U.S. patent application number 13/341717 was filed with the patent office on 2013-07-04 for golf ball dimple profile.
The applicant listed for this patent is Chris Hixenbaugh, Michael R. Madson, Nicholas M. Nardacci. Invention is credited to Chris Hixenbaugh, Michael R. Madson, Nicholas M. Nardacci.
Application Number | 20130172124 13/341717 |
Document ID | / |
Family ID | 48695254 |
Filed Date | 2013-07-04 |
United States Patent
Application |
20130172124 |
Kind Code |
A1 |
Hixenbaugh; Chris ; et
al. |
July 4, 2013 |
GOLF BALL DIMPLE PROFILE
Abstract
Golf ball dimples having a cross-sectional profile shape
partially defined by a Gabriel's Horn curve are disclosed.
Inventors: |
Hixenbaugh; Chris;
(Dartmouth, MA) ; Nardacci; Nicholas M.; (Bristol,
RI) ; Madson; Michael R.; (Wrentham, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Hixenbaugh; Chris
Nardacci; Nicholas M.
Madson; Michael R. |
Dartmouth
Bristol
Wrentham |
MA
RI
MA |
US
US
US |
|
|
Family ID: |
48695254 |
Appl. No.: |
13/341717 |
Filed: |
December 30, 2011 |
Current U.S.
Class: |
473/383 |
Current CPC
Class: |
A63B 37/0019 20130101;
A63B 37/0003 20130101; A63B 37/002 20130101; A63B 37/0018 20130101;
A63B 37/0021 20130101; A63B 37/0012 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 including a base portion and a
Gabriel's Horn portion, the base portion being defined by the
equation: y(x)=-C.sub.d,0.ltoreq.x<x.sub.0, where C.sub.d is the
chord depth, and the Gabriel's Horn portion being defined by the
equation: y ( x ) = C d ( 2 d d - 1 x ) ( d d 2 ) ( H F - 1 ) , x 0
.ltoreq. x .ltoreq. d d 2 , ##EQU00011## where C.sub.d is the chord
depth, d.sub.d is the dimple diameter, and HF is the horn factor
defined as: H F = d d d b , ##EQU00012## where d.sub.d is the
dimple diameter and d.sub.b is the dimple base diameter.
2. The golf ball of claim 1, wherein the horn factor, HF, is from
1.3 to 30.
3. The golf ball of claim 1, wherein the horn factor, HF, is from
1.3 to 15.
4. The golf ball of claim 1, wherein the horn factor, HF, is from
1.5 to 4.
5. The golf ball of claim 1, wherein the chord depth, C.sub.d, is
from 0.001 inches to 0.030 inches.
6. The golf ball of claim 1, wherein the chord depth, C.sub.d, is
from 0.005 inches to 0.015 inches.
7. The golf ball of claim 1, wherein the chord depth, C.sub.d, is
from 0.007 inches to 0.010 inches.
8. The golf ball of claim 1, wherein the dimple has a volume ratio
of from 0.03 to 1.00.
9. The golf ball of claim 1, wherein the dimple has a volume ratio
of from 0.07 to 0.80.
10. The golf ball of claim 1, wherein the dimple has a volume ratio
of from 0.25 to 0.70.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to a golf ball dimple
cross-sectional profile a portion of which is defined by a
Gabriel's Horn curve.
BACKGROUND OF THE INVENTION
[0002] Golf ball dimples are known to have a significant effect on
the aerodynamic forces acting on the ball during flight. For
example, the dimples on a golf ball create a turbulent boundary
layer around the ball. The turbulence energizes the boundary layer
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. Based on the role that
dimples play in reducing drag, golf ball manufacturers continually
seek to develop novel dimple patterns, sizes, shapes, volumes,
cross-sections, etc., in order to optimize flight performance.
