This application claims priority on Patent Application No. 2011-228414 filed in JAPAN on Oct. 18, 2011. The entire contents of this Japanese Patent Application are hereby incorporated by reference.
1. Field of the Invention
The present invention relates to golf balls. Specifically, the present invention relates to processes for designing dimple patterns of golf balls.
2. Description of the Related Art
Golf balls have a large number of dimples on the surface thereof. The dimples disturb the air flow around the golf ball during flight to cause turbulent flow separation. By causing the turbulent flow separation, separation points of the air from the golf ball shift backwards leading to a reduction of drag. The turbulent flow separation promotes the displacement between the separation point on the upper side and the separation point on the lower side of the golf ball, which results from the backspin, thereby enhancing the lift force that acts upon the golf ball. The reduction of drag and the enhancement of lift force are referred to as a “dimple effect”.
The United States Golf Association (USGA) has established the rules about symmetry of golf balls. According to the rules, the trajectory during PH (pole horizontal) rotation and the trajectory during POP (pole over pole) rotation are compared with each other. A golf ball having a large difference between these two trajectories does not conform to the rules. In other words, a golf ball having inferior aerodynamic symmetry does not conform to the rules. A golf ball with inferior aerodynamic symmetry has a short flight distance because the aerodynamic characteristic of the golf ball for PH rotation or for POP rotation is inferior. The rotation axis for PH rotation extends through the poles of the golf ball, and the rotation axis for POP rotation is orthogonal to the rotation axis for PH rotation.
The dimples can be arranged by using a regular polyhedron that is inscribed in the phantom sphere of a golf ball. In this arrangement method, the surface of the phantom sphere is divided into a plurality of units by division lines obtained by projecting the sides of the polyhedron on the spherical surface. The dimple pattern of one unit is developed all over the phantom sphere. According to this dimple pattern, the aerodynamic characteristic in the case where a line passing through a vertex of the regular polyhedron is a rotation axis is different from that in the case where a line passing through the center of a surface of the regular polyhedron is a rotation axis. Such a golf ball has inferior aerodynamic symmetry.
JP50-8630 (U.S. Pat No. 4,729,861, U.S. Pat. No. 4,936,587, and U.S. Pat. No. 5,080,367) discloses a golf ball having an improved dimple pattern. The surface of the golf ball is divided by an icosahedron that is inscribed in the phantom sphere thereof. On the basis of this division, dimples are arranged on the surface of the golf ball. According to this dimple pattern, the number of great circles that do not intersect any dimples is 1. This great circle coincides with the equator of the golf ball. The region near the equator is a unique region.
Generally, a golf ball is formed by a mold including upper and lower mold halves. The mold has a parting line. A golf ball obtained by this mold has a seam at a position along the parting line. Through this forming, spew occurs along the seam. The spew is removed by means of cutting. By cutting the spew, the dimples near the seam are deformed. In addition, the dimples near the seam tend to be orderly arranged. The seam is located along the equator of the golf ball. The region near the equator is a unique region.
A mold having an uneven parting line has been used. A golf ball obtained by this mold has dimples on the equator thereof. The dimples on the equator contribute to eliminating the uniqueness of the region near the equator. However, the uniqueness is not sufficiently eliminated. This golf ball has insufficient aerodynamic symmetry.
JP61-284264 (U.S. Pat. No. 4,744,564) discloses a golf ball in which the dimples near the seam are greater in volume than the dimples near the poles. This volume difference contributes to eliminating the uniqueness of the region near the equator. This golf ball eliminates, by the volume difference of dimples, the disadvantage caused by the dimple pattern. The disadvantage caused by the dimple pattern is eliminated not by modification of the dimple pattern. In the golf ball, the potential of the dimple pattern is sacrificed. The flight distance of the golf ball is insufficient.
JP9-164223 (U.S. Pat. No. 5,688,194 and U.S. Pat. No. 5,772,532) discloses a golf ball in which a large number of dimples are randomly arranged. The random arrangement enhances aerodynamic symmetry. JP2000-189542 also discloses a golf ball in which a large number of dimples are randomly arranged.
