.85946


4
22.29791
84.58636


5
1.15E−13
44.66932


6
337.7021
84.58636


7
142.2979
84.58636


8
120
44.66932


9
457.7021
84.58636


10
262.2979
84.58636


11
240
44.66932


12
577.7021
84.58636






Dimple #
2



Type
truncated



Radius
0.0800



SCD
0.0138



TCD
0.0050


#
Phi
Theta





1
19.46456
17.6616


2
100.5354
17.6616


3
139.4646
17.6616


4
220.5354
17.6616


5
259.4646
17.6616


6
340.5354
17.6616


7
18.02112
74.614


8
7.175662
54.03317


9
352.8243
54.03317


10
341.9789
74.614


11
348.5695
84.24771


12
11.43052
84.24771


13
138.0211
74.614


14
127.1757
54.03317


15
472.8243
54.03317


16
461.9789
74.614


17
468.5695
84.24771


18
131.4305
84.24771


19
258.0211
74.614


20
247.1757
54.03317


21
592.8243
54.03317


22
581.9789
74.614


23
588.5695
84.24771


24
251.4305
84.24771






Dimple #
3



Type
truncated



Radius
0.0825



SCD
0.0141



TCD
0.0050


#
Phi
Theta





1
0
6.707467


2
60
13.5496


3
120
6.707467


4
180
13.5496


5
240
6.707467


6
300
13.5496


7
6.04096
73.97888


8
13.01903
64.24653


9
2.41E−14
63.82131


10
346.981
64.24653


11
353.959
73.97888


12
360
84.07838


13
126.041
73.97888


14
133.019
64.24653


15
120
63.82131


16
466.981
64.24653


17
473.959
73.97888


18
480
84.07838


19
246.041
73.97888


20
253.019
64.24653


21
240
63.82131


22
586.981
64.24653


23
593.959
73.97888


24
600
84.07838






Dimple #
4



Type
spherical



Radius
0.0550



SCD
0.0075



TCD
—


#
Phi
Theta





1
89.81848
78.25196


2
92.38721
71.10446


3
95.11429
63.96444


4
105.6986
42.86305


5
101.558
49.81178


6
98.11364
56.8624


7
100.3784
30.02626


8
86.62335
26.05789


9
69.339
23.82453


10
19.62155
30.03626


11
33.37665
26.05789


12
50.601
23.82453


13
14.30135
42.86305


14
18.44204
49.81178


15
21.38636
56.8624


16
38.18152
78.25196


17
27.61279
71.10446


18
24.88571
63.96444


19
41.03508
85.94042


20
48.61817
85.94042


21
56.20813
85.94042


22
78.96492
85.94042


23
71.38183
85.94042


24
63.79187
85.94042


25
209.8185
78.25196


26
212.3872
71.10446


27
215.1143
63.96444


28
225.6986
42.86305


29
221.558
49.81178


30
218.1136
56.8624


31
220.3784
30.02626


32
206.6234
26.05789


33
189.399
23.82453


34
139.6216
30.02626


35
153.3765
26.05789


36
170.601
23.82453


37
134.3014
42.86305


38
133.442
49.81178


39
141.8864
56.8624


40
150.1815
78.25196


41
147.6128
71.10446


42
144.8857
53.96444


43
161.0351
85.94042


44
168.6182
85.94042


45
176.2081
85.94042


46
198.9649
85.94042


47
191.3818
85.94042


48
193.7919
85.94042


49
329.8185
78.25196


50
332.3872
71.10446


51
335.1143
63.96444


52
345.6986
42.86305


53
341.558
49.81178


54
338.1136
56.8624


55
340.3784
30.02626


56
326.6234
26.05789


57
309.399
23.82453


58
259.6216
30.02626


59
273.3765
26.05789


60
290.601
23.82453


61
254.3014
42.86305


62
258.442
49.81178


63
261.8864
56.8624


64
270.1815
78.25196


65
267.6128
71.10446


66
264.8857
63.36444


67
281.0351
85.94042


68
238.6182
85.94042


69
296.2081
85.94042


70
318.9649
85.94042


71
311.3919
85.94042


72
303.7919
85.94042






Dimple #
5



Type
spherical



Radius
0.0575



