# 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 comprising at least two groups of areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, the areas in the first group being triangular and the areas in the second group being square, the first and second groups of areas being arranged to form a cuboctahedron shape, 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 first and second groups of areas produce different aerodynamic effects, and the first dimples being of different dimensions from the second dimples.

## Background
RELATED APPLICATIONS INFORMATION
This application claims the benefit under 35 U.S.C. §120 of 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 §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 comprising at least two groups of areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, the areas in the first group being triangular and the areas in the second group being square, the first and second groups of areas being arranged to form a cuboctahedron shape, 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 first and second groups of areas produce different aerodynamic effects, and the first dimples being of different dimensions from the second dimples.
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 & 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


surface

%
%
%





area


area


area

surface
surface
surface



# of

for all


for all


for all
Total
area
area
area


Name of
Re-

of the
# of

of the
# of

of the
number
per
per
per


Archimedean
gion
Region A
Region
Region
Region B
Region
Region
Region C
Region
of
single A
single B
single C


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























truncated
30
triangles
17%
20
Hexagons
30%
12
decagons
53%
62
0.6%
1.5%
4.4%


icosidodecahedron


Rhombicos
20
triangles
15%
30
squares
51%
12
pentagons
35%
62
0.7%
1.7%
2.9%


idodecahedron


snub
80
triangles
63%
12
Pentagons
37%



92
0.8%
3.1%


dodecahedron


truncated
12
pentagons
28%
20
Hexagons
72%



32
2.4%
3.6%


icosahedron


truncated
12
squares
19%
8
Hexagons
34%
6
octagons
47%
26
1.6%
4.2%
7.8%


cuboctahedron


Rhombicub-
8
triangles
16%
18
squares
84%



26
2.0%
4.7%


octahedron


snub cube
32
triangles
70%
6
squares
30%



38
2.2%
5.0%


Icosado-
20
triangles
30%
12
Pentagons
70%



32
1.5%
5.9%


decahedron


truncated
20
triangles
 9%
12
Decagons
91%



32
0.4%
7.6%


dodecahedron


truncated
6
squares
22%
8
Hexagons
78%



14
3.7%
9.7%


octahedron


Cuboctahedron
8
triangles
37%
6
squares
63%



14
4.6%
10.6%


truncated
8
triangles
11%
6
Octagons
89%



14
1.3%
14.9%


cube


truncated
4
triangles
14%
4
Hexagons
86%



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.
It should also be understood that a golf ball designed in accordance with the embodiments described herein can be configured such that the average volume per dimple in one region or area, e.g., region A, is greater than the average volume per dimple in another region or area, e.g., region B. Also, a first parameter based on dimple volume in the one area, e.g region A can be greater, e.g., 5% greater, 15% greater, etc., than a second, equivalent parameter based on dimple volume in the other region or area, e.g., region B. Each of the foregoing parameters based on dimple volume can be defined as the volume of the dimples in the respective region divided by the surface area of the region. Also, the regions do not have to be perfect geometric shapes. For example, the triangle areas can incorporate, and therefore extend into, a small number of dimples from the adjacent square region, or vice versa. Thus, an edge of the triangle region can extend out in a tab like fashion into the adjacent square region. This could happen on one or more than one edge of one or more than one region. In this way, the areas can be said to be derived based on certain geometric shapes, i.e., the underlying shape is still a triangle or square, but with some irregularities at the edges. Accordingly, in the specification and claims that follow when a region is said to be, e.g., a triangle region, this should also be understood to cover a region that is of a shape derived from a triangle.
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
Dimple # 2
Dimple # 3


Type spherical
Type spherical
Type spherical


Radius 0.05
Radius 0.0525
Radius 0.055


SCD 0.0075
SCD 0.0075
SCD 0.0075


TCD n/a
TCD n/a
TCD n/a















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
28.81007
1
3.606874
86.10963
1
0
17.13539


 2
0
41.7187
2
4.773603
59.66486
2
0
79.62325


 3
5.308533
47.46948
3
7.485123
79.72027
3
0
53.39339


 4
9.848338
23.49139
4
9.566953
53.68971
4
8.604739
66.19316


 5
17.85912
86.27884
5
10.81146
86.10963
5
15.03312
79.65081


 6
22.3436
79.84939
6
12.08533
72.79786
6
60
9.094473


 7
24.72264
86.27886
7
13.37932
60.13101
7
104.9669
79.65081


 8
95.27736
86.27886
8
16.66723
66.70139
8
111.3953
66.19316


 9
97.6564
79.84939
9
19.58024
73.34845
9
120
17.13539


10
102.1409
86.27884
10
20.76038
11.6909
10
120
53.39339


11
110.1517
23.49139
11
24.53367
18.8166
11
120
79.62325


12
114.6915
47.46948
12
46.81607
15.97349
12
128.6047
66.19316


13
120
28.81007
13
73.18393
15.97349
13
135.0331
79.65081


14
120
41.7187
14
95.46633
18.8166
14
180
9.094473


15
125.3085
47.46948
15
99.23962
11.6909
15
224.9669
79.65081


16
129.8483
23.49139
16
100.4198
73.34845
16
231.3953
66.19316


17
137.8591
86.27884
17
103.3328
66.70139
17
240
17.13539


18
142.3436
79.84939
18
106.6207
60.13101
18
240
53.39339


19
144.7226
86.27886
19
107.9147
72.79786
19
240
79.62325


20
215.2774
86.27886
20
109.1885
86.10963
20
248.6047
66.19316


21
217.6564
79.84939
21
110.433
53.68971
21
255.0331
79.65081


22
222.1409
86.27884
22
112.5149
79.72027
22
300
9.094473


23
230.1517
23.49139
23
115.2264
59.66486
23
344.9669
79.65081


24
234.6915
47.46948
24
116.3931
86.10963
24
351.3953
66.19316


25
240
28.81007
25
123.6069
86.10963


26
240
41.7187
26
124.7736
59.66486


27
245.3085
47.46948
27
127.4851
79.72027


28
249.8483
23.49139
28
129.567
53.68971


29
257.8591
86.27884
29
130.8115
86.10963


30
262.3436
79.84939
30
132.0853
72.79786


31
264.7226
86.27886
31
133.3793
60.13101


32
335.2774
86.27886
32
136.6672
66.70139


33
337.6564
79.84939
33
139.5802
73.34845


34
342.1409
86.27884
34
140.7604
11.6909


35
350.1517
23.49139
35
144.5337
18.8166


36
354.6915
47.46948
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
223.3328
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
86.10963