JP2010-213741 (US2010/0234141) discloses a golf ball having a rugged pattern obtained by a Cellular Automaton method. In the rugged pattern, dimples are randomly arranged.
In a method disclosed in JP9-164223, a process of trial and error is conducted in order to obtain a desired dimple pattern. In a method disclosed in JP2000-189542 as well, a process of trial and error is conducted in order to obtain a desired dimple pattern.
In the golf ball disclosed in JP2010-213741, the dimples are non-circular. The dimple effect of the dimples is insufficient.
An object of the present invention is to provide a golf ball having circular dimples and excellent aerodynamic symmetry.
A process for designing a dimple pattern of a golf ball according to the present invention comprises the steps of:
(1) randomly arranging a large number of points on a surface of a phantom sphere;
(2) calculating a distance between a first point and a second point which is a point closest to the first point;
(3) deciding a radius on the basis of the distance;
(4) assuming a circle which has a center at the first point and has the radius; and
(5) assuming a dimple whose contour coincides with the circle.
Preferably, at the step (3), half of the distance is set as the radius.
Preferably, at the step (1), the large number of points are randomly arranged on the basis of a Cellular Automaton method. Preferably, at the step (1), the large number of points are randomly arranged on the basis of a reaction-diffusion model of the Cellular Automaton method.
Preferably, the step (1) comprises the steps of:
(1.1) assuming a plurality of states;
(1.2) assuming a large number of cells on the surface of the phantom sphere;
(1.3) assigning any one of the states to each cell;
(1.4) assigning, as an attribute of said each cell, any one of INSIDE, OUTSIDE, and BOUNDARY to said each cell on the basis of the state of said each cell and states of a plurality of cells located adjacent to said each cell;
(1.5) assuming a loop by connecting cells of BOUNDARY; and (1.6) deciding a point on the basis of the loop or another loop obtained on the basis of this loop.
A golf ball according to the present invention has a large number of dimples on a surface thereof. These dimples are randomly arranged. A pattern of these dimples is designed by the process described above.
Preferably, in the golf ball, a fluctuation range Rh and a fluctuation range Ro are equal to or less than 3.3 mm and are obtained by the steps of:
(1) assuming a line which connects both poles of the golf ball, as a first rotation axis;
(2) assuming a great circle which exists on a surface of a phantom sphere of the golf ball and is orthogonal to the first rotation axis;
(3) assuming two small circles which exist on the surface of the phantom sphere of the golf ball, which are orthogonal to the first rotation axis, and of which an absolute value of a central angle with the great circle is 30°;
(4) defining a region, of the surface of the golf ball, which is obtained by dividing the golf ball at the two small circles and which is sandwiched between the two small circles;
(5) determining 30240 points on the region at intervals of a central angle of 3° in a direction of the first rotation axis and at intervals of a central angle of 0.25° in a direction of rotation about the first rotation axis;
(6) calculating a length L1 of a perpendicular line which extends from each point to the first rotation axis;
(7) calculating a total length L2 by summing twenty-one lengths L1 calculated on the basis of twenty-one perpendicular lines arranged in the direction of the first rotation axis;
(8) determining a maximum value and a minimum value among 1440 total lengths L2 calculated along the direction of rotation about the first rotation axis, and calculating a fluctuation range Rh by subtracting the minimum value from the maximum value;
(9) assuming a second rotation axis orthogonal to the first rotation axis assumed at the step (1);
(10) assuming a great circle which exists on the surface of the phantom sphere of the golf ball and is orthogonal to the second rotation axis;
(11) assuming two small circles which exist on the surface of the phantom sphere of the golf ball, which are orthogonal to the second rotation axis, and of which an absolute value of a central angle with the great circle is 30°;
(12) defining a region, of the surface of the golf ball, which is obtained by dividing the golf ball at the two small circles and which is sandwiched between the two small circles;
(13) determining 30240 points on the region at intervals of a central angle of 3° in a direction of the second rotation axis and at intervals of a central angle of 0.25° in a direction of rotation about the second rotation axis;
(14) calculating a length L1 of a perpendicular line which extends from each point to the second rotation axis;
(15) calculating a total length L2 by summing twenty-one lengths L1 calculated on the basis of twenty-one perpendicular lines arranged in the direction of the second rotation axis; and (16) determining a maximum value and a minimum value among 1440 total lengths L2 calculated along the direction of rotation about the second rotation axis, and calculating a fluctuation range Ro by subtracting the minimum value from the maximum value.
