JP4993639B2 - Method for designing uneven pattern on golf ball surface - Google Patents

Description

  The present invention relates to a golf ball. More specifically, the present invention relates to a method for designing an uneven pattern on the surface 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 them, in other words, a golf ball having 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. Note that 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 phantom sphere surface 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 rotation axis is different from the aerodynamic characteristic when the line passing through the surface center of the regular polyhedron is the rotation 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.

Japanese Patent Laid-Open No. 50-8630 Japanese Patent Laid-Open No. 61-284264

  In the golf ball disclosed in Japanese Patent Laid-Open No. 61-284264, 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.

  Efforts have been made to determine the cause of the singularity near the equator as well as the insufficient symmetry resulting from it. However, the cause is not yet clear, and no universal theory for improvement has been established.

  An object of the present invention is to provide a golf ball excellent in aerodynamic symmetry.

The present inventors have found that a golf ball excellent in aerodynamic symmetry can be obtained by devising the uneven pattern on the surface of the golf ball. The uneven pattern design method according to the present invention includes:
Steps where multiple states are assumed,
A step where a large number of cells are assumed on the sphere,
A step in which the initial state of each cell is determined;
Determining whether or not the state of the cell needs to be changed based on the states of a plurality of cells located in the vicinity of the cell;
Based on the above determination, the method includes the step of updating the state of the cell and the step of assigning a land or recess to the cell according to the state.

  Preferably, the initial state is determined randomly. Preferably, after the determination and update are repeated three or more times, each cell is assigned a land or recess depending on its state.

  Preferably, the determination and update are performed by a cell automaton method. Preferably, the determination and update are performed by a reaction / diffusion model of a cell automaton method. Preferably, the number of cells is 5000 or more and 100,000 or less.

Preferably, whether or not the state needs to be changed is determined based on a value E calculated by the following mathematical formula (1).
_{E = W 1 * N R1 +} W 2 * N R1-R2 (1)
In Formula (1), W ₁ is the first concentration, N _R1 is the number of cells in a specific state that are included in the first circle and are not located at the center of the first circle, and W ₂ is the second concentration. N _R1-R2 is the number of cells in a specific state that are included in the second circle and not included in the first circle. The first concentration is positive and the second concentration is negative. First circle is centered on the cell, the index radius of the circle is R _1. Second circle is centered on the cell, the index radius of the circle is R _2. Radius _{R 2} is greater than the radius _{R 1.}

Preferably, the initial state of each cell is differentiated or undifferentiated. When the value E calculated by the following mathematical formula (1) is positive, this state is maintained if the cell state is differentiated, and this state is changed to differentiation if the cell state is undifferentiated. When this value E is zero, the cell state is maintained. When this value E is negative, if the cell state is differentiated, this state is changed to undifferentiated, and if the cell state is undifferentiated, this state is maintained.
_{E = W 1 * N R1 +} W 2 * N R1-R2 (1)
In this equation (1), W ₁ is the first concentration, N _R1 is the total number of differentiated cells included in the first circle and not located at the center of the first circle, and W ₂ is the second concentration. Yes, _NR1-R2 is the total number of differentiated cells that are included in the second circle and not included in the first circle. The first concentration is positive and the second concentration is negative. First circle is centered on the cell, the index radius of the circle is R _1. Second circle is centered on the cell, the index radius of the circle is R _2. Radius _{R 2} is greater than the radius _{R 1.}

Preferably, the first concentration W1 is not less than 0.80 and not more than 1.20. Preferably, the second concentration W2 is −0.70 or more and −0.50 or less. Preferably, the index radius R ₁ is 2.20 or more and 2.60 or less. Preferably, the index radius _{R 2} is 3.0 to 5.0.

  The golf ball according to the present invention has an uneven pattern on the surface thereof. This uneven pattern is designed by the method described above.

