Golf ball dimple plan shapes and methods of generating same
The present invention is directed to golf balls having improved aerodynamic performance due, at least in part, to the selection of the plan shapes of the dimples thereon. In particular, the present invention is directed to a golf ball that includes at least a portion of its dimples having a plan shape defined by low frequency periodic functions along a closed simple path. In addition, the present invention provides methods for designing dimples having a plan shape defined by a low frequency periodic function along a closed simple path.
1. A golf ball having a generally spherical surface and comprising a plurality of dimples on the spherical surface, wherein at least a portion of the plurality of dimples have a non-circular plan shape defined by a low frequency periodic function along a simple closed path, wherein the periodic function is selected from at least one of a sine, cosine, saw tooth wave, triangle wave, or square wave and a simple path is select from a circle, ellipse, polygon, or arbitrary closed curve.
2. The golf ball of claim 1 , wherein at least a portion comprises about 50 percent or more of the dimples on the golf ball.
3. The golf ball of claim 1 , wherein at least a portion comprises about 80 percent or more of the dimples on the golf ball.
4. The golf ball of claim 1 , wherein the periodic function is selected from a cosine, saw tooth wave, triangle wave, or square wave function.
5. The golf ball of claim 1 , wherein the periodic function is a combination of two or more periodic functions.
6. The golf ball of claim 1 , wherein the simple closed path is selected from a circle, ellipse, or square.
7. The golf ball of claim 1 , wherein the simple closed path is an arbitrary closed curve.
8. The golf ball of claim 1 , wherein the plan shape is defined according to the following function:
Q ( x ) = F path ( l, scl, x ) * F periodic ( s, a, p, x )
Where F path is the simple closed path of length l, with scale factor scl, defined along the vertices x; and F periodic is the periodic function with sharpness factor s, amplitude a, and period p defined at the vertices x, and
wherein the sharpness factor, s, is about 10 to about 60, amplitude, a, is about 1 or less, and period, p, is about 15 or less.
9. The golf ball of claim 8 , wherein the low frequency periodic function has a period of about 12 or less.
10. A golf ball having a generally spherical surface and comprising a plurality of dimples on the surface, wherein at least a portion of the plurality of dimples have a plan shape defined by a low frequency periodic function along a simple closed path according to the following function:
Q ( x ) = F path ( l, scl, x ) * F periodic ( s, a, p, x )
wherein F path is a path function of length l, with scale factor scl, defined along the vertices x, and F periodic is a periodic function with sharpness factor s, amplitude a, and period p defined at the vertices x,
wherein the path function is selected from a circle, ellipse, polygon, or arbitrary closed curve and the periodic function is selected from at least one of a sine, cosine, saw-tooth wave, triangle wave, or square wave, and
wherein the sharpness factor, s, is about 10 to about 60, amplitude, a, is about 1 or less, and period, p, is about 15 or less.
11. The golf ball of claim 10 , wherein at least a portion comprises about 50 percent or more of the dimples on the golf ball.
12. The golf ball of claim 10 , wherein at least a portion comprises about 80 percent or more of the dimples on the golf ball.
13. The golf ball of claim 10 , wherein the path function is any simple closed path that is symmetrical about two orthogonal axes.
14. The golf ball of claim 10 , wherein the path function is selected from a circle, ellipse, or square.
15. The golf ball of claim 10 , wherein the period, p, is about 12 or less.
16. The golf ball of claim 10 , wherein the period, p, is about 9 or less.
17. The golf ball of claim 10 , wherein the amplitude, a, is about 0.1 to about 1.
18. The golf ball of claim 10 , wherein the plan shape has an amplitude A of less than about 0.500.
19. A golf ball having a surface with a plurality of recessed dimples thereon, wherein at least one of the dimples have a plan shape defined by a low frequency periodic function along a simple closed path symmetrical about wo orthogonal axes according to the following function:
Q ( x ) = F path ( l, scl, x ) * F periodic ( s, a, p, x )
wherein F path is a path function of length l, with scale factor scl, defined along the vertices x, and F periodic is a periodic function with sharpness factor s, amplitude a, and period p defined at the vertices x,
wherein the path function is selected from a circle, ellipse, polygon, or arbitrary closed curve and the periodic function is selected from at least one of a sine, cosine, saw-tooth wave, triangle wave, or square wave, and
wherein the sharpness factor, s, is about 10 to about 60, amplitude, a, is about 0.1 to 1, and period, p, is about 12 or less.
20. The golf ball of claim 19 , wherein the periodic function is a sawtooth wave form.
21. The golf ball of claim 19 , wherein the periodic function is a square wave form.
22. The golf ball of claim 19 , wherein the periodic function is a cosine wave form.
23. The golf ball of claim 19 , wherein the periodic function is a triangle wave form.
24. The golf ball of claim 19 , wherein the plan shape has an amplitude A of about 0.0005 inches to about 0.100 inches.