Abstract:
A golf ball having dimples on its spherical surface, the dimples close to each pole being smaller in volume than those close to the parting line while maintaining total effectiveness of dimple volume substantially equal in relation to a first axis passing through the center of the ball defining a pair of poles and to a second axis passing through the center of the ball perpendicular to the first axis, so as to minimize variations in the aerodynamic characteristics of the ball despite changes of the axis of rotation. The effectiveness of dimple volume means a product obtained by multiplying the volume of a dimple by the sine value of an angle made by a radius from the center of the ball to the center of that dimple and the first or second axis of the ball.

Description:
TECHNICAL FIELD 
     The present invention relates to improvements in golf balls. 
     PRIOR ART 
     Various proposals have heretofore been made as to the pattern and shape of dimples in golf balls. Golf balls are divided generally into the following six types according to the dimple pattern. 
     (1) Those having about 336 dimples in a regular octahedral arrangement. 
     (2) Those having 360 dimples in a regular dodecahedral arrangement (Examined Japanese Patent Publication No. SHO 57-22595). 
     (3) Those having 320 dimples equidistantly arranged at a constant center-to-center spacing (equal pitch arrangement) (Unexamined Japanese Patent Publication No. SHO 57-107170). 
     (4) Those having 252 or 492 dimples in a quasi-icosahedral arrangement (Unexamined Japanese Patent Publication No. SHO 49-52029). 
     (5) Those having 332 or 392 dimples in a quasi-icosahedral arrangement (Examined Japanese Patent Publication No. SHO 58-50744). 
     (6) Those having 280 to 350 dimples arranged on concentric circles centered about the opposite poles (concentric circular arrangement) (Unexamined Japanese Patent Publication No. SHO 53-115330). 
     In any of the arrangements of dimples mentioned above, the dimples on the spherical surface of the ball are all of the same dimension (volume), and none of the dimples have different dimension (volumes) at different portions of the spherical surface. 
     It is required that the golf ball exhibit the same flight characteristics from whatever direction it may be hit. That is, the ball must always behave with spherical symmetry when hit with different axes of rotation (as prescribed in Rules of Japan Golf Association, Supplementary Rule III, Ball (C) and also in like rules of U.S. Golf Association). In other words, it is required that the golf ball exhibit definite aerodynamic characteristics when hit with any optional axis of rotation. 
     Of the foregoing dimple patterns, (1), (2) and (3) are based on a polyhedral arrangement, have a plurality of planes of symmetry and are excellent in the uniformity of arrangement, number and dimension of dimples (that is, the ball surface is excellent in equivalency to a spherical surface), so that the variations in the aerodynamic characteristics due to changes of the axis of rotation of the ball are small. 
     However, the fabrication of golf balls involves the problem that since the golf ball is molded using a pair of upper and lower dies, dimples can not be arranged at the junction of the dies (i.e., on the parting line to be mentioned below). Accordingly, even if it is attempted to design a highly symmetric dimple arrangement, there are cases wherein the symmetry is sacrificed. 
     The arrangements (4), (5) and (6) are typical of such cases; each of these arrangement has only one plane of symmetry through the parting line and is therefore low in equivalency to a spherical surface (roundness). Consequently, if dimples of the same dimension are arranged over the entire ball surface, changes of the axis of rotation of the ball result in variations of aerodynamic characteristics. Thus, it is impossible to obtain the desired flight performance with stable directionality. It is therefore undesirable to arrange dimples of identical dimension (volume) in the case of dimple arrangements having a small number of planes of symmetry. 
     SUMMARY OF THE INVENTION 
     The main object of the present invention is to provide a golf ball which, even having a dimple arrangement of a small number of planes of symmetry, is adapted to exhibit definite aerodynamic characteristics despite changes of the axis of rotation of the ball, by ingeniously designing the dimension of individual dimples. 
     To fulfill the above object, not all dimples of the golf ball of the present invention are uniform in volume, and when dimples in optional positions are compared, the volume of the dimple closer to either pole is smaller than or equal to the volume of the dimple closer to the parting line. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a front view showing a first embodiment; 
     FIG. 2 is a plan view of the same; 
     FIG. 3 is a front view of a second embodiment; 