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 # 4
Dimple # 5
Dimple # 6


Type spherical
Type spherical
Type spherical


Radius 0.0575
Radius 0.075
Radius 0.0775


SCD 0.0075
SCD 0.005
SCD 0.005


TCD n/a
TCD n/a
TCD n/a















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
4.637001
1
11.39176
35.80355
1
22.97427
54.90551


 2
0
65.89178
2
17.86771
45.18952
2
27.03771
64.89835


 3
4.200798
72.89446
3
26.35389
29.36327
3
47.66575
25.59568


 4
115.7992
72.89446
4
30.46014
74.86406
4
54.6796
84.41703


 5
120
4.637001
5
33.84232
84.58637
5
65.3204
84.41703


 6
120
65.89178
6
44.16317
84.58634
6
72.33425
25.59568


 7
124.2008
72.89446
7
75.83683
84.58634
7
92.96229
64.89835


 8
235.7992
72.89446
8
86.15768
84.58637
8
97.02573
54.90551


 9
240
4.637001
9
89.53986
74.86406
9
142.9743
54.90551


10
240
65.89178
10
93.64611
29.36327
10
147.0377
64.89835


11
244.2008
72.89446
11
102.1323
45.18952
11
167.6657
25.59568


12
355.7992
72.89446
12
108.6082
35.80355
12
174.6796
84.41703





13
131.3918
35.80355
13
185.3204
84.41703





14
137.8677
45.18952
14
192.3343
25.59568





15
146.3539
29.36327
15
212.9623
64.89835





16
150.4601
74.86406
16
217.0257
54.90551





17
153.8423
84.58637
17
262.9743
54.90551





18
164.1632
84.58634
18
267.0377
64.89835





19
195.8368
84.58634
19
287.6657
25.59568





20
206.1577
84.85637
20
294.6796
84.41703





21
209.5399
74.86406
21
305.3204
84.41703





22
213.6461
29.36327
22
312.3343
25.59568





23
222.1323
45.18952
23
332.9623
64.89835





24
228.6082
35.80355
24
337.0257
54.90551





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
284.1632
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 # 7
Dimple # 8
Dimple # 9


Type spherical
Type spherical
Type spherical


Radius 0.0825
Radius 0.0875
Radius 0.095


SCD 0.005
SCD 0.005
SCD 0.005


TCD n/a
TCD n/a
TCD n/a















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
35.91413
51.35559
1
32.46033
39.96433
1
51.33861
48.53996


 2
38.90934
62.34835
2
41.97126
73.6516
2
52.61871
61.45814


 3
50.48062
36.43373
3
78.02874
73.6516
3
67.38129
61.45814


 4
54.12044
73.49879
4
87.53967
39.96433
4
68.66139
48.53996


 5
65.87956
73.49879
5
152.4603
39.96433
5
171.3386
48.53996


 6
69.51938
36.43373
6
161.9713
73.6516
6
172.6187
61.45814


 7
81.09066
62.34835
7
198.0287
73.6516
7
187.3813
61.45814


 8
84.08587
51.35559
8
207.5397
39.96433
8
188.6614
48.53996


 9
155.9141
51.35559
9
272.4603
39.96433
9
291.3386
48.53996


10
158.9093
62.34835
10
281.9713
73.6516
10
292.6187
61.45814


11
170.4806
36.43373
11
318.0287
73.6516
11
307.3813
61.45814


12
174.1204
73.49879
12
327.5397
39.96433
12
308.6614
48.53996


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
















TABLE 7





(Dimple Pattern 173)

















Dimple # 1
Dimple # 2
Dimple # 3


Type spherical
Type spherical
Type spherical


Radius 0.05
Radius 0.0525
Radius 0.055


SCD 0.0075
SCD 0.0075
SCD 0.0075


TCD n/a
TCD n/a
TCD n/a















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
28.81007
1
3.606873831
86.10963
1
0
17.13539