Preferably, an absolute value of a difference dR between the fluctuation range Rh and the fluctuation range Ro is equal to or less than 1.0 mm.
The following will describe in detail the present invention on the basis of preferred embodiments with reference to the accompanying drawings.
A golf ball 2 shown in
The golf ball 2 preferably has a diameter of 40 mm or greater but 45 mm or less. From the standpoint of conformity to the rules established by the United States Golf Association (USGA), the diameter is particularly preferably equal to or greater than 42.67 mm. In light of suppression of air resistance, the diameter is more preferably equal to or less than 44 mm and particularly preferably equal to or less than 42.80 mm. The golf ball 2 preferably has a weight of 40 g or greater but 50 g or less. In light of attainment of great inertia, the weight is more preferably equal to or greater than 44 g and particularly preferably equal to or greater than 45.00 g. From the standpoint of conformity to the rules established by the USGA, the weight is particularly preferably equal to or less than 45.93 g.
The core 4 is formed by crosslinking a rubber composition. Examples of base rubbers for use in the rubber composition include polybutadienes, polyisoprenes, styrene-butadiene copolymers, ethylene-propylene-diene copolymers, and natural rubbers. Two or more rubbers may be used in combination. In light of resilience performance, polybutadienes are preferred, and, high-cis polybutadienes are particularly preferred.
In order to crosslink the core 4, a co-crosslinking agent can be used. Examples of preferable co-crosslinking agents in light of resilience performance include zinc acrylate, magnesium acrylate, zinc methacrylate, and magnesium methacrylate. Preferably, the rubber composition includes an organic peroxide together with a co-crosslinking agent. Examples of suitable organic peroxides include dicumyl peroxide, 1,1-bis(t-butylperoxy)-3,3,5-trimethylcyclohexane, 2,5-dimethyl-2,5-di(t-butylperoxy)hexane, and di-t-butyl peroxide.
According to need, various additives such as sulfur, a sulfur compound, a filler, an anti-aging agent, a coloring agent, a plasticizer, a dispersant, and the like are included in the rubber composition of the core 4 in an adequate amount. Crosslinked rubber powder or synthetic resin powder may also be included in the rubber composition.
The core 4 has a diameter of 30.0 mm or greater and particularly 38.0 mm or greater. The diameter of the core 4 is equal to or less than 42.0 mm and particularly equal to or less than 41.5 mm. The core 4 may be composed of two or more layers. The core 4 may have a rib on its surface.
A suitable polymer for the cover 6 is an ionomer resin. Examples of preferable ionomer resins include binary copolymers formed with an α-olefin and an α,β-unsaturated carboxylic acid having 3 to 8 carbon atoms. Examples of other preferable ionomer resins include ternary copolymers formed with: an α-olefin; an α,α-unsaturated carboxylic acid having 3 to 8 carbon atoms; and an α,β-unsaturated carboxylate ester having 2 to 22 carbon atoms.
For the binary copolymers and ternary copolymers, preferable α-olefins are ethylene and propylene, while preferable α,β-unsaturated carboxylic acids are acrylic acid and methacrylic acid. In the binary copolymers and ternary copolymers, some of the carboxyl groups are neutralized with metal ions. Examples of metal ions for use in neutralization include sodium ion, potassium ion, lithium ion, zinc ion, calcium ion, magnesium ion, aluminum ion, and neodymium ion.
Another polymer may be used instead of or together with an ionomer resin. Examples of the other polymer include thermoplastic polyurethane elastomers, thermoplastic styrene elastomers, thermoplastic polyamide elastomers, thermoplastic polyester elastomers, and thermoplastic polyolefin elastomers. In light of spin performance, thermoplastic polyurethane elastomers are preferred.
