GOLF BALL

This application claims priority on Patent Application No. 2016-242133 filed in JAPAN on Dec. 14, 2016. The entire contents of this Japanese Patent Application are hereby incorporated by reference.

BACKGROUND OF THE INVENTION
Field of the Invention

The present invention relates to golf balls. Specifically, the present invention relates to dimple patterns of golf balls.

Description of the Related Art

The face of a golf club has a loft angle. When a golf ball is hit with the golf club, backspin due to the loft angle occurs in the golf ball. The golf ball flies with the backspin.

Golf balls have a large number of dimples on the surfaces thereof. The dimples disturb the air flow around the golf ball during flight to cause turbulent flow separation. This phenomenon is referred to as “turbulization”. Due to the turbulization, separation points of the air from the golf ball shift backwards leading to a reduction of drag. The turbulization promotes the displacement between the separation point on the upper side and the separation point on the lower side of the golf ball, which results from the backspin, thereby enhancing the lift force that acts upon the golf ball. The reduction of drag and the enhancement of lift force are referred to as a “dimple effect”. Excellent dimples efficiently disturb the air flow. The excellent dimples produce a long flight distance.

There have been various proposals for dimples. JPH4-109968 discloses a golf ball in which the dimple pattern of each hemisphere can be divided into six units. JP2004-243124 (US2004/0157682) discloses a golf ball in which the dimple pattern near each pole can be divided into four units and the dimple pattern near the equator can be divided into five units. JP2011-10667 (US2010/0326175) discloses a golf ball in which a parameter dependent on the shapes of dimples falls within a predetermined range.

The greatest interest to golf players concerning golf balls is flight performance. Golf players desire golf balls having excellent flight performance. In light of flight performance, there is room for improvement of dimples.

An object of the present invention is to provide a golf ball having excellent flight performance.

SUMMARY OF THE INVENTION

A golf ball according to the present invention has a plurality of dimples on a surface thereof. A minimum value of 15 peak values obtained by executing steps (a) to (h) for each of 15 axes Ax is not less than 95 mm, when spherical polar coordinates of a point that is located on a surface of a phantom sphere of the golf ball and has a latitude of θ (degrees) and a longitude of ϕ (degrees) are represented by (θ, ϕ), the 15 axes Ax being

(1) a first axis Ax1 passing through a point Pn1 coordinates of which are (75, 270) and a point Ps1 coordinates of which are (−75, 90),

(2) a second axis Ax2 passing through a point Pn2 coordinates of which are (60, 270) and a point Ps2 coordinates of which are (−60, 90)

(3) a third axis Ax3 passing through a point Pn3 coordinates of which are (45, 270) and a point Ps3 coordinates of which are (−45, 90),

(4) a fourth axis Ax4 passing through a point Pn4 coordinates of which are (30, 270) and a point Ps4 coordinates of which are (−30, 90),

(5) a fifth axis Ax5 passing through a point Pn5 coordinates of which are (15, 270) and a point Ps5 coordinates of which are (−15, 90),

(6) a sixth axis Ax6 passing through a point Pn6 coordinates of which are (75, 0) and a point Ps6 coordinates of which are (−75, 180),

(7) a seventh axis Ax1 passing through a point Pn7 coordinates of which are (60, 0) and a point Ps7 coordinates of which are (−60, 180),

(8) an eighth axis Ax8 passing through a point Pn8 coordinates of which are (45, 0) and a point Ps8 coordinates of which are (−45, 180),

(9) a ninth axis Ax9 passing through a point Pn9 coordinates of which are (30, 0) and a point Ps9 coordinates of which are (−30, 180),

(10) a tenth axis Ax10 passing through a point Pn10 coordinates of which are (15, 0) and a point Ps10 coordinates of which are (−15, 180),

(11) an eleventh axis Ax11 passing through a point Pn11 coordinates of which are (75, 90) and a point Ps11 coordinates of which are (−75, 270),

(12) a twelfth axis Ax12 passing through a point Pn12 coordinates of which are (60, 90) and a point Ps12 coordinates of which are (−60, 270),

(13) a thirteenth axis Ax13 passing through a point Pn13 coordinates of which are (45, 90) and a point Ps13 coordinates of which are (−45, 270),

