Golf balls including at least one modified dimple group are disclosed. The modified dimple group comprises one or more modified dimples forming an axially symmetric pattern about a Correction Area Centroid located on an axis of symmetry at a latitude greater than 0°, where 0° represents the hemispherical pole and 90° represents the equator. The modified dimples can be altered, for example, by changing dimple coverage, dimple diameter, dimple depth, dimple edge angle, dimple volume, dimple cross-sectional shape, and/or dimple plan shape. Optionally, the dimples have a catenary cross-sectional shape and the modified dimples are altered by changing the shape factor and/or chord depth. Such modifications preferably produce a golf ball that flies more consistently regardless of orientation when struck than a corresponding golf ball without such modifications.
1. A golf ball having dimples on the outermost surface thereof, wherein the dimples have a catenary cross-sectional shape and consist of a majority of unmodified dimples and a plurality of modified dimples;
wherein the catenary cross-sectional shape of each unmodified dimple is expressed by the following formula:
Y
=
d
(
cosh
(
a
U
x
)
-
1
)
cosh
(
a
U
r
)
-
1
where:
Y is the vertical distance from the dimple apex;
x is the radial distance from the dimple apex to the dimple surface;
a U is a constant from 20 to 100, and is the same for all of the unmodified dimples;
d is the depth of the dimple; and
r is the radius of the dimple;
wherein the catenary cross-sectional shape of each modified dimple is expressed by the following formula:
Y
=
d
(
cosh
(
a
M
x
)
-
1
)
cosh
(
a
M
r
)
-
1
where:
Y is the vertical distance from the dimple apex;
x is the radial distance from the dimple apex to the dimple surface;
a M is a constant from 20 to 100;
d is the depth of the dimple; and
r is the radius of the dimple;
wherein a M is at least 10% greater than or at least 10% less than a U ; and
wherein the modified dimples are arranged in two or more groups, each group consisting of the modified dimples and forming an axially symmetric pattern about a different geometric center.
2. The golf ball of claim 1 , wherein the geometric center of each group of modified dimples is located on a non-polar axis of the ball.
3. The golf ball of claim 1 , wherein the geometric center of each group of modified dimples is located on an axis of the ball located at a latitude angle of greater than 5°.
4. The golf ball of claim 1 , wherein the geometric center of each group of modified dimples is located on an axis of the ball located at a latitude angle of greater than 15°.
5. The golf ball of claim 1 , wherein the geometric center of each group of modified dimples is located on an axis of the ball located at a latitude angle of greater than 30°.
6. The golf ball of claim 1 , wherein the geometric center of each group of modified dimples is located on an axis of the ball located at a latitude angle of greater than 45°.
7. The golf ball of claim 1 , wherein the geometric center of each group of modified dimples is located on an axis of the ball located at a latitude angle of greater than 50°.
8. The golf ball of claim 1 , wherein the modified dimples are arranged in six to eight groups.
9. The golf ball of claim 1 , wherein the pattern of one group of modified dimples is different from the pattern of another group of modified dimples.