Preferably, the absolute value of the difference dR of this golf ball is 2.5 mm or less. The difference dR is obtained by the following steps (1) to (17).
(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) The virtual sphere is defined by these small circles, and a region sandwiched between these small circles is specified on the surface of the virtual sphere. (5) The above regions are axially centered in 3 ° increments. 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 Calculated based on 21 vertical lines arranged in the axial direction Step 21 where 21 lengths L1 are totaled and total length L2 is calculated (8) From 1440 total lengths L2 calculated along the rotation direction, a maximum value and a minimum value are determined. Step (9) of calculating fluctuation range Rh, which is a value obtained by subtracting the minimum value Step of assuming second rotation axis orthogonal to first rotation axis assumed in step (1) (10) Golf ball A great circle that is present on the surface of the phantom sphere and is orthogonal to the second rotation axis is assumed (11) is present on the surface of the phantom sphere of the golf ball, is orthogonal to the second rotation axis, and Step (12) in which two small circles whose absolute value of the central angle with the great circle is 30 ° is assumed (12) The virtual sphere is defined by these small circles, and is sandwiched between these small circles on the surface of the virtual sphere Step (13) in which the region is specified Step (14) in which 30240 points are determined in 3 ° increments in the central direction in the axial direction and in 0.25 ° increments in the central angle in the rotational direction (14) The length of the perpendicular drawn from each point to the second rotational axis Step (15) in which the length L1 is calculated Step 21 in which the 21 lengths L1 calculated based on the 21 vertical lines arranged in the axial direction are summed, and the total length L2 is calculated (16) along the rotational direction A maximum value and a minimum value are determined from the calculated 1440 total lengths L2, and a fluctuation range Ro that is a value obtained by subtracting the minimum value from the maximum value is calculated (17) The fluctuation ranges Rh and Ro Step of calculating the difference dR between

  Preferably, the absolute value of the difference dR is 1.0 mm or less.

  A large number of craters are formed by recesses on the surface of the golf ball according to the present invention. These craters promote turbulent separation. These craters contribute to the flight performance of the golf ball. Since these craters are randomly arranged, this pattern has no directionality. This golf ball is excellent in aerodynamic symmetry.

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

  FIG. 1 is a schematic cross-sectional view showing a golf ball 2 according to an embodiment of the present invention. The golf ball 2 includes a spherical core 4 and a cover 6. A large number of craters 8 are formed on the surface of the cover 6. A portion of the surface of the golf ball 2 other than the crater 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 has a diameter of 40 mm or greater and 45 mm or less. From the viewpoint of satisfying the standards of the US Golf Association (USGA), the diameter is more preferably 42.67 mm or more. 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 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. From the viewpoint that the USGA standard is satisfied, the mass is more preferably 45.93 g or less.

  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 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.

  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.

  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 0.3 mm or more, particularly 0.5 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. As is clear from FIG. 2, a large number of craters 8 are randomly arranged. The crater 8 and the land 10 form an uneven pattern on the surface of the golf ball 2.

  A cellular automaton method is used to design the uneven pattern. 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.

  The reaction / diffusion model of the cell automaton method is suitable for designing the uneven 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 concavo-convex pattern in which a large number of craters 8 are randomly arranged is obtained. Any model can be used as long as this feature is maintained. The design method according to the present invention 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. Hereinafter, a design method using a reaction diffusion model of the cell automaton method will be described in detail.

  FIG. 3 is a flowchart illustrating a design method according to an embodiment of the present invention. FIG. 4 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. 5 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. 6 is an enlarged view showing a part of the mesh 12 of FIG. For convenience, in FIG. 6, the mesh 12 is drawn in two dimensions. In the center of FIG. 6, a cell 16 to be determined is shown. FIG. 6 further shows a first circle 18 and a second circle 20. First circle 18, centered on the cell 16, the index radius of the circle is R _1. The second circle 20, centered on the cell 16, the index radius of the circle is R _2. What is indicated by a filled circle is a cell other than the cell 16 included in the first circle 18. What is indicated by a filled rectangle is a cell that is included in the second circle 20 and not included in the first circle 18. The solid triangles indicate cells that are not included in the second circle 20.

In this design method, the number N _{R1 of} cells 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 whose state is differentiated is counted and a total N _R1 is calculated. In this design method, the number N _{R1-R2 of} cells 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 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 16 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 16 is updated (STEP 5). In the update, the cell 16 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 16 is differentiated, and this state is changed to differentiation if the state of the cell 16 is undifferentiated. When this value E is zero, the state of the cell 16 is maintained. When the value E is negative, if the state of the cell 16 is differentiated, this state is changed to undifferentiated. If the state of the cell 16 is undifferentiated, this state is maintained. The mesh 12 that has been updated for the first time for all cells is in 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 18 whose state is differentiated (excluding the cell 16): 8
Number of cells that are included in the second circle 20 and not included in the first circle 18 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 16 is differentiated, and this state is changed to differentiation if the state of the cell 16 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 18 whose state is differentiated (excluding the cell 16): 5
Number of cells that are included in the second circle 20 and not included in the first circle 18 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, this state is changed to undifferentiated if the state of the cell 16 is differentiated, and this state is maintained if the state of the cell 16 is undifferentiated.