(14) a fourteenth axis Ax14 passing through a point Pn14 coordinates of which are (30, 90) and a point Ps14 coordinates of which are (−30, 270), and

(15) a fifteenth axis Ax15 passing through a point Pn15 coordinates of which are (15, 90) and a point Ps15 coordinates of which are (−15, 270), the steps (a) to (h) being the steps of

(a) assuming a great circle that is present on the surface of the phantom sphere and is orthogonal to the axis Ax,

(b) assuming two small circles that are present on the surface of the phantom sphere, that are orthogonal to the axis Ax, and of which absolute values of central angles with the great circle are each 30°,

(c) defining a region, of the surface of the golf ball, which is obtained by dividing the surface of the golf ball at these small circles and which is sandwiched between these small circles,

(d) determining 30240 points, on the region, arranged at intervals of a central angle of 3° in a direction of the axis Ax and at intervals of a central angle of 0.25° in a direction of rotation about the axis Ax,

(e) calculating a length L1 of a perpendicular line that extends from each point to the axis Ax,

(f) calculating a total length L2 by summing 21 lengths L1 calculated on the basis of 21 perpendicular lines arranged in the direction of the axis Ax,

(g) obtaining a transformed data constellation by performing Fourier transformation on a data constellation of 1440 total lengths L2 calculated along the direction of rotation about the axis Ax, and

(h) calculating a peak value and an order of a maximum peak of the transformed data constellation. A minimum value of 15 orders obtained by executing the steps (a) to (h) is not less than 27. A maximum value of the 15 orders obtained by executing the steps (a) to (h) is not greater than 37. An average of the 15 orders obtained by executing the steps (a) to (h) is not less than 30 and not greater than 34.

When the golf ball according to the present invention flies, the lift force coefficient and the drag coefficient are appropriate. The golf ball has excellent flight performance.

Preferably, an average of the 15 peak values obtained by executing the steps (a) to (h) is not less than 200 mm.

Preferably, a total volume of the dimples is not less than 450 mm³and not greater than 750 mm³.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view of a golf ball according to an embodiment of the present invention;

FIG. 2 is an enlarged front view of the golf ball in FIG. 1;

FIG. 3 is a plan view of the golf ball in FIG. 2;

FIG. 4 is a partially enlarged cross-sectional view of the golf ball in FIG. 1;

FIG. 5 is a schematic diagram for explaining an evaluation method for the golf ball in FIG. 2;

FIG. 6 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 7 is a schematic cross-sectional view for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 8 is a schematic cross-sectional view for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 9 is a graph showing an evaluation result of the golf ball in FIG. 2;

FIG. 10 is a graph showing another evaluation result of the golf ball in FIG. 2;

FIG. 11 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 12 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 13 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 14 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 15 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 16 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 17 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 18 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 19 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 20 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 21 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 22 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 23 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 24 is a schematic diagram for explaining the evaluation method for the golf ball in FIG. 2;

FIG. 25 is a front view of a golf ball according to Example 2 of the present invention;

FIG. 26 is a plan view of the golf ball in FIG. 25;

FIG. 27 is a front view of a golf ball according to Example 3 of the present invention;

FIG. 28 is a plan view of the golf ball in FIG. 27;

FIG. 29 is a front view of a golf ball according to Comparative Example 1;

FIG. 30 is a plan view of the golf ball in FIG. 29;

FIG. 31 is a front view of a golf ball according to Comparative Example 2;

FIG. 32 is a plan view of the golf ball in FIG. 31;

FIG. 33 is a front view of a golf ball according to Comparative Example 3;

FIG. 34 is a plan view of the golf ball in FIG. 33;

FIG. 35 is a front view of a golf ball according to Comparative Example 4; and

FIG. 36 is a plan view of the golf ball in FIG. 35.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following will describe in detail the present invention based on preferred embodiments with appropriate reference to the drawings.

A golf ball 2 shown in FIG. 1 includes a spherical core 4, a mid layer 6 positioned outside the core 4, and a cover 8 positioned outside the mid layer 6. The golf ball 2 has a large number of dimples 10 on the surface thereof. Of the surface of the golf ball 2, a part other than the dimples 10 is a land 12. The golf ball 2 includes a paint layer and a mark layer on the external side of the cover 8 although these layers are not shown in the drawing.