SCD
0.0075



TCD
—


#
Phi
Theta





1
83.35856
69.4058


2
85.57977
61.65549


3
91.04137
46.06539


4
88.0815
53.82973


5
81.86535
34.37733


6
67.54444
32.56834


7
38.13465
34.37733


8
52.45556
32.56834


9
28.95863
46.06539


10
31.9185
53.02973


11
36.64144
69.4858


12
34.42023
61.65549


13
47.55421
77.35324


14
55.84333
77.16119


15
72.44579
77.35324


16
64.15697
77.16119


17
203.3586
69.4858


18
205.5798
61.65549


19
211.0414
46.06539


20
200.0815
53.82973


21
201.8653
34.37733


22
187.5444
32.56834


23
158.1347
34.37733


24
172.4556
32.56834


25
148.9586
46.06539


26
151.9185
53.82973


27
156.6414
69.4858


28
154.4202
61.65549


29
167.5642
77.35324


30
175.843
77.16119


31
192.4458
77.35324


32
184.157
77.16119


33
323.3586
69.4858


34
325.5798
61.65549


35
331.0414
46.06539


36
328.0815
53.82973


37
321.8653
34.37733


38
307.5444
32.56834


39
278.1347
34.37733


40
292.4556
32.56834


41
268.9586
46.06539


42
271.9185
53.82973


43
275.6414
69.4858


44
274.4202
61.65549


45
287.5542
77.35324


46
235.843
77.16119


47
312.4458
77.35324


48
304.157
77.16119






Dimple #
6



Type
spherical



Radius
0.0600



SCD
0.0075



TCD
—


#
Phi
Theta





1
86.88247
85.60198


2
110.7202
35.62098


3
9.279821
35.62098


4
33.11753
85.60198


5
206.8825
85.60198


6
230.7202
35.62098


7
129.2798
35.62098


8
153.1175
85.60198


9
326.8825
85.60198


10
350.7202
35.62098


11
249.2798
35.62098


12
273.1175
85.60198






Dimple #
7



Type
spherical



Radius
0.0625



SCD
0.0075



TCD
—


#
Phi
Theta





1
80.92949
77.43144


2
76.22245
60.1768


3
77.98598
51.7127


4
94.40845
38.09724


5
66.573
40.85577


6
53.427
40.85577


7
25.59155
38.09724


8
42.01402
51.7127


9
43.77755
60.1763


10
39.07051
77.43144


11
55.39527
68.86469


12
64.60473
68.86469


13
200.9295
77.43144


14
196.2224
60.1768


15
197.986
51.7127


16
214.4085
38.09724


17
186.573
40.85577


18
173.427
40.85577


19
145.5915
38.09724


20
162.014
51.7127


21
163.7776
60.1768


22
159.0705
77.43144


23
175.3953
68.86469


24
184.6047
68.86469


25
320.9295
77.43144


26
316.2224
60.1768


27
317.986
51.7127


28
334.4085
38.09724


29
306.573
40.85577


30
293.427
40.85577


31
265.5915
38.09724


32
282.014
51.7127


33
283.7776
60.1768


34
279.0705
77.43144


35
295.3953
68.86469


36
304.6047
68.86469






Dimple #
8



Type
spherical



Radius
00675



SCD
0.0075



TCD
—


#
Phi
Theta





1
74.18416
68.92141


2
79.64177
42.85974


3
40.35823
42.85974


4
45.81584
68.92141


5
194.1842
68.92141


6
199.6418
42.85974


7
160.3582
42.85974


8
165.8158
68.92141


9
314.1842
68.92141


10
319.6418
42.85974


11
280.3582
42.85974


12
285.8158
68.92141






Dimple #
9



Type
spherical



Radius
0.0700



SCD
0.0075



TCD
—


#
Phi
Theta





1
65.60484
59.710409


2
66.31567
50.052318


3
53.68433
50.052318


4
54.39516
59.710409


5
185.6048
59.710409


6
186.3157
50.052318


7
173.6843
50.052318


8
174.3952
59.710409


9
305.6048
59.710409


10
306.3157
50.052318


11
293.6843
50.052318


12
294.3952
59.710409
















TABLE 11





(Dimple Pattern 2-3)


















