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 from 250 to 400 dimples on the spherical surface, wherein at least 80% of the dimples are non-circular plan shape dimples having a plan shape defined by a periodic function mapped along a simple closed path, wherein:
the periodic function is selected from sine, cosine, sawtooth wave, triangle wave, and square wave functions;
the periodic function has a period of 15 or less;
the simple closed path is selected from a circle, an ellipse, and a square; and
the non-circular plan shape dimples include dimples having at least three different plan shape areas.
2. The golf ball of claim 1 , wherein the surface of each of the non-circular plan shape dimples includes a protruding center portion.
3. The golf ball of claim 2 , wherein the non-circular plan shape dimples having a protruding center portion have a profile shape defined by the function:
y=x 3 −⅗ x 2 .
4. The golf ball of claim 3 , wherein, for each one of the non-circular plan shape dimples, the average of the edge angles of all of the dimple profiles of that dimple is from 14° to 18°.
5. The golf ball of claim 1 , wherein the absolute distance, d, of any point on the non-circular plan shape from the simple closed 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 simple closed path, and the maximum value, d max , for all calculated distances, d, is 0.007 inches or less.
6. The golf ball of claim 1 , wherein the non-circular plan shape dimples include dimples having at least four different plan shape areas.
7. The golf ball of claim 1 , wherein the non-circular plan shape dimples include dimples having at least five different plan shape areas.
8. The golf ball of claim 1 , wherein the golf ball has a total of 312 dimples on the spherical surface thereof.
9. The golf ball of claim 1 , wherein all of the dimples are non-circular plan shape dimples.
10. The golf ball of claim 9 , wherein the dimples have a plan shape defined by a periodic sawtooth function mapped along a circular simple closed path, and wherein the periodic function has a period of 3.
11. 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 from 3 to 6; and
the non-circular plan shape dimples include dimples having at least three different plan shape areas.
12. The golf ball of claim 11 , wherein p=3.
13. The golf ball of claim 11 , wherein the surface of each of the non-circular plan shape dimples includes a protruding center portion.
14. The golf ball of claim 13 , wherein the non-circular plan shape dimples having a protruding center portion have a profile shape defined by the function:
y=x 3 −⅗ x 2 .
15. The golf ball of claim 14 , wherein, for each one of the non-circular plan shape dimples, the average of the edge angles of all of the dimple profiles of that dimple is from 14° to 18°.
16. The golf ball of claim 11 , wherein 80 percent or more of the dimples on the golf ball are non-circular plan shape dimples.
17. The golf ball of claim 11 , wherein the non-circular plan shape dimples include dimples having at least four different plan shape areas.
18. The golf ball of claim 11 , wherein the non-circular plan shape dimples include dimples having at least five different plan shape areas.
19. The golf ball of claim 11 , 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.
20. The golf ball of claim 19 , wherein the maximum value, d max , for all calculated distances, d, is from 0.003 inches to 0.007 inches.