The golf ball 2 preferably has a diameter of not less than 40 mm and not greater than 45 mm. From the standpoint of conformity to the rules established by the United States Golf Association (USGA), the diameter is particularly preferably not less than 42.67 mm. In light of suppression of air resistance, the diameter is more preferably not greater than 44 mm and particularly preferably not greater than 42.80 mm.

The golf ball 2 preferably has a weight of not less than 40 g and not greater than 50 g. In light of attainment of great inertia, the weight is more preferably not less than 44 g and particularly preferably not less than 45.00 g. From the standpoint of conformity to the rules established by the USGA, the weight is particularly preferably not greater than 45.93 g.

The core 4 is formed by crosslinking a rubber composition. Examples of the base rubber of the rubber composition include polybutadienes, polyisoprenes, styrene-butadiene copolymers, ethylene-propylene-diene copolymers, and natural rubbers. Two or more rubbers may be used in combination. In light of resilience performance, polybutadienes are preferable, and high-cis polybutadienes are particularly preferable.

The rubber composition of the core 4 includes a co-crosslinking agent. Examples of preferable co-crosslinking agents in light of resilience performance include zinc acrylate, magnesium acrylate, zinc methacrylate, and magnesium methacrylate. The rubber composition preferably includes an organic peroxide together with a co-crosslinking agent. Examples of preferable organic peroxides include dicumyl peroxide, 1,1-bis(t-butylperoxy)-3,3,5-trimethylcyclohexane, 2,5-dimethyl-2,5-di(t-butylperoxy)hexane, and di-t-butyl peroxide.

The rubber composition of the core 4 may include additives such as a filler, sulfur, a vulcanization accelerator, a sulfur compound, an anti-aging agent, a coloring agent, a plasticizer, and a dispersant. The rubber composition may include a carboxylic acid or a carboxylate. The rubber composition may include synthetic resin powder or crosslinked rubber powder.

The core 4 has a diameter of preferably not less than 30.0 mm and particularly preferably not less than 38.0 mm. The diameter of the core 4 is preferably not greater than 42.0 mm and particularly preferably not greater than 41.5 mm. The core 4 may have two or more layers. The core 4 may have a rib on the surface thereof. The core 4 may be hollow.

The mid layer 6 is formed from a resin composition. A preferable base polymer of the resin composition is an ionomer resin. Examples of preferable ionomer resins include binary copolymers formed with an α-olefin and an α,β-unsaturated carboxylic acid having 3 to 8 carbon atoms. Examples of other preferable ionomer resins include ternary copolymers formed with: an α-olefin; an α,β-unsaturated carboxylic acid having 3 to 8 carbon atoms; and an α,β-unsaturated carboxylate ester having 2 to 22 carbon atoms. For the binary copolymer and the ternary copolymer, preferable α-olefins are ethylene and propylene, while preferable α,β-unsaturated carboxylic acids are acrylic acid and methacrylic acid. In the binary copolymer and the ternary copolymer, some of the carboxyl groups are neutralized with metal ions. Examples of metal ions for use in neutralization include sodium ion, potassium ion, lithium ion, zinc ion, calcium ion, magnesium ion, aluminum ion, and neodymium ion.

Instead of an ionomer resin, the resin composition of the mid layer 6 may include another polymer. Examples of the other polymer include polystyrenes, polyamides, polyesters, polyolefins, and polyurethanes. The resin composition may include two or more polymers.

The resin composition of the mid layer 6 may include a coloring agent such as titanium dioxide, a filler such as barium sulfate, a dispersant, an antioxidant, an ultraviolet absorber, a light stabilizer, a fluorescent material, a fluorescent brightener, and the like. For the purpose of adjusting specific gravity, the resin composition may include powder of a metal with a high specific gravity such as tungsten, molybdenum, and the like.

