Golf ball dimple plan shape
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 periodic sawtooth function mapped along a circular simple closed path, wherein the periodic sawtooth function is defined by the equation:
f
(
x
)
=
s
-
a
π
(
sin
(
π
px
)
+
1
2
sin
(
2
π
px
)
+
1
3
sin
(
3
π
px
)
+
1
4
sin
(
4
π
px
)
)
where s is the sharpness factor of the periodic sawtooth function and is defined by a constant value of from 10 to 60; a is the amplitude of the periodic sawtooth function and is a value from 0.1 to 1; and p is the period of the periodic sawtooth function and is equal to 3.
2. The golf ball of claim 1 , wherein each one of the dimples having said non-circular plan shape comprises a first dimple profile and a second dimple profile, the first dimple profile having a first edge angle (Φ EDGE1 ) and a second edge angle (Φ EDGE2 ) and the second dimple profile having a third edge angle (Φ EDGE3 ) and a fourth edge angle (Φ EDGE4 ), wherein at least two of Φ EDGE1 , Φ EDGE2 , Φ EDGE3 and Φ EDGE4 have different values.
3. The golf ball of claim 2 , wherein Φ EDGE1 ≠Φ EDGE2 and Φ EDGE3 ≠Φ EDGE4 .
4. The golf ball of claim 2 , wherein, for each one of the dimples having said non-circular plan shape, the difference between the maximum edge angle and the minimum edge angle of all of the dimple profiles of that dimple is from 0.30° to 3.00°.
5. The golf ball of claim 2 , wherein, for each one of the dimples having said non-circular plan shape, the difference between the maximum edge angle and the minimum edge angle of all of the dimple profiles of that dimple is from 0.50° to 3.00°.
6. The golf ball of claim 5 , wherein, for each one of the dimples having said non-circular plan shape, the difference between the first edge angle and the second edge angle of each of the dimple profiles of that dimple is from 0.30° to 2.00°.
7. The golf ball of claim 2 , wherein, for each one of the dimples having said non-circular plan shape, the average of the edge angles of all of the dimple profiles of that dimple is from 11° to 16°.
8. The golf ball of claim 1 , wherein the surface of said dimples having non-circular plan shape includes a protruding center portion.
9. The golf ball of claim 8 , wherein the protruding center portion lies below the nominal chord plane of the dimple.
10. The golf ball of claim 1 , wherein 50 percent or more of the dimples on the golf ball are dimples having said non-circular plan shape.
11. The golf ball of claim 1 , wherein 80 percent or more of the dimples on the golf ball are dimples having said non-circular plan shape.
12. The golf ball of claim 1 , wherein the circular path has a radius of from 0.025 inches to 0.150 inches.
13. The golf ball of claim 1 , wherein the absolute distance, d, of any point on the non-circular plan shape from the circular path is defined by the following equation:
d =√{square root over (( x circle −x plan ) 2 +( y circle −y plan ) 2 )}
where d is a directed distance calculated along a line from the plan shape centroid through corresponding points on the plan shape and circular path, and the maximum value, d max , for all calculated distances, d, is 0.007 inches or less.
14. The golf ball of claim 13 , wherein the maximum value, d max , for all calculated distances, d, is from 0.003 inches to 0.007 inches.
15. The golf ball of claim 14 , wherein the non-circular plan shape has a total of six points wherein the distance, d, of the point on the plan shape from the circular path equals d max .
16. The golf ball of claim 14 , wherein a first line is drawn from the plan shape centroid to a first point on the plan shape having a distance, d, equal to d max ; a second line is drawn from the plan shape centroid to a second point on the plan shape having a distance, d, equal to d max ; and the angle between the first line and the second line is 24°, 96°, or 120°.
17. The golf ball of claim 14 , wherein a first line is drawn from the plan shape centroid to a first point on the plan shape having a distance, d, equal to d max ; a second line is drawn from the plan shape centroid to a second point on the plan shape having a distance, d, equal to d max ; and the angle between the first line and the second line is 60°, 120°, or 180°.