SUMMARY OF THE INVENTION
[0003] In a particular embodiment, the present invention is
directed to a golf ball having a plurality of recessed dimples on
the surface thereof, at least a portion of which have a
cross-sectional profile including a base portion and a Gabriel's
Horn portion. The base portion of the profile is defined by a first
equation in the form of:
y(x)=-C.sub.d,0.ltoreq.x<x.sub.0,
where C.sub.d is the chord depth. The Gabriel's Horn portion of the
profile is defined by a second equation in the form of:
y ( x ) = C d ( 2 d d - 1 x ) ( d d 2 ) ( H F - 1 ) , x 0 .ltoreq.
x .ltoreq. d d 2 , ##EQU00001##
where C.sub.d is the chord depth, d.sub.d is the dimple diameter,
and HF is the horn factor. The horn factor is defined as:
H F = d d d b , ##EQU00002##
where d.sub.d is the dimple diameter and d.sub.b is the dimple base
diameter.
BRIEF DESCRIPTION OF DRAWINGS
[0004] 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:
[0005] FIG. 1 shows a portion of a dimple cross-sectional profile
of the present invention.
DETAILED DESCRIPTION
[0006] Golf balls of the present invention include dimples having a
cross-sectional profile partially defined by a Gabriel's Horn
curve. Gabriel's Horn, also known as Torricelli's Trumpet, is a
curve defined by the Cartesian equation:
y ( x ) = 1 x , x .gtoreq. 1 , x .ltoreq. - 1. ##EQU00003##
This equation is manipulated to provide the following equation,
which defines the Gabriel's horn portion of a dimple
cross-sectional profile:
y ( x ) = C d ( 2 d d - 1 x ) ( d d 2 ) ( H F - 1 ) , x 0 .ltoreq.
x .ltoreq. d d 2 , ##EQU00004##
where C.sub.d is the chord depth, d.sub.d is the dimple diameter,
and HF is the horn factor. The remaining portion of the dimple
cross-sectional profile, i.e., the base portion of the dimple, is
defined by the following equation:
y(x)=-C.sub.d,0.ltoreq.x<x.sub.0
where C.sub.d is the chord depth. The following are also taken into
account: [0007] 1) the chord plane of the dimple represents y=0,
and [0008] 2) the vertical axis in the center of the dimple
represents x=0.
[0009] FIG. 1 illustrates a dimple profile resulting from a
combination of a Gabriel's horn portion and a base portion, each
being defined according to the respective equations above. The
profile is then rotated 360.degree. about the Y (vertical) axis to
define the dimple surface.
[0010] For purposes of the present invention, the horn factor is
defined as:
H F = d d d b , ##EQU00005##
where d.sub.d is the dimple diameter and d.sub.b is the dimple base
diameter. The horn factor, HF, can be any real number greater than
1. In a particular embodiment, HF is within a range having a lower
limit of 1.3 or 1.5 and an upper limit of 4 or 15 or 30.
[0011] Dimples of the present invention typically have a base
diameter within a range having a lower limit of 0.003 inches or
0.010 inches or 0.030 inches and an upper limit of 0.120 inches or
0.190 inches or 0.225 inches.
[0012] The chord depth, C.sub.d, of dimples of the present
invention is typically within a range having a lower limit of 0.001
inches or 0.005 inches or 0.007 inches and an upper limit of 0.010
inches or 0.015 inches or 0.030 inches.
[0013] The second derivative of the defining function of Gabriel's
Horn is negative, thus indicating that the dimple profile is
defined by a concave down curve:
d d 2 C d ( 2 d d - 1 x ) ( d d 2 ) ( H F - 1 ) d d x 2 = - C d d d
x 3 ( H F - 1 ) ##EQU00006##
where C.sub.d is the chord depth, d.sub.d is the dimple diameter,
and HF is the horn factor.
[0014] The dimple volume of dimples of the present invention is
typically within a range having a lower limit of 2.673*10.sup.-7 or
3.184*10.sup.-6 or 2.303*10.sup.-5 and an upper limit of
1.676*10.sup.-4 or 3.581*10.sup.-4 or 1.166* 10.sup.-3.
[0015] The volume ratio of the dimple, V.sub.0 is the fractional
ratio of the dimple volume divided by the volume of a cylinder
defined by a diameter and chord depth similar to that of the
dimple, and is defined by:
V 0 = V .pi. ( d d 2 ) 2 C d ##EQU00007##
where V is dimple volume, C.sub.d is the chord depth, and d.sub.d
is the dimple diameter. The volume ratio of dimples of the present
invention is typically within a range having a lower limit of 0.03
or 0.07 or 0.25 and an upper limit of 0.70 or 0.80 or 1.00.
[0016] The dimple profile dimensions preferably adhere to the Bell
Ratio, BR, such that:
B R = d d d b * C d ##EQU00008## or ##EQU00008.2## B R = H F * C d
##EQU00008.3##
where C.sub.d is the chord depth, d.sub.d is the dimple diameter,
d.sub.b is the dimple base diameter, and HF is the horn factor. For
purposes of the present invention, the Bell Ratio is typically
within a range having a lower limit of 0.01 or 0.02 and an upper
limit of 0.03 or 0.07.
[0017] The tangential angle, .theta..sub.T, at any point on the
Gabriel's Horn portion of the profile is calculated as follows:
.theta. T = 180 .pi. tan - 1 ( C d * d d 2 ( H F - 1 ) x 2 )
##EQU00009##
where C.sub.d is the chord depth, d.sub.d is the dimple diameter,
and HF is the horn factor.
[0018] The chord angle, .theta..sub.CHORD, is the tangential angle
of the curve at the dimple perimeter, and is calculated as
follows:
.theta. CHORD = 180 .pi. tan - 1 ( C d * d d 2 ( H F - 1 ) ( d d 2
) 2 ) ##EQU00010##
where C.sub.d is the chord depth, d.sub.d is the dimple diameter,
and HF is the horn factor.
[0019] Dimples of the present invention typically have an edge
angle within a range having a lower limit of 3.degree. or 5.degree.
and an upper limit of 50.degree. or 80.degree.. Such edge angles
can produce a preferred equivalent edge angle for a spherical
dimple with like volume of from 12.degree. to 16.degree..
[0020] Dimples of the present invention typically have an angle
relative to the chord plane within a lower limit of 0.03.degree. or
0.30.degree. or 2.degree. and an upper limit of 15.degree. or
30.degree. or 90.degree..
[0021] 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.
[0022] 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.
[0023] 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.
[0024] Preferably, at least 30%, or at least 50%, or at least 60%,
or at least 80%, or at least 90%, or at least 95% of the total
number of dimples have a cross-sectional profile partially defined
by a Gabriel's Horn curve, with the remaining dimples, if any,
having a cross-sectional profile based on any known dimple profile
shape including, but not limited to, parabolic curves, ellipses,
spherical curves, saucer-shapes, sine curves, truncated cones,
flattened trapezoids, and catenary curves. Among the dimples having
a cross-sectional profile defined by the present invention, the
profile of one dimple may be the same as or different from the
profile of another dimple. Similarly, among the remaining dimples,
if any, having a known dimple profile shape, the profile of one
dimple may be the same as or different from the profile of another
dimple.
[0025] 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.
[0026] The present invention is not limited by any particular golf
ball construction or any particular composition for forming the
golf ball layers. For example, functionally weighted curves of the
present invention can be used to form dimple profiles on one-piece,
two-piece (i.e., a core and a cover), multi-layer (i.e., a core of
one or more layers and a cover of one or more layers), and wound
golf balls, having a variety of core structures, intermediate
layers, covers, and coatings.
[0027] When numerical lower limits and numerical upper limits are
set forth herein, it is contemplated that any combination of these
values may be used.
[0028] All patents, publications, test procedures, and other
references cited herein, including priority documents, are fully
incorporated by reference to the extent such disclosure is not
inconsistent with this invention and for all jurisdictions in which
such incorporation is permitted.
[0029] While the illustrative embodiments of the invention have
been described with particularity, it will be understood that
various other modifications will be apparent to and can be readily
made by those of ordinary skill in the art without departing from
the spirit and scope of the invention. Accordingly, it is not
intended that the scope of the claims appended hereto be limited to
the examples and descriptions set forth herein, but rather that the
claims be construed as encompassing all of the features of
patentable novelty which reside in the present invention, including
all features which would be treated as equivalents thereof by those
of ordinary skill in the art to which the invention pertains.
* * * * *