The mid layer 6 has a thickness of preferably not less than 0.2 mm and particularly preferably not less than 0.3 mm. The thickness of the mid layer 6 is preferably not greater than 2.5 mm and particularly preferably not greater than 2.2 mm. The mid layer 6 has a specific gravity of preferably not less than 0.90 and particularly preferably not less than 0.95. The specific gravity of the mid layer 6 is preferably not greater than 1.10 and particularly preferably not greater than 1.05. The mid layer 6 may have two or more layers.

The cover 8 is formed from a resin composition. A preferable base polymer of the resin composition is a polyurethane. The resin composition may include a thermoplastic polyurethane or may include a thermosetting polyurethane. In light of productivity, the thermoplastic polyurethane is preferable. The thermoplastic polyurethane includes a polyurethane component as a hard segment, and a polyester component or a polyether component as a soft segment.

The polyurethane has a urethane bond within the molecule. The urethane bond can be formed by reacting a polyol with a polyisocyanate.

The polyol, which is a material for the urethane bond, has a plurality of hydroxyl groups. Low-molecular-weight polyols and high-molecular-weight polyols can be used.

Examples of an isocyanate for the polyurethane component include alicyclic diisocyanates, aromatic diisocyanates, and aliphatic diisocyanates. Alicyclic diisocyanates are particularly preferable. Since an alicyclic diisocyanate does not have any double bond in the main chain, the alicyclic diisocyanate suppresses yellowing of the cover 8. Examples of alicyclic diisocyanates include 4,4′-dicyclohexylmethane diisocyanate (H₁₂MDI), 1,3-bis(isocyanatomethyl)cyclohexane (H₆XDI), isophorone diisocyanate (IPDI), and trans-1,4-cyclohexane diisocyanate (CHDI). In light of versatility and processability, H₁₂MDI is preferable.

Instead of a polyurethane, the resin composition of the cover 8 may include another polymer. Examples of the other polymer include ionomer resins, polystyrenes, polyamides, polyesters, and polyolefins. The resin composition may include two or more polymers.

The resin composition of the cover 8 may include a coloring agent such as titanium dioxide, a filler such as barium sulfate, a dispersant, an antioxidant, an ultraviolet absorber, a light stabilizer, a fluorescent material, a fluorescent brightener, and the like.

The cover 8 has a thickness of preferably not less than 0.2 mm and particularly preferably not less than 0.3 mm. The thickness of the cover 8 is preferably not greater than 2.5 mm and particularly preferably not greater than 2.2 mm. The cover 8 has a specific gravity of preferably not less than 0.90 and particularly preferably not less than 0.95. The specific gravity of the cover 8 is preferably not greater than 1.10 and particularly preferably not greater than 1.05. The cover 8 may have two or more layers.

The golf ball 2 may include a reinforcing layer between the mid layer 6 and the cover 8. The reinforcing layer firmly adheres to the mid layer 6 and also to the cover 8. The reinforcing layer suppresses separation of the cover 8 from the mid layer 6. The reinforcing layer is formed from a polymer composition. Examples of the base polymer of the reinforcing layer include two-component curing type epoxy resins and two-component curing type urethane resins.

As shown in FIGS. 2 and 3, the contour of each dimple 10 is circular. The golf ball 2 has dimples A each having a diameter of 4.40 mm; dimples B each having a diameter of 4.30 mm; dimples C each having a diameter of 4.15 mm; dimples D each having a diameter of 3.90 mm; and dimples E each having a diameter of 3.00 mm. The number of types of the dimples 10 is five. The golf ball 2 may have non-circular dimples instead of the circular dimples 10 or together with the circular dimples 10.

The number of the dimples A is 60; the number of the dimples B is 158; the number of the dimples C is 72; the number of the dimples D is 36; and the number of the dimples E is 12. The total number of the dimples 10 is 338. A dimple pattern is formed by these dimples 10 and the land 12.

FIG. 4 shows a cross section of the golf ball 2 along a plane passing through the central point of the dimple 10 and the central point of the golf ball 2. In FIG. 4, the top-to-bottom direction is the depth direction of the dimple 10. In FIG. 4, a chain double-dashed line 14 indicates a phantom sphere 14. The surface of the phantom sphere 14 is the surface of the golf ball 2 when it is postulated that no dimple 10 exists. The diameter of the phantom sphere 14 is equal to the diameter of the golf ball 2. The dimple 10 is recessed from the surface of the phantom sphere 14. The land 12 coincides with the surface of the phantom sphere 14. In the present embodiment, the cross-sectional shape of each dimple 10 is substantially a circular arc. The curvature radius of this circular arc is shown by reference character CR in FIG. 4.