According to need, a coloring agent such as titanium dioxide, a filler such as barium sulfate, a dispersant, an antioxidant, an ultraviolet absorber, a light stabilizer, a fluorescent material, a fluorescent brightener, and the like are included in the cover 6 in an adequate amount. For the purpose of adjusting specific gravity, powder of a metal with a high specific gravity such as tungsten, molybdenum, and the like may be included in the cover 6.
The cover 6 has a thickness of 0.1 mm or greater and particularly 0.3 mm or greater. The thickness of the cover 6 is equal to or less than 2.5 mm and particularly equal to or less than 2.2 mm. The cover 6 has a specific gravity of 0.90 or greater and particularly. 0.95 or greater. The specific gravity of the cover 6 is equal to or less than 1.10 and particularly equal to or less than 1.05. The cover 6 may be composed of two or more layers.
In the dimple pattern, a large number of dimples are randomly arranged. In a process for designing the dimple pattern, a large number of points are randomly arranged on the surface of a phantom sphere 14 of the golf ball. Circles having centers at the points, respectively, are assumed. Dimples whose contours coincide with the circles, respectively, are assumed. Since the arrangement of the points is random, the arrangement of the dimples is also random. The designing process is preferably executed using a computer and software in light of efficiency. Of course, the present invention is practicable even by hand calculation. The essence of the present invention is not in a computer and software.
Preferably, a Cellular Automaton method is used for arranging the points. By the Cellular Automaton method, a pattern in which a large number of loops are randomly arranged on the surface of the phantom sphere 14 is obtained. The central points of these loops are obtained. Since the arrangement of the loops is random, the arrangement of the central points is also random.
The Cellular Automaton method is widely used in the fields of computability theory, mathematics, theoretical biology, and the like. A model of the Cellular Automaton method consists of a large number of cells and simple rules. By this model, natural phenomena such as life phenomena, crystal growth, turbulent flow, and the like can be simulated. In this model, each cell has a state. This state can change to another state as a stage proceeds. The state of a cell at stage (t+1) is decided by the state of this cell and the states of a plurality of cells adjacent to this cell at stage (t). This decision is performed according to a rule. This rule is equally applied to all the cells.
For designing the dimple pattern, a reaction-diffusion model of the Cellular Automaton method is suitable. This model is used for simulating patterns on body surfaces of beasts, birds, fish, insects, and the like. In this model, a plurality of states are assumed. The number of states is normally equal to or greater than 2 but equal to or less than 8. For each cell, an initial state is decided. As a stage proceeds, the state is updated according to a rule. There are cells whose states change by this update, while there are also cells whose states do not change by this update. The Cellular Automaton method is disclosed at Pages 25 to 28 of “Seru Otomaton Hou, Fukuzatsukei No Jikososhikika To Chouheiretsushori (Cellular Automaton method, Self-organization of Complex Systems and Massively Parallel Processing)” (written by Yasuyoshi Kato et al, published by Morikita Publishing Co., Ltd.).
A designing process according to the present invention is characterized in that the state of a cell is updated under the influence of other cells adjacent to this cell. By this update, a pattern in which a large number of loops are randomly arranged is obtained. As long as this characteristic is maintained, any model can be used. The following will describe in detail a designing process using a reaction-diffusion model of the Cellular Automaton method.
In the designing process, two states, a differentiated state and an undifferentiated state, are assumed. For each cell, either state (an initial state) is decided (STEP 3). The decision is preferably performed in a random manner. For the random decision, random numbers and a residue system are used. Because the number of states is 2, a residue system having a base of 2 is used. Specifically, a random number to 5 decimal places, which is equal to or greater than 0 and less than 1, is generated by a computer. The random number is multiplied by 100000, and the product is divided by 2. The remainder for the division is “1” or “0”. On the basis of the remainder, the state of the cell is decided. For example, when the remainder is “1”, the differentiated state is selected, and when the remainder is “0”, the undifferentiated state is selected. For all the cells, this decision is performed. The mesh 12 after the decision is at stage 1.
For each cell, whether or not to change the state is determined (STEP 4). This determination is performed according to a rule.