     FIG. 4 is a plan view of the same; 
     FIG. 5 is a front view of a third embodiment; 
     FIG. 6 is a plan view of the same; 
     FIG. 7 is a front view of a fourth embodiment; 
     FIG. 8 is a plan view of the same; 
     FIG. 9 is a front view of a first reference example; 
     FIG. 10 is a plan view of the same; 
     FIG. 11 is a front view of a second reference example; 
     FIG. 12 is a plan view of the same; 
     FIG. 13 is a diagram for illustrating &#34;POP&#34;; 
     FIG. 14 is a diagram for illustrating &#34;PH&#34;; 
     FIG. 15 is a diagram for illustrating a dimple portion; 
     FIG. 16 is a diagram for illustrating how to express the position of a dimple; 
     FIG. 17 is a front view of an embodiment having 392 dimples; 
     FIG. 18 is a plan view of an embodiment having 392 dimples; 
     FIG. 19 is a front view of an embodiment having 332 dimples; 
     FIG. 20 is a plan view of an embodiment having 332 dimples; 
     FIG. 21 is a front view of an embodiment having 492 dimples; 
     FIG. 22 is a plan view of an embodiment having 492 dimples; 
     FIG. 23 is a front view of an embodiment having 446 dimples; 
     FIG. 24 is a plan view of an embodiment having 446 dimples. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     As is known for a long time, the arrangement, dimension, etc. of dimples are important for the flight of the golf ball. These factors are used for controlling the lift characteristics, etc. We checked the flight characteristics of balls having dimples in an asymmetric arrangement (as shown in FIGS. 1 to 8, etc. to be described later) and found that a greater lift and higher trajectory can be obtained when the ball is hit with rotation about an axis L1 through the seam (parting line) S as shown in FIG. 13 (pole over pole or &#34;POP&#34; rotation) than when it is hit with rotation about an axis L2 through the poles P as shown in FIG. 14 (pole horizontal or &#34;PH&#34; rotation). (Comparative Examples 11, 12, 13 and 14 given later show that POP achieves a longer duration of flight than PH.) 
     Presumably, the reason is that with the above arrangement, the effect of the dimples is greater in POP direction than in PH direction. We assumed that elimination of the variations in the dimple effect will be directly effective for obviating the variations in the flight characteristics of the ball, and introduced the concept of total effectiveness of dimple volume in order to substantiate the assumption. 
     The total effectiveness of dimple volume means a volume obtained by multiplying the sine value of an angle made by a straight line through the center of the dimple in an optional position and the center of the ball with the axis of rotation, by the volume of the dimple in the optional position. Thus, the effect of dimples is analyzed based on the effect of the dimple on the axis of rotation of the ball which is taken as a minimum of zero and the effect of a dimple on the large circle of rotation which is taken as a maximum of 1. 
     When the total effectiveness of dimple volumes of balls having an asymmetric arrangement (FIGS. 1 to 8, etc.) of dimples of uniform dimension are calculated in POP and PH directions, the effective total volume of each ball is greater in POP direction as shown in Comparative Examples 11 to 14. To substantiate the above assumption, we conducted experiments using balls in which without changing the total volume of the dimples, dimples closer to the pole which are more effective in POP direction in respective of effective volume were made smaller in volume than those closer to the parting line, with dimples closer to the parting line made correspondingly larger in volume. Consequently, the assumption was verified. 
     The effect of the dimples will be clarified with reference to the following embodiments and the data thereof. 
     EMBODIMENTS 
     In the drawings of embodiments of golf balls, dimples are shown over a quarter area of the ball surface. 
     Table 1 below shows examples of the invention. Table 1 sets forth the dimple design and flight characteristics of the examples of applicants&#39; invention. Table 2 shows comparative examples. Table 2 sets forth the dimple design and flight characteristics of examples known in the prior art. In each comparative example, the dimples are all identical in dimension and are arranged in the same pattern as the corresponding example of the invention as will be mentioned later. Table 3 shows an arrangement of dimples 392 in total number, with the position of each dimple expressed in terms of angle θ (theta) and angle φ (phi) these angles being defined on page 9 herein. 
     The terms in the following tables and description have the following meanings. 
     DIMPLE VOLUME 
     The volume of the cavity portion (shown by hatching in FIG. 15) beneath a horizontal plane containing the dimple edge. When the dimple is defined by a portion of a perfect sphere, the volume, V, is expressed by: 
     
