Golf ball dimples defined by superposed curve with decaying feature
A golf ball having a plurality of dimples on a surface thereof is disclosed herein. At least a first group of the plurality of dimples has a cross-sectional dimple profile defined by a superposed function resulting from a sum of at least a first function and a second function. The first function can be defined by at least one of: a circular arc or a catenary curve, and the second function can be defined by a decaying sinusoidal function.
1. A golf ball having a plurality of dimples on a surface thereof, wherein at least a first group of the plurality of dimples has a cross-sectional dimple profile defined by a superposed function resulting from a sum of at least a first function and a second function,
wherein the first function is defined by at least one of: a circular arc or a catenary curve, and
the second function is a decaying sinusoidal function.
2. The golf ball according to claim 1 , wherein the first function is defined by the circular arc.
3. The golf ball according to claim 1 , wherein the second function is a positive decaying sinusoidal function defined by:
y
(
x
)
=
α
c
d
e
-
k
x
cos
(
b
x
)
where α is an amplitude factor, and 0.01≤α≤1,
c d is a chord depth (in inches) of the first function,
k is a decay constant,
b is an oscillation frequency constant, and
x is a radial distance (in inches) from a centroid of the cross-sectional dimple profile,
wherein x=0 corresponds to the centroid of the cross-sectional dimple profile, and a three-dimensional dimple geometry is generated via rotation about x=0.
4. The golf ball according to claim 3 , wherein an amplitude of a sinusoidal oscillation defined at a center of the cross-sectional dimple profile is 10%-90% of the chord depth c d .
5. The golf ball according to claim 3 , wherein an amplitude of a sinusoidal oscillation defined at a center of the cross-sectional dimple profile is 10%-50% of the chord depth c d .
6. The golf ball according to claim 3 , wherein the oscillation frequency constant b is defined by:
b
=
2
π
n
D
D
where D D is a diameter (in inches) of the cross-sectional dimple profile, and
n is a quantity of sinusoidal oscillations defined by the cross-sectional dimple profile between x=0 and x=(D D /2).
7. The golf ball according to claim 6 , wherein n is an integer.
8. The golf ball according to claim 6 , wherein n is not an integer.
9. The golf ball according to claim 3 , wherein the oscillation frequency constant b is within the range defined by: 25≤b≤650.
10. The golf ball according to claim 3 , wherein the decay constant k is within the range defined by: 1≤k≤30.
11. The golf ball according to claim 1 , wherein the first function is defined by a catenary curve, the catenary curve being defined by:
y
1
=
c
d
(
cosh
(
SF
·
x
)
-
1
)
cosh
(
SF
·
D
D
2
)
-
1
where D D is a diameter (in inches) of the cross-sectional dimple profile, and
SF is a shape factor of the catenary curve.
12. The golf ball according to claim 1 , wherein the second function is a negative decaying sinusoidal function defined by:
y
(
x
)
=
-
α
c
d
e
-
k
x
cos
(
b
x
)
where α is an amplitude factor, and 0.01≤α≤1,
c d is a chord depth (in inches) of the first function,
k is a decay constant,
b is an oscillation frequency constant, and
x is a radial distance (in inches) from a centroid of the cross-sectional dimple profile,
wherein x=0 corresponds to the centroid of the cross-sectional dimple profile, and a three-dimensional dimple geometry is generated via rotation about x=0.
13. The golf ball according to claim 12 , wherein the oscillation frequency constant b is defined by:
b
=
2
π
n
D
D
where D D is a diameter (in inches) of the cross-sectional dimple profile, and
n is a quantity of sinusoidal oscillations defined by the cross-sectional dimple profile between x=0 and x=(D D /2).
14. The golf ball according to claim 13 , wherein the oscillation frequency constant b is within the range defined by: 25≤b≤650.
15. The golf ball according to claim 12 , wherein the decay constant k is within the range defined by: 1≤k≤30.
16. A golf ball having a plurality of dimples on a surface thereof, wherein at least a first group of the plurality of dimples has a cross-sectional dimple profile defined by a sum of at least a first function and a second function,
wherein the first function is defined by a circular arc or a catenary curve; and
the second function is defined by one of the following:
y
(
x
)
=
α
c
d
e
-
k
x
cos
(
bx
)
;
or
(
i
)
y
(
x
)
=
-
α
c
d
e
-
k
x
cos
(
bx
)
,
(
ii
)
where α is an amplitude factor, and 0.01≤α≤1,
c d is a chord depth (in inches) of the first function,
k is a decay constant,
b is an oscillation frequency constant, and
x is a radial distance (in inches) from a centroid of the cross-sectional dimple profile; and
wherein x=0 corresponds to the centroid of the cross-sectional dimple profile, and a three-dimensional dimple geometry is generated via rotation about x=0.
17. The golf ball according to claim 16 , wherein the first function is defined by the catenary curve, and the catenary curve is defined by:
y
1
=
c
d
(
cosh
(
SF
·
x
)
-
1
)
cosh
(
SF
·
D
D
2
)
-
1
where D D is a diameter (in inches) of the cross-sectional dimple profile, and
SF is a shape factor of the catenary curve.
18. The golf ball according to claim 16 , wherein the oscillation frequency constant b is defined by:
b
=
2
π
n
D
D
where D D is a diameter (in inches) of the cross-sectional dimple profile, and
n is a quantity of sinusoidal oscillations defined by the cross-sectional dimple profile between x=0 and x=(D D /2).
19. The golf ball according to claim 18 , wherein the quantity of sinusoidal oscillations is 1.5-15.5.
20. The golf ball according to claim 18 , wherein an amplitude of a sinusoidal oscillation defined at a center of the cross-sectional dimple profile is 10%-50% of the chord depth c d .