Golf ball

Description

TECHNICAL FIELD
The present invention relates to golf balls, and more particularly to a golf ball which is optimized in the shape, number and arrangement of dimples and which is thereby adapted to give an increased distance in the low-speed region of its trajectory, i.e. the descending portion thereof from the peak point to the ground.
BACKGROUND OF THE INVENTION
Golf balls having varying numbers of dimples in different arrangements are known. With many of golf balls, the arrangement dimples is determined in the following manner. On a spherical surface externally in contact with a reqular polyhedron, the ridge lines of the polyhedron are projected to obtain lines of projection as phantom lines 2 dividing the spherical surface as seen in FIG. 3. Dimples 1 are formed in an identical arrangement in each of the portions 3 of the spherical surface divided by the phantom dividing lines 2. The regular polyhedron may be a regular octahedron, regular dodecahedron or regular icosahedron, and the corresponding dimple arrangement will hereinafter be referred to as a "regular octahedral arrangement," "regular dodecahedral arrangement" or "regular icosahedral arrangement."
Golf balls heretofore proposed are divided generally into the following five types according to the arrangement pattern and total number of dimples.
A: Golf balls having about 336 dimples 1 in a regular octahedral arrangement as seen in FIG. 3 (showing only the dimples in substantially 1/8 part of the whole area of the spherical surface).
B: Those having about 332 dimples or about 392 dimples generally in an icosahedral arrangement symmetric with respect to the parting line.
C: Those having about 330 to 344 dimples as arranged on concentric circles or in a similar arrangement.
D: Those having 360 dimples in a regular dodecahedral arrangement.
E: Those having 252 dimples in a regular icosahedral arrangement.
Of these, the balls B and C are poor in symmetrical pattern of dimple arrangements because the plane of symmetry containing the center of the ball is limited only to the parting line and thus have some directionality.
The balls A, D and E, each having a regular polyhedral dimple arrangement, are symmetric with respect to planes containing the center of the sphere and the phantom dividing lines 2 and are therefore high in equivalency and superior to the balls B and C.
However, the balls D and E in which the planes of symmetry containing the center of the ball do not intersect one another at right angles are difficult to address, to tee up for making tee shots and to putt along the desired line and accordingly have not been widely accepted.
The ball A having a regular octahedral dimple arrangement is symmetric with respect to planes intersecting one another, is free of the above drawbacks, has been traditionally used and is primarily used at present.
Almost all the balls having this dimple arrangement are provided with 336 dimples although the number of dimples somewhat differs, for example, because the space for the print of brand name has varying sizes.
On the other hand, the golf ball flies at a high speed of 40 to 80 m/sec while rotating also at a high speed of 2000 to 10,000 r.p.m. For the golf ball to achieve an added distance during flying in a low-speed region of its trajectory, i.e. the descending portion thereof from the peak point to the ground, it is required that the change from turbulent air flow separation to laminar air flow separation should take place in a region of the lowest possible speed. The dimples formed in the surface of the ball must fulfill this requirement among other physical functions. In order to maintain the condition of such turbulent air separation as long as possible, it is proposed to lengthen the dimple edge to the greatest possible extent. This can be obtained by giving a larger diameter to the dimples and/or forming an increased number of dimples.
With the ball A having 336 dimples, the above effect can be achieved by increasing the diameter of the dimples. In the case of the dimple arrangement of this ball, the pitch of dimples differs from location to location and is only 3.9 mm when small. Accordingly with small-sized balls having a diameter of 41.15 mm, it is impossible to form too large dimples in view of the number of dimples.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a golf ball which is balanced in respect of the shape, total number and arrangement of dimples and which is thereby adapted to achieve an added distance while flying at a low speed from the highest point to the ground to give an increased flight distance.
Another object of the invention is to provide a golf ball having 400 to 550 dimples in a regular octahedral arrangement.
Another object of the invention is to provide the following experimental equation representing the relationship between the dimples and the increase of flight distance in the low-speed region. ##EQU2## wherein D: the diameter(mm) of dimples,
N: the total number of dimples,
R: the diameter(mm) of golf ball,
Ek: the diameter(mm) of dimple at a point k microns away from the dimple edge downward, i.e. in the direction of depth of dimple (apparent diameter of dimple when the dimpled land portion is cut in parallel with the plane containing the dimple edge at its opening), and
n: the depth of dimple (in microns).
Still another object of the present invention is to provide a golf ball ranging from 500 to 1000 in the above mentioned .alpha. value.

BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a view showing a golf ball embodying the invention showing an arrangement pattern having 416 dimples in a regular octahedral arrangement, the dimples only in substantially 1/8 part of the whole surface area of the ball being shown;
FIG. 2 is a view showing a golf ball embodying the invention showing an arrangement pattern having 504 dimples in a regular octahedral arrangement, the view showing the dimples only in substantially 1/8 part of the whole surface area of the ball;
FIG. 3 is a view showing a conventional golf ball having 336 dimples in a regular octahedral arrangement, the view showing the dimples only in substantial 1/8 part of the whole surface area of the ball;
FIG. 4 is an enlarged view in section showing a dimple;
FIG. 5 is a graph showing the relationship between the .alpha. value and the total distance of flight; and
FIG. 6 is a graph showing the relationship between the .alpha. value and the aerodynamic characteristic values as determined by a wind tunnel experiment.

DETAILED DESCRIPTION OF THE INVENTION
The increase of distance in a low-speed region of the trajectory of the golf ball, i.e. the descending portion thereof from the peak point to the ground is dependent largely on the size of the ball and the diameter and number of dimples. The present inventor has repeatedly conducted various experiments on the relationship between these factors and found that the greater the K value of the following experimental equation, i.e. the larger the length of the dimple edge per unit surface area of the golf ball, the greater is the increase of distance in the low-speed region to give a larger total flight distance.
K=D.times.N/R.sup.2 (i)
wherein
D: the diameter(mm) of dimples,
N: the total number of dimples, and
R: the diameter(mm) of golf ball.
The present inventor has further found that the .alpha. value of the following experimental equation is preferably in the range of 500 to 1000. ##EQU3## wherein Ek: the diameter(mm) of dimple at a point k microns away from the dimple edge downward, i.e. in the direction of depth of dimple (apparent diameter of dimple when the dimpled land portion is cut in parallel with the plane containing the dimple edge at its opening), and
n: the depth of dimple (in microns).
As used herein the term "the diameter of dimple", in the case of a circular shaped dimple, refers to a diameter of the circle provided on a phantom plane which comes into contact with the dimple, or to a diameter between both contact points passing both dimple edges when the dimple is cut in a plane including the center points of the dimple and the ball. In the case of a non-circular shaped dimple, "the diameter of dimple" refers to a diameter as the circular shaped dimple having a circumferential dimension equal to total length of the dimple edge sides.
As used herein the term "the depth of dimple" refers to a depth at the deepest point away from the horizontal plane including the dimple edge.
As used herein the term "the pitch of dimple" indicates the distance calculated in the following manner. On the spherical surface of the ball, the center-to-center distances between a specified dimple and other dimples adjacent to the specified dimple were measured to obtain only 4 values taken out in order of the shortest distance therebetween. The dimple pitch is defined by the average obtained by these 4 values. Hereupon, the center-to-center distance indicates the length of the larger circular arc connected with two points where each center point of the two dimples is projected on the spherical surface of the ball.
The .alpha. value serves as an index of the dimple size.
The volume of a dimple having the depth of n micron is approximately determined by the following formula: ##EQU4## With respect to the equation (ii) mentioned in the foregoing, the expression in the bracket is obtained by deleting a constant part of 0.001/12.pi. and indicates the relative volume per one dimple. A way to obtain the formula (iii) will be described below.
With reference to FIG. 4, a frustoconical portion with two surfaces having diameters of Ek-1 and Ek and parallel to the plane of the dimple opening has a volume .DELTA.V (mm.sup.3) which is represented by
.DELTA.V=0.001/12.pi.(Ek-1.sup.2 +Ek-1.multidot.Ek+Ek.sup.2)
The effective volume ##EQU5## with respect to a dimple having a depth of n microns is expressed as follows, when Eo.sup.2 is omitted and En-1.sup.2 is made approximate to En.sup.2 through calculating thereof: ##EQU6## When the constant portion (0.001/12.pi.) is omitted, the foregoing calculation equation is obtained.
So far as the circular shaped dimple is concerned, the .alpha. value provides following considerations;
