Golf ball dimple based on witch of Agnesi curve
View Patent ↗A golf ball having the contour wherein at least one dimple has the cross-section of the dimple surface based on a modified witch of Agnesi curve and defined by the equation in the form of: y ( x ) = - C 1 a 3 x 2 + C 2 a 2 + C 1 a 3 ( d 2 ) 2 + C 2 a 2 wherein: y is the vertical distance from the dimple apex, x is the radial distance from the dimple apex, a is equal to the radius of the circle in the witch of Agnesi, d is the dimple diameter, and C 1 and C 2 are constants that will produce a variety of dimple surfaces from a variety of functions.
1. A golf ball having a surface with a plurality of recessed dimples thereon, wherein the cross-section of at least one dimple is a curve defined by the equation:
y
(
x
)
=
-
C
1
a
3
x
2
+
C
2
a
2
+
C
1
a
3
(
d
2
)
2
+
C
2
a
2
where the chord plane represents y=0,
the center axis of the dimple represents x=0,
a is a constant equal to the radius of a circle having a center at x=0 and tangent to the curve at the center of the dimple,
C 1 and C 2 are constants, and
d is the dimple diameter; and
wherein the ratio between the chord volume, V c , of the dimple profile and the square of the dimple diameter, having a profile as defined d 2 , is:
0.0010
≤
V
c
d
2
≤
0.0040
.
2. The golf ball according to claim 1 , wherein the ratio between the chord volume, V c , of the dimple profile and the square of the dimple diameter, d 2 , is:
0.0015
≤
V
c
d
2
≤
0.0030
.
3. The golf ball according to claim 1 , wherein the curvature is unique at every point x when 0≦x≦d/2.
4. The golf ball according to claim 3 , wherein the maximum curvature as an absolute value at any point in the dimple profile is equal to or less than 200.
5. The golf ball according to claim 3 , wherein the maximum curvature as an absolute value at any point in the dimple profile is equal to or less than 100.
6. The golf ball according to claim 3 , wherein the maximum curvature as an absolute value at any point in the dimple profile is equal to or less than 50.
7. The golf ball according to claim 3 , wherein the volume ratio, R V , is from 0.01 to 0.50, as defined by the equation:
R
V
=
V
c
π
(
d
2
)
2
D
c
,
where D c , is the chord depth.
8. The golf ball according to claim 7 , wherein the volume ratio is from 0.15 to 0.35.