  This determination and update are repeated. In the flowchart of FIG. 3, the number of repetitions is N. The mesh 12 after N repetitions are in the stage (N + 1). As the stage progresses, the number of cells whose state changes due to the update decreases.

FIG. 7 is a photograph showing a change in state due to repetition. Note that the photograph in FIG. 7 is not for the golf ball 2 shown in FIG. In FIG. 7, for convenience, differentiated cells are colored black, and undifferentiated cells are colored white. Details of each photo are as follows.
(a) Stage 1 Number of repetitions: 0 Initial state
(b) Stage 2 Number of repetitions: 1
(c) Stage 3 Number of repetitions: 2
(d) Stage 4 Number of repetitions: 3
(e) Stage 5 Number of repetitions: 4
(f) Stage 6 Number of repetitions: 5
(g) Stage 31 Number of repetitions: 30

  As is clear from FIG. 7, in the stage where the number of repetitions is small, the pattern change due to the update is severe. The pattern converges by being updated many times. As is clear from FIG. 7, 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.

  After completion of the repetition, a concavo-convex pattern is formed (STEP 6). In the formation of the concavo-convex pattern, each cell is assigned a land 10 or a recess depending on the state. Specifically, a recess is assigned to a differentiated cell, and a land 10 is assigned to an undifferentiated cell. A land 10 may be assigned to a differentiated cell, and a recess may be assigned to an undifferentiated cell.

  Hereinafter, the land 10 and recess allocation method will be described. FIG. 8 is an enlarged view showing a part of the mesh after the update is completed. 9 is a cross-sectional view taken along line IX-IX in FIG. In FIG. 8 and FIG. 9, the cells indicated by circles are differentiated cells, and the cells indicated by squares are undifferentiated cells. As shown in FIG. 9, the radius of the phantom sphere 14 is Ra. In FIG. 9, a second sphere 22 is also shown. The second sphere 22 is concentric with the phantom sphere 14. The radius Rb of the second sphere 22 is smaller than the radius Ra. Differentiation cells (indicated by circles) are moved to the surface of the second sphere 22 along the radial direction of the phantom sphere 14. The moving distance is (Ra−Rb). In FIG. 9, the triangle indicates the cell after movement. Since the radius Rb is smaller than the radius Ra, this movement corresponds to a recess allocation. As shown in FIG. 9, a crater 8 is formed from a series of recesses. The crater 8 may consist of a single recess. Undifferentiated cells (indicated by squares) do not move. The absence of movement corresponds to the land 10 assignment. An uneven pattern is formed by the assignment of the recess and the land 10. In a place where the differentiated cell and the undifferentiated cell are adjacent to each other, a slope 24 is formed from the undifferentiated cell toward the differentiated cell after movement. The slope 24 may be arcuate. The movement distance of one cell may be different from the movement distance of another cell. In this case, the crater 8 may have a non-flat bottom surface.

  In the golf ball 2 shown in FIG. 2, craters 8 are randomly arranged. This uneven | corrugated pattern does not have directionality. This golf ball 2 is excellent in aerodynamic symmetry.

In this design method, the following two items affect the determination of whether or not state change is necessary.
(I) State of the cell 16 (II) State of other cells located in the vicinity of the cell 16 In this design method, determination is made based on the following assumptions.
(1) The differentiation cell generates an activation substance that promotes differentiation of the cell 16.
(2) The differentiation cell generates an inhibitor that returns the cell 16 from the differentiated state to the undifferentiated state.
(3) An undifferentiated cell does not affect the cell 16.
(4) Activating substances have a great influence and inhibitors have a small influence.
(5) The activating substance does not diffuse far, and the inhibitor diffuses far.
In the graph shown in FIG. 5, the absolute value of the density W ₁ is greater than the absolute value of the density W _2. This reflects the assumption (4) above. In the graph shown in FIG. 5, the index radius R ₂ is larger than the index radius R ₁ . This reflects the assumption (5) above. The effect of the activator and the effect of the inhibitor cancel each other. If the effect of the activating substance acting on the cell 16 whose state is undifferentiated is greater than the influence of the inhibitor acting on the cell 16, the cell 16 differentiates. When the influence of the inhibitor acting on the cell 16 whose state is differentiation is greater than the influence of the activating substance acting on the cell 16, the state of the cell 16 changes to undifferentiated.