Dimple #
1



Type
spherical



Radius
0.0550



SCD
0.0080



TCD
—


#
Phi
Theta





1
89.818
78.252


2
92.387
71.104


3
95.114
63.964


4
105.699
42.863


5
101.558
49.812


6
98.114
56.862


7
100.378
30.026


8
86.623
26.058


9
69.3989
23.825


10
19.622
30.026


11
33.377
26.858


12
50.601
29.825


13
14.301
42.863


14
18.442
49.812


15
21.886
56.862


16
30.182
78.252


17
27.613
71.104


18
24.886
63.964


19
41.035
85.940


20
48.618
85.940


21
56.208
85.940


22
78.985
85.940


23
71.382
85.940


24
63.792
85.940


25
209.818
78.252


26
212.387
71.104


27
215.114
63.964


28
225.699
42.863


29
221.558
49.812


30
218.114
56.862


31
220.376
30.026


32
206.623
26.058


33
189.399
23.825


34
149.622
30.026


35
153.377
26.058


36
170.601
23.825


37
134.301
42.863


38
130.442
49.812


39
141.885
56.862


40
150.182
78.252


41
147.613
71.104


42
144.886
63.954


43
161.035
85.940


44
168.618
85.940


45
176.208
85.940


46
198.965
85.940


47
191.382
85.940


48
183.792
85.940


49
329.818
78.252


50
332.387
71.104


51
335.114
63.964


52
345.699
42.863


53
341.558
49.812


54
338.114
56.862


55
340.378
30.026


56
326.623
26.058


57
309.399
23.825


58
259.622
30.026


59
273.377
26.058


60
290.601
23.825


61
254.301
42.863


62
258.442
49.812


63
261.886
56.862


64
270.182
78.252


65
267.613
71.104


66
264.886
63.964


67
281.035
85.940


68
288.618
85.940


69
296.208
85.940


70
318.965
85.940


71
311.382
85.940


72
303.792
85.940






Dimple #
2



Type
spherical



Radius
0.0575



SCD
0.0080



TCD
—


#
Phi
Theta





1
83.359
69.486


2
85.580
61.655


3
91.041
46.065


4
88.081
53.830


5
81.865
34.377


6
67.544
32.568


7
38.135
34.377


8
52.456
32.568


9
28.959
46.065


10
31.919
53.830


11
36.641
69.486


12
34.420
61.655


13
47.554
77.353


14
55.843
77.161


15
72.446
77.363


16
64.157
77.161


17
203.359
69.485


18
205.580
61.655


19
211.041
46.065


20
208.081
53.830


21
201.865
34.377


22
187.544
32.568


23
158.135
34.377


24
172.456
32.568


25
148.959
46.065


26
151.919
53.830


27
156.641
63.486


28
154.420
61.655


29
167.554
77.353


30
175.843
77.161


31
132.446
77.353


32
184.157
77.161


33
323.359
63.486


34
325.580
61.655


35
331.041
46.065


36
328.081
53.830


37
321.865
34.377


38
307.544
32.568


39
278.135
34.377


40
292.456
32.568


41
268.959
46.065


42
271.919
53.830


43
276.641
69.485


44
274.420
61.655


45
287.554
77.353


46
295.843
77.161


47
312.446
77.363


48
304.157
77.161






Dimple #
3



Type
spherical



Radius
0.0600



SCD
0.0080



TCD
—


#
Phi
Theta





1
86.882
85.602


2
110.720
35.621


3
9.280
35.621


4
33.116
85.602


5
205.882
85.602


6
230.720
35.621


7
129.280
35.621


8
153.118
85.602


9
326.682
85.602


10
350.720
35.621


11
249.280
35.621


12
273.118
85.602






Dimple #
4



Type
spherical



Radius
0.0625



SCD
0.0080



TCD
—


#
Phi
Theta





1
80.929
77.431


2
76.222
60.177


3
77.986
51.713


4
94.408
38.097


5
66.573
40.856


6
53.427
40.856


7
25.592
38.097


8
42.014
51.713


9
43.778
60.177


10
39.071
77.431


11
55.395
68.865


12
64.605
68.865


13
200.929
77.431


14
196.222
60.177


15
197.986
51.717


16
214.408
38.097


17
136.573
40.856


18
173.427
40.856


19
145.592
38.097


20
162.014
51.713


21
163.778
60.177


22
159.071
77.431


23
175.395
68.865


24
184.605
68.865


25
320.929
77.431


26
316.222
60.177


27
317.986
51.713


28
334.408
38.037


29
306.573
40.856


30
293.427
40.856


31
265.592
38.097


32
282.014
51.713


33
233.778
60.177


34
279.071
77.431


35
295.395
68.865


36
304.605
68.865






Dimple #
5



Type
spherical



Radius
0.0675



SCD
0.0080



TCD
—


#
Phi
Theta





1
74.184
68.921


2
79.642
42.860


3
40.358
42.860


4
45.816
68.921


5
194.184
68.921


6
199.642
42.860


7
160.358
42.860


8
165.816
68.921


9
314.184
68.921


10
319.842
42.860


11
280.358
42.860


12
285.816
68.921






Dimple #
6



Type
spherical



Radius
0.0700



SCD
0.0080



TCD
—


#
Phi
Theta





1
65.605
59.710


2
66.316
50.052


3
53.684
50.052


4
54.395
59.710


5
185.605
59.710


6
186.316
50.052


7
173.634
50.052


8
174.395
59.710


9
305.605
59.710


10
306.316
50.052


11
293.684
50.052


12
294.395
59.710






Dimple #
7



Type
truncated



Radius
0.0750



SCD
0.0132



TCD
0.0055


#
Phi
Theta





1
0.000
25.859


2
120.000
25.859


3
240.000
25.859


4
22.298
84.586


