JP2013106937A - Method for designing dimple pattern of golf ball - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a golf ball 2 excellent in aerodynamic symmetry property.SOLUTION: The golf ball 2 has, on a surface thereof, a dimple pattern consisting of a land 10 and a large number of dimples 8. A method for designing the dimple pattern includes the steps of: (1) randomly arranging a large number of points on the surface of a virtual sphere; (2) calculating a distance between a first point and a second point which is the closest point 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. The dimples 8 are randomly arranged.

Description

  The present invention relates to a golf ball. Specifically, the present invention relates to a method for designing a dimple pattern of a golf ball.

  The golf ball has a large number of dimples on its surface. The dimples disturb the air flow around the golf ball during flight and cause turbulent separation. Turbulent separation shifts the separation point of air from the golf ball backwards, reducing drag. Turbulent separation promotes the deviation between the upper separation point and the lower separation point of the golf ball due to backspin, and increases the lift acting on the golf ball. The reduction of drag and the improvement of lift are referred to as “dimple effect”.

  The United States Golf Association (USGA) has established rules regarding the symmetry of golf balls. In this rule, the trajectory during PH rotation and the trajectory during POP rotation are compared. A golf ball having a large difference between the two does not conform to this rule. In other words, a golf ball with poor aerodynamic symmetry does not conform to this rule. A golf ball with poor aerodynamic symmetry is inferior in flight distance due to poor aerodynamic characteristics during PH rotation or aerodynamic characteristics during POP rotation. The rotation axis of PH rotation passes through both poles of the golf ball. The rotation axis of POP rotation is orthogonal to the rotation axis of PH rotation.

  A dimple may be arranged by using a regular polyhedron inscribed in a virtual sphere of a golf ball. In this arrangement method, the surface of the phantom sphere is partitioned into a plurality of units by partition lines obtained by projecting the sides of the polyhedron onto a spherical surface. A dimple pattern of one unit is developed on the entire virtual sphere. In this dimple pattern, the aerodynamic characteristic when the line passing through the apex of the regular polyhedron is the rotational axis is different from the aerodynamic characteristic when the line passing through the center of the regular polyhedron is the rotational axis. This golf ball is inferior in aerodynamic symmetry.

  JP-A-50-8630 discloses a golf ball having an improved dimple pattern. The surface of this golf ball is partitioned by an icosahedron inscribed in the phantom sphere. Based on this section, dimples are arranged on the surface of the golf ball. In this dimple pattern, the number of great circles that do not intersect with the dimples is one. This great circle coincides with the equator. The vicinity of the equator is a unique area.

  A golf ball is formed by a mold including an upper mold and a lower mold. This mold has a parting line. The golf ball obtained by this mold has a seam at a position corresponding to the parting line. Due to the molding, burrs are generated in the seam. The burrs are cut and removed. Due to the cutting of burrs, the dimples near the seam are deformed. Furthermore, dimples tend to be arranged in an orderly manner in the vicinity of the seam. The seam is located on the equator. The vicinity of the equator is a unique area.

  A mold having an uneven parting line is used. The golf ball obtained with this mold has dimples on the equator. The dimples on the equator contribute to the elimination of singularities near the equator. However, specificity is not fully resolved. The aerodynamic symmetry of this golf ball is not sufficient.

  Japanese Patent Application Laid-Open No. 61-284264 discloses a golf ball in which the dimple volume near the seam is larger than the dimple volume near the pole. The difference in volume contributes to the elimination of specificity near the equator. In this golf ball, the inconvenience due to the dimple pattern is eliminated by the difference in volume. The inconvenience caused by the dimple pattern is not solved by the idea of the dimple pattern itself. In this golf ball, the potential inherent in the dimple pattern is sacrificed. The flight distance of this golf ball is not sufficient.

  Japanese Patent Application Laid-Open No. 9-164223 discloses a golf ball in which a large number of dimples are randomly arranged. Random placement increases aerodynamic symmetry. Japanese Patent Application Laid-Open No. 2000-189542 also discloses a golf ball in which a large number of dimples are randomly arranged.

  JP 2010-213741 A discloses a golf ball having a concavo-convex pattern obtained by a cell automaton method. In this uneven pattern, dimples are randomly arranged.

Japanese Patent Laid-Open No. 50-8630 Japanese Patent Laid-Open No. 61-284264 JP-A-9-164223 JP 2000-189542 A JP 2010-213741 A

  In the method disclosed in JP-A-9-164223, trial and error are repeated to obtain a dimple pattern. In the method disclosed in Japanese Patent Laid-Open No. 2000-189542, trial and error are repeated to obtain a dimple pattern.

  In the golf ball disclosed in Japanese Patent Application Laid-Open No. 2010-213741, the dimples are non-circular. The dimple effect of this dimple is not sufficient.

  An object of the present invention is to provide a golf ball having a circular dimple and having excellent aerodynamic symmetry.

A golf ball dimple pattern design method according to the present invention includes:
(1) a step of randomly arranging a number of points on the surface of the phantom sphere;
(2) calculating a distance between the first point and a second point which is the closest point to the first point;
(3) determining a radius based on the distance;
(4) assuming a circle centered on the first point and having the radius;
And (5) including a step of assuming a dimple having the circle as an outline.

  Preferably, in step (3), a half value of the distance is set as the radius.

  Preferably, in step (1), a large number of points are randomly arranged based on the cell automaton method. Preferably, in step (1), a large number of points are randomly arranged based on the reaction / diffusion model of the cell automaton method.

Preferably, step (1) comprises
(1.1) a step in which a plurality of states are assumed;
(1.2) a step where a large number of cells are assumed on the surface of the phantom sphere;
(1.3) a step in which any state is given to each cell;
(1.4) Based on the state of the cell and the state of a plurality of cells located in the vicinity of the cell, any one of inside, outside, and boundary is given as an attribute of the cell,
(1.5) a step in which a loop is assumed by connecting cells at the boundary; and (1.6) a step in which a point is determined based on the loop or another loop obtained based on the loop. including.

Step (1)
(1.1) generating a random number;
(1.2) determining coordinates on the surface of the phantom sphere based on the random number;
(1.3) calculating a distance between a point having this coordinate and a point already existing on the surface of the virtual sphere;
And (1.4) If this distance is within a predetermined range, the method may include the step of identifying a point having this coordinate as a point existing on the surface of the phantom sphere. Preferably, step (1) comprises
(1.5) taking one point on the surface of the phantom sphere as a reference point;
(1.6) determining a plurality of adjacent points adjacent to the reference point;
(1.7) calculating an average of the coordinates of the plurality of adjacent points;
And (1.8) further comprising replacing the coordinates of the reference point with the average coordinates. Preferably, step (1.6) comprises
(1.6.1) a step where a number of triangles are assumed by Delaunay triangulation using all points on the surface of the phantom sphere;
And (1.6.2) the step of considering other vertices of the triangle having the reference point as a vertex as neighboring points.

  The golf ball according to the present invention has a large number of dimples on the surface thereof. These dimples are randomly arranged. These dimple patterns are designed by the method described above.