If the diameter and depth of dimples are definite, the .alpha. value increases with an increase in the number of dimples and decreases with a decrease in the dimple number. When the diameter and number of dimples are definite, the .alpha. value increases with an increase in the depth of dimples and decreases with a decrease in the dimple depth. Further when depth and number of dimples are definite, the .alpha. value increases with an increase in the diameter of dimples and decreases with a decrease in the dimple diameter.
FIG. 3 shows a small-sized conventional ball having a diameter of 41.15 mm and 336 dimples in a regular octahedral arrangement. With this ball, the center-to-center distance 4 between adjacent dimples which are closest to each other is about 3.9 mm. When D, the diameter of the dimples is 3.9, the K value is 0.774.
When the dimple diameter is larger than 3.9, adjacent dimples will overlap. Thus, the K value may be as great as 0.774.
When the number of dimples is increased to 416 according to a regular octahedral arrangement pattern as shown in FIG. 1, D can be 3.5. In this case, the K value is 0.860 which is 11% higher than the corresponding value of the 336-dimple arrangement.
The K value increases with a further increase in the number of dimples in the octahedral arrangement pattern, giving a further increased distance in the descending portion of the trajectory of the ball. However, if the number of dimples is more than 550, the pitch of dimples becomes smaller than 2.87 mm, with the result that the dimples that can be arranged are as small as less than 2.8 mm in diameter.
Further to achieve the .alpha. value defined by the equation (ii), the depth of dimples must be as small as less than 0.15 mm in the above case, that is, as described in the immediately preceding sentence. This is not desirable since when the ball is repeatedly shot, the dimples will deform greatly to produce a difference between the initial performance thereof and the performance after repeated use. Optimally, the number of dimples is about 400 to about 550.
The number of dimples to be in the octahedral arrangement can be various multiples of 8. However, to obtain dimple pitches within the smallest range of variations, it is desirable that the total number of dimples be 416 or 504 as shown in FIG. 1 or 2.
A golf ball having 416 dimples with a diameter of 42.67 mm is also in the range of 3.7 to 4.2 mm in respect of the pitch of dimples.
A golf ball having 504 dimples with a diameter of 42.67 mm ranges from 3.3 to 3.7 mm in the dimple pitch.
Examples are given below to show that the golf balls of the invention achieve increased distances.
The golf ball was tested for distance by hitting the ball at a speed of 45 m/sec with a No. 1 wood club set on a hitting test machine. The results are given in Tables 1 to 3, in which each test value is the average obtained by shooting 8 samples twice.
The terms in Tables 1 to 3 mean the following.
Carrying distance: The distance of flight of the ball from the hitting point to the point where the ball hit the ground.
Rolling distance: The distance the ball ran from the landing point to the point where the ball came to rest.
Total distance: The carrying distance plus the rolling distance.
Shape of trajectory: "Good" means that the ball hit achieve an appreciable extra distance. "Hop" means that the ball hopped at peak point of the trajectory. "Weak ball" means that the ball hit failed to achieve any noticeable extra distance, describing a markedly descending trajectory.
EXAMPLE 1
Thread-wound balata-covered balls, 41.2 mm in diameter, were tested for distance. Table 1 shows the results. Sample Nos. 1 to 10 are golf balls according to the invention, while sample Nos. 101 to 114 are those prepared for comparison.
Sample Nos. 1 to 5, 111 and 112 are golf balls having 416 dimples. FIG. 5, curve AA shows the relationship between the total distance and the .alpha. value as determined with sample Nos. 1 to 5, 111 and 112. Sample Nos. 6 to 10, 113 and 114 are golf balls having 504 dimples. FIG. 5, curve BB shows the relationship between the total distance and the .alpha. value as achieved by sample Nos. 6 to 8, 113 and 114.
Table 1 reveals the following. Sample Nos. 1 to 4 (having 416 dimples with a diameter of about 3.45 mm) are at least 5 m longer in total distance than sample Nos. 101 to 110 having 336 dimples. The former balls exhibit a satisfactory trajectory with an extra distance without hopping in the vicinity of the peak point or without a rapid descent with reduced power.
Sample No. 5, which has a small K value, is slightly inferior to sample Nos. 1 to 4 but superior to sample Nos. 101 to 110 in total distance.
Sample Nos. 6 to 10 (having 504 dimples with a diameter of about 3.05 mm) are at least 7 m longer than sample Nos. 101 to 110 having 336 dimples in total distance and are superior thereto also in the form of trajectory.