In FIG. 4, an arrow Dm indicates the diameter of the dimple 10. The diameter Dm is the distance between two tangent points Ed appearing on a tangent line Tg that is drawn tangent to the far opposite ends of the dimple 10. Each tangent point Ed is also the edge of the dimple 10. The edge Ed defines the contour of the dimple 10.

The diameter Dm of each dimple 10 is preferably not less than 2.0 mm and not greater than 6.0 mm. The dimple 10 having a diameter Dm of not less than 2.0 mm contributes to turbulization. In this respect, the diameter Dm is more preferably not less than 2.5 mm and particularly preferably not less than 2.8 mm. The dimple 10 having a diameter Dm of not greater than 6.0 mm does not impair a fundamental feature of the golf ball 2 being substantially a sphere. In this respect, the diameter Dm is more preferably not greater than 5.5 mm and particularly preferably not greater than 5.0 mm.

In the case of a non-circular dimple, a circular dimple 10 having the same area as that of the non-circular dimple is assumed. The diameter of the assumed circular dimple 10 can be regarded as the diameter of the non-circular dimple.

In FIG. 4, a double ended arrow Dp1 indicates a first depth of the dimple 10. The first depth Dp1 is the distance between the deepest part of the dimple 10 and the surface of the phantom sphere 14. In FIG. 4, a double ended arrow Dp2 indicates a second depth of the dimple 10. The second depth Dp2 is the distance between the deepest part of the dimple 10 and the tangent line Tg.

In light of suppression of rising of the golf ball 2 during flight, the first depth Dp1 of each dimple 10 is preferably not less than 0.10 mm, more preferably not less than 0.13 mm, and particularly preferably not less than 0.15 mm. In light of suppression of dropping of the golf ball 2 during flight, the first depth Dp1 is preferably not greater than 0.65 mm, more preferably not greater than 0.60 mm, and particularly preferably not greater than 0.55 mm.

The area S of the dimple 10 is the area of a region surrounded by the contour line of the dimple 10 when the central point of the golf ball 2 is viewed at infinity. In the case of a circular dimple 10, the area S is calculated by the following mathematical formula.

S=(Dm/2)²*n

In the golf ball 2 shown in FIGS. 2 and 3, the area of each dimple A is 15.20 mm²; the area of each dimple B is 14.52 mm²; the area of each dimple C is 13.53 mm²; the area of each dimple D is 11.95 mm²; and the area of each dimple E is 7.07 mm².

In the present invention, the ratio of the sum of the areas S of all the dimples 10 relative to the surface area of the phantom sphere 14 is referred to as an occupation ratio. From the standpoint of achieving sufficient turbulization, the occupation ratio is preferably not less than 78%, more preferably not less than 80%, and particularly preferably not less than 82%. The occupation ratio is preferably not greater than 95%. In the golf ball 2 shown in FIGS. 2 and 3, the total area of the dimples 10 is 4695.4 mm². The surface area of the phantom sphere 14 of the golf ball 2 is 5728 mm², so that the occupation ratio is 82.0%.

From the standpoint of achieving a sufficient occupation ratio, the total number N of the dimples 10 is preferably not less than 250, more preferably not less than 280, and particularly preferably not less than 300.

From the standpoint that each dimple 10 can contribute to turbulization, the total number N of the dimples 10 is preferably not greater than 450, more preferably not greater than 400, and particularly preferably not greater than 380.

In the present invention, the “volume V of the dimple” means the volume of a portion surrounded by the surface of the phantom sphere 14 and the surface of the dimple 10. The total volume TV of the dimples 10 is preferably not less than 450 mm³and not greater than 750 mm³. With the golf ball 2 having a total volume TV of not less than 450 mm³, rising of the golf ball 2 during flight is suppressed. In this respect, the total volume TV is more preferably not less than 480 mm³and particularly preferably not less than 500 mm³. With the golf ball 2 having a total volume TV of not greater than 750 mm³, dropping of the golf ball 2 during flight is suppressed. In this respect, the total volume TV is more preferably not greater than 730 mm³and particularly preferably not greater than 710 mm³.