         V=πd1.sup.2 {R-d1/3} 
    
     wherein 
     d1=depth from the dimple edge 
     R=radius of the dimple sphere. 
     RATIO OF TOTAL EFFECTIVENESS OF DIMPLE VOLUME 
     The ratio of the total effectiveness of the dimple volume (A) in POP direction to the total effectiveness of dimple volume (B) in PH direction, expressed by: 
     
         |(A/B-1)×100|(%) 
    
     CONVERTED DIMPLE DEPTH 
     The depth of the dimple as measured from the top of a phantom extension of the spherical ball surface to the bottom of the dimple and indicated at d2 in FIG. 15. 
     FLIGHT DISTANCE TEST 
     The same hitting test machine as used by U.S. Golf Associattion (USGA) for flight distance tests was used with a No. 1 wood club set thereon for hitting the ball at 48.8 m/sec (160 ft/sec). For each kind of ball, 20 samples were hit twice in each of POP and PH directions. The test result is given in terms of the average of the distances measured. 
     CARRY 
     The distance of flight of the ball from the hitting point to the point where the ball hit the ground. 
     RUN 
     The distance the ball rolled along from the ground hitting point to the point where the ball stopped. 
     TOTAL 
     The total distance which is carry plus run. 
     ANGLES θ and φ 
     Suppose the ball has a three-dimensional coordinate system including Z-axis through the pole and the center of the ball, and X-axis and Y-axis on the plane containing the parting line. In this coordinate system, the position of a dimple D is indicated by (θ,φ). 
     The angles θ and φ are counterclockwise angles from Z-axis and X-axis, respectively. The pole has an angle θ of 0 deg, and a point on the parting line S has an angle θ of 90 deg. 
     
                                           TABLE 1__________________________________________________________________________             Examples of the Invention             Specimen Nos.             1       2       3       4             Back-spin Direction             POP PH  POP PH  POP PH  POP PH__________________________________________________________________________Total Number of Dimples             392     332     492     446Dimple Diameter (mm)             3.50    3.80    3.30    3.55Total Dimple Volume (mm.sup.3)             349     390     321     345Effective Total Volume (mm.sup.3)             277 277 309 309 252 252 272 272Effective Total Dimple Volume Ratio                  0%      0%      0%      0%Converted Dimple Depth0 ≦ 60°             0.247   0.279   0.211   0.2280 &gt; 60°    0.269   0.302   0.221   0.232Volume Ratio of Dimples Having                 1.13    1.12    1.07    1.020 &gt; 60° to Dimples Having 0 ≦ 60°Flight Distance TestCarrying Distance (m)             218.4                 218.8                     217.4                         217.8                             219.4                                 219.1                                     218.2                                         218.4RunningDistance (m)             18.0                 17.8                     16.1                         15.8                             18.1                                 18.0                                     18.7                                         18.4Total Distance (m)             236.4                 236.6                     233.5                         233.6                             237.5                                 237.1                                     236.9                                         236.8Flight Duration (sec.)             5.93                 5.90                     5.93                         5.91                             5.99                                 6.01                                     5.94                                         5.96__________________________________________________________________________ 
    
