U.S. patent application number 13/433337 was filed with the patent office on 2013-07-04 for golf ball dimples defined by superposed curves.
The applicant listed for this patent is Michael R. Madson, Nicholas M. Nardacci. Invention is credited to Michael R. Madson, Nicholas M. Nardacci.
Application Number | 20130172125 13/433337 |
Document ID | / |
Family ID | 48695255 |
Filed Date | 2013-07-04 |
United States Patent
Application |
20130172125 |
Kind Code |
A1 |
Nardacci; Nicholas M. ; et
al. |
July 4, 2013 |
GOLF BALL DIMPLES DEFINED BY SUPERPOSED CURVES
Abstract
The present invention is a golf ball which comprises dimples
having a cross-sectional shape defined by the superposition of a
weighted profile and one or more additional profiles. The dimples
preferably have a circular boundary and maintain an axis coincident
with the center of the circular boundary.
Inventors: |
Nardacci; Nicholas M.;
(Bristol, RI) ; Madson; Michael R.; (Wrentham,
MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Nardacci; Nicholas M.
Madson; Michael R. |
Bristol
Wrentham |
RI
MA |
US
US |
|
|
Family ID: |
48695255 |
Appl. No.: |
13/433337 |
Filed: |
March 29, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
13341652 |
Dec 30, 2011 |
|
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|
13433337 |
|
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Current U.S.
Class: |
473/383 |
Current CPC
Class: |
A63B 37/0012 20130101;
A63B 37/0021 20130101; A63B 37/0018 20130101; A63B 37/0019
20130101; A63B 37/0003 20130101; A63B 37/002 20130101 |
Class at
Publication: |
473/383 |
International
Class: |
A63B 37/14 20060101
A63B037/14 |
Claims
1. A golf ball having a plurality of recessed dimples on the
surface thereof, wherein at least a portion of the recessed dimples
have a cross-sectional profile defined by the superposition of a
weighted profile and one or more additional profiles, wherein the
weighted profile is the product of a base profile and at least one
weighting function, and wherein the base profile is defined by a
single function.
2. The golf ball of claim 1, wherein the cross-sectional profile is
defined by the superposition of a weighted profile and a spherical
profile.
3. The golf ball of claim 1, wherein the cross-sectional profile is
defined by the superposition of a weighted profile and a conical
profile.
4. The golf ball of claim 1, wherein the cross-sectional profile is
defined by the superposition of a weighted profile and a catenary
profile.
5. The golf ball of claim 1, wherein the cross-sectional profile is
defined by the superposition of a weighted profile and an
elliptical profile.
6. The golf ball of claim 1, wherein the cross-sectional profile is
defined by the superposition of a weighted profile and a polynomial
profile.
7. The golf ball of claim 1, wherein the cross-sectional profile is
defined by the superposition of a weighted profile and a
trigonometric profile.
8. The golf ball of claim 1, wherein the base profile of the
weighted profile is selected from the group consisting of
spherical, conical, catenary, elliptical, polynomial, and
trigonometric functions.
9. The golf ball of claim 1, wherein the base profile of the
weighted profile is selected from the group consisting of Witch of
Agnesi, frequency, Neiles parabola, and trigonometric
functions.
10. The golf ball of claim 1, wherein the weighting function of the
weighted profile is selected from the group consisting of
polynomial, exponential, and trigonometric functions.
11. The golf ball of claim 1, wherein the weighted profile is the
product of the base profile and a linear combination of two or more
weighting functions.
12. The golf ball of claim 1, wherein the weighted profile is
continuous and differentiable.
13. The golf ball of claim 1, wherein the base profile is a single
continuous and differentiable function.
14. The golf ball of claim 1, wherein the cross-sectional profile
is continuous and differentiable.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation-in-part of co-pending
U.S. patent application Ser. No. 13/341,652, filed Dec. 30, 2011,
the entire disclosure of which is hereby incorporated herein by
reference.
FIELD OF THE INVENTION
[0002] The present invention is directed to a golf ball dimple
cross-sectional shape defined by the superposition of a weighted
profile and one or more additional profiles.
BACKGROUND OF THE INVENTION
[0003] Golf balls were originally made with smooth outer surfaces.
In the late nineteenth century, players observed that the
gutta-percha golf balls traveled further as they got older and more
gouged up. The players then began to roughen the surface of new
golf balls with a hammer to increase flight distance. Manufacturers
soon caught on and began molding non-smooth outer surfaces on golf
balls.