Sample Nos. 111 to 114, although similar to sample Nos. 1 to 4 and 6 to 10 in K value, are outside the range of 500 to 1000 in .alpha. value and are inferior to the golf balls of the invention in total distance.
TABLE 1__________________________________________________________________________Dimples Carrying Rolling Total Flight Diameter Distance Distance Distance Height of Time Shape ofNo. Number (mm) K value .alpha. value (m) (m) (m) Trajectory (sec) Trajectory__________________________________________________________________________ 1 416 3.45 0.846 530 208 14 222 Slightly 5.99 Good high 2 416 3.44 0.843 965 199 24 223 Slightly 5.16 Good low 3 416 3.49 0.855 690 207 19 226 Usual -- Good 4 416 3.41 0.836 740 204 21 225 Usual 5.51 Good 5 416 3.22 0.789 697 204 16 220 Usual -- Good 6 504 3.06 0.909 515 208 16 224 Slightly 5.89 Good high 7 504 3.03 0.900 635 206 20 226 Usual 5.68 Good 8 504 3.05 0.906 790 201 23 224 Usual 5.36 Good 9 504 3.03 0.900 635 207 21 228 Usual -- Good 10 504 2.91 0.864 630 206 18 224 Usual -- Good101 336 3.55 0.703 400 181 14 195 Varying 6.15 Unstable102 336 3.45 0.683 534 197 8 205 High 6.35 Marked hop103 336 3.51 0.695 700 200 13 213 Usual 5.70 Slight hop104 336 3.52 0.697 960 197 16 213 Slightly 5.32 Slightly low weak ball105 336 3.53 0.699 1050 190 20 210 Low 5.14 Weak ball106 336 3.76 0.744 470 189 3 192 Very high 6.46 Unstable Hop107 336 3.77 0.746 576 201 6 207 High 6.18 Hop108 336 3.79 0.750 740 199 18 217 Usual 5.71 Slight hop109 336 3.78 0.748 855 197 20 217 Usual 5.55 Slightly weak ball110 336 3.78 0.748 1150 185 26 211 Low 4.95 Weak ball111 416 3.42 0.838 453 202 10 213 High 6.23 Slight hop112 416 3.45 0.846 1055 192 26 218 Low 4.90 Weak ball113 504 3.08 0.915 401 196 14 210 High 6.38 Slight hop114 504 3.04 0.903 1104 189 28 217 Low 4.55 Weak ball__________________________________________________________________________
EXAMPLE 2
Two-piece balls, 41.2 mm in diameter, were tested for distance. Table 2 shows the results. Sample Nos. 11 to 13 are golf balls according to the invention, while sample Nos. 115 to 121 are those prepared for comparison.
FIG. 5, curve CC represents the relationship between the total distance and the .alpha. value as determined by sample Nos. 11 to 13, 120 and 121.
Table 2 shows that sample Nos. 11 to 13 (having 416 dimples with a diameter of about 3.45 mm) are at least 6 m longer in total distance than sample Nos. 115 to 119 having 336 dimples and have a satisfactory trajectory.
Sample Nos. 120 and 121 have 416 dimples, are similar to sample Nos. 11 to 13 in K value, but are outside the range of 500 to 1000 in .alpha. value, and are therefore inferior to the golf balls of the invention in total distance.
TABLE 2__________________________________________________________________________Dimples Carrying Rolling Total Flight Diameter Distance Distance Distance Height of Time Shape ofNo. Number (mm) K value .alpha. value (m) (m) (m) Trajectory (sec) Trajectory__________________________________________________________________________ 11 416 3.47 0.850 521 208 21 229 Slightly -- Good high 12 416 3.44 0.843 629 204 29 233 Usual -- Good 13 416 3.46 0.848 780 201 31 232 Usual -- Good115 336 3.79 0.750 470 195 10 205 Varying -- Unstable116 336 3.81 0.754 550 201 14 215 High -- Slight hop117 336 3.77 0.746 618 202 21 223 Usual -- Slightly weak ball118 336 3.81 0.754 960 194 27 221 Low -- Weak ball119 336 3.80 0.752 1025 188 31 219 Very low -- Weak ball120 416 3.45 0.846 466 204 17 221 High -- Slight hop121 416 3.47 0.850 1080 190 33 223 Low -- Weak ball__________________________________________________________________________
EXAMPLE 3
Thread-wound balata-covered balls, 42.7 mm in diameter were tested for distance. Table 3 shows the results. Sample Nos. 14 to 16 are golf balls according to the invention, while sample Nos. 122 to 128 are those prepared for comparison.
FIG. 5, curve DD represents the relationship between the total distance and the .alpha. value as determined by sample Nos. 14 to 16, 127 and 128.
Table 3 shows that sample Nos. 14 to 16 (having 416 dimples with a diameter of about 3.55 mm) are at least 5 m longer in total distance than sample Nos. 122 to 126 having 336 dimples and have a satisfactory trajectory.
Samples Nos. 127 and 128, although having 416 dimples and similar to sample Nos. 14 to 16 in K value, are outside the range of 500 to 1000 in .alpha. value and are therefore inferior to the golf balls of the invention in total distance.