5
0.000
44.669


6
337.702
84.586


7
142.298
84.586


8
120.000
44.669


9
457.702
84.586


10
262.298
84.586


11
240.000
44.659


12
577.702
84.586






Dimple #
8



Type
truncated



Radius
0.0800



SCD
0.0138



TCD
0.0055


#
Phi
Theta





1
19.465
17.662


2
100.535
17.662


3
139.465
17.662


4
220.535
17.662


5
259.465
17.662


6
340.535
17.662


7
18.021
74.614


8
7.176
54.033


9
352.824
54.033


10
341.979
74.614


11
348.569
84.248


12
11.431
84.248


13
138.021
74.614


14
127.176
54.033


15
472.824
54.033


16
461.979
74.614


17
468.569
84.248


18
131.431
84.248


19
258.021
74.614


20
247.176
54.033


21
592.824
54.033


22
581.979
74.614


23
588.569
84.248


24
251.431
84.248






Dimple #
9



Type
truncated



Radius
0.0825



SCD
0.0141



TCD
0.0055


#
Phi
Theta





1
0.000
6.707


2
60.000
13.550


3
120.000
6.707


4
180.000
13.550


5
240.000
6.707


6
300.000
13.550


7
6.041
73.979


8
13.019
64.247


9
0.000
63.821


10
346.931
64.247


11
353.959
73.979


12
360.000
84.078


13
126.041
73.979


14
133.019
64.247


15
120.000
63.821


16
466.981
64.247


17
473.959
73.979


18
480.000
84.078


19
246.041
73.979


20
355.019
64.247


21
240.000
63.821


22
586.981
64.247


23
593.959
73.979


24
600.000
84.078









The geometric and dimple patterns 172-175, 273 and 2-3 described above have been shown to reduce dispersion. Moreover, the geometric and dimple patterns can be selected to achieve lower dispersion based on other ball design parameters as well. For example, for the case of a golf ball that is constructed in such a way as to generate relatively low driver spin, a cuboctahedral dimple pattern with the dimple profiles of the 172-175 series golf balls, shown in Table 5, or the 273 and 2-3 series golf balls shown in Tables 10 and 11, provides for a spherically symmetrical golf ball having less dispersion than other golf balls with similar driver spin rates. This translates into a ball that slices less when struck in such a way that the ball's spin axis corresponds to that of a slice shot. To achieve lower driver spin, a ball can be constructed from e.g., a cover made from an ionomer resin utilizing high-performance ethylene copolymers containing acid groups partially neutralized by using metal salts such as zinc, sodium and others and having a rubber-based core, such as constructed from, for example, a hard DupontTM Surlyn® covered two-piece ball with a polybutadiene rubber-based core such as the TopFlite XL Straight or a three-piece ball construction with a soft thin cover, e.g., less than about 0.04 inches, with a relatively high flexural modulus mantle layer and with a polybutadiene rubber-based core such as the Titleist ProV1®.
Similarly, when certain dimple pattern and dimple profiles describe above are used on a ball constructed to generate relatively high driver spin, a spherically symmetrical golf ball that has the short iron control of a higher spinning golf ball and when imparted with a relatively high driver spin causes the golf ball to have a trajectory similar to that of a driver shot trajectory for most lower spinning golf balls and yet will have the control around the green more like a higher spinning golf ball is produced. To achieve higher driver spin, a ball can be constructed from e.g., a soft DupontTM Surlyn® covered two-piece ball with a hard polybutadiene rubber-based core or a relatively hard DupontTM Surlyn® covered two-piece ball with a plastic core made of 30-100% DuPontTM HPF 2000®, or a three-piece ball construction with a soft thicker cove, e.g., greater than about 0.04 inches, with a relatively stiff mantle layer and with a polybutadiene rubber-based core.
It should be appreciated that the dimple patterns and dimple profiles used for 172-175, 273, and 2-3 series golf balls causes these golf balls to generate a lower lift force under various conditions of flight, and reduces the slice dispersion.