 2
0
41.7187
2
4.773603104
59.66486
2
0
79.62325


 3
5.30853345
47.46948
3
7.485123389
79.72027
3
0
53.39339


 4
9.848337904
23.49139
4
9.566952638
53.68971
4
8.604738835
66.19316


 5
17.85912075
86.27884
5
10.81146128
86.10963
5
15.03312161
79.65081


 6
22.34360082
79.84939
6
12.08533241
72.79786
6
60
9.094473


 7
24.72264341
86.27886
7
13.37931975
60.13101
7
104.9668784
79.65081


 8
95.27735659
86.27886
8
16.66723032
66.70139
8
111.3952612
66.19316


 9
97.65639918
79.84939
9
19.58024114
73.34845
9
120
17.13539


10
102.1408793
86.27884
10
20.76038062
11.6909
10
120
53.39339


11
110.1516621
23.49139
11
24.53367306
18.8166
11
120
79.62325


12
114.6914665
47.46948
12
46.81607116
15.97349
12
128.6047388
66.19316


13
120
28.81007
13
73.18392884
15.97349
13
135.0331216
79.65081


14
120
41.7187
14
95.46632694
18.8166
14
180
9.094473


15
125.3085335
47.46948
15
99.23961938
11.6909
15
224.9668784
79.65081


16
129.8483379
23.49139
16
100.4197589
73.34845
16
231.3952612
66.19316


17
137.8591207
86.27884
17
103.3327697
66.70139
17
240
17.13539


18
142.3436008
79.84939
18
106.6206802
60.13101
18
240
53.39339


19
144.7226434
86.27886
19
107.9146676
72.79786
19
240
79.62325


20
215.2773566
86.27886
20
109.1885387
86.10963
20
248.6047388
66.19316


21
217.6563991
79.84939
21
110.4330474
53.68971
21
255.0331216
79.65081


22
222.1408793
86.27884
22
112.5148766
79.72027
22
300
9.094473


23
230.1516621
23.49139
23
115.2263969
59.66486
23
344.9668784
79.65081


24
234.6914665
47.46948
24
116.3931262
86.10963
24
351.3952612
66.19316


25
240
28.81007
25
123.6068738
86.10963


26
240
41.7187
26
124.7736031
59.66486


27
245.3085335
47.46948
27
127.4851234
79.72027


28
249.8483379
23.49139
28
129.5669526
53.68971


29
257.8591207
86.27884
29
130.8114613
86.10963


30
262.3436008
79.84939
30
132.0853324
72.79786


31
264.7226434
86.27886
31
133.3793198
60.13101


32
335.2773566
86.27886
32
136.6672303
66.70139


33
337.6563992
79.84939
33
139.5802411
73.34845


34
342.1408793
86.27884
34
140.7603806
11.6909


35
350.1516621
23.49139
35
144.5336731
18.8166


36
354.6914665
47.46948
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
229.1885387
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
86.10963





50
244.7736031
59.66486





51
247.4851234
79.72027





52
249.5669526
53.68971





53
250.6114613
86.10963





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
355.2663969
59.66486





72
356.3931262
86.10953












Dimple # 4
Dimple # 5
Dimple # 6


Type spherical
Type truncated
Type truncated


Radius 0.0575
Radius 0.075
Radius 0.0775


SCD 0.0075
SCD 0.0119
SCD 0.0122


TCD n/a
TCD 0.005
TCD 0.005















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
4.637001
1
11.39176224
35.80355
1
22.97426943
54.90551


 2
0
65.89178
2
17.86771474
45.18952
2
27.03771469
64.89835


 3
4.200798314
72.89446
3
26.35389345
29.36327
3
47.6657487
25.59568


 4
115.7992017
72.89446
4
30.46014274
74.86406
4
54.67960187
84.41703


 5
120
4.637001
5
33.84232422
84.58637
5
65.32039813
84.41703


 6
120
65.89178
6
44.16316958
84.58634
6
72.3342513
25.59568


 7
124.2007983
72.89446
7
75.83683042
84.58634
7
92.96228531
64.89835


 8
235.7992017
72.89446
8
86.15767578
84.58637
8
97.02573057
54.90551


 9
240
4.637001
9
89.53985726
74.86406
9
142.9742694
54.90551


10
240
65.89178
10
93.64610655
29.36327
10
147.0377147
64.89835


11
244.2007983
72.89446
11
102.1322853
45.18952
11
167.6657487
25.59568


12
355.7992017
72.89446
12
108.6082378
35.80355
12
174.6796019
84.41703





13
131.3917622
35.80355
13
185.3203981
84.41703





14
137.8677147
45.18952
14
192.3342513
25.59568





15
146.3538935
29.36327
15
212.9622853
64.89835





16
150.4601427
74.86406
16
217.0257306
54.90551





17
153.8423242
84.58637
17
262.9742694
54.90551





18
164.1631696
84.58634
18
267.0377147
64.89835





19
195.8368304
84.58634
19
297.6657487
25.59568





20
206.1576759
84.58637
20
294.6796019
84.41703





21
209.5398573
74.86406
21
305.3203981
84.41703





22
213.6461065
29.36327
22
312.3342513
25.59568





23
222.1322853
45.18952
23
332.9622853
64.89835





24
228.6082378
35.80355
24
337.0257306
54.90551





25
251.3917622
35.80355





26
257.8677147
45.18952





27
266.3538935
29.36327





28
270.4801427
74.86406





29
273.8423242
84.58637





30
284.1631696
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 # 7
Dimple # 8
Dimple # 9


Type truncated
Type truncated
Type truncated


Radius 0.0825
Radius 0.0875
Radius 0.095


SCD 0.0128
SCD 0.0133
SCD 0.014


TCD 0.005
TCD 0.005
TCD 0.005















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
35.91413117
51.35559
1
32.46032855
39.96433
1
51.33861068
48.53996


 2
38.90934195
62.34835
2
41.97126436
73.6516
2
52.61871427
61.45814


 3
50.48062345
36.43373
3
78.02873564
73.6516
3
67.38128573
61.45814


 4
54.12044072
73.49879
4
87.53967145
39.96433
4
68.66138932
48.53996


 5
65.87955928
73.49879
5
152.4603285
39.96433
5
171.3386107
48.53996


 6
69.51937655
36.43373
6
161.9712644
73.6516
6
172.6187143
61.45814


 7
81.09065805
62.34835
7
198.0287356
73.6516
7
187.3812857
61.45814


 8
084.08586883
51.35559
8
207.5396715
39.96433
8
188.6613893
48.53996


 9
155.9141312
51.35559
9
272.4603285
39.96433
9
291.3386107
48.53996


10
158.909342
62.34835
10
281.9712644
73.6516
10
292.6187143
61.45814


11
170.4806234
36.43373
11
318.0287356
73.6516
11
307.3812857
61.45814


12
174.1204407
73.49879
12
327.5396715
39.96433
12
308.6613893
48.53996


13
185.8795593
73.49879


14
189.5193766
36.43373


15
201.090658
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
324.0858688
51.35559
















TABLE 8





(Dimple Pattern 174)

















Dimple # 1
Dimple # 2
Dimple # 3


Type truncated
Type truncated
Type truncated


Radius 0.05
Radius 0.0525
Radius 0.055


SCD 0.0087
SCD 0.0091
SCD 0.0094


TCD 0.0035
TCD 0.0035
TCD 0.0035















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
28.81007
1
3.606874
86.10963
1
0
17.13539