Preferably, in this golf ball, the fluctuation range Rh and the fluctuation range Ro obtained by the following steps (1) to (16) are 3.3 mm or less.
(1) Step where a line connecting both poles of the golf ball is assumed to be the first rotation axis (2) A great circle that exists on the surface of the phantom sphere of the golf ball and is orthogonal to the first rotation axis is assumed Step (3) A step in which two small circles that exist on the surface of the phantom sphere of the golf ball, are orthogonal to the first rotation axis, and have an absolute value of the central angle with the great circle of 30 ° are assumed ( 4) A step of defining a region between these small circles in which a golf ball is partitioned by these small circles and (5) a region sandwiched between these small circles in the surface of the golf ball. Step (6) where 30240 points are determined in steps of 0.25 ° in the central angle in the rotational direction (6) Step (7) where the length L1 of the perpendicular drawn from the respective points to the first rotation axis is calculated Based on 21 vertical lines in the axial direction Step 21 where the 21 lengths L1 calculated in this way are totaled and the total length L2 is calculated (8) From the 1440 total lengths L2 calculated along the rotation direction, the maximum value and the minimum value are determined. Step of calculating fluctuation range Rh which is a value obtained by subtracting minimum value from maximum value (9) Step of assuming second rotation axis orthogonal to first rotation axis assumed in step (1) above ( 10) A step in which a great circle that exists on the surface of the phantom sphere of the golf ball and is orthogonal to the second rotation axis is assumed (11) It exists on the surface of the phantom sphere of the golf ball and is orthogonal to the second rotation axis And a step (12) in which two small circles having an absolute value of the central angle with the great circle of 30 ° are assumed. (12) A golf ball is defined by these small circles. Steps to identify the area between (13) Step (14) in which 30240 points are determined in the above-mentioned region in units of 3 ° in the central direction in the axial direction and in units of 0.25 ° in the central direction in the rotational direction (14) The second rotation from each point Step (15) of calculating the length L1 of the vertical line drawn down on the axis Step of calculating the total length L2 by summing the 21 lengths L1 calculated based on the 21 vertical lines arranged in the axial direction ( 16) A step of determining a maximum value and a minimum value from 1440 total lengths L2 calculated along the rotation direction, and calculating a fluctuation range Ro that is a value obtained by subtracting the minimum value from the maximum value.

  Preferably, the absolute value of the difference dR between the fluctuation range Rh and the fluctuation range Ro is 1.0 mm or less.

  By the design method according to the present invention, a golf ball excellent in aerodynamic symmetry can be easily obtained.

FIG. 1 is a schematic cross-sectional view showing a golf ball according to an embodiment of the present invention. FIG. 2 is an enlarged front view showing the golf ball of FIG. FIG. 3 is a plan view showing the golf ball of FIG. FIG. 4 is a flowchart showing a loop pattern design method. FIG. 5 is a front view showing a mesh used in the design method of FIG. FIG. 6 is a graph for explaining the rules of the design method of FIG. FIG. 7 is an enlarged view showing a part of the mesh of FIG. FIG. 8 is an enlarged view showing a part of the mesh after the update is completed. FIG. 9 is a front view showing a pattern having a first loop. FIG. 10 is an enlarged view showing a part of the mesh after the attribute assignment is completed. FIG. 11 is a front view showing a pattern having a second loop. FIG. 12 is a front view showing a pattern having a third loop. FIG. 13 is a front view showing the third loop. FIG. 14 is a front view showing a loop obtained by connecting the cells of the third loop of FIG. 13 with a spline curve. FIG. 15 is a front view showing a loop obtained by connecting reference points obtained by a three-point moving average with a spline curve. FIG. 16 is a front view showing a loop obtained by connecting the reference points obtained by the five-point moving average with spline curves. FIG. 17 is a front view showing a loop obtained by connecting the reference points obtained by the seven-point moving average with spline curves. FIG. 18 is a front view showing a loop obtained by thinning the reference point obtained by the 5-point moving average by half. FIG. 19 is a front view showing a loop obtained by thinning the reference point obtained by the 5-point moving average to 1/3. 20 is a front view showing a pattern including the loop of FIG. FIG. 21 is a plan view showing the pattern of FIG. FIG. 22 is a front view showing many points. FIG. 23 is an enlarged view showing the points of FIG. FIG. 24 is a schematic diagram for explaining the golf ball evaluation method of FIG. FIG. 25 is a schematic diagram for explaining the golf ball evaluation method of FIG. FIG. 26 is a schematic diagram for explaining the golf ball evaluation method of FIG. FIG. 27 is a graph showing the evaluation results of the golf ball according to Example 1 of the present invention. FIG. 28 is a graph showing the evaluation results of the golf ball according to Example 1 of the present invention. FIG. 29 is a front view showing a golf ball according to another embodiment of the present invention. FIG. 30 is a plan view showing the golf ball of FIG. FIG. 31 is a front view showing a virtual sphere in which a large number of points are randomly arranged. FIG. 32 is a plan view showing the phantom sphere of FIG. FIG. 33 is a graph showing the evaluation results of the golf balls of FIGS. 29 and 30. FIG. 34 is a graph showing the evaluation results of the golf balls of FIGS. FIG. 35 is a front view showing a golf ball according to still another embodiment of the present invention. FIG. 36 is a plan view showing the golf ball of FIG. FIG. 37 is a front view showing a state where the phantom sphere shown in FIG. 31 is divided into Delaunay regions. FIG. 38 is an enlarged view showing a part of the phantom sphere of FIG. FIG. 39 is a front view showing a part of the phantom sphere after the reference point replacement. FIG. 40 is a front view showing a state in which the phantom sphere after the reference point replacement is divided into Delaunay regions. FIG. 41 is a front view showing the virtual sphere together with the reference point after replacement. FIG. 42 is a plan view showing the phantom sphere of FIG. FIG. 43 is a graph showing the evaluation results of the golf ball according to Example 3 of the present invention. FIG. 44 is a graph showing the evaluation results of the golf ball according to Example 3 of the present invention. 45 is a front view showing a golf ball according to Comparative Example 1. FIG. FIG. 46 is a plan view showing the golf ball of FIG. FIG. 47 is a graph showing the evaluation results of the golf ball according to Comparative Example 1. FIG. 48 is a graph showing the evaluation results of the golf ball according to Comparative Example 1.

  Hereinafter, the present invention will be described in detail based on preferred embodiments with appropriate reference to the drawings.

  A golf ball 2 shown in FIG. 1 includes a spherical core 4 and a cover 6. A large number of dimples 8 are formed on the surface of the cover 6. A portion of the surface of the golf ball 2 other than the dimples 8 is a land 10. The golf ball 2 includes a paint layer and a mark layer outside the cover 6, but these layers are not shown. An intermediate layer may be provided between the core 4 and the cover 6.

  The golf ball 2 preferably has a diameter of 40 mm or greater and 45 mm or less. The diameter is particularly preferably equal to or greater than 42.67 mm from the viewpoint that US Golf Association (USGA) standards are satisfied. 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 mass of 40 g or more and 50 g or less. In light of attainment of great inertia, the mass is more preferably equal to or greater than 44 g, and particularly preferably equal to or greater than 45.00 g. In light of satisfying the USGA standard, the mass is particularly preferably equal to or less than 45.93 g.

  The core 4 is formed by crosslinking a rubber composition. Examples of the base rubber of the rubber composition include polybutadiene, polyisoprene, styrene-butadiene copolymer, ethylene-propylene-diene copolymer, and natural rubber. Two or more kinds of rubbers may be used in combination. From the viewpoint of resilience performance, polybutadiene is preferred, and high cis polybutadiene is particularly preferred.