Golf balls dimple patterns 172-175 were subjected to several tests under industry standard laboratory conditions to demonstrate the better performance that the dimple configurations described herein obtain over competing golf balls. In these tests, the flight characteristics and distance performance for golf balls with the 173-175 dimple patterns were conducted and compared with a Titleist Pro V1® made by Acushnet. Also, each of the golf balls with the 172-175 patterns were tested in the Poles-Forward-Backward (PFB) and Pole Horizontal (PH) orientations. The Pro V1® being a USGA conforming ball and thus known to be spherically symmetrical was tested in no particular orientation (random orientation). Golf balls with the 172-175 patterns were all made from basically the same materials and had a standard polybutadiene-based rubber core having 90-105 compression with 45-55 Shore D hardness. The cover was a SurlynTM blend (38% 9150, 38% 8150, 24% 6320) with a 58-62 Shore D hardness, with an overall ball compression of approximately 110-115.
The tests were conducted with a “Golf Laboratories” robot and hit with the same Taylor Made® driver at varying club head speeds. The Taylor Made® driver had a 10.5° r7 425 club head with a lie angle of 54 degrees and a REAX 65 ‘R’ shaft. The golf balls were hit in a random-block order, approximately 18-20 shots for each type ball-orientation combination. Further, the balls were tested under conditions to simulate a 20-25 degree slice, e.g., a negative spin axis of 20-25 degrees.
The testing revealed that the 172-175 dimple patterns produced a ball speed of about 125 miles per hour, while the Pro V1® produced a ball speed of between 127 and 128 miles per hour.
The data for each ball with patterns 172-175 also indicates that velocity is independent of orientation of the golf balls on the tee.
The testing also indicated that the 172-175 patterns had a total spin of between 4200 rpm and 4400 rpm, whereas the Pro V1® had a total spin of about 4000 rpm. Thus, the core/cover combination used for balls with the 172-175 patterns produced a slower velocity and higher spinning ball.
Keeping everything else constant, an increase in a ball's spin rate causes an increase in its lift. Increased lift caused by higher spin would be expected to translate into higher trajectory and greater dispersion than would be expected, e.g., at 200-500 rpm less total spin; however, the testing indicates that the 172-175 patterns have lower maximum trajectory heights than expected. Specifically, the testing revealed that the 172-175 series of balls achieve a max height of about 21 yards, while the Pro V1® is closer to 25 yards.
The data for each of golf balls with the 172-175 patterns indicated that total spin and max height was independent of orientation, which further indicates that the 172-175 series golf balls were spherically symmetrical.
Despite the higher spin rate of a golf ball with, e.g., pattern 173, it had a significantly lower maximum trajectory height (max height) than the Pro V1®. Of course, higher velocity will result in a higher ball flight. Thus, one would expect the Pro V1® to achieve a higher max height, since it had a higher velocity. If a core/cover combination had been used for the 172-175 series of golf balls that produced velocities in the range of that achieved by the Pro V1®, then one would expect a higher max height. But the fact that the max height was so low for the 172-175 series of golf balls despite the higher total spin suggests that the 172-175 Vballs would still not achieve as high a max height as the Pro V1® even if the initial velocities for the 172-175 series of golf balls were 2-3 mph higher.
FIG. 11 is a graph of the maximum trajectory height (Max Height) versus initial total spin rate for all of the 172-175 series golf balls and the Pro V1®. These balls were when hit with Golf Labs robot using a 10.5 degree Taylor Made r7 425 driver with a club head speed of approximately 90 mph imparting an approximately 20 degree spin axis slice. As can be seen, the 172-175 series of golf balls had max heights of between 18-24 yards over a range of initial total spin rates of between about 3700 rpm and 4100 rpm, while the Pro V1® had a max height of between about 23.5 and 26 yards over the same range.
The maximum trajectory height data correlates directly with the CL produced by each golf ball. These results indicate that the Pro V1® golf ball generated more lift than any of the 172-175 series balls. Further, some of balls with the 172-175 patterns climb more slowly to the maximum trajectory height during flight, indicating they have a slightly lower lift exerted over a longer time period. In operation, a golf ball with the 173 pattern exhibits lower maximum trajectory height than the leading comparison golf balls for the same spin, as the dimple profile of the dimples in the square and triangular regions of the cuboctahedral pattern on the surface of the golf ball cause the air layer to be manipulated differently during flight of the golf ball.