 2
0
41.7187
2
4.773603
59.66486
2
0
79.62325


 3
5.308533
47.46948
3
7.485123
79.72027
3
0
53.39339


 4
9.848338
23.49139
4
9.566953
53.68971
4
8.604739
66.19316


 5
17.85912
86.27884
5
10.81146
86.10963
5
15.03312
79.65081


 6
22.3436
79.84939
6
12.08533
72.79786
6
60
9.094473


 7
24.72264
86.27886
7
13.37932
60.13101
7
104.9669
79.65081


 8
95.27736
86.27886
8
16.66723
66.70139
8
111.3953
66.19316


 9
97.6564
79.84939
9
19.58024
73.34545
9
120
17.13539


10
102.1409
86.27884
10
20.76038
11.6909
10
120
53.39339


11
110.1517
23.49139
11
24.53367
18.8166
11
120
79.62325


12
114.6915
47.46948
12
46.81607
15.97349
12
128.6047
66.19316


13
120
28.81007
13
73.18393
15.97349
13
135.0331
79.65081


14
120
41.7187
14
95.46633
18.8166
14
180
9.094473


15
125.3085
47.46948
15
99.23962
11.6909
15
224.9669
79.65081


16
129.8483
23.49139
16
100.4198
73.34845
16
231.3953
66.19316


17
137.8591
86.27884
17
103.3328
66.70139
17
240
17.13539


18
142.3436
79.84939
18
106.6207
60.13101
18
240
53.39339


19
144.7226
86.27886
19
107.9147
72.79786
19
240
79.62325


20
215.2774
86.27886
20
109.1885
86.10963
20
248.6047
66.19316


21
217.6564
79.84939
21
110.433
53.68971
21
255.0331
79.65081


22
222.1409
86.27884
22
112.5149
79.72027
22
300
9.094473


23
230.1517
23.49139
23
115.2264
59.66486
23
344.9669
79.65081


24
234.6915
47.46948
24
116.3931
86.10963
24
351.3953
66.19316


25
240
28.81007
25
123.6069
86.10963


26
240
41.7187
26
124.7736
59.66486


27
345.3085
47.46948
27
127.4851
79.72027


28
249.8483
23.49139
28
129.567
53.68971


29
257.8591
86.27884
29
130.8115
86.10963


30
262.3436
79.84939
30
132.0853
72.79786


31
264.7226
86.27886
31
133.3793
60.13101


32
335.2774
86.27886
32
136.6672
66.70139


33
337.6564
79.84939
33
139.5802
73.34845


34
342.1409
86.27884
34
140.7604
11.6909


35
350.1517
23.49139
35
144.5337
18.8166


36
354.6915
47.46948
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
223.3328
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
86.10963





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 # 4
Dimple # 5
Dimple # 6


Type truncated
Type spherical
Type spherical


Radius 0.0575
Radius 0.075
Radius 0.0775


SCD 0.0098
SCD 0.008
SCD 0.008


TCD 0.0035
TCD n/a
TCD n/a















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
4.637001
1
11.39176
35.80355
1
22.97427
54.90551


 2
0
65.89178
2
17.86771
45.18952
2
27.03771
64.89835


 3
4.200798
72.89446
3
26.35389
29.36327
3
47.66575
25.59568


 4
115.7992
72.89446
4
30.46014
74.86406
4
54.6796
84.41703


 5
120
4.637001
5
33.84232
84.58637
5
65.3204
84.41703


 6
120
65.89178
6
44.16317
84.58634
6
72.33425
25.59568


 7
124.2008
72.89446
7
75.83683
84.58634
7
92.96229
64.89835


 8
235.7992
72.79446
8
86.15768
84.58637
8
97.02573
54.90551


 9
240
4.637001
9
89.53986
74.86406
9
142.9743
54.90551


10
240
65.89178
10
93.64611
29.36327
10
147.0377
64.89835


11
244.2008
72.89446
11
102.1323
45.18952
11
167.6657
25.59568


12
355.7992
72.89446
12
108.6082
35.80355
12
174.6796
84.41703





13
131.3918
35.80355
13
185.3204
84.41703





14
137.8677
45.18952
14
192.3343
25.59568





15
146.3539
29.36327
15
212.9623
64.89835





16
150.4601
74.86406
16
217.0257
54.90551





17
153.8423
84.58637
17
262.9743
54.90551





18
164.1632
84.58634
18
267.0377
64.89835





19
195.8368
84.58634
19
287.6657
25.59568





20
206.1577
84.58637
20
294.6796
84.41703





21
209.5399
74.86406
21
305.3204
84.41703





22
213.6461
29.36327
22
312.3343
25.59568





23
222.1323
45.18952
23
332.9623
64.89835





24
228.6082
35.80355
24
337.0257
54.90551





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
284.1632
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 # 7
Dimple # 8
Dimple # 9


Type spherical
Type spherical
Type spherical


Radius 0.0825
Radius 0.0875
Radius 0.095


SCD 0.008
SCD 0.008
SCD 0.008


TCD n/a
TCD n/a
TCD n/a















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
35.91413
51.35559
1
32.46033
39.96433
1
51.33861
48.53996


 2
38.90934
62.34835
2
41.97126
73.6516
2
52.61871
61.45814


 3
50.48062
36.43373
3
78.02874
73.6516
3
67.38129
61.45814


 4
54.12044
73.49879
4
87.53967
39.96433
4
68.66139
48.53996


 5
65.87956
73.49879
5
152.4603
39.96433
5
171.3386
48.53996


 6
69.51938
36.43373
6
161.9713
73.6516
6
172.6187
61.45814


 7
81.09066
62.34835
7
198.0287
73.6516
7
187.3813
61.45814


 8
84.08587
51.35559
8
207.5397
39.96433
8
188.6614
48.53996


 9
155.9141
51.35559
9
272.4603
39.96433
9
291.3386
48.53996


10
158.9093
62.34835
10
281.9713
73.6516
10
292.6187
61.45814


11
170.4806
36.43373
11
318.0287
73.6516
11
307.3813
61.45814


12
174.1204
73.49879
12
327.5397
39.96433
12
308.6614
48.53996


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
















TABLE 9





(Dimple Pattern 175)

















Dimple # 1
Dimple # 2
Dimple # 3


Type spherical
Type spherical
Type spherical


Radius 0.05
Radius 0.0525
Radius 0.055


SCD 0.008
SCD 0.008
SCD 0.008


TCD n/a
TCD n/a
TCD n/a















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
28.81007
1
3.606874
86.10963
1
0
17.13539