  A co-crosslinking agent may be used for crosslinking the core 4. From the viewpoint of resilience performance, preferred co-crosslinking agents are zinc acrylate, magnesium acrylate, zinc methacrylate and magnesium methacrylate. It is preferable that an organic peroxide is blended with the co-crosslinking agent in the rubber composition. Suitable organic peroxides include dicumyl peroxide, 1,1-bis (t-butylperoxy) -3,3,5-trimethylcyclohexane, 2,5-dimethyl-2,5-di (t- Butyl peroxy) hexane and di-t-butyl peroxide.

  Various additives such as sulfur, sulfur compounds, fillers, anti-aging agents, colorants, plasticizers, and dispersants are blended in the rubber composition of the core 4 as necessary. Crosslinked rubber powder or synthetic resin powder may be blended with the rubber composition.

  The diameter of the core 4 is 30.0 mm or more, particularly 38.0 mm or more. The diameter of the core 4 is 42.0 mm or less, particularly 41.5 mm or less. The core 4 may be composed of two or more layers. The core 4 may be provided with ribs on the surface thereof.

  A suitable polymer for the cover 6 is an ionomer resin. A preferable ionomer resin includes a binary copolymer of an α-olefin and an α, β-unsaturated carboxylic acid having 3 to 8 carbon atoms. Other preferable ionomer resins include ternary α-olefin, α, β-unsaturated carboxylic acid having 3 to 8 carbon atoms and α, β-unsaturated carboxylic acid ester having 2 to 22 carbon atoms. A copolymer is mentioned. In the binary copolymer and ternary copolymer, preferred α-olefins are ethylene and propylene, and preferred α, β-unsaturated carboxylic acids are acrylic acid and methacrylic acid. In the binary copolymer and ternary copolymer, some of the carboxyl groups are neutralized with metal ions. Examples of the metal ions for neutralization include sodium ions, potassium ions, lithium ions, zinc ions, calcium ions, magnesium ions, aluminum ions, and neodymium ions.

  Other polymers may be used in place of or in conjunction with the ionomer resin. Examples of other polymers include thermoplastic polyurethane elastomers, thermoplastic styrene elastomers, thermoplastic polyamide elastomers, thermoplastic polyester elastomers, and thermoplastic polyolefin elastomers. From the viewpoint of spin performance, a thermoplastic polyurethane elastomer is preferred.

  If necessary, the cover 6 may contain an appropriate amount of a colorant such as titanium dioxide, a filler such as barium sulfate, a dispersant, an antioxidant, an ultraviolet absorber, a light stabilizer, a fluorescent agent, and a fluorescent brightening agent. Blended. For the purpose of adjusting the specific gravity, the cover 6 may be mixed with powder of a high specific gravity metal such as tungsten or molybdenum.

  The cover 6 has a thickness of 0.1 mm or more, particularly 0.3 mm or more. The cover 6 has a thickness of 2.5 mm or less, particularly 2.2 mm or less. The specific gravity of the cover 6 is 0.90 or more, particularly 0.95 or more. The specific gravity of the cover 6 is 1.10 or less, particularly 1.05 or less. The cover 6 may be composed of two or more layers.

  FIG. 2 is an enlarged front view showing the golf ball 2 of FIG. FIG. 3 is a plan view showing the golf ball 2 of FIG. As apparent from FIGS. 2 and 3, the golf ball 2 includes a large number of dimples 8. The outline of each dimple 8 is a circle. These dimples 8 and lands 10 form a dimple pattern on the surface of the golf ball 2.

  In this dimple pattern, a large number of dimples are randomly arranged. In this dimple pattern design, a large number of points are arranged on the surface of the phantom sphere 14 of the golf ball. A circle around each point is assumed. A dimple having an outline of this circle is assumed. Since the arrangement of points is random, the arrangement of dimples is also random. This design method is preferably implemented using a computer and software from the viewpoint of efficiency. Of course, the present invention can also be implemented by hand calculation. The essence of the present invention is not in computer software.

  Preferably, a cellular automaton method is used for the arrangement of the points. A pattern in which a large number of loops are randomly arranged on the surface of the phantom sphere 14 is obtained by the cell automaton method. The center point of these loops is determined. Since the loop arrangement is random, the arrangement of the center points is also random.

  The cell automaton method is widely used in the fields of computability theory, mathematics, theoretical biology and the like. The model of the cell automaton method consists of a large number of cells and simple rules. This model can simulate natural phenomena such as life phenomena, crystal growth, and turbulence. In this model, each cell has a state. This state can change to other states as the stage progresses. The state of a certain cell at stage (t + 1) is determined by the state of the cell at stage (t) and the states of a plurality of cells in the vicinity of this cell. Decisions are made according to certain rules. This rule applies equally to all cells.

  A cell-automaton reaction / diffusion model is suitable for designing the dimple pattern. This model is used for simulating patterns of body surfaces such as beasts, birds, fish and insects. In this model, multiple states are assumed. The number of states is usually 2 or more and 8 or less. In each cell, the initial state is determined. As the stage progresses, the state is updated based on the rules. There is a cell whose state changes due to the update. Some cells do not change state due to the update. The cell automaton method is disclosed on pages 25-28 of “Cell automaton method Self-organization and massively parallel processing of complex systems (written by Yasuyoshi Kato et al., Published by Morikita Publishing Co., Ltd.)”.

  The design method according to the present invention is characterized in that the state of a cell is updated under the influence of another cell located in the vicinity of the cell. By this update, a pattern in which a large number of loops are randomly arranged is obtained. Any model can be used as long as this feature is maintained. Hereinafter, a design method using a reaction diffusion model of the cell automaton method will be described in detail.

  FIG. 4 is a flowchart showing a loop pattern design method. FIG. 5 is a front view showing the mesh 12 used in the design method of FIG. The sphere 14 is hypothesized to form the mesh 12 (STEP 1). The diameter of the phantom sphere 14 is the same as the diameter of the golf ball 2. The surface of the phantom sphere 14 is divided into a large number of triangles (STEP 2). The division is based on an advancing front method. The advanced advanced method is disclosed on pages 195 to 197 of “Graduate School of Information Science and Technology 3 Computational Mechanics” (published by Junichi Ito, published by Kodansha). In this mesh 12, the number of triangles is 176528 and the number of vertices is 88266. Each vertex is defined as a cell (or cell center). In this mesh 12, the number of cells is 88266. The virtual sphere 14 may be divided by other methods.

  In this design method, two states are assumed, differentiated and undifferentiated. In each cell, any state (initial state) is determined (STEP 3). The decision is preferably made at random. For random decisions, random numbers and residue systems are used. Since the number of states is 2, a residue system with a radix of 2 is used. Specifically, a random number of the last 5 digits is generated by a computer, which is 0 or more and less than 1. This random number is multiplied by 100,000, and this product is further divided by two. The remainder of this quotient is “1” or “0”. Based on this remainder, the state of the cell is determined. For example, differentiation is selected when the remainder is “1”, and undifferentiation is selected when the remainder is “0”. Decisions are made for all cells. The mesh 12 after the determination is in stage 1.