The number of cells, the first concentration W ₁ , the second concentration W ₂ , the exponent radius R ₁ and the exponent radius R ₂ are factors that affect the pattern. FIG. 10 shows 11 patterns. For convenience, differentiated cells are colored black and undifferentiated cells are colored white. The factors for each pattern are shown in Table 1 below.

  From the standpoint that a crater 8 having an excessive width is obtained, the number of cells is preferably 5000 or more, more preferably 9000 or more, further preferably 20000 or more, and particularly preferably 40000 or more. In light of obtaining a crater 8 having a width that is not too small, the number of cells is preferably 100,000 or less, and more preferably 90000 or less. The crater 8 having an appropriate width promotes turbulent separation.

The first concentration _{W 1} is preferably 0.80 or more, more preferably 0.95 or more. The first concentration W ₁ is preferably 1.20 or less, and more preferably 1.05 or less. Second concentration _{W 2} is preferably at least -0.70, more preferably not less than -0.65. Second concentration _{W 2} is preferably -0.50 or less, more preferably -0.55 or less. The index radius R ₁ is preferably 2.20 or more, and more preferably 2.45 or more. The index radius R ₁ is preferably 2.60 or less, and more preferably 2.55 or less. Index radius _{R 2} is preferably 3.0 or more, 3.5 or more is more preferable. Index radius _{R 2} is preferably 5.0 or less, 4.5 or less is more preferable.

  In the present invention, the ratio of the total area of all craters 8 to the surface area of the phantom sphere 14 is referred to as an occupation ratio. From the viewpoint of promoting turbulent separation, the occupation ratio is preferably 55% or more, more preferably 65% or more, and particularly preferably 82% or more. The occupation ratio is preferably 95% or less.

  From the viewpoint that hops of the golf ball 2 are suppressed, the depth (Ra-Rb) of the crater 8 is preferably 0.05 mm or more, more preferably 0.08 mm or more, and particularly preferably 0.10 mm or more. In light of suppression of dropping of the golf ball 2, the depth (Ra-Rb) 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.

In the present invention, the “volume of the crater” means the volume of the portion surrounded by the phantom sphere 14 and the surface of the crater 8. The sum (total volume) of all craters 8 is preferably 400 mm ³ or more, more preferably 450 mm ³ or more, and particularly preferably 500 mm ³ or more from the viewpoint that hops of the golf ball 2 are suppressed. In view of dropping of the golf ball 2 is suppressed, the total volume is preferably 700 mm ³ or less, more preferably 650 mm ³ or less, particularly preferably 600 mm ³ or less.

  Preferably, the absolute value of the difference dR of the golf ball 2 is 2.5 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. In this respect, the absolute value is more preferably equal to or less than 1.0 mm, and particularly preferably equal to or less than 0.80 mm. Hereinafter, an evaluation method based on the difference dR will be described.

  FIG. 11 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 part of the mold used for molding the golf ball 2. One pole Po is the deepest part of the upper mold, and the other pole Po is the deepest part 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. 12 schematically shows a partial cross section of the golf ball 2 of FIG. The left-right direction in FIG. 12 is the axial direction. As shown in FIG. 12, 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 sandwiched between the small circles C1 and C2 on the surface of the phantom sphere 14 is specified.

  A point P (α) in FIG. 12 is a point located on the surface of the golf ball 2 and having a central angle with the great circle GC of 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. 13 shows a partial cross section of the golf ball 2. In FIG. 13, the direction perpendicular to the paper surface is the axial direction. In FIG. 13, 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 FIG. 2 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 °. In the region between the surfaces of the phantom sphere 14 and these small circles, the total length L2 of 1440 is calculated. 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. A graph in which a data group of the golf ball 2 shown in FIG. 2 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 Ro is calculated. The fluctuation range Ro is a numerical value representing an aerodynamic characteristic in 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 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.

  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 crater 8 is selected, and the fluctuation range Ro and the difference dR are calculated. Instead of this, 20 fluctuation ranges Ro may be calculated based on 20 great circles GC randomly extracted. In this case, the difference dR is calculated based on the maximum value among the 20 pieces of data.