 2
0
41.7187
2
4.773603
59.66486
2
0
79.62325


 3
5.308533
47.46948
3
7.485123
79.72027
3
0
53.39339


 4
9.848338
23.49139
4
9.566953
53.68971
4
8.604739
66.19316


 5
17.85912
86.27884
5
10.81146
86.10963
5
15.03312
79.65081


 6
22.3436
79.84939
6
12.08533
72.79786
6
60
9.094473


 7
24.72264
86.27886
7
13.37932
60.13101
7
104.9669
79.65081


 8
95.27736
86.27886
8
16.66723
66.70139
8
111.3953
66.19316


 9
97.6564
79.84939
9
19.58024
73.34845
9
120
17.13539


10
102.1409
86.27884
10
20.76038
11.6909
10
120
53.39339


11
110.1517
23.49139
11
24.53367
18.8166
11
120
79.62325


12
114.6915
47.46948
12
46.81607
15.97349
12
128.6047
66.19316


13
120
28.81007
13
73.18393
15.97349
13
135.0331
79.65081


14
120
41.7187
14
95.46633
18.8166
14
180
9.094473


15
125.3085
47.46948
15
99.23962
11.6909
15
224.9669
79.65081


16
129.8483
23.49139
16
100.4198
73.34845
16
231.3953
66.19316


17
137.8591
86.27884
17
103.3328
66.70139
17
240
17.13539


18
142.3436
79.84939
18
106.6207
60.13101
18
240
53.39339


19
144.7226
86.27886
19
107.9147
72.79786
19
240
79.62325


20
215.2774
86.27886
20
109.1885
86.10963
20
248.6047
66.19316


21
217.6564
79.84939
21
110.433
53.68971
21
255.0331
79.65081


22
222.1409
86.27884
22
112.5149
79.72027
22
300
9.094473


23
230.1517
23.49139
23
115.2264
59.66486
23
344.9669
79.65081


24
234.6915
47.46948
24
116.3931
86.10963
24
351.3953
66.19316


25
240
28.81007
25
123.6069
86.10963


26
240
41.7187
26
124.7736
59.66486


27
245.3085
47.46948
27
127.4851
79.72027


28
249.8483
23.49139
28
129.567
53.68971


29
257.8591
86.27884
29
130.8115
86.10963


30
262.3436
79.84939
30
132.0853
72.79786


31
264.7226
86.27886
31
133.3793
60.13101


32
335.2774
86.27886
32
136.6672
66.70139


33
337.6564
79.84939
33
139.5802
73.34845


34
342.1409
86.27884
34
140.7604
11.6909


35
350.1517
23.49139
35
144.5337
18.8166


36
354.6915
47.46948
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
223.3328
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
86.10963





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 # 4
Dimple # 5
Dimple # 6


Type spherical
Type truncated
Type truncated


Radius 0.0575
Radius 0.075
Radius 0.0775


SCD 0.008
SCD 0.012
SCD 0.0122


TCD n/a
TCD 0.0035
TCD 0.0035















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
4.637001
1
11.39176
35.80355
1
22.97427
54.90551


 2
0
65.89178
2
17.86771
45.18952
2
27.03771
64.89835


 3
4.200798
72.89446
3
26.35389
29.36327
3
47.66575
25.59568


 4
115.7992
72.89446
4
30.46014
74.86406
4
54.6796
84.41703


 5
120
4.637001
5
33.84232
84.58637
5
65.3204
84.41703


 6
120
65.89178
6
44.16317
84.58634
6
72.33425
25.59568


 7
124.2008
72.89446
7
75.83683
84.58634
7
92.96229
64.89835


 8
235.7992
72.89446
8
86.15768
84.58637
8
97.02573
54.90551


 9
240
4.637001
9
89.53986
74.86406
9
142.9743
54.90551


10
240
65.89178
10
93.64611
29.36327
10
147.0377
64.89835


11
244.2008
72.89446
11
102.1323
45.18952
11
167.6657
25.59568


12
355.7992
72.89446
12
108.6082
35.80355
12
174.6796
84.41703





13
131.3918
35.80355
13
185.3204
84.41703





14
137.8677
45.18952
14
192.3343
25.59568





15
146.3539
29.36327
15
212.9623
64.89835





16
150.4601
74.86406
16
217.0257
54.90551





17
153.8423
84.58637
17
262.9743
54.90551





18
164.1632
84.58634
18
267.0377
64.89835





19
195.8368
84.58634
19
287.6657
25.59568





20
206.1577
84.58637
20
294.6796
84.41703





21
209.5399
74.86406
21
305.3204
84.41703





22
213.6461
29.36327
22
312.3343
25.59568





23
222.1323
45.18952
23
332.9623
64.89835





24
228.6082
35.80355
24
337.0257
54.90551





25
251.3918
35.80355





26
257.8677
45.18952





27
266.3539
29.36327





28
270.4501
74.86406





29
273.8423
84.58637





30
284.1632
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 # 7
Dimple # 8
Dimple # 9


Type truncated
Type truncated
Type truncated


Radius 0.0825
Radius 0.0875
Radius 0.095


SCD 0.0128
SCD 0.0133
SCD 0.014


TCD 0.0035
TCD 0.0035
TCD 0.0035















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
35.91413
51.35559
1
32.46033
39.96433
1
51.33861
48.53996


 2
38.90934
62.34835
2
41.97126
73.6516
2
52.61871
61.45814


 3
50.48062
36.43373
3
78.02874
73.6516
3
67.38129
61.45814


 4
54.12044
73.49879
4
87.53967
39.96433
4
68.66139
48.53996


 5
65.87956
73.49879
5
152.4603
39.96433
5
171.3386
48.53996


 6
69.51938
36.43373
6
161.9713
73.6516
6
172.6187
61.45814


 7
81.09066
62.34835
7
198.0287
73.6516
7
187.3813
61.45814


 8
84.08587
51.35559
8
207.5397
39.96433
8
188.6614
48.53996


 9
155.9141
51.35559
9
272.4603
39.96433
9
291.3386
48.53996


10
158.9093
62.34835
10
281.9713
73.6516
10
292.6187
61.45814


11
170.4806
36.43373
11
318.0287
73.6516
11
307.3813
61.45814


12
174.1204
73.49879
12
327.5397
39.96433
12
308.6614
48.53996


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
















TABLE 10





(Dimple Pattern 273

















Dimple # 1
Dimple # 2
Dimple # 3


Type truncated
Type truncated
Type truncated


Radius 0.0750
Radius 0.0800
Radius 0.0825


SCD 0.0132
SCD 0.0138
SCD 0.0141


TCD 0.0050
TCD 0.0050
TCD 0.0050















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0
25.85946
1
19.46456
17.6616
1
0
6.707467