In each cell, it is determined whether or not the state needs to be changed (STEP 4). The judgment is made according to the rules. FIG. 6 is a graph for explaining this rule. In this graph, the vertical axis represents the concentration, and the horizontal axis represents the index radius. The exponent radius is a value obtained by dividing the distance from the cell by the reference value. This reference value is the distance between the cell closest to the cell and the cell. Concentration _{W 1} is positive, the concentration _{W 2} is negative. The absolute value of the density W ₁ is greater than the absolute value of the density W _2. Index radius _{R 2} is greater than the index radius _{R 1.} The R ₁ following areas exponent radius greater than 0, the concentration is W _1. The _{R 2} below area index radius exceeds the _{R 1,} concentration is _{W 2.}

FIG. 7 is an enlarged view showing a part of the mesh 12 of FIG. For convenience, in FIG. 7, the mesh 12 is drawn in two dimensions. In the center of FIG. 7, a cell 16a that is a determination target is shown. FIG. 7 further shows a first circle 18 and a second circle 20. First circle 18, centered on the cell 16a, the index radius of the circle is R _1. The second circle 20, centered on the cell 16a, the index radius of the circle is R _2. What is indicated by a filled circle is a cell 16 included in the first circle 18 other than the cell 16a. What is indicated by a filled rectangle is a cell 16 included in the second circle 20 and not included in the first circle 18. The cells 16 not included in the second circle 20 are indicated by filled triangles.

In this design method, the number N _{R1 of} cells 16 in a specific state that are included in the first circle 18 and are not located at the center of the first circle 18 is counted. According to a preferred aspect, the number of cells 16 whose state is differentiated is counted and a total N _R1 is calculated. In this design method, the number N _{R1-R2 of} cells 16 in a specific state that are included in the second circle 20 and not included in the first circle 18 is counted. According to a preferred embodiment, the number of cells 16 whose state is differentiated is counted and a total N _R1-R2 is calculated. These numbers N _R1 and N _R1-R2 are substituted into the following mathematical formula (1) to calculate the value E. Based on this value E, whether or not the state of the cell 16a needs to be changed is determined.
_{E = W 1 * N R1 +} W 2 * N R1-R2 (1)

  Based on this determination, the state of the cell 16a is updated (STEP 5). In the update, the cell 16a state may or may not change. According to a preferred embodiment, when the value E is positive, this state is maintained if the state of the cell 16a is differentiated, and this state is changed to differentiation if the state of the cell 16a is undifferentiated. When this value E is zero, the state of the cell 16a is maintained. When the value E is negative, if the state of the cell 16a is differentiated, this state is changed to undifferentiated, and if the state of the cell 16a is undifferentiated, this state is maintained. The mesh 12 for which the first update for all the cells 16 has been completed is in the stage 2.

In the following, calculation examples of determination and update are shown.
Condition First concentration W ₁ : 1.00
Second concentration W ₂ : −0.60
Number of cells included in the first circle and whose state is differentiated (excluding the cell 16a): 8
Number of cells that are included in the second circle but not in the first circle and whose state is differentiation: 13
Calculation example E = 1.00 * 8−0.60 * 13
= 0.2
In this case, since the value E is positive, this state is maintained if the state of the cell 16a is differentiated, and this state is changed to differentiation if the state of the cell 16a is undifferentiated.

In the following, other calculation examples of determination and update will be shown.
Condition First concentration W ₁ : 1.00
Second concentration W ₂ : −0.60
Number of cells included in the first circle and whose state is differentiated (excluding the cell 16a): 5
Number of cells 16 included in the second circle and not included in the first circle and whose state is differentiation: 9
Calculation example E = 1.00 * 5-0.60 * 9
= -0.4
In this case, since the value E is negative, if the state of the cell 16a is differentiated, this state is changed to undifferentiated, and if the state of the cell 16a is undifferentiated, this state is maintained.

  This determination and update are repeated. In the flowchart of FIG. The mesh 12 after completing M times is in the stage (M + 1). As the stage progresses, the number of cells 16 whose state changes due to the update decreases. In the stage with a small number of repetitions, the pattern change due to the update is severe. The pattern converges by being updated many times. The number of repetitions is preferably 3 or more, and more preferably 5 or more. If the number of repetitions is excessive, the load on the computer is large. In this respect, the number of repetitions is preferably 30 or less, and more preferably 10 or less.

The state of each cell 16 is determined by repeating the determination and updating M times. This confirmation is “assignment of state” to the cell 16. FIG. 8 is an enlarged view showing a part of the mesh 12 after the completion of the state assignment. In FIG. 8, the differentiated cells 16 are indicated by circles, and the undifferentiated cells 16 are indicated by squares. Based on this state, iflag is given to the cell 16. First, provisionally, “0” is assigned to all the cells 16 as iflag. Next, iflag is changed for the cell 16 whose state is differentiation. The cell 16 indicated by reference numeral 16b in FIG. 8 is adjacent to the six cells 16c-16h. In the present invention, when the other cell 16 exists at the other vertex of the triangle having one cell 16 as a vertex, it is referred to as “one cell 16 is adjacent to the other cell 16”. The state of these cells 16c-16h is differentiation. When the state of all adjacent cells 16c-16h is differentiated, the iflag of the cell 16b is changed from “0” to “1”. A cell 16 indicated by a reference numeral 16n in FIG. 8 is adjacent to six cells 16h-16m. The states of the cells 16h, 16i, 16l, and 16m are differentiation. The states of the cells 16j and 16k are undifferentiated. When adjacent to one or more cells 16 whose state is undifferentiated, the flag of the cell 16n is changed from “0” to “2”. The ifflag is changed for all the cells 16 whose state is differentiation. The iflag of the cell 16 whose state is undifferentiated is not changed. Based on this iflag, attributes are assigned to all the cells 16 (STEP 6). The attribute is assigned based on the following rules.
iflag: 0 attribute: outside iflag: 1 attribute: inside iflag: 2 attribute: The mesh 12 that has been given the boundary attribute is in the first phase. The first loop 21 is completed by connecting a plurality of cells 16 whose attributes are boundaries. In FIG. 8, the first loop 21 is indicated by a bold line.

A pattern having multiple first loops 21 is shown in FIG. This pattern was obtained using the following parameters.
W1: 1.0
W2: -0.6
R1: 4.5
R2: 8.0

  The occupation ratio of this pattern is calculated (STEP 7). In this calculation, the area surrounded by the first loop 21 is calculated. The areas of all the first loops 21 are summed up. The ratio of the total to the surface area of the phantom sphere 14 is the occupation ratio. A large number of triangles shown in FIG. 5 may be used, and the occupation ratio may be calculated approximately. In the approximate calculation, the total area of the triangles included in the first loop 21 is divided by the total area of all the triangles.

  A determination is made based on the obtained occupancy (STEP 8). In 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 FIG. 4, it is determined whether or not the occupation ratio Y is 65% or more.

If the occupation ratio Y is less than 65%, the attribute is updated (STEP 9). Hereinafter, this update method will be described in detail. FIG. 10 is an enlarged view showing a part of the mesh 12 after the attribute assignment is completed. The cell 16 indicated by the reference numeral 16n exists on the first loop 21. Six cells 16h-16m are adjacent to the cell 16n. The iflag of the cell 16h is “1”, and its attribute is inside. In the cell 16 whose attribute is inside, the ifflag is not changed. The iflag of the cells 16i, 16l, and 16m is 2, and its attribute is a boundary. In the cell 16 adjacent to the other cell 16 whose attribute is the boundary and the attribute is the boundary, the ifflag is not changed. The iflag of the cells 16j and 16k is “0”, and the attribute is outside. In the cell 16 adjacent to the other cell 16 whose attribute is the outside and whose attribute is the boundary, the ifflag is changed from “0” to “3”. With respect to all the cells 16 existing on the first loop 21, the flag of the cell 16 adjacent to the cell 16 is determined. Based on this iflag, the attribute is updated (STEP 9). The attribute is updated based on the following rules.
iflag: 0 attribute: outside iflag: 1-2 attribute: inside iflag: 3 attribute: The mesh 12 after the boundary attribute is updated once is in the second phase.