TABLE 3__________________________________________________________________________Dimples Carrying Rolling Total Flight Diameter Distance Distance Distance Height of Time Shape ofNo. Number (mm) K value .alpha. value (m) (m) (m) Trajectory (sec) Trajectory__________________________________________________________________________ 14 416 3.56 0.812 625 202 11 213 Slightly -- Good high 15 416 3.54 0.808 781 201 17 218 Usual -- Good 16 416 3.57 0.815 981 194 20 214 Slightly -- Good low122 336 3.89 0.717 465 179 2 181 Varying -- Unstable High123 336 3.88 0.715 585 197 7 204 Markedly -- Hop high124 336 3.89 0.717 755 198 10 208 High -- Hop125 336 3.86 0.711 933 194 12 206 Usual -- Slight hop126 336 3.86 0.711 1055 186 18 204 Low -- Weak ball127 416 3.57 0.815 487 197 7 204 High -- Hop128 416 3.57 0.815 1120 182 25 207 Low -- Weak ball__________________________________________________________________________
EXAMPLE 4
Two kinds of thread-wound balata-covered golf balls having 41.2 mm in diameter and 504 or 600 dimples were tested for the decrease in distance that would result from repeated shooting. The ball was checked before and after being hammered 20 times. Table 4 shows the specifications of the balls tested, and Table 5 the test results.
A grooved metal plate substantially equivalent to the club face was caused to strike the ball at a speed of 45 m/sec by an air gun for hammering to check the ball for durability. The procedure including hammering 20 times corresponds to about 1 to 2 usual golf rounds.
TABLE 4______________________________________ Ball of Ball for invention comparison______________________________________Diameter of ball (mm) 41.2 41.2Number of dimples 504 600Diameter of dimples (mm) 3.03 2.79K value 0.900 0.986.alpha. Value 635 601______________________________________
TABLE 5______________________________________ Ball of invention Ball for comparison Before After Before After hammering hammering hammering hammering______________________________________Carrying 206 208 208 204distance (m)Rolling 19 15 21 12distance (m)Total distance 225 223 229 216(m)Height of Usual Slightly Usual Hightrajectory highShape of Good Good Good Hoptrajectory______________________________________
Table 5 reveals that the hammering (20 times) produced a difference of only 2 m in total distance in the case of the balls of the invention but that the corresponding difference in the comparison balls was as large as 13 m, hence undesirable for playing golf.
The poor result achieved by the comparison balls (having 600 dimples) appears attributable to the following reason. In order to obtain an .alpha. value within the optimum range, the dimples must have a reduced depth, so that even if exhibiting high performance initially, the ball undergoes a marked change in performance as the number of shots increases due to the resulting wear of the dimple edge and reduction in the depth of the dimple.
Golf balls having such shallow dimples also encounter many problems in the manufacturing process because even slight variations in the thickness of the coating usually formed over the golf ball greatly influence the performance.
EXAMPLE 6
A wind tunnel experiment was conducted to substantiate the importance of limiting the .alpha. value to the range of 500 to 1000, with the results shown in FIG. 6.
The wind tunnel experiment was performed by known means (Proceedings of the 19th Japan National Congress for Applied Mechanics, 1969, pp. 167-170).
Four golf balls were tested three times under 24 conditions (6 conditions for Reynolds number and 4 spin conditions) to obtain 288 points, from which a curve was obtained statistically. Each point in FIG. 6 was determined by reading a value for a Reynolds number of 1.5.times.10.sup.5 and spin of 4000 r.p.m. from the curve.
The drag coefficient index and lift coefficient index are expressed in terms of lift coefficient ratio of a sample having an .alpha. value of 700.
While wind tunnel experiments afford the lift coefficient and the drag coefficient, it is generally thought that golf balls have better aerodynamic characteristics if the lift coefficient is greater and the drag coefficient is smaller. Since the characteristics are more dependent on the drag coefficient, .alpha. of about 600 to about 800 is most desirable at which the drag coefficient is lowest in FIG. 6. Furthermore .alpha. of 500 to 600 is also effective in that the lift-drag ratio is great. It is also generally known that even if the lift coefficient is somewhat lower, golf balls have a good trajectory provided that the drag coefficient is small. Accordingly, when considering the condition that the lift coefficient index should be at least 0.6 and the drag coefficient index should be up to 1.5, the .alpha. value is preferably in the range of 500 to 1000.
If the .alpha. value is below 500, the drag coefficient is great although the lift coefficient is high, so that a reduced distance and variations in the trajectory will result.
Although the optimum range of .alpha. values slightly differs according to the diameter and structure of golf ball, it is desirable that the .alpha. value be in the range of 500 to 1000.