Despite having higher spin rates, the 172-175 series golf balls have Carry Dispersions that are on average less than that of the Pro V1® golf ball. The data in FIGS. 12-16 clearly shows that the 172-175 series golf balls have Carry Dispersions that are on average less than that of the Pro V1® golf ball. It should be noted that the 172-175 series of balls are spherically symmetrical and conform to the USGA Rules of Golf.
FIG. 12 is a graph illustrating the carry dispersion for the balls tested and shown in FIG. 11. As can be seen, the average carry dispersion for the 172-175 balls is between 50-60 ft, whereas it is over 60 feet for the Pro V1®.
FIGS. 13-16 are graphs of the Carry Dispersion versus Total Spin rate for the 172-175 golf balls versus the Pro V1®. The graphs illustrate that for each of the balls with the 172-175 patterns and for a given spin rate, the balls with the 172-175 patterns have a lower Carry Dispersion than the Pro V1®. For example, for a given spin rate, a ball with the 173 pattern appears to have 10-12 ft lower carry dispersion than the Pro V1® golf ball. In fact, a 173 golf ball had the lowest dispersion performance on average of the 172-175 series of golf balls.
The overall performance of the 173 golf ball as compared to the Pro V1® golf ball is illustrated in FIGS. 17 and 18. The data in these figures shows that the 173 golf ball has lower lift than the Pro V1® golf ball over the same range of Dimensionless Spin Parameter (DSP) and Reynolds Numbers.
FIG. 17 is a graph of the wind tunnel testing results showing of the Lift Coefficient (CL) versus DSP for the 173 golf ball against different Reynolds Numbers. The DSP values are in the range of 0.0 to 0.4. The wind tunnel testing was performed using a spindle of 1/16th inch in diameter.
FIG. 18 is a graph of the wind tunnel test results showing the CL versus DSP for the Pro V1 golf ball against different Reynolds Numbers.
In operation and as illustrated in FIGS. 17 and 18, for a DSP of 0.20 and a Re of greater than about 60,000, the CL for the 173 golf ball is approximately 0.19-0.21, whereas for the Pro V1® golf ball under the same DSP and Re conditions, the CL is about 0.25-0.27. On a percentage basis, the 173 golf ball is generating about 20-25% less lift than the Pro V1® golf ball. Also, as the Reynolds Number drops down to the 60,000 range, the difference in CL is pronounced—the Pro V1® golf ball lift remains positive while the 173 golf ball becomes negative. Over the entire range of DSP and Reynolds Numbers, the 173 golf ball has a lower lift coefficient at a given DSP and Reynolds pair than does the Pro V1® golf ball. Furthermore, the DSP for the 173 golf ball has to rise from 0.2 to more than 0.3 before CL is equal to that of CL for the Pro V1® golf ball. Therefore, the 173 golf ball performs better than the Pro V1® golf ball in terms of lift-induced dispersion (non-zero spin axis).
Therefore, it should be appreciated that the cuboctahedron dimple pattern on the 173 golf ball with large truncated dimples in the square sections and small spherical dimples in the triangular sections exhibits low lift for normal driver spin and velocity conditions. The lower lift of the 173 golf ball translates directly into lower dispersion and, thus, more accuracy for slice shots.
“Premium category” golf balls like the Pro V1® golf ball often use a three-piece construction to reduce the spin rate for driver shots so that the ball has a longer distance yet still has good spin from the short irons. The 173 dimple pattern can cause the golf ball to exhibit relatively low lift even at relatively high spin conditions. Using the low-lift dimple pattern of the 173 golf ball on a higher spinning two-piece ball results in a two-piece ball that performs nearly as well on short iron shots as the “premium category” golf balls currently being used.
The 173 golf ball's better distance-spin performance has important implications for ball design in that a ball with a higher spin off the driver will not sacrifice as much distance loss using a low-lift dimple pattern like that of the 173 golf ball. Thus the 173 dimple pattern or ones with similar low-lift can be used on higher spinning and less expensive two-piece golf balls that have higher spin off a PW but also have higher spin off a driver. A two-piece golf ball construction in general uses less expensive materials, is less expensive, and easier to manufacture. The same idea of using the 173 dimple pattern on a higher spinning golf ball can also be applied to a higher spinning one-piece golf ball.