The golf ball 2 according to the present invention has an excellent aerodynamic characteristic. In an evaluation method for the aerodynamic characteristic, the following steps (a) to (h) are executed:

(a) assuming a great circle that is present on the surface of the phantom sphere 14 and is orthogonal to an axis Ax;

(b) assuming two small circles that are present on the surface of the phantom sphere 14, that are orthogonal to the axis Ax, and of which the absolute values of central angles with the great circle are each 30°;

(c) defining a region, of the surface of the golf ball 2, which is obtained by dividing the surface of the golf ball 2 at these small circles and which is sandwiched between these small circles;

(e) calculating the length L1 of a perpendicular line that extends from each point to the axis Ax;

(f) calculating a total length L2 by summing 21 lengths L1 calculated on the basis of 21 perpendicular lines arranged in the direction of the axis Ax;

(g) obtaining a transformed data constellation by performing Fourier transformation on a data constellation of 1440 total lengths L2 calculated along the direction of rotation about the axis Ax; and

(h) calculating the peak value and the order of the maximum peak of the transformed data constellation. The following will describe each step in detail.

FIG. 5 is a schematic diagram for explaining this evaluation method. FIG. 5 shows the phantom sphere 14 of the golf ball 2. In FIG. 5, reference character NP represents a north pole. The north pole NP corresponds to the top of a cavity face formed by an upper mold half for molding the golf ball 2. Reference character SP represents a south pole. The south pole SP corresponds to the deepest part of a cavity face formed by a lower mold half for molding the golf ball 2. Reference character Eq represents an equator. The phantom sphere 14 can be divided into a northern hemisphere NH and a southern hemisphere SH by the equator Eq.

The latitude of the north pole NP is 90° (degrees). The latitude θ of the equator Eq is zero. The latitude of the south pole SP is −90°. The counterclockwise direction when the phantom sphere 14 is seen from the north pole NP is a positive direction of longitude ϕ. The minimum value of ϕ is zero. The maximum value of ϕ is 360°. The spherical polar coordinates of a point present on the surface of the phantom sphere 14 are represented by (θ, ϕ). In FIG. 5, a point (0, 0) is located in the front.

In FIG. 5, reference character Loa represents a first longitude line. The longitude ϕ of the first longitude line Loa is 0° and also 360°. The phantom sphere 14 has numerous longitude lines. A longitude line that contains the maximum number of dimples 10 that centrally intersect the longitude line is defined as the first longitude line Loa. At a dimple 10 that centrally intersects a longitude line, the longitude line passes through the area center of gravity of the dimple 10.

In this evaluation method, a first axis Ax1 is assumed. The first axis Ax1 passes through a point Pn1 and a point Ps1. The point Pn1 and the point Ps1 are present on the surface of the phantom sphere 14. The point Pn1 is present on the northern hemisphere NH. The coordinates of the point Pn1 are (75, 270). The point Ps1 is present on the southern hemisphere SH. The coordinates of the point Ps1 are (−75, 90). The first axis Ax1 is tilted relative to the earth axis. The angle of the tilt is 15°. The earth axis is a line passing through the north pole NP and the south pole SP.

In this evaluation method, a first great circle GC1 that is present on the surface of the phantom sphere 14 of the golf ball 2 is assumed. The first axis Ax1 is orthogonal to the first great circle GC1. In other words, the first axis Ax1 is orthogonal to the plane including the first great circle GC1. In FIG. 5, the first great circle GC1 is tilted relative to the equator Eq. The angle of the tilt is 15°. The great circle is a circle that is present on the surface of the phantom sphere 14 and has a diameter equal to the diameter of the phantom sphere 14.

The golf ball 2 rotates about the first axis Ax1. During this rotation, the circumferential speed of the first great circle GC1 is high. Therefore, the surface roughness of the golf ball 2 at and near the first great circle GC1 greatly influences the flight performance of the golf ball 2.