  A second loop 28 is obtained by connecting a plurality of cells 16 whose attributes are boundaries. The second loop 28 has an area that is greater than or equal to the area of the first loop 21. In other words, the occupation rate is increased by the attribute update (STEP 9).

A pattern having multiple second loops 28 is shown in FIG. As is clear from the comparison between FIGS. 9 and 11, the occupation ratio of the pattern in FIG. 11 is larger than that in FIG. The occupation ratio of this pattern is calculated (STEP 7). A determination is made based on the obtained occupancy (STEP 8). In 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 FIG. 4, it is determined whether or not the occupation ratio Y is 65% or more. Similarly, the attribute update (STEP 9), the occupation rate calculation (STEP 7), and the determination (STEP 8) are repeated until the occupation rate Y reaches 65% or more. Prior to the Nth attribute update, iflag is changed from “0” to “N + 2” in a cell 16 adjacent to another cell 16 whose attribute is outside and whose attribute is a boundary. The Nth attribute update is performed based on the following rules.
iflag: 0 attribute: outside iflag: 1 to N + 1 attribute: inside iflag: N + 2 attribute: The mesh 12 after the boundary attribute has been updated N times is in the (N + 1) th phase.

  A pattern obtained by updating the attribute twice is shown in FIG. This pattern of mesh 12 is in the third phase. This pattern comprises a number of third loops 29. The third loop 29 has an area that is greater than or equal to the area of the second loop 28. As is clear from the comparison between FIGS. 9, 11 and 12, the occupation ratio of the pattern shown in FIG. 12 is large. The occupation ratio of this pattern is 79%.

  In FIG. 13, one third loop 29 is shown. The third loop 29 is obtained by connecting 25 cells 16 whose attributes are boundaries. The third loop 29 has a large number of vertices.

  In FIG. 14, 25 cells 16 are connected by a spline curve. A spline curve is a smooth curve that passes through a plurality of points. In the spline curve, a line between two adjacent cells 16 is defined by a polynomial. In general, a cubic polynomial is used. As is clear from the comparison between FIGS. 13 and 14, a smooth loop can be obtained by using a spline curve.

  Preferably, the coordinates of the cell 16 on the loop are smoothed to obtain a reference point corresponding to the cell 16 (STEP 10). By connecting a large number of reference points with spline curves, a new loop is assumed (STEP 11).

  A typical smoothing is a moving average. FIG. 15 shows a loop obtained by connecting the reference points obtained by the three-point moving average with a spline curve. FIG. 16 shows a loop obtained by connecting the reference points obtained by the five-point moving average with a spline curve. FIG. 17 shows a loop obtained by connecting the reference points obtained by the 7-point moving average with a spline curve. As is clear from the comparison of FIGS. 14 to 17, the smoothness of the contour can be achieved by the moving average.

In the three-point moving average, the coordinates of the following three cells 16 are averaged.
(1) The cell 16
(2) Cell 16 closest to the cell 16 in the clockwise direction of the loop
(3) Cell 16 closest to the cell 16 in the counterclockwise direction of the loop

In the 5-point moving average, the coordinates of the following five cells 16 are averaged.
(1) The cell 16
(2) Cell 16 closest to the cell 16 in the clockwise direction of the loop
(3) Cell 16 closest to the cell 16 in the counterclockwise direction of the loop
(4) Cell 16 that is second closest to the cell 16 in the clockwise direction of the loop
(5) Cell 16 that is second closest to the cell 16 in the counterclockwise direction of the loop

In the 7-point moving average, the coordinates of the following seven cells 16 are averaged.
(1) The cell 16
(2) Cell 16 closest to the cell 16 in the clockwise direction of the loop
(3) Cell 16 closest to the cell 16 in the counterclockwise direction of the loop
(4) Cell 16 that is second closest to the cell 16 in the clockwise direction of the loop
(5) Cell 16 that is second closest to the cell 16 in the counterclockwise direction of the loop
(6) Cell 16 closest to the cell 16 in the clockwise direction of the loop
(7) Cell 16 third closest to the cell 16 in the counterclockwise direction of the loop

  When the loop is formed, a part of the reference point may be thinned out to draw a spline curve. FIG. 18 shows a loop obtained by thinning out the reference point obtained by the five-point moving average to half (one skipped point). FIG. 19 shows a loop obtained by thinning the reference point obtained by the 5-point moving average to 1/3 (2 points skipped). A pattern with the loop of FIG. 19 is shown in FIGS. This pattern includes a number of loops 30. The loops 30 are randomly arranged on the surface of the phantom sphere 14.

  The center point of each loop 30 is determined. The coordinates of the center point are obtained by obtaining the average value of the coordinates of the cells on the contour of the loop 30 and the cells existing inside the contour. The coordinates of the center point may be obtained by obtaining the average value of the coordinates of only the cells existing inside the outline of the loop 30. The coordinates of the center point may be obtained by obtaining an average value of the coordinates of only the cells existing on the contour of the loop 30. In FIG. 22, the center point 32 is shown. Since the loops 30 are randomly arranged, the center points 32 are also randomly arranged on the surface of the phantom sphere 14.

  Based on the first loop 21 shown in FIG. 9, the point 32 may be determined. Also in this case, a large number of points 32 arranged at random are obtained. Based on the second loop 28 shown in FIG. 11, the point 32 may be determined. Also in this case, a large number of points 32 arranged at random are obtained. Based on the third loop 29 shown in FIG. 12, the point 32 may be determined. Also in this case, a large number of points 32 arranged at random are obtained. The point 32 may be determined based on a loop (see FIG. 14) obtained by connecting the cells 16 with a spline curve. Also in this case, a large number of points 32 arranged at random are obtained. The point 32 may be determined based on a loop obtained by smoothing (see FIGS. 15 to 17). Also in this case, a large number of points 32 arranged at random are obtained.

  FIG. 23 shows a first point 32a and five points (32b-32f) adjacent to the first point 32a. Of these points 32b-32f, the point closest to the first point 32a is the point 32b. Hereinafter, this point 32b is referred to as a second point. In FIG. 23, the reference numeral 34 indicates a virtual line connecting the first point 32 a and the second point 32 b, and the arrow L indicates the length of the virtual line 34. The length L is the distance between the first point 32a and the second point 32b. Since the first point 32a and the second point 32b are located on the spherical surface, the distance L can be calculated as an arc length. The distance L may be calculated as the chord length.

  In FIG. 23, what is indicated by reference numeral 36 is a circle centered on the first point 32a. This circle has a radius R. The radius R is determined based on the distance L. In this embodiment, radius R is half of distance L. A dimple 8 having this circle as an outline is assumed. In other words, the inside of the circle is recessed from the surface of the phantom sphere 14. The cross-sectional shape of the dimple 8 is arbitrary. A dimple 8 whose cross-sectional shape is a single radius may be assumed, and a dimple 8 whose cross-sectional shape is a double radius may be assumed. Dimples 8 having other cross-sectional shapes may be assumed.