  As the fluctuation range Rh is smaller, a greater flight distance can be obtained during PH rotation. In this respect, the fluctuation range Rh is preferably 3.0 mm or less, and more preferably 2.8 mm or less. The smaller the fluctuation range Ro, the larger the flight distance can be obtained during POP rotation. In this respect, the fluctuation range Ro is preferably 3.0 mm or less, and more preferably 2.7 mm or less.

  Hereinafter, the effects of the present invention will be clarified by examples. However, the present invention should not be construed in a limited manner based on the description of the examples.

[Example 1]
The concavo-convex pattern shown in FIG. 2 was designed by the method shown in FIG. Details of the factors affecting the pattern are as follows.
Number of cells: 47415 First concentration W ₁ : 1.00
Second concentration W ₂ : −0.60
Exponential radius R ₁ : 2.5
Exponential radius R ₂ : 4.0
Crater depth (Ra-Rb): 0.213mm

[Examples 2 to 4]
The concavo-convex patterns of Examples 2 to 4 were designed in the same manner as Example 1 except that the factor values were as shown in Table 2 below. The uneven pattern of Example 2 is shown in FIG. The uneven pattern of Example 3 is shown in FIG. The concavo-convex pattern of Example 4 is shown in FIG.

[Comparative Example 1]
The dimple pattern shown in FIG. 19 was designed. In FIG. 19, the type of dimple is indicated by a symbol for one unit. This unit is obtained by dividing the spherical surface into ten parts. The pattern of this unit is developed on the entire spherical surface. This dimple 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. ing. 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 0.184 1.737
B 152 3.70 0.184 1.414
C 60 3.40 0.184 1.137
D 60 3.20 0.184 0.977

[Evaluation]
The difference dR of each pattern was calculated by the method described above. Details of the results are shown in Table 3 below.

  As shown in Table 3, the absolute value of the difference dR in each example is smaller than that in Comparative Example 1. From this evaluation result, the superiority of the present invention is clear.

  The uneven 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.

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 flowchart illustrating a design method according to an embodiment of the present invention. FIG. 4 is a front view showing a mesh used in the design method of FIG. FIG. 5 is a graph for explaining the rules of the design method of FIG. FIG. 6 is an enlarged view showing a part of the mesh of FIG. FIG. 7 is a photograph showing seven patterns in the course of the design method of FIG. FIG. 8 is an enlarged view showing a part of the mesh after the update is completed. 9 is a cross-sectional view taken along line IX-IX in FIG. FIG. 10 is a photograph showing 11 patterns obtained by the design method of FIG. FIG. 11 is a schematic diagram for explaining the golf ball evaluation method of FIG. FIG. 12 is a schematic diagram for explaining the evaluation method of FIG. FIG. 13 is a schematic diagram for explaining the evaluation method of FIG. FIG. 14 is a graph showing the evaluation results of the golf ball in FIG. FIG. 15 is a graph showing the evaluation results of the golf ball in FIG. FIG. 16 is a front view showing a golf ball according to Example 2 of the present invention. FIG. 17 is a front view showing a golf ball according to Example 3 of the present invention. FIG. 18 is a front view showing a golf ball according to Example 4 of the present invention. FIG. 19 is a front view showing a golf ball according to Comparative Example 1. FIG. FIG. 20 is a graph showing the evaluation results of the golf ball in FIG. FIG. 21 is a graph showing the evaluation results of the golf ball in FIG. FIG. 22 is a graph showing the evaluation results of the golf ball in FIG. FIG. 23 is a graph showing the evaluation results of the golf ball in FIG. FIG. 24 is a graph showing the evaluation results of the golf ball in FIG. FIG. 25 is a graph showing the evaluation results of the golf ball in FIG. FIG. 26 is a graph showing the evaluation results of the golf ball in FIG. FIG. 27 is a graph showing the evaluation results of the golf ball in FIG.

2 ... Golf ball 4 ... Core 6 ... Cover 8 ... Crater 10 ... Land 12 ... Mesh 14 ... Virtual sphere 16 ... Cell 18 ... First circle 20 ... Second circle 22 ... Sphere 24 ... Slope

Claims (9)

Steps where multiple states are assumed,
A step where a large number of cells are assumed on the sphere,
A step in which the initial state of each cell is determined;
Determining whether or not the state of the cell needs to be changed based on the states of a plurality of cells located in the vicinity of the cell;
A method for designing a concavo-convex pattern on the surface of a golf ball, comprising: a step of updating the state of the cell based on the determination; and a step of assigning a land or a recess to the cell according to the state,
A design method in which the determination and update are performed by a reaction / diffusion model of the cell automaton method.   The design method according to claim 1, wherein the initial state is determined at random.   The design method according to claim 1 or 2, wherein a land or a recess is assigned to each cell according to the state after the determination and the update are repeated three times or more.   The design method according to any one of claims 1 to 3, wherein the number of the cells is 5000 or more and 100000 or less. The design method according to any one of claims 1 to 4, wherein whether or not the state needs to be changed is determined based on a value E calculated by the following mathematical formula (1).
_{E = W 1 * N R1 +} W 2 * N R1-R2 (1)
(In this formula (1), W ₁ is the first concentration, N _R1 is the number of cells in a specific state of not located in the first circle center of the contained in the first circle, W ₂ is the N _R1-R2 is the number of cells in a particular state that are included in the second circle and not included in the first circle, where the first concentration is positive and the second concentration is negative. The first circle is a circle centered on the cell and the index radius is R _1. The second circle is a circle centered on the cell and the index radius is R _{2. The} radius R ₂ is larger than the radius _{R 1.)} The initial state of each cell is differentiated or undifferentiated,
When the value E calculated by the following formula (1) is positive, if the cell state is differentiated, this state is maintained, and if the cell state is undifferentiated, this state is changed to differentiated,
When this value E is zero, the state of the cell is maintained,
The design method according to claim 5, wherein when the value E is negative, if the cell state is differentiated, the state is changed to undifferentiated, and if the cell state is undifferentiated, the state is maintained.
_{E = W 1 * N R1 +} W 2 * N R1-R2 (1)
(In this equation (1), W ₁ is the first concentration, N _R1 is the total number of differentiated cells that are included in the first circle and are not located in the center of the first circle, and W ₂ is the second concentration. N _R1-R2 is the total number of differentiated cells that are included in the second circle but not in the first circle, the first concentration is positive and the second concentration is negative. The second circle is a circle centered on the cell with an index radius of R _1. The second circle is a circle centered on the cell with an index radius of R _{2. The} radius R ₂ is a radius R _1. Bigger than.) A golf ball having a concavo-convex pattern on a surface thereof, the concavo-convex pattern being designed by the method according to claim 1 . The golf ball according to claim 7 , wherein an absolute value of the difference dR obtained by the following steps (1) to (17) is 2.5 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) The virtual sphere is defined by these small circles, and a region sandwiched between these small circles is specified on the surface of the virtual sphere. (5) The above regions are axially centered in 3 ° increments. 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 Calculated based on 21 vertical lines arranged in the axial direction Step 21 where 21 lengths L1 are totaled and total length L2 is calculated (8) From 1440 total lengths L2 calculated along the rotation direction, a maximum value and a minimum value are determined. Step (9) of calculating fluctuation range Rh, which is a value obtained by subtracting the minimum value Step of assuming second rotation axis orthogonal to first rotation axis assumed in step (1) (10) Golf ball A great circle that is present on the surface of the phantom sphere and is orthogonal to the second rotation axis is assumed (11) is present on the surface of the phantom sphere of the golf ball, is orthogonal to the second rotation axis, and Step (12) in which two small circles whose absolute value of the central angle with the great circle is 30 ° is assumed (12) The virtual sphere is defined by these small circles, and is sandwiched between these small circles on the surface of the virtual sphere Step (13) in which the region is specified Step (14) in which 30240 points are determined in 3 ° increments in the central direction in the axial direction and in 0.25 ° increments in the central angle in the rotational direction (14) The length of the perpendicular drawn from each point to the second rotational axis Step (15) in which the length L1 is calculated Step 21 in which the 21 lengths L1 calculated based on the 21 vertical lines arranged in the axial direction are summed, and the total length L2 is calculated (16) along the rotational direction A maximum value and a minimum value are determined from the calculated 1440 total lengths L2, and a fluctuation range Ro that is a value obtained by subtracting the minimum value from the maximum value is calculated (17) The fluctuation ranges Rh and Ro Step of calculating the difference dR between The golf ball according to claim 8 , wherein an absolute value of the difference dR is 1.0 mm or less.

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