 2
120
25.85946
2
100.5354
17.6616
2
60
13.5496


 3
240
25.85946
3
139.4646
17.6616
3
120
6.707467


 4
22.29791
84.58636
4
220.5354
17.6616
4
180
13.5496


 5
1.15E−13
44.66932
5
259.4646
17.6616
5
240
6.707467


 6
337.7021
84.58636
6
340.5354
17.6616
6
300
13.5496


 7
142.2979
84.58636
7
18.02112
74.614
7
6.04096
73.97888


 8
120
44.66932
8
7.175662
54.03317
8
13.01903
64.24653


 9
457.7021
84.58636
9
352.8243
54.03317
9
2.41E−14
63.82131


10
262.2979
84.58636
10
341.9789
74.614
10
346.981
64.24653


11
240
44.66932
11
348.5695
84.24771
11
353.959
73.97888


12
577.7021
84.58636
12
11.43052
84.24771
12
360
84.07838





13
138.0211
74.614
13
126.041
73.97888





14
127.1757
54.03317
14
133.019
64.24653





15
472.8243
54.03317
15
120
63.82131





16
461.9789
74.614
16
466.981
64.24653





17
468.5695
84.24771
17
473.959
73.97888





18
131.4305
84.24771
18
480
84.07838





19
258.0211
74.614
19
246.041
73.97888





20
247.1757
54.03317
20
253.019
64.24653





21
592.8243
54.03317
21
240
63.82131





22
581.9789
74.614
22
586.981
64.24653





23
588.5695
84.24771
23
593.959
73.97888





24
251.4305
84.24771
24
600
84.07838












Dimple # 4
Dimple # 5
Dimple # 6


Type spherical
Type spherical
Type spherical


Radius 0.0550
Radius 0.0575
Radius 0.0600


SCD 0.0075
SCD 0.0075
SCD 0.0075


TCD —
TCD —
TCD —















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
89.81848
78.25196
1
83.35856
69.4858
1
86.88247
85.60198


 2
92.38721
71.10446
2
85.57977
61.65549
2
110.7202
35.62098


 3
95.11429
63.96444
3
91.04137
46.06539
3
9.279821
35.62098


 4
105.6986
42.86305
4
88.0815
53.82973
4
33.11753
85.60198


 5
101.558
49.81178
5
81.86536
34.37733
5
206.8825
85.60198


 6
98.11364
56.8624
6
67.54444
32.56834
6
230.7202
35.62098


 7
100.3784
30.02626
7
38.13465
34.37733
7
129.2798
35.62098


 8
86.62335
26.05789
8
52.45556
32.56834
8
153.1175
85.60198


 9
69.399
23.82453
9
28.95863
46.06539
9
326.8825
85.60198


10
19.62155
30.02626
10
31.9185
53.82973
10
350.7202
35.62098


11
33.37665
26.05789
11
36.64144
69.4858
11
249.2798
35.62098


12
50.601
23.82453
12
34.42023
61.65549
12
273.1175
85.60198


13
14.30135
42.86305
13
47.55421
77.35324


14
18.44204
49.81178
14
55.84303
77.16119


15
21.88636
56.8624
15
72.44579
77.35324


16
30.18152
78.25196
16
64.15697
77.16119


17
27.61279
71.10446
17
203.3586
69.4858


18
24.88571
63.96444
18
205.5798
61.65549


19
41.03508
85.94042
19
211.0414
46.06539


20
48.61817
85.94042
20
208.0815
53.82973


21
56.20813
85.94042
21
201.8653
34.34433


22
78.96492
85.94042
22
187.5444
32.56834


23
71.38183
85.94042
23
158.1347
34.37733


24
63.79187
85.94042
24
172.4556
32.56834


25
209.8185
78.25196
25
148.9586
46.06539


26
212.3872
71.10446
26
151.9185
63.82973


27
215.1143
63.96444
27
156.6414
69.4858


28
225.6986
42.86305
28
154.4202
61.65549


29
221.558
49.81178
29
167.5542
77.35324


30
218.1136
56.8624
30
175.843
77.16119


31
220.3784
30.02626
31
192.4458
77.35324


32
206.6234
26.05789
32
184.157
77.16119


33
189.399
23.82453
33
323.3586
69.4858


34
139.6216
30.02626
34
325.5796
61.65549


35
153.3766
26.05789
35
331.0414
46.06539


36
170.601
23.82453
36
328.0815
53.82973


37
134.3014
42.86305
37
321.8653
34.37733


38
138.442
49.81178
38
307.5444
32.56834


39
141.8864
56.8624
39
278.1347
34.37733


40
150.1815
78.25196
40
292.4556
32.56834


41
147.6128
71.10446
41
268.9586
46.06539


42
144.8857
63.96444
42
281.9185
53.82973


43
161.0351
85.94042
43
276.6414
69.4858


44
166.6182
85.94042
44
274.4202
61.65549


45
176.2081
85.94042
45
287.5542
77.35324


46
198.9649
85.94042
46
295.843
77.16119


47
191.3818
85.94042
47
312.4458
77.35324


48
183.7919
85.94042
48
304.157
77.16119


49
329.8185
78.25196


50
332.3872
71.10446


51
336.1143
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
373.3766
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
63.96444


67
281.0351
85.94042


68
288.6182
85.94042


69
296.2081
85.94042


70
318.9649
85.94042


71
311.3818
85.94042


72
303.7919
85.94042












Dimple # 7
Dimple # 8
Dimple # 9


Type spherical
Type spherical
Type spherical


Radius 0.0625
Radius 0.0675
Radius 0.0700


SCD 0.0075
SCD 0.0075
SCD 0.0075


TCD —
TCD —
TCD —















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
80.92949
77.43144
1
74.16416
68.92141
1
65.6084
59.710409