In this evaluation method, two small circles C1 and C2 that are present on the surface of the phantom sphere 14 and are orthogonal to the first axis Ax1 are assumed. FIG. 6 shows these small circles C1 and C2. Each small circle is parallel to the first great circle GC1.

FIG. 7 schematically shows a partial cross section of the golf ball 2 in FIG. 6. FIG. 7 shows a cross-section passing through the center O of the golf ball 2. The right-left direction in FIG. 7 is the direction of the first axis Ax1. As shown in FIG. 7, the absolute value of the central angle between the small circle C1 and the first great circle GC1 is 30°. Although not shown, the absolute value of the central angle between the small circle C2 and the first great circle GC1 is also 30°. The golf ball 2 is divided at the small circles C1 and C2, and of the surface of the golf ball 2, a region sandwiched between the small circles C1 and C2 is defined. Since the circumferential speed of the first great circle GC1 is high, the dimples 10 present in this region greatly influence the aerodynamic characteristic of the golf ball 2.

In FIG. 7, a point P(α) is the point that is located on the surface of the golf ball 2 and of which the central angle with the first great circle GC1 is α° (degrees). A point F(α) is the foot of a perpendicular line Pe(α) that extends downward from the point P(α) to the first axis Ax1. An arrow L1(α) represents 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 axis Ax1. For one cross section, the lengths L1(α) are calculated at 21 points P(α). Specifically, the lengths L1(α) are calculated at angles α of −30°, −27°, −24°, −21°, −18°, −15°, −12°, −9°, −6°, −3°, 0°, 3°, 6°, 9°, 12°, 15°, 18°, 21°, 24°, 27°, and 30°. The 21 lengths L1(α) are summed, thereby obtaining a total length L2 (mm). The total length L2 is a parameter dependent on the surface shape in the cross section shown in FIG. 7.

FIG. 8 shows a partial cross section of the golf ball 2. In FIG. 8, a direction perpendicular to the surface of the sheet is the direction of the first axis Ax1. In FIG. 8, reference character β represents a rotation angle of the golf ball 2. In a range of equal to or greater than 0° and less than 360°, the rotation angles β are set at an interval of an angle of 0.25°. At each rotation angle, the total length L2 is calculated. As a result, 1440 total lengths L2 are obtained along the rotation direction. These total lengths L2 are a data constellation calculated through one rotation of the golf ball 2. This data constellation is calculated on the basis of 30240 lengths L1.

FIG. 9 shows a graph plotting the data constellation, for the first axis Ax1, of the golf ball 2 shown in FIGS. 2 and 3. In this graph, the horizontal axis represents the rotation angle β, and the vertical axis represents the total length L2. Fourier transformation is performed on the data constellation. By the Fourier transformation, a frequency spectrum is obtained. In other words, by the Fourier transformation, a coefficient of a Fourier series represented by the following formula is obtained.

$F_{k} = \sum_{n = 0}^{N - 1} (a_{n} \cos 2 π \frac{nk}{N} + b_{n} \sin 2 π \frac{nk}{N})$

The above mathematical formula is a combination of two trigonometric functions having different periods. In the above mathematical formula, a_nand b_nare Fourier coefficients. The magnitude of each component to be combined is determined depending on these Fourier coefficients. Each coefficient is represented by the following mathematical formula.

$a_{n} = \frac{1}{N} \sum_{k = 0}^{N - 1} F_{k} \cos 2 π \frac{nk}{N}$

$b_{n} = \frac{1}{N} \sum_{k = 0}^{N - 1} F_{k} \sin 2 π \frac{nk}{N}$

In the above mathematical formulas, N is the total number of pieces of data of the data constellation, and F_kis the kth value in the data constellation. The spectrum is represented by the following mathematical formula.

P
_n=√{square root over (a_n²+b_n²)}

By the Fourier transformation, a transformed data constellation is obtained. FIG. 10 shows a graph plotting the transformed data constellation. In this graph, the horizontal axis represents an order, and the vertical axis represents an amplitude. From this graph, the maximum peak is determined. Furthermore, the peak value Pd1 of the maximum peak and the order Fd1 of the maximum peak are determined. