Golf ball dimples defined by superposed curves
The present invention is a golf ball which comprises dimples having a cross section defined by the superposition of two or more continuous and differentiable functions, and particularly the superposition of a catenary function and a Witch of Agnesi function. Additionally, the dimples preferably have a circular boundary and maintain an axis coincident with the center of the circular boundary.
1. A golf ball having a surface with a plurality of recessed dimples thereon, including a plurality of axially symmetric cat-witch dimples having a profile defined by a function resulting from the sum of a catenary function and a Witch of Agnesi function, wherein the plurality of cat-witch dimples comprises:
at least one cat-witch dimple having a first diameter (D D1 ) and a first chord depth, and
at least one cat-witch dimple having a second diameter (D D2 ) and a second chord depth;
wherein D D1 is at least 0.005 inches greater than D D2 ;
wherein the chord depth difference, δ CD1 , between the first chord depth and the second chord depth is at least 0.001 inches; and
wherein the profile depth difference, δ PD1 , between the profile depth of the cat-witch dimple having the first diameter and the profile depth of the cat-witch dimple having the second diameter, at every distance D C from the center of the dimple, where
0
<
D
C
≤
D
D
2
4
,
is from
(
δ
CD
1
-
δ
CD
1
2
)
to
(
δ
CD
1
+
δ
CD
1
2
)
.
2. The golf ball of claim 1 , wherein the superposed dimple has a circular plan shape.
3. The golf ball of claim 1 , wherein the superposed dimple has a dimple diameter of from 0.100 inches to 0.220 inches.
4. The golf ball of claim 1 , wherein the plurality of cat-witch dimples additionally comprise at least one cat-witch dimple having a third diameter (D D3 ) and a third chord depth, and wherein D D3 is at least 0.005 inches less than D D2 .
5. The golf ball of claim 4 , wherein the chord depth difference, δ CD2 , between the first chord depth and the third chord depth is at least 0.002 inches.
6. The golf ball of claim 5 , wherein the profile depth difference, δ PD2 , between the profile depth of the cat-witch dimple having the first diameter and the profile depth of the cat-witch dimple having the third diameter, at every distance D C from the center of the dimple, where
0
≤
D
C
≤
D
D
3
4
,
is from
(
δ
CD
2
-
δ
CD
2
2
)
to
(
δ
CD
2
+
δ
CD
2
2
)
.
7. The golf ball of claim 6 , wherein the chord depth difference, δ CD3 , between the second chord depth and the third chord depth is at least 0.001 inches, and wherein the profile depth difference, δ PD3 , between the profile depth of the cat-witch dimple having the second diameter and the profile depth of the cat-witch dimple having the third diameter, at every distance D C from the center of the dimple, where
0
≤
D
C
≤
D
D
3
4
,
is from
(
δ
CD
3
-
δ
CD
3
2
)
to
(
δ
CD
3
+
δ
CD
3
2
)
.