  For each point 32, a circle 36 is assumed when the point 32 is the first point 32a. Further, for each circle 36, a dimple 8 having the circle 36 as an outline is assumed. In this way, the dimple pattern shown in FIGS. 2 and 3 is obtained. Since the points 32 are randomly arranged, the dimples 8 are also randomly arranged.

  As described above, since the radius R is half of the distance L, the adjacent dimples 8 do not overlap each other. Adjacent dimples 8 are in contact with each other or separated from each other.

  For the purpose of overlapping adjacent dimples 8, 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 a value smaller than half of the distance L.

  In light of suppression of hops of the golf ball 2, the depth of the dimple 8 is preferably 0.05 mm or more, more preferably 0.08 mm or more, and particularly preferably 0.10 mm or more. From the viewpoint of suppressing the drop of the golf ball 2, the depth is preferably 0.60 mm or less, more preferably 0.45 mm or less, and particularly preferably 0.40 mm or less. 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 “dimple volume” means a volume of a portion surrounded by a plane including the outline of the dimple 8 and the surface of the dimple 8. The total volume of all the dimples 8 (total volume) is, 260 mm ³ or more is preferred from the viewpoint of rising of the golf ball 2 is suppressed, 280 mm ³ or more is particularly preferable. In view of dropping of the golf ball 2 is suppressed, the sum is preferably 380 mm ³ or less, more preferably 350 mm ³ or less, 320 mm ³ or less is particularly preferred.

  From the viewpoint of flight performance, the ratio (occupancy) of the total area of the dimples 8 to the surface area of the phantom sphere 14 is preferably 55% or more, and particularly preferably 60% or more.

  From the viewpoint that the essence of the golf ball 2 that is substantially a sphere is not impaired, the total number of the dimples 8 is preferably 250 or more, and particularly preferably 300 or more. From the viewpoint that each dimple 8 exhibits a sufficient dimple effect, the total number is preferably 450 or less, and particularly preferably 400 or less.

  Preferably, the absolute value of the difference dR of the golf ball 2 is 1.0 mm or less. This absolute value is a parameter that correlates with the aerodynamic symmetry of the golf ball 2. The smaller the absolute value, the smaller the difference between the trajectory during PH rotation and the trajectory during POP rotation. Hereinafter, an evaluation method based on the difference dR will be described.

  FIG. 24 is a schematic diagram for explaining this evaluation method. In this evaluation method, the first rotation axis Ax1 is assumed. The first rotation axis Ax1 passes through the two pole points Po of the golf ball 2. Each pole Po is the deepest point of the mold used for molding the golf ball 2. One pole point Po is the deepest point of the upper mold, and the other pole Po is the deepest point of the lower mold. The golf ball 2 rotates about the first rotation axis Ax1. This rotation is a PH rotation.

  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 is assumed. When the golf ball 2 rotates, the circumferential speed of the great circle GC is the fastest. Furthermore, 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 are assumed. FIG. 25 schematically shows a partial cross section of the golf ball 2 of FIG. The left-right direction in FIG. 25 is the axial direction. As shown in FIG. 25, the absolute value of the central angle between the small circle C1 and the great circle GC is 30 °. Although not shown, the absolute value of the central angle between the small circle C2 and the great circle GC is also 30 °. The phantom sphere 14 is partitioned by these small circles C1 and C2, and a region between the small circles C1 and C2 on the surface of the golf ball 2 is specified.

  A point P (α) in FIG. 25 is a point that is located on the surface of the golf ball 2 and that the central angle with the great circle GC is α ° (degree). A point F (α) is a foot of a perpendicular line Pe (α) drawn from the point P (α) to the first rotation axis Ax1. What is indicated by the arrow L1 (α) is the length of the perpendicular line Pe (α). In other words, the length L1 (α) is the distance between the point P (α) and the first rotation axis Ax1. In one cross section, the length L1 (α) is calculated for 21 points P (α). Specifically, −30 °, −27 °, −24 °, −21 °, −18 °, −15 °, −12 °, −9 °, −6 °, −3 °, 0 °, and 3 °. , 6 °, 9 °, 12 °, 15 °, 18 °, 21 °, 24 °, 27 ° and 30 °, the length L1 (α) is calculated. The 21 lengths L1 (α) are summed to obtain a total length L2 (mm). The total length L2 is a parameter depending on the shape of the surface in the cross section shown in FIG.

  FIG. 26 shows a partial cross section of the golf ball 2. In FIG. 26, the direction perpendicular to the paper surface is the axial direction. In FIG. 26, what is indicated by a symbol β is the rotation angle of the golf ball 2. In the range from 0 ° to less than 360 °, the rotation angle β is set in increments of 0.25 °. The total length L2 is calculated for each rotation angle. As a result, a total length L2 of 1440 is obtained along the rotational direction. In other words, a data group relating to a parameter depending on the shape of the surface that appears every moment at a predetermined location by one rotation of the golf ball 2 is calculated. This data group is calculated based on 30240 lengths L1. A graph in which the data group of the golf ball 2 shown in FIGS. 2 and 3 is plotted is shown in FIG. In this graph, the horizontal axis is the rotation angle β, and the vertical axis is the total length L2. From this graph, the maximum value and the minimum value of the total length L2 are determined. The minimum value is subtracted from the maximum value, and the fluctuation range Rh is calculated. The fluctuation range Rh is a numerical value representing an aerodynamic characteristic in PH rotation.

  Furthermore, a second rotation axis Ax2 orthogonal to the first rotation axis Ax1 is determined. The rotation of the golf ball 2 around the second rotation axis Ax2 is POP rotation. As with the PH rotation, a great circle GC and two small circles C1 and C2 are assumed for the POP rotation. 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 °. A total length L2 of 1440 is calculated in a region sandwiched between these small circles on the surface of the golf ball 2. In other words, a data group relating to a parameter depending on the shape of the surface that appears every moment at a predetermined location by one rotation of the golf ball 2 is calculated. FIG. 27 shows a graph in which the data group of the golf ball 2 shown in FIGS. 2 and 3 is plotted. In this graph, the horizontal axis is the rotation angle β, and the vertical axis is the total length L2. From this graph, the maximum value and the minimum value of the total length L2 are determined. The minimum value is subtracted from the maximum value, and the fluctuation range Ro is calculated. The fluctuation range Ro is a numerical value representing an aerodynamic characteristic in POP rotation.

  There are an infinite number of straight lines orthogonal to the first rotation axis Ax1. Accordingly, there are an infinite number of great circles GC. The great circle GC having the longest portion included in the dimple 8 is selected, and the fluctuation range Ro and the difference dR are calculated. Instead of this, 20 fluctuation ranges may be calculated based on 20 great circles GC randomly extracted. In this case, the maximum value among the 20 pieces of data is Ro.