[0004] By the mid 1900's, almost every golf ball being made had 336
dimples arranged in an octahedral pattern. Generally, these balls
had about 60 percent of their outer surface covered by dimples.
Over time, improvements in ball performance were developed by
utilizing different dimple patterns. In 1983, for instance,
Titleist introduced the TITLEIST 384, which, not surprisingly, had
384 dimples that were arranged in an icosahedral pattern. About 76
percent of its outer surface was covered with dimples and the golf
ball exhibited improved aerodynamic performance. Today, dimpled
golf balls travel nearly two times farther than a similar ball
without dimples.
[0005] The dimples on a golf ball are important in reducing drag
and increasing lift. Drag is the air resistance that acts on the
golf ball in the opposite direction from the ball flight direction.
As the ball travels through the air, the air surrounding the ball
has different velocities and, thus, different pressures. The air
exerts maximum pressure at the stagnation point on the front of the
ball. The air then flows over the sides of the ball and has
increased velocity and reduced pressure. At some point it separates
from the surface of the ball, leaving a large turbulent flow area
called the wake that has low pressure. The difference in the high
pressure in front of the ball and the low pressure behind the ball
slows the ball down. This is the primary source of drag for a golf
ball.
[0006] The dimples on the ball create a turbulent boundary layer
around the ball, i.e., a thin layer of air adjacent to the ball
flows in a turbulent manner. The turbulence energizes the boundary
layer of air around the ball and helps it stay attached further
around the ball to reduce the area of the wake. This greatly
increases the pressure behind the ball and substantially reduces
the drag.
[0007] Lift is the upward force on the ball that is created from a
difference in pressure on the top of the ball to the bottom of the
ball. The difference in pressure is created by a warpage in the air
flow resulting from the ball's back spin. Due to the back spin, the
top of the ball moves with the air flow, which delays the
separation to a point further aft. Conversely, the bottom of the
ball moves against the air flow, moving the separation point
forward. This asymmetrical separation creates an arch in the flow
pattern, requiring the air over the top of the ball to move faster,
and thus have lower pressure than the air underneath the ball.
[0008] Almost every golf ball manufacturer researches dimple
patterns in order to improve the aerodynamic forces on the ball
during flight and increase the distance traveled by a golf ball. A
high degree of dimple coverage is generally beneficial to flight
distance, but only if the dimples are of preferred size and shape.
For example, dimple coverage gained by filling spaces with tiny
dimples is generally not very effective, since tiny dimples are not
good turbulence generators.
[0009] In addition to researching dimple pattern and size, golf
ball manufacturers also study the effect of dimple shape, volume,
and cross-section on overall flight performance of the ball. One
example is U.S. Pat. No. 5,737,757, which discusses dimples using
two different spherical radii with an inflection point where the
two curves meet. In most cases, however, the cross-sectional
profiles of dimples in prior art golf balls are parabolic curves,
ellipses, semi-spherical curves, saucer-shaped, a sine curve, a
truncated cone, or a flattened trapezoid. One disadvantage of these
shapes is that they can sharply intrude into the surface of the
ball, which may cause the drag to become greater than the lift. As
a result, the ball may not make best use of momentum initially
imparted thereto, resulting in an insufficient carry of the ball.
Despite all the cross-sectional profiles disclosed in the prior
art, there has been no disclosure of a golf ball having dimples
with a cross-sectional shape defined by the superposition of a
weighted profile and one or more additional profiles.
SUMMARY OF THE INVENTION
[0010] The present invention is a golf ball having a surface with a
plurality of recessed dimples thereon, wherein the dimples have a
cross-section defined by the superposition of a weighted profile
and one or more additional profiles. In a particular embodiment,
the weighted profile is the product of a base profile and at least
one weighting function wherein the base profile is defined by a
single function. In another particular embodiment, the weighted
profile is the product of a base profile and at least one weighting
function wherein the base profile is defined by a single
continuous, differentiable function.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] In the accompanying drawings, which form a part of the
specification and are to be read in conjunction therewith, and
which are given by way of illustration only, and thus are not meant
to limit the present invention.
[0012] FIG. 1 shows a dimple cross-sectional profile defined by the
superposition of a spherical profile and weighted catenary profile
according to one embodiment of the present invention.