Golf balls like the MC Lady and MaxFli Noodle use a soft core (approximately 50-70 PGA compression) and a soft cover (approximately 48-60 Shore D) to achieve a golf ball with fairly good driver distance and reasonable spin off the short irons. Placing a low-lift dimple pattern on these balls allows the core hardness to be raised while still keeping the cover hardness relatively low. A ball with this design has increased velocity, increased driver spin rate, and is easier to manufacture; the low-lift dimple pattern lessens several of the negative effects of the higher spin rate.
The 172-175 dimple patterns provide the advantage of a higher spin two-piece construction ball as well as being spherically symmetrical. Accordingly, the 172-175 series of golf balls perform essentially the same regardless of orientation.
In an alternate embodiment, a non-Conforming Distance Ball having a thermoplastic core and using the low-lift dimple pattern, e.g., the 173 pattern, can be provided. In this alternate embodiment golf ball, a core, e.g., made with DuPontTM Surlyn® HPF 2000 is used in a two- or multi-piece golf ball. The HPF 2000 gives a core with a very high COR and this directly translates into a very fast initial ball velocity—higher than allowed by the USGA regulations.
In yet another embodiment, as shown in FIG. 19, golf ball 600 is provided having a spherically symmetrical low-lift pattern that has two types of regions with distinctly different dimples. As one non-limiting example of the dimple pattern used for golf ball 600, the surface of golf ball 600 is arranged in an octahedron pattern having eight symmetrical triangular shaped regions 602, which contain substantially the same types of dimples. The eight regions 602 are created by encircling golf ball 600 with three orthogonal great circles 604, 606 and 608 and the eight regions 602 are bordered by the intersecting great circles 604, 606 and 608. If dimples were placed on each side of the orthogonal great circles 604, 606 and 608, these “great circle dimples” would then define one type of dimple region two dimples wide and the other type region would be defined by the areas between the great circle dimples. Therefore, the dimple pattern in the octahedron design would have two distinct dimple areas created by placing one type of dimple in the great circle regions 604, 606 and 608 and a second type dimple in the eight regions 602 defined by the area between the great circles 604, 606 and 608.
As can be seen in FIG. 19, the dimples in the region defined by circles 604, 606, and 608 can be truncated dimples, while the dimples in the triangular regions 602 can be spherical dimples. In other embodiments, the dimple type can be reversed. Further, the radius of the dimples in the two regions can be substantially similar or can vary relative to each other.
FIGS. 25 and 26 are graphs which were generated for balls 273 and 2-3 in a similar manner to the graphs illustrated in FIGS. 20 to 24 for some known balls and the 173 and 273 balls. FIGS. 25 and 26 show the lift coefficient versus Reynolds Number at initial spin rates of 4,000 rpm and 4,500 rpm, respectively, for the 273 and 2-3 dimple pattern. FIGS. 27 and 28 are graphs illustrating the drag coefficient versus Reynolds number at initial spin rates of 4000 rpm and 4500 rpm, respectively, for the 273 and 2-3 dimple pattern. FIGS. 25 to 28 compare the lift and drag performance of the 273 and 2-3 dimple patterns over a range of 120,000 to 140,000 Re and for 4000 and 4500 rpm. This illustrates that balls with dimple pattern 2-3 perform better than balls with dimple pattern 273. Balls with dimple pattern 2-3 were found to have the lowest lift and drag of all the ball designs which were tested.
While certain embodiments have been described above, it will be understood that the embodiments described are by way of example only. Accordingly, the systems and methods described herein should not be limited based on the described embodiments. Rather, the systems and methods described herein should only be limited in light of the claims that follow when taken in conjunction with the above description and accompanying drawings.