In the designing process, the number NR1 of cells 16 in a specific state which are included in the first circle 18 and not located at the center of the first circle 18, is counted. In a preferred embodiment, the number of cells 16 whose states are differentiated is counted to obtain the total number NR1. Furthermore, in the designing process, the number NR1-R2 of cells 16 in a specific state which are included in the second circle 20 and not included in the first circle 18, is counted. In a preferred embodiment, the number of cells 16 whose states are differentiated is counted to obtain the total number NR1-R2. The numbers NR1 and NR1-R2 are substituted into the following mathematical formula (1) to obtain a value E. On the basis of the value E, whether or not to change the state of the cell 16a is determined.
E=W
1
*N
R1
+W
2
*N
R1-R2 (1)
On the basis of the determination, the state of the cell 16a is updated (STEP 5). In the update, the state of the cell 16a may change or may not change. In a preferred embodiment, when the value E is positive, the state of the cell 16a is maintained if the state of the cell 16a is differentiated, and the state of the cell 16a is changed to be differentiated if the state of the cell 16a is undifferentiated. When the value E is zero, the state of the cell 16a is maintained. When the value E is negative, the state of the cell 16a is changed to be undifferentiated if the state of the cell 16a is differentiated, and the state of the cell 16a is maintained if the state of the cell 16a is undifferentiated. The mesh 12 in which the update for the first time is completed for all the cells 16 is at stage 2.
The following will describe a calculation example for the determination and the update.
First concentration W1: 1.00
Second concentration W2: −0.60
Number of cells which are included in the first circle and whose states are differentiated (except for the cell 16a): 8
Number of cells which are included in the second circle and not included in the first circle and whose states are differentiated: 13
In this case, because the value E is positive, the state of the cell 16a is maintained if the state of the cell 16a is differentiated, and the state of the cell 16a is changed to be differentiated if the state of the cell 16a is undifferentiated.
The following will describe another calculation example for the determination and the update.
First concentration W1: 1.00
Second concentration W2: −0.60
Number of cells which are included in the first circle and whose states are differentiated (except for the cell 16a): 5
Number of cells 16 which are included in the second circle and not included in the first circle and whose states are differentiated: 9
In this case, because the value E is negative, the state of the cell 16a is changed to be undifferentiated if the state of the cell 16a is differentiated, and the state of the cell 16a is maintained if the state of the cell 16a is undifferentiated.
The determination and the update are repeated. The number of times of the repetition is M in the flowchart in
The determination and the update are repeated M times to fix the state of each cell 16. This fixing is “to assign a state” to the cell 16.
iflag: 0 attribute: OUTSIDE
iflag: 1 attribute: INSIDE
iflag: 2 attribute: BOUNDARY
The mesh 12 in which the assignment of attribute is completed is at first phase. By connecting a plurality of cells 16 whose attributes are BOUNDARY, a first loop 21 is completed. In
A pattern having a large number of first loops 21 is shown in
W1: 1.0
W2: −0.6
R1: 4.5
R2: 8.0
An occupation ratio of the pattern is calculated (STEP 7). In this calculation, the area surrounded by each first loop 21 is calculated. The areas of all the first loops 21 are summed. The ratio of the sum to the surface area of the phantom sphere 14 is the occupation ratio. The occupation ratio may be approximately calculated by using a large number of triangles shown in
On the basis of the obtained occupation ratio, a determination is performed (STEP 8). At this STEP, it is determined whether or not the occupation ratio is equal to or greater than a predetermined value. In the embodiment shown in
When the occupation ratio Y is less than 65%, update of attribute is performed (STEP 9). The following will describe a method of this update in detail.
iflag: 0 attribute: OUTSIDE
iflag: 1-2 attribute: INSIDE
iflag: 3 attribute: BOUNDARY
The mesh 12 in which the update of attribute has been performed once is at second phase.
By connecting a plurality of cells 16 whose attributes are BOUNDARY, a second loop 28 is obtained. The second loop 28 has an area larger than the area of the first loop 21. In other words, the occupation ratio becomes great due to the update of attribute (STEP 9).
A pattern having a large number of second loops 28 is shown in
iflag: 0 attribute: OUTSIDE
iflag: 1 to N+1 attribute: INSIDE
iflag: N+2 attribute: BOUNDARY
The mesh 12 in which the update of attribute has been performed N times is at (N+1)th phase.