[0013] FIG. 2 shows a dimple cross-sectional profile defined by the
superposition of a spherical profile and a weighted catenary
profile according to another embodiment of the present
invention.
[0014] FIG. 3 shows a dimple cross-sectional profile defined by the
superposition of a spherical profile and a weighted conical profile
according to another embodiment of the present invention.
[0015] FIG. 4 shows a dimple cross-sectional profile defined by the
superposition of a spherical profile and a weighted conical profile
according to another embodiment of the present invention.
[0016] FIG. 5 shows a dimple cross-sectional profile defined by the
superposition of a catenary profile and a weighted conical profile
according to another embodiment of the present invention.
[0017] FIG. 6 shows a dimple cross-sectional profile defined by the
superposition of a catenary profile and a weighted spherical
profile according to another embodiment of the present
invention.
[0018] FIG. 7 shows a dimple cross-sectional profile defined by the
superposition of a weighted spherical profile and a weighted
catenary profile according to another embodiment of the present
invention.
[0019] FIG. 8 shows a dimple cross-sectional profile defined by the
superposition of a weighted spherical profile and a weighted
catenary profile according to another embodiment of the present
invention.
DETAILED DESCRIPTION OF THE INVENTION
[0020] The present invention is directed to a golf ball which
comprises dimples having a cross-sectional shape defined by the
superposition of a weighted profile and one or more additional
profiles. The weighted profile is the product of a base profile and
at least one weighting function. Each additional profile can be an
un-weighted or a weighted profile. In embodiments of the present
invention wherein the cross-sectional shape is defined by the
superposition of at least two weighted profiles, the base profile
of one weighted profile can be the same as or different from the
base profile of another weighted profile, and the weighting
function of one weighted profile can be the same as or different
than the weighting function of another weighted profile.
[0021] Suitable profiles for use as an un-weighted profile or as
the base profile of a weighted profile include those that can be
defined by a single function, including, but not limited to,
spherical, conical, catenary, elliptical, polynomial, Witch of
Agnesi, frequency, Neiles parabola, and trigonometric profiles, and
those that are defined by two or more functions, including, but not
limited to, profiles comprising a top conical edge and a bottom
spherical cap. Profiles comprising a top conical edge and a bottom
spherical cap are further disclosed, for example, in U.S. Patent
Application Publication No. 2010/0240474, the entire disclosure of
which is hereby incorporated herein by reference.
[0022] Typical weighting function forms include, but are not
limited to, polynomial, exponential, and trigonometric and linear
combinations thereof.
[0023] In a particular embodiment, the present invention is
directed to dimples having a cross-sectional shape defined by the
superposition of a weighted profile and one or more additional
profiles, wherein the weighted profile is the product of a base
dimple profile defined by a single continuous, differentiable
function, and a continuous weighting function, resulting in a
continuous, differentiable weighted dimple profile. In a particular
aspect of this embodiment, each of the one or more additional
profiles is defined by a single continuous, differentiable
function.
[0024] Weighted profiles are further disclosed in U.S. patent
application Ser. No. 13/341,652, filed Dec. 30, 2011, the entire
disclosure of which is hereby incorporated herein by reference.
[0025] Non-limiting examples of particularly suitable weighting
functions are shown in Table 1 below.
TABLE-US-00001 TABLE 1 Example No. Weighting Function 1 w = 1 2 w =
x 3 w = x.sup.2 4 w = x.sup.3 5 w = x.sup.4 6 w = x.sup.4 + x.sup.3
7 w = x.sup.2/5 + 3x.sup.3 + x.sup.4 8 w = 10x.sup.2 + 3x.sup.4 9 w
= 3x.sup.4 + x.sup.3/2 + 10x 10 w = -x 11 w = -x.sup.3 12 w =
x.sup.3 - x.sup.4 - 2x 13 w = sin(x) 14 w = cos(x) 15 w = -x.sup.5
16 w = e.sup.x 17 w = -e.sup.x 18 w = (-e.sup.2x)sin(x) 19 w =
e.sup.2xx.sup.3
[0026] FIGS. 1-8 show the dimple cross-sections resulting from the
superposition of a weighted profile and one additional profile. In
each figure, the individual profiles are shown along with the final
dimple profile. FIGS. 1-8 show various combinations of weighted
base profiles and one additional profile. The figures consider a
golf ball with a diameter of 1.680 inches and a dimple diameter of
0.165 inches. The base profiles and weighting functions used to
create the superposed profile along with chord depth, chord volume
and equivalent spherical edge angle of the final profile are
tabularized in Table 2. Weighting functions are numerically
referenced from Table 1.