  As the fluctuation range Rh is smaller, a greater flight distance can be obtained during PH rotation. The reason is presumed that the smaller the fluctuation range Rh, the smoother the turbulent transition is continued. In this respect, the fluctuation range Rh is preferably 3.3 mm or less. The smaller the fluctuation range Ro, the larger the flight distance can be obtained during POP rotation. The reason is presumed that the smaller the fluctuation range Ro, the smoother the turbulent transition is continued. In this respect, the fluctuation range Ro is preferably 3.3 mm or less. It is preferable that both the fluctuation range Rh and the fluctuation range Ro are 3.3 mm or less from the viewpoint that a large flight distance can be obtained both during PH rotation and POP rotation.

. The fluctuation range Ro is subtracted from the fluctuation range Rh, and the difference dR is calculated. The difference dR is an index representing the aerodynamic symmetry of the golf ball 2. According to the knowledge obtained by the present inventor, the golf ball 2 having a small absolute value of the difference dR is excellent in aerodynamic symmetry. The reason is presumed that the similarity between the surface shape during PH rotation and the surface shape during POP rotation is high.

  The dimples may be randomly arranged by a method other than the cell automaton method. For example, a human may randomly determine the position of a point on the surface of the phantom sphere, and a circle centered on this point may be assumed.

  FIG. 29 is a front view showing a golf ball 102 according to another embodiment of the present invention. FIG. 30 is a plan view showing the golf ball 102 of FIG. As apparent from FIGS. 29 and 30, the golf ball 102 includes a large number of dimples 108. The outline of each dimple 108 is a circle. These dimples 108 and lands 110 form a dimple pattern on the surface of the golf ball 102.

  In this dimple pattern, a large number of dimples 108 are randomly arranged. In this dimple pattern design, a large number of points are arranged on the surface of the phantom sphere of the golf ball 102. A circle around each point is assumed. A dimple 108 having this circle as an outline is assumed. Since the arrangement of the points is random, the arrangement of the dimples 108 is also random. This design method is preferably implemented using a computer and software from the viewpoint of efficiency. Of course, the present invention can also be implemented by hand calculation. The essence of the present invention is not in computer software.

A random number is used for the arrangement of the points. A point on the surface of the phantom sphere is represented by spherical coordinates (θ, φ). Here, θ represents latitude and φ represents longitude. According to Robin Green's paper “Spherical Harmonic Lighting: The Gritty Details”, the spherical coordinates (θ, φ) can be calculated by the following equation.
(Θ, φ) = (2 cos ⁻¹ (1-ξ _x ) ^1/2 , 2πξ _y )
In the above formula, ξ _x and ξ _y are real random numbers of 0 or more and 1 or less, respectively.

Random numbers ξ _x and ξ _y are sequentially generated to calculate spherical coordinates (θ, φ), and a point having the spherical coordinates (θ, φ) is arranged on the surface of the virtual sphere. At this time, if the arrangement is performed indefinitely, a zone where points are concentrated may be generated. In other words, a zone where the dimples 108 are concentrated can occur. In order to avoid the occurrence of this zone, restrictions are placed on the arrangement of points. Specifically, the distance between a point having spherical coordinates (θ, φ) and a point closest to the point already existing on the surface of the phantom sphere and having spherical coordinates (θ, φ) Is calculated. When this distance is within a predetermined range, a point having spherical coordinates (θ, φ) is recognized as a point existing on the surface of the phantom sphere. If the distance between the point having the spherical coordinates (θ, φ) and the point already existing on the surface of the phantom sphere is outside the predetermined range, the point having the spherical coordinates (θ, φ) It is not recognized as a point on the surface of the virtual sphere. The distance may be the length of a straight line connecting the points, or the length of an arc connecting the points and existing on the surface of the phantom sphere.

  When the distance is a length of a straight line, the range of the distance that is recognized as a point where a point having spherical coordinates (θ, φ) exists on the surface of the phantom sphere is preferably 2.5 mm or more. 0 mm or more is particularly preferable. This range is preferably 6.0 mm or less, and particularly preferably 5.5 mm or less.

Until the number of points on the surface of the phantom sphere reaches a predetermined number,
(A) Generation of random numbers ξ _x and ξ _y (b) Calculation of distance (c) The determination of whether or not the distance is within a predetermined range is repeated.

  31 and 32 show a virtual sphere 114 in which a large number of points 112 are randomly arranged by the above-described method. In this embodiment, the number of points 112 is 324. In this embodiment, when the distance from the closest point 112 already existing on the surface of the phantom sphere 114 is not less than 3.7 mm and not more than 4.0 mm, the point having the spherical coordinate (θ, φ) 112 is identified as a point 112 present on the surface of the phantom sphere 114. Based on these points, the diameter of the dimple 108 is determined by the method shown in FIG. By this determination, the dimple pattern shown in FIGS. 29 and 30 is obtained.

  FIG. 35 is a front view showing a golf ball 122 according to still another embodiment of the present invention. FIG. 36 is a plan view showing the golf ball 122 of FIG. The golf ball 122 also has a large number of dimples 108 on the surface thereof. A dimple pattern is formed on the surface of the golf ball 122 by the dimple 108 and the land 110.

  Also in this dimple pattern design method, a large number of points 112 shown in FIGS. 31 and 32 are assumed on the surface of the phantom sphere 114. In this embodiment, the coordinates of these points 112 are corrected. The correction can be achieved by Delaunay triangulation. In this method, the surface of the phantom sphere 114 is divided into a large number of triangles (Droney regions). Hereinafter, this division method will be described.

  In this method, arbitrary three points 112 are selected from a large number of points 112. A triangle having these three points 112 as vertices is assumed. This triangular circumscribed circle is assumed. When a point 112 other than these three points 112 is not included in the circumscribed circle, this triangle is determined to be a Delaunay region. A determination is made for all combinations of three points 112. As a result, the entire surface of the phantom sphere 114 is divided into a number of Delaunay regions. FIG. 37 shows a state in which the phantom sphere 114 shown in FIG. 31 is divided into Delaunay regions 124.

  FIG. 38 shows a part of the phantom sphere 114 of FIG. In FIG. 38, seven points 112A-112G are shown. FIG. 38 further shows six Delaunay regions 124A-124F. Each Delaunay region 124 is used for determining whether or not the point 112 and another point 112 are adjacent to each other. One vertex 112 of the Delaunay region 124 and another vertex 112 of the Delaunay region 124 are considered to be adjacent.

  The point 112B is a vertex of the Delaunay region 124B, and the point 112A is also a vertex of the Delaunay region 124B. Therefore, the point 112B is adjacent to the point 112A. The point 112C is the apex of the Delaunay area 124C, and the point 112A is also the apex of the Delaunay area 124C. Therefore, the point 112C is adjacent to the point 112A. The point 112D is a vertex of the Delaunay region 124D, and the point 112A is also a vertex of the Delaunay region 124D. Therefore, the point 112D is adjacent to the point 112A. The point 112E is the apex of the Delaunay area 124E, and the point 112A is also the apex of the Delaunay area 124E. Therefore, the point 112E is adjacent to the point 112A. The point 112F is a vertex of the Delaunay region 124F, and the point 112A is also a vertex of the Delaunay region 124F. Therefore, the point 112F is adjacent to the point 112A. The point 112G is the apex of the Delaunay area 124A, and the point 112A is also the apex of the Delaunay area 124A. Therefore, the point 112G is adjacent to the point 112A. There is no point 112 adjacent to the point 112A other than the points 112B to 112G. Hereinafter, the point 112A is referred to as a reference point, and the points 112B-112G are referred to as adjacent points.