A pattern obtained by performing the update of attribute twice is shown in
In
Preferably, smoothing is performed on coordinates of the cells 16 on the loop, to obtain reference points corresponding to the cells 16 (STEP 10). By connecting a large number of the reference points by a spline curve, a new loop is assumed (STEP 11).
Typical smoothing is moving averaging.
In the three-point moving averaging, coordinates of the following three cells 16 are averaged:
(1) a cell 16;
(2) a cell 16 that is closest to the cell 16 in the clockwise direction of the loop; and
(3) a cell 16 that is closest to the cell 16 in the counterclockwise direction of the loop.
In the five-point moving averaging, coordinates of the following five cells 16 are averaged:
(1) a cell 16;
(2) a cell 16 that is closest to the cell 16 in the clockwise direction of the loop;
(3) a cell 16 that is closest to the cell 16 in the counterclockwise direction of the loop;
(4) a cell 16 that is second closest to the cell 16 in the clockwise direction of the loop; and
(5) a cell 16 that is second closest to the cell 16 in the counterclockwise direction of the loop.
In the seven-point moving averaging, coordinates of the following seven cells 16 are averaged:
(1) a cell 16;
(2) a cell 16 that is closest to the cell 16 in the clockwise direction of the loop;
(3) a cell 16 that is closest to the cell 16 in the counterclockwise direction of the loop;
(4) a cell 16 that is second closest to the cell 16 in the clockwise direction of the loop;
(5) a cell 16 that is second closest to the cell 16 in the counterclockwise direction of the loop;
(6) a cell 16 that is third closest to the cell 16 in the clockwise direction of the loop;
(7) a cell 16 that is third closest to the cell 16 in the counterclockwise direction of the loop.
When forming a loop, a part of the reference points may be removed, and a spline curve may be drawn.
The central point of each loop 30 is obtained. A coordinate of the central point is obtained by calculating the average of coordinates of: cells on the contour of the loop 30; and cells present inside the contour. The coordinate of the central point may be obtained by calculating the average of the coordinates of only the cells present inside the contour of the loop 30. The coordinate of the central point may be obtained by calculating the average of the coordinates of only the cells present on the contour of the loop 30.
On the basis of the first loops 21 shown in
In
For each point 32, a circle 36 obtained when this point 32 is set as the first point 32a is assumed. Furthermore, for each circle 36, a dimple 8 whose contour coincides with this circle 36 is assumed. In this manner, the dimple pattern shown in
Since the radius R is half of the distance L as described above, the adjacent dimples 8 do not overlap each other. The adjacent dimples 8 are in contact with or spaced apart from each other.
For the purpose of causing the adjacent dimples 8 to overlap each other, the radius R may be larger than half of the distance L. For the purpose of increasing the area of the land 10, the radius R may be smaller than half of the distance L.
In light of suppression of rising of the golf ball 2 during flight, each dimple 8 has a depth of preferably 0.05 mm or greater, more preferably 0.08 mm or greater, and particularly preferably 0.10 mm or greater. In light of suppression of dropping of the golf ball 2 during flight, the depth is preferably equal to or less than 0.60 mm, more preferably equal to or less than 0.45 mm, and particularly preferably equal to or less than 0.40 mm. The depth is the distance between the deepest point of the dimple 8 and the surface of the phantom sphere 14.
In the present invention, the term “volume of dimple” means the volume of the portion surrounded by the surface of the dimple 8 and the plane including the contour of the dimple 8. In light of suppression of rising of the golf ball 2 during flight, the sum of the volumes (total volume) of all the dimples 8 is preferably equal to or greater than 260 mm3 and particularly preferably equal to or greater than 280 mm3. In light of suppression of dropping of the golf ball 2 during flight, the sum is preferably equal to or less than 380 mm3, more preferably equal to or less than 350 mm3, and particularly preferably equal to or less than 320 mm3.
In light of flight performance, the ratio (occupation ratio) of the sum of the areas of the dimples 8 to the surface area of the phantom sphere 14 is preferably equal to or greater than 55% and particularly preferably equal to or greater than 60%.
From the standpoint that a fundamental feature of the golf ball 2 being substantially a sphere is not impaired, the total number of the dimples 8 is preferably equal to or greater than 250 and particularly preferably equal to or greater than 300. From the standpoint that each dimple 8 exerts a sufficient dimple effect, the total number is preferably equal to or less than 450 and particularly preferably equal to or less than 400.
Preferably, the golf ball 2 has a difference dR whose absolute value is equal to or less than 1.0 mm. The absolute value is a parameter that correlates with the aerodynamic symmetry of the golf ball 2. The smaller the absolute value is, the smaller the difference between the trajectory during PH rotation and the trajectory during POP rotation is. The following will describe an evaluation method based on the difference dR.
There is assumed a great circle GC that exists on the surface of the phantom sphere 14 of the golf ball 2 and is orthogonal to the first rotation axis Ax1. The circumferential speed of the great circle GC is faster than any other part of the golf ball 2 during rotation of the golf ball 2. In addition, there are assumed two small circles C1 and C2 that exist on the surface of the phantom sphere 14 of the golf ball 2 and are orthogonal to the first rotation axis Ax1.
In
Furthermore, a second rotation axis Ax2 orthogonal to the first rotation axis Ax1 is decided. Rotation of the golf ball 2 about the second rotation axis Ax2 is referred to as POP rotation. Similarly as for PH rotation, for POP rotation, a great circle GC and two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the great circle GC is 30°. The absolute value of the central angle between the small circle C2 and the great circle GC is also 30°. For a region, sandwiched between the small circles C1 and C2, of the surface of the golf ball 2, 1440 total lengths L2 are calculated. In other words, a data constellation regarding a parameter dependent on a surface shape appearing at a predetermined point moment by moment during one rotation of the golf ball 2, is calculated.
There are numerous straight lines orthogonal to the first rotation axis Ax1. Thus, there are also numerous great circles GC. A great circle GC, whose part included in the dimples 8 is the longest, is selected, and a fluctuation range Ro and a difference dR are calculated. Instead of this, twenty great circles GC may be extracted in a random manner, and twenty fluctuation ranges may be calculated on the basis of the extracted twenty great circles GC. In this case, the maximum value among twenty pieces of data is set as Ro.
The smaller the fluctuation range Rh is, the larger the flight distance at PH rotation is. The reason is inferred to be that the smaller the fluctuation range Rh is, the more smoothly transition of a turbulent flow continues. In this respect, the fluctuation range Rh is preferably equal to or less than 3.3 mm. The smaller the fluctuation range Ro is, the larger the flight distance at POP rotation is. The reason is inferred to be that the smaller the fluctuation range Ro is, the more smoothly transition of a turbulent flow continues. In this respect, the fluctuation range Ro is preferably equal to or less than 3.3 mm. In light of attainment of a large flight distance at any of PH rotation and POP rotation, both the fluctuation range Rh and the fluctuation range Ro are preferably equal to or less than 3.3 mm.
The fluctuation range Ro is subtracted from the fluctuation range Rh to calculate the difference dR. The difference dR is a parameter indicating the aerodynamic symmetry of the golf ball 2. According to the finding by the inventor of the present invention, the golf ball 2 in which the absolute value of the difference dR is small has excellent aerodynamic symmetry. It is inferred that this is because the similarity between the surface shape during PH rotation and the surface shape during POP rotation is high.
Dimples may be randomly arranged by a method other than the Cellular Automaton method. For example, a person may randomly decide the positions of points on the surface of the phantom sphere, and circles having centers at these points, respectively, may be assumed.
A pattern of Example 1 shown in
Furthermore, a pattern of Comparative Example 1 shown in
By the aforementioned method, fluctuation ranges Ro and Rh of each pattern were calculated. The results are shown in Table 1 below.
As shown in Table 1, dR of the pattern of Example 1 is small. From the results of evaluation, advantages of the present invention are clear.
The dimple pattern described above is applicable to a one-piece golf ball, a multi-piece golf ball, and a thread-wound golf ball, in addition to a two-piece golf ball. The above descriptions are merely for illustrative examples, and various modifications can be made without departing from the principles of the present invention.
Number | Date | Country | Kind |
---|---|---|---|
2011-228414 | Oct 2011 | JP | national |