Claims

1. A golf ball having a spherical surface containing therein eight triangular areas divided by phantom lines and extended over the spherical surface, each of the triangular areas comprising three sides of equal spherical length,
the golf ball being provided on the spherical surface to form 52 dimples in each of the triangular areas without adjacent dimples overlapping each other and to form totally 416 dimples,
said 52 dimples being so arranged that a first spherically shaped triangle formed inside and along the triangular area defined by the phantom lines comprises three sides of equal spherical length and includes 9 dimples formed on each of the side lines to provide totally 24 dimples, a second spherically shaped triangle formed inside and along the first triangle comprises three sides of equal spherical length and includes 7 dimples formed on each of the side lines to provide totally 18 dimples, and a third spherically shaped triangle formed inside and along the second triangle includes 4 dimples formed on each of the side lines to provide totally 9 dimples and further includes 1 dimple inside thereof,
said golf ball having a diameter of the dimples being 3.2 to 3.6 l mm and of a dimple depth such that the total volume of the dimples is in the range of 222 to 476 mm.sup.3.
2. The golf ball as defined in claim 1 wherein the ball having 41.2 mm diameter is in the range of 238 to 476 mm.sup.3 in the total volume of the dimples.
3. The golf ball as defined in claim 1 wherein the ball having 42.7 mm diameter is in the range of 238 to 476 mm.sup.3 in the total volume of the dimples.

Priority Claims (1)

Number	Date	Country	Kind
58-220277	Nov 1983	JPX

US Referenced Citations (3)

Number	Name	Date
878254	Taylor	Feb 1908
4090716	Martin et al.	May 1978
4141559	Melvin et al.	Feb 1979

Foreign Referenced Citations (3)

Number	Date	Country
967188	May 1975	CAX
377354	Jul 1932	GBX
2103939A	Mar 1983	GBX

Non-Patent Literature Citations (1)

Entry
"The Curious History of the Golf Ball" by John Stuart Martin, Horizon Press, New York--1968--pp. 126-131.

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