  The coordinates of these adjacent points 112B-112G are averaged. The coordinates of the reference point 112A are replaced with the obtained average value. The reference point 112A 'after replacement is shown in FIG. In FIG. 38, the distance from the point 112D to the point 112A is small. In FIG. 39, there is no point 112 having a small distance to the point 112A '.

  Such a replacement is made for all points 112 on the surface of the phantom sphere 114. The replaced phantom sphere 114 is shown in FIGS. 40-42. FIG. 40 shows a Delaunay region 124 ′ based on the replaced point 112 ′. 41 and 42 show the point 112 'after replacement. Based on these points 112 ', the diameter of the dimple 108 is determined by the method shown in FIG. By this determination, the dimple pattern shown in FIGS. 35 and 36 is obtained. As is clear from the comparison between FIG. 35 and FIG. 29, the occupation ratio can be increased by correcting the coordinates.

  Coordinate correction may be performed on the point 32 (see FIG. 22) obtained by the cell automaton method.

  The pattern of Example 1 shown in FIGS. 2 and 3 was designed. This pattern has 391 dimples. The pattern of Example 2 shown in FIGS. 29 and 30 was designed. This pattern has 324 dimples. The pattern of Example 3 shown in FIGS. 35 and 36 was designed. This pattern has 324 dimples.

Furthermore, the dimple pattern of Comparative Example 1 shown in FIGS. 45 and 46 was designed. This pattern includes a dimple A having a diameter of 4.00 mm, a dimple B having a diameter of 3.70 mm, a dimple C having a diameter of 3.40 mm, and a dimple D having a diameter of 3.20 mm. Yes. The cross-sectional shape of each dimple is an arc. The details of the dimple are as follows.
Type Number Diameter (mm) Depth (mm) Volume (mm ³ )
A 120 4.00 0.1532 0.964
B 152 3.70 0.1532 0.825
C 60 3.40 0.1532 0.697
D 60 3.20 0.1532 0.618

  The fluctuation ranges Ro and Rh of each pattern were calculated by the method described above. The results are shown in Table 1 below.

  As shown in Table 1, the dR of the pattern of Example 1-3 is small. From this evaluation result, the superiority of the present invention is clear.

  The dimple pattern described above can be applied not only to a two-piece golf ball but also to a one-piece golf ball, a multi-piece golf ball, and a thread wound golf ball.

2, 102, 122 ... Golf ball 8, 108 ... Dimple 10, 110 ... Land 12 ... Mesh 14, 114 ... Virtual sphere 16 ... Cell 21 ... First loop 28 ... Second loop 29 ... Third loop 30 ... Loop 32, 112 ... Point

Claims (11)

(1) a step of randomly arranging a number of points on the surface of the phantom sphere;
(2) calculating a distance between the first point and a second point which is the closest point to the first point;
(3) determining a radius based on the distance;
(4) assuming a circle centered on the first point and having the radius;
And (5) A method for designing a dimple pattern for a golf ball, including the step of assuming a dimple having an outline of the circle.   The design method according to claim 1, wherein, in the step (3), a half value of the distance is set as a radius.   The design method according to claim 1 or 2, wherein in the step (1), a large number of points are randomly arranged based on a cell automaton method.   4. The design method according to claim 3, wherein in the step (1), a large number of points are randomly arranged based on a reaction / diffusion model of a cell automaton method. Step (1) above is
(1.1) a step in which a plurality of states are assumed;
(1.2) a step where a large number of cells are assumed on the surface of the phantom sphere;
(1.3) a step in which any state is given to each cell;
(1.4) Based on the state of the cell and the state of a plurality of cells located in the vicinity of the cell, any one of inside, outside, and boundary is given as an attribute of the cell,
(1.5) a step in which a loop is assumed by connecting cells at the boundary; and (1.6) a step in which a point is determined based on the loop or another loop obtained based on the loop. The design method of Claim 4 containing these. Step (1) above is
(1.1) generating a random number;
(1.2) determining coordinates on the surface of the phantom sphere based on the random number;
(1.3) calculating a distance between a point having the coordinates and a point already existing on the surface of the virtual sphere;
And (1.4) when the distance is within a predetermined range, the step of identifying the point having the coordinates as a point existing on the surface of the phantom sphere, . Step (1) above is
(1.5) taking one point on the surface of the phantom sphere as a reference point;
(1.6) determining a plurality of adjacent points adjacent to the reference point;
(1.7) calculating an average of the coordinates of the plurality of adjacent points;
And (1.8) The design method according to claim 6, further comprising the step of replacing the coordinates of the reference point with the average coordinates. The above step (1.6)
(1.6.1) a step in which a large number of triangles are assumed by Delaunay triangulation using all points on the surface of the phantom sphere;
(1.6.2) The design method according to claim 7, further comprising the step of considering other vertices of the triangle having the reference point as a vertex as the adjacent points. It has many dimples on its surface,
These dimples are arranged randomly,
A golf ball in which the pattern of these dimples is designed by the method according to claim 1. The golf ball according to claim 9, wherein the fluctuation range Rh and the fluctuation range Ro obtained by the following steps (1) to (16) are 3.3 mm or less.
(1) Step where a line connecting both poles of the golf ball is assumed to be the first rotation axis (2) A great circle that exists on the surface of the phantom sphere of the golf ball and is orthogonal to the first rotation axis is assumed Step (3) A step in which two small circles that exist on the surface of the phantom sphere of the golf ball, are orthogonal to the first rotation axis, and have an absolute value of the central angle with the great circle of 30 ° are assumed ( 4) A step of defining a region between these small circles in which a golf ball is partitioned by these small circles and (5) a region sandwiched between these small circles in the surface of the golf ball. Step (6) where 30240 points are determined in steps of 0.25 ° in the central angle in the rotational direction (6) Step (7) where the length L1 of the perpendicular drawn from the respective points to the first rotation axis is calculated Based on 21 vertical lines in the axial direction Step 21 where the 21 lengths L1 calculated in this way are totaled and the total length L2 is calculated (8) From the 1440 total lengths L2 calculated along the rotation direction, the maximum value and the minimum value are determined. Step of calculating fluctuation range Rh which is a value obtained by subtracting minimum value from maximum value (9) Step of assuming second rotation axis orthogonal to first rotation axis assumed in step (1) above ( 10) A step in which a great circle that exists on the surface of the phantom sphere of the golf ball and is orthogonal to the second rotation axis is assumed (11) It exists on the surface of the phantom sphere of the golf ball and is orthogonal to the second rotation axis And a step (12) in which two small circles having an absolute value of the central angle with the great circle of 30 ° are assumed. (12) A golf ball is defined by these small circles. Steps to identify the area between (13) Step (14) in which 30240 points are determined in the above-mentioned region in units of 3 ° in the central direction in the axial direction and in units of 0.25 ° in the central direction in the rotational direction (14) The second rotation from each point Step (15) of calculating the length L1 of the vertical line drawn down on the axis Step of calculating the total length L2 by summing the 21 lengths L1 calculated based on the 21 vertical lines arranged in the axial direction ( 16) A step of determining a maximum value and a minimum value from 1440 total lengths L2 calculated along the rotation direction, and calculating a fluctuation range Ro that is a value obtained by subtracting the minimum value from the maximum value.   The golf ball according to claim 10, wherein an absolute value of a difference dR between the fluctuation range Rh and the fluctuation range Ro is 1.0 mm or less.

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