## Claims

1. A golf ball having a plurality of dimples formed on its outer surface, the outer surface of the golf ball being divided into plural areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, each area of the second group abutting one or more areas of the first group, the first and second groups of areas and dimple shapes and dimensions being configured such that the golf ball is spherically symmetrical as defined by the United States Golf Association (USGA) Symmetry Rules, and such that the golf ball exhibits a lift coefficient (CL) of less than about 0.250 over a range of Reynolds Number (Re) from about 120,000 to about 180,000 and at a spin rate of about 3,500 rpm, and a CL of less than about 0.166 at a Re of 180,000 and at a spin rate of about 3,500 rpm.

2. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.220 over a range of Re from about 120,000 to about 180,000 and at a spin rate of about 3,500 rpm.

3. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.220 over a range of Re from about 130,000 to about 180,000 and at a spin rate of about 3,500 rpm.

4. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.210 over a range of Re from about 130,000 to about 180,000 and at a spin rate of about 3,500 rpm.

5. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.212 over a range of Re from about 140,000 to about 180,000 and at a spin rate of about 3,500 rpm.

6. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.210 over a range of Re from about 140,000 to about 180,000 and at a spin rate of about 3,500 rpm.

7. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.196 over a range of Re from about 140,000 to about 180,000 and at a spin rate of about 3,500 rpm.

8. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.205 over a range of Re from about 150,000 to about 180,000 and at a spin rate of about 3,500 rpm.

9. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.200 over a range of Re from about 150,000 to about 180,000 and at a spin rate of about 3,500 rpm.

10. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.185 over a range of Re from about 150,000 to about 180,000 and at a spin rate of about 3,500 rpm.

11. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.198 over a range of Re from about 160,000 to about 180,000 and at a spin rate of about 3,500 rpm.

12. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.190 over a range of Re from about 160,000 to about 180,000 and at a spin rate of about 3,500 rpm.

13. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.175 over a range of Re from about 160,000 to about 180,000 and at a spin rate of about 3,500 rpm.

14. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.186 over a range of Re from about 170,000 to about 180,000 and at a spin rate of about 3,500 rpm.

15. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.180 over a range of Re from about 170,000 to about 180,000 and at a spin rate of about 3000 rpm.

16. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.166 over a range of Re from about 170,000 to about 180,000 and at a spin rate of about 3,500 rpm.

17. The golf ball of claim 1, wherein the first and second groups of areas and dimple shapes and dimensions are configured such that the golf ball exhibits a CL of less than about 0.160 at a Re of about 180,000 and at a spin rate of about 3,500 rpm.

18. The golf ball of claim 1, wherein the areas in the first group are of different shape from the areas in the second group.

19. The golf ball of claim 1, wherein the areas are arranged to form a spherical polyhedron.

20. The golf ball of claim 19, wherein the areas of the first group are triangular and the areas of the second group are square.

21. The golf ball of claim 20, wherein the areas together form a cuboctahedral shape.

22. The golf ball of claim 20, wherein the first dimples are of smaller diameter than the second dimples.

23. The golf ball of claim 22 wherein the first dimples are of deeper depth than the second dimples.

24. The golf ball of claim 20 wherein each triangular shape area borders at least one square shape area.

25. The golf ball of claim 1, wherein some of the dimples are spherical dimples and some are spherical truncated dimples.

26. The golf ball of claim 1, wherein each area contains the same number of dimples.

27. The golf ball of claim 1, wherein the outer surface has a total of 504 dimples or less.

28. The golf ball of claim 1, wherein the dimples in each area are of at least two different sizes.

29. The golf ball of claim 1, wherein the dimple radius of each dimple in the first areas is in the range from about 0.05 to about 0.06 inches.

30. The golf ball of claim 29 wherein the dimple radius of each dimple in the second areas is in the range from about 0.075 to about 0.095 inches.

31. The golf ball of claim 29 wherein the dimple chord depth in the first areas is in the range from about 0.0075 to about 0.01 inches.

32. The golf ball of claim 31 wherein the dimple chord depth in the second areas is in the range from about 0.0035 to about 0.008 inches.

33. The golf ball of claim 1, wherein the areas together form a spherical polyhedron shape selected from the group consisting of cuboctahedron, truncated tetrahedron, truncated cube, truncated octahedron, truncated dodecahedron, truncated icosahedron, truncated icosahedron, truncated cuboctahedron, icosidodecahedron, rhombicuboctahedron, rhombicosidodecahedron, rhombitruncated cuboctahedron, rhombitruncated icosidodecahedron, snub cube, snub dodecahedron, cube, dodecahedron, hexahedron, icosahedron, octahedron, and tetrahedron.

34. The golf ball of claim 1, wherein the outer surface is divided into at least four areas of dimples.

35. The golf ball of claim 34 wherein the outer surface is divided into a plurality of areas of dimples in the range from four to thirty two areas of dimples.

36. The golf ball of claim 35, wherein the areas are of the same shape.

37. The golf ball of claim 35, wherein the areas are of at least two different shapes.

38. The golf ball of claim 35, wherein the areas are of three different shapes.

39. The golf ball of claim 37, wherein the areas include at least two different shapes selected from triangles, squares, pentagons, hexagons, octagons, and decagons.