 2
76.22245
60.1768
2
79.64177
42.85974
2
66.31567
50.052318


 3
77.98598
51.7127
3
40.35823
42.85974
3
53.68433
50.052318


 4
94.40845
38.09724
4
45.81584
68.92141
4
54.39516
59.710409


 5
66.573
40.85577
5
194.1842
68.92141
5
185.6048
59.710409


 6
53.427
40.85577
6
199.6418
42.85974
6
186.3157
50.052318


 7
25.59155
38.09724
7
160.3582
42.85974
7
173.6843
50.052318


 8
42.01402
51.7127
8
165.8158
68.92141
8
174.3952
59.710409


 9
43.77755
60.1768
9
314.1842
68.92141
9
305.6048
59.710409


10
39.07051
77.43144
10
319.6418
42.85974
10
306.3157
50.052318


11
55.39527
68.86469
11
280.3582
42.85974
11
293.6843
50.052318


12
64.60473
68.86469
12
385.8158
68.92141
12
294.3952
59.710409


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
61.7127


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
















TABLE 11





(Dimple Pattern 2-3)

















Dimple # 1
Dimple # 2
Dimple # 3


Type spherical
Type spherical
Type spherical


Radius 0.0550
Radius 0.0575
Radius 0.0600


SCD 0.0080
SCD 0.0080
SCD 0.0080


TCD —
TCD —
TCD —















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
89.818
78.252
1
83.359
69.486
1
86.882
85.602


 2
92.387
71.104
2
85.580
61.655
2
110.720
35.621


 3
95.114
63.964
3
91.041
46.065
3
9.280
35.621


 4
105.699
42.863
4
88.081
53.830
4
33.118
85.602


 5
101.558
49.812
5
81.865
34.377
5
206.882
85.602


 6
98.114
56.862
6
67.544
32.568
6
230.720
35.621


 7
100.378
30.026
7
38.135
34.377
7
129.280
35.621


 8
86.623
26.058
8
52.456
32.568
8
153.118
85.602


 9
69.399
23.825
9
28.959
46.065
9
326.882
85.602


10
19.622
30.026
10
31.919
53.830
10
350.720
35.621


11
33.377
26.058
11
36.641
69.486
11
249.280
35.621


12
50.601
23.825
12
34.420
61.655
12
273.118
85.602


13
14.301
42.863
13
47.554
77.353


14
18.442
49.812
14
55.843
77.161


15
21.886
56.862
15
72.446
77.353


16
30.182
78.252
16
64.157
77.161


17
27.613
71.104
17
203.359
69.486


18
24.886
63.964
18
205.580
61.655


19
41.035
85.940
19
211.041
46.065


20
48.618
85.940
20
208.081
53.830


21
56.208
85.940
21
201.865
34.377


22
78.965
85.940
22
187.544
32.568


23
71.382
85.940
23
158.135
34.377


24
63.792
85.940
24
172.456
32.568


25
209.818
78.252
25
148.959
46.065


26
212.387
71.104
26
151.919
53.830


27
215.114
63.964
27
156.641
69.486


28
225.699
42.863
28
154.420
61.655


29
221.558
49.812
29
167.554
77.353


30
218.114
56.862
30
175.843
77.161


31
220.378
30.026
31
192.446
77.353


32
206.623
26.058
32
184.157
77.161


33
189.399
30.026
33
323.359
69.486


34
139.622
30.026
34
325.580
61.655


35
153.377
26.058
35
331.041
46.065


36
170.601
23.825
36
328.081
53.830


37
134.301
42.863
37
321.865
34.377


38
138.442
49.812
38
307.544
32.568


39
141.886
56.862
39
278.135
34.377


40
150.182
78.252
40
292.456
32.568


41
147.613
71.104
41
268.959
46.065


42
144.886
63.964
42
271.919
53.830


43
161.035
85.940
43
276.641
69.486


44
168.618
85.940
44
274.420
61.655


45
176.208
85.940
45
287.554
77.353


46
198.965
85.940
46
295.843
77.161


47
191.382
85.940
47
312.446
77.353


48
183.792
85.940
48
304.157
77.161


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 # 4
Dimple # 5
Dimple # 6


Type spherical
Type spherical
Type spherical


Radius 0.0625
Radius 0.0675
Radius 0.0700


SCD 0.0080
SCD 0.0080
SCD 0.0080


TCD —
TCD —
TCD —















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
80.929
77.431
1
74.184
68.921
1
65.605
59.710


 2
76.222
60.177
2
79.642
42.860
2
66.316
50.052


 3
77.986
51.713
3
40.358
42.860
3
53.684
50.052


 4
94.408
38.097
4
45.816
68.921
4
54.395
59.710


 5
66.573
40.856
5
194.184
68.921
5
185.605
59.710


 6
53.427
40.856
6
199.642
42.860
6
186.316
50.052


 7
25.592
38.097
7
160.358
42.860
7
173.684
50.052


 8
42.014
51.713
8
165.816
68.921
8
174.395
59.710


 9
43.778
60.177
9
314.184
68.921
9
305.605
59.710


10
39.071
77.431
10
319.642
42.860
10
306.316
50.052


11
55.395
68.865
11
280.358
42.860
11
293.684
50.052


12
64.605
68.865
12
285.816
68.921
12
294.395
59.710


13
200.929
77.431


14
196.222
60.177


15
197.986
51.713


16
214.408
38.097


17
186.573
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
38.097


29
306.573
40.856


30
293.427
40.856


31
265.592
38.097


32
282.014
51.713


33
283.778
60.177


34
279.071
77.431


35
295.395
68.865


36
304.605
68.865












Dimple # 7
Dimple # 8
Dimple # 9


Type truncated
Type truncated
Type truncated


Radius 0.075
Radius 0.0800
Radius 0.0825


SCD 0.0132
SCD 0.0138
SCD 0.0141


TCD 0.0055
TCD 0.0055
TCD 0.0055















#
Phi
Theta
#
Phi
Theta
#
Phi
Theta





 1
0.000
25.859
1
19.465
17.662
1
0.000
6.707


 2
120.000
25.859
2
100.535
17.662
2
60.000
13.550


 3
240.000
28.859
3
139.465
17.662
3
120.000
6.707


 4
22.298
84.586
4
220.535
17.662
4
180.000
13.550


 5
0.000
44.669
5
259.465
17.662
5
240.000
6.707


 6
337.702
84.586
6
340.535
17.662
6
300.000
13.550


 7
142.298
84.586
7
18.021
74.614
7
6.041
73.979


 8
120.000
44.669
8
7.176
54.033
8
13.019
64.247


 9
457.702
84.586
9
352.824
54.033
9
0.000
63.821


10
262.298
84.586
10
341.979
74.614
10
346.981
64.247


11
240.000
44.669
11
348.569
84.248
11
353.959
73.979


12
577.702
84.586
12
11.431
84.248
12
360.000
84.078





13
138.021
74.614
13
126.041
73.979





14
127.176
54.033
14
133.019
64.247





15
472.824
54.033
15
120.000
63.821





16
461.979
74.614
16
466.981
64.247





17
468.569
84.248
17
473.959
73.979





18
131.431
84.248
18
480.000
84.078





19
258.021
74.614
19
246.041
73.979





20
247.176
54.033
20
253.019
64.247





21
592.824
54.033
21
240.000
63.821





22
581.979
74.614
22
586.981
64.247





23
588.569
84.248
23
593.959
73.979





24
251.431
84.248
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®.
FIG. 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 comprising at least two groups of areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, the areas in the first group being triangular and the areas in the second group being square, the first and second groups of areas being arranged to form a cuboctahedron shape, 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 first and second groups of areas produce different aerodynamic effects, the first dimples are of different dimensions from the second dimples, the dimples are arranged along geodesic lines, and there are six dimples along each edge of the square areas and eight dimples along each edge of the triangular areas.

2. The golf ball of claim 1, wherein the first dimples are of smaller diameter than the second dimples.

3. 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 comprising at least two groups of areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, the areas in the first group being triangular and the areas in the second group being square, the first and second groups of areas being arranged to form a cuboctahedron shape, 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 first and second groups of areas produce different aerodynamic effects, the first dimples are of different dimensions from the second dimples, and at least most of the first dimples are of deeper depth than at least most of the second dimples.

4. The golf ball of claim 3, wherein the dimples are arranged along geodesic lines.

5. The golf ball of claim 3, wherein the ball has an equator, opposite poles, and first and second hemispheres on opposite sides of the equator, and the first hemisphere is offset by 60 degrees from the second hemisphere.

6. The golf ball of claim 5, wherein the dimple pattern repeats every 120 degrees.

7. The golf ball of claim 5, wherein the equator comprises a seam of the ball.

8. The golf ball of claim 5, wherein each pole is located in a triangular area.

9. The golf ball of claim 6, wherein each square region of one hemisphere borders each triangular region of the other hemisphere.

10. The golf ball of claim 3, wherein the first group of areas cover a surface area of approximately 37% of the total surface area of the ball and the second group of areas cover a surface area of approximately 63% of the total surface area.

11. The golf ball of claim 3, wherein some of the dimples are spherical and some are truncated.

12. The golf ball of claim 11, wherein all first dimples in the triangular areas are spherical dimples and all second dimples in the square areas are truncated dimples.

13. The golf ball of claim 3, wherein each area contains the same number of dimples.

14. The golf ball of claim 3, wherein the outer surface has a total of 504 dimples or less.

15. The golf ball of claim 3, wherein the dimples in each area are of at least two different sizes.

16. The golf ball of claim 15, wherein the dimples in each area are of at least two different diameters.

17. The golf ball of claim 3, wherein the dimple radius in the first areas is in the range from about 0.05 to about 0.06 inches.

18. The golf ball of claim 17 wherein the dimple radius in the second areas is in the range from about 0.075 to about 0.095 inches.

19. The golf ball of claim 18, wherein the second areas include at least some dimples having a radius of approximately 0.075 inches.

20. The golf ball of claim 17 wherein the dimple chord depth in the first areas is in the range from about 0.0075 to about 0.0035 inches.

21. The golf ball of claim 19 wherein the dimple chord depth in the second areas is in the range from about 0.0035 to about 0.008 inches.

22. The golf ball of claim 3, wherein the first dimples are of different dimensions from the second dimples such that the first and second groups of areas are visually contrasting.

23. The golf ball of claim 3, wherein the average volume per dimple is greater in one of the groups of areas relative to the other.

24. The golf ball of claim 3, wherein a first parameter based on dimple volume in one area of one of the groups of areas is greater than a second parameter based on dimple volume in one area of the other group of areas, and wherein the first and second parameters based on dimple volume are each defined as the volume of the dimples in the respective area divided by the surface area in that area.

25. The golf ball of claim 24, wherein the first parameter is at least 5% greater than the second parameter.

26. The golf ball of claim 24, wherein the first parameter is at least 15% greater than the second parameter.

27. The golf ball of claim 3, wherein the first group of areas is formed by adding a portion of the second group of areas to the first group of areas or vice versa.

28. 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 comprising at least two groups of areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, the areas in the first group being triangular and the areas in the second group being square, the first and second groups of areas being arranged to form a cuboctahedron shape, 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 first and second groups of areas produce different aerodynamic effects, the first dimples are of different dimensions from the second dimples, and at least most of the first dimples are of smaller diameter and shallower depth than at least most of the second dimples.

29. 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 comprising at least two groups of areas, a first group of areas containing a plurality of first dimples and a second group of areas containing a plurality of second dimples, the areas in the first group being triangular and the areas in the second group being square, the first and second groups of areas being arranged to form a cuboctahedron shape, 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 first and second groups of areas produce different aerodynamic effects, and the first dimples being of different dimensions from the second dimples, the dimples are arranged along geodesic lines, and the dimples in the first area are of four different sizes and the dimples in the second area are of five different sizes.