     
                                           TABLE 2__________________________________________________________________________             Comparative Examples             Specimen Nos.             11      12      13      14             Back-spin Direction             POP PH  POP PH  POP PH  POP PH__________________________________________________________________________Total Number of Dimples             392     332     492     446Dimple Diameter (mm)             3.50    3.80    3.30    3.55Total Dimple Volume (mm.sup.3)             350     390     320     345Effective Total Volume (mm.sup.3)             279 273 312 305 254 250 272 271Effective Total Dimple Volume Ratio                 2.2%    2.3%    1.6%    0.4%Converted Dimple Depth0 ≦ 60°             0.257   0.291   0.216   0.2300 &gt; 60°Volume Ratio of Dimples Having                 1       1       1       10 &gt; 60° to Dimples Having 0 ≦ 60°Flight Distance TestCarrying Distance (m)             215.3                 218.1                     214.6                         217.7                             216.4                                 218.2                                     216.7                                         217.9Running Distance (m)             15.3                 18.3                     13.4                         15.7                             12.1                                 15.0                                     14.8                                         16.1Total Distance (m)             230.6                 236.4                     228.0                         233.4                             228.5                                 233.2                                     231.5                                         234.0Flight Duration (sec.)             6.00                 5.77                     6.05                         5.80                             6.14                                 5.99                                     5.96                                         5.90__________________________________________________________________________ 
    
     
                       TABLE 3______________________________________Theta  Phi-1    Phi-2    Phi-3  Phi-4  Phi-5______________________________________84.900 6.000    18.000   30.000 42.000 54.00084.900 66.000   78.000   90.000 102.000                                  114.00084.900 126.000  138.000  150.000                           162.000                                  174.00084.000 186.000  198.000  210.000                           222.000                                  234.00084.900 246.000  258.000  270.000                           282.000                                  294.00084.900 306.000  318.000  330.000                           342.000                                  354.00076.840 0.000    72.000   144.000                           216.000                                  288.00076.600 12.000   59.600   84.000 131.600                                  156.00076.600 203.600  228.000  275.600                           300.000                                  347.60075.740 24.000   48.000   96.000 120.000                                  168.00075.740 192.000  240.000  264.000                           312.000                                  336.00074.870 36.000   108.000  180.000                           252.000                                  324.00068.200 6.510    65.490   78.510 137.490                                  150.51068.200 209.490  222.510  281.490                           294.510                                  353.49066.240 18.050   53.950   90.050 125.950                                  162.05066.240 197.950  234.050  269.950                           306.050                                  341.95065.160 29.730   42.270   101.730                           114.270                                  173.73065.160 186.270  245.730  258.270                           317.730                                  330.27059.970 0.000    72.000   144.000                           216.000                                  288.00057.330 11.550   60.450   83.550 132.450                                  155.55057.320 204.450  227.550  276.450                           299.550                                  348.45055.670 23.620   48.380   95.620 120.380                                  167.62055.670 192.380  239.620  264.380                           311.620                                  336.38055.100 36.000   108.000  180.000                           252.000                                  324.00049.980 0.000    72.000   144.000                           216.000                                  288.00046.950 13.660   58.330   85.660 130.330                                  157.66046.950 202.330  229.660  274.330                           301.660                                  346.33045.860 28.500   43.500   100.500                           115.500                                  172.50045.860 187.500  244.500  259.500                           316.500                                  331.50039.990 0.000    72.000   144.000                           216.000                                  288.00036.450 17.110   54.890   89.110 126.890                                  161.11036.450 198.890  233.110  270.890                           305.110                                  342.89035.340 36.000   108.000  180.000                           252.000                                  324.00029.990 0.000    72.000   144.000                           216.000                                  288.00026.435 23.050   48.950   95.050 120.950                                  167.05026.435 192.950  439.050  264.950                           311.050                                  336.95019.990 0.000    72.000   144.000                           216.000                                  288.00016.860 36.000   108.000  180.000                           252.000                                  324.0009.990  0.000    72.000   144.000                           216.000                                  288.0000.000  0.000______________________________________ 
    