TABLE-US-00002 TABLE 2 Effective Chord Edge Base Weighting Base
Weighting Depth Chord Vol Angle FIG. profile Function Profile
Function (inch) (in.sup.3) (degs) 1 Spherical none Catenary 19
0.0090 1.2284E-04 21.43 2 Spherical none Catenary 7 0.0069
9.2868E-05 17.57 3 Spherical none Conical 19 0.0082 7.6391E-05
15.45 4 Spherical none Conical 2 0.0089 8.5137E-05 16.57 5 Catenary
none Conical 14 0.0059 8.1103E-05 16.05 6 Catenary none Spherical 9
0.0061 9.0453E-05 17.26 7 Spherical 5 Catenary 5 0.0061 1.0184E-04
18.73 8 Spherical 5 Catenary 13 0.0051 6.1605E-05 13.54
[0027] The present invention is not limited by any particular
dimple pattern. Examples of suitable dimple patterns include, but
are not limited to, phyllotaxis-based patterns; polyhedron-based
patterns; and patterns based on multiple copies of one or more
irregular domain(s) as disclosed in U.S. Pat. No. 8,029,388, the
entire disclosure of which is hereby incorporated herein by
reference; and particularly dimple patterns suitable for packing
dimples on seamless golf balls. Non-limiting examples of suitable
dimple patterns are further disclosed in U.S. Pat. Nos. 7,927,234,
7,887,439, 7,503,856, 7,258,632, 7,179,178, 6,969,327, 6,702,696,
6,699,143, 6,533,684, 6,338,684, 5,842,937, 5,562,552, 5,575,477,
5,957,787, 5,249,804, 5,060,953, 4,960,283, and 4,925,193, and U.S.
Patent Application Publication Nos. 2006/0025245, 2011/0021292,
2011/0165968, and 2011/0183778, the entire disclosures of which are
hereby incorporated herein by reference. Non-limiting examples of
seamless golf balls and methods of producing such are further
disclosed, for example, in U.S. Pat. Nos. 6,849,007 and 7,422,529,
the entire disclosures of which are hereby incorporated herein by
reference.
[0028] In a particular embodiment, the dimple pattern provides for
overall dimple coverage of 60% or greater, or 65% or greater, or
75% or greater, or 80% or greater, or 85% or greater, or 90% or
greater.
[0029] Golf balls of the present invention typically have a dimple
count within a limit having a lower limit of 250 and an upper limit
of 350 or 400 or 450 or 500. In a particular embodiment, the dimple
count is 252 or 272 or 302 or 312 or 320 or 328 or 332 or 336 or
340 or 352 or 360 or 362 or 364 or 372 or 376 or 384 or 390 or 392
or 432.
[0030] The diameter of the dimples is preferably within a range
having a lower limit of 0.090 inches or 0.100 inches or 0.115
inches or 0.125 inches and an upper limit of 0.185 inches or 0.200
inches or 0.225 inches.
[0031] The chord depth of the dimples is preferably within a range
having a lower limit of 0.002 inches or 0.004 inches or 0.006
inches and an upper limit of 0.008 inches or 0.010 inches or 0.012
inches or 0.014 inches or 0.016 inches.
[0032] The present invention may be used with any type of ball
construction. For instance, the ball may have a 2-piece
construction, a double cover or veneer cover construction or other
multi-layer constructions depending on the type of performance
desired of the ball. Examples of these and other types of ball
constructions that may be used with the present invention include
those described in U.S. Pat. Nos. 5,713,801, 5,803,831, 5,885,172,
5,919,100, 5,965,669, 5,981,654, 5,981,658, and 6,149,535, with the
construction and materials disclosed in the patents being expressly
incorporated herein. Different materials also may be used in the
construction of the golf balls made with the present invention. For
example, the cover of the ball may be made of polyurethane,
polyurea, ionomer resin, balata or any other suitable cover
material known to those skilled in the art. Different materials
also may be used for forming core and intermediate layers of the
ball.
[0033] While the invention has been described in conjunction with
specific embodiments, it is evident that numerous alternatives,
modifications, and variations will be apparent to those skilled in
the art in light of the foregoing description.
* * * * *