     FIRST EMBODIMENT (FIGS. 1 AND 2) 
     This embodiment is a thread-wound balata-covered ball of 1.68 inch (42.67 mm) diameter having 392 dimples in the same arrangement as the conventional arrangement (5). 
     Without changing the total dimple volume, dimples D2 closer to the parting line S are made deeper and dimples D1 closer to each pole P are made shallower so that the effectiveness of total dimple volume in POP direction is equal to that in PH direction. 
     The dimple diameter is 3.50 mm, the converted dimple depth is 0.247 mm at positions with an angle θ of up to 60 deg or 0.269 mm at positions with θ of greater than 60 deg, the total dimple volume is 349 mm 3 , and the effectiveness of total volume is 277 mm 3  in both POP and PH. Between POP and PH, the difference in carry is 0.4 m, and the difference in duration of flight is 0.03 sec. 
     The ball of Comparative Example 11 is identical with the first embodiment in dimple arrangement, dimple diameter and total dimple volume, but all dimples have the same depth. Between POP and PH, the difference in carry is 2.8 m, and the difference in duration of flight is 0.23 sec. 
     Although the first embodiment is 0.13 sec longer than Comparative Example 11 in duration of flight in PH, there is no difference in total distance. This is considered to be one of the effects resulting from the approximately equal effectiveness of total dimple volumes for POP and PH. 
     SECOND EMBODIMENT (FIGS. 3 AND 4) 
     This embodiment is a thread-wound balata-covered ball of large size having 332 dimples in the same arrangement as the conventional arrangement (5). 
     The effective total volume is 309 mm 3  in both POP and PH. 
     The dimple diameter is 3.80 mm, the converted dimple depth is 0.279 mm at positions with an angle θ of up to 60 deg or 0.302 mm at positions with an angle θ of greater than 60 deg, and the total dimple volume is 390 mm 3 . Between POP and PH, the difference in carry is 0.4 m and the difference in duration of flight is 0.02 sec. 
     The ball of Comparative Example 12 is identical with the second embodiment in dimple arrangement, dimple diameter and total dimple volume, but all dimples have the same depth. Between POP and PH, the difference in carry is 3.1 m, and the difference in duration of flight is 0.25 sec, hence great differences. The equal total effectiveness of dimple volume according to the second embodiment achieve an apparent effect. 
     THIRD EMBODIMENT (FIGS. 5 AND 6) 
     This embodiment is a thread-wound balata-covered ball of large size having 492 dimples in the same arrangement as the conventional arrangement (4). 
     The total effectiveness of dimple volume is 252 mm 3  in both POP and PH. 
     The dimple diameter is 3.30 mm, the converted dimple depth is 0.211 mm at positions with an angle θ of up to 60 deg or 0.221 mm at positions with an angle θ of greater than 60 deg, and the total dimple volume is 321 mm 3 . Between POP and PH, the difference in carry is 0.3 m, and the difference in duration of flight is 0.02 sec. 
     The ball of Comparative Example 13 is identical with the third embodiment in dimple arrangement, dimple diameter and total dimple volume, but all the dimples are made to have the same depth. Between POP and PH, the difference in carry is 1.8 m, and the difference in duration of flight is 0.15 sec. 
     The equal total effectiveness of dimple according to the third embodiment achieve an apparent effect. 
     FOURTH EMBODIMENT (FIGS. 7 AND 8) 
     This embodiment is a thread-wound balata-covered golf ball having 446 dimples with a diameter of 3.55 mm and a total dimple volume of 345 mm 3 . 
     The effective total volume is 272 mm 3  in both POP and PH. 
     The converted dimple depth is 0.228 mm at positions with an angle θ of up to 60 deg or 0.232 at positions with an angle θ of greater than 60 deg. Between POP and PH, the difference in carry is 0.2 m, and the difference in duration of flight is 0.02 sec. 
     The ball of Comparative Example 14 is identical with the fourth embodiment in dimple arrangement, dimple diameter and total dimple volume, but all the dimples have the same depth. Between POP and PH, the difference in carry is 1.2 m, and the difference in duration of flight is 0.06 sec. 
     The equal total effectiveness of dimple volume according to the fourth embodiment achieve an apparent effect. 
     We carried out further experiments and found that the variations in the aerodynamic characteristics due to the change of the axis of rotation of the ball are small insofar as the effective total dimple volume ratio is within 0.3%. 
     Therefore, good results will be given to the balls also having dimple arrangements other than those of the first to fourth embodiments in the above, when any one of the following requirements is satisfied. 
     * The dimple volume at positions with an angle θ of up 60 deg is 2 to 20% smaller than the dimple volume at positions with an angle θ of greater than 60 deg. 
     * The dimple volume gradually decreases toward each pole, and the volume of the dimple most proximate to the pole differs from that of the dimple most proximate to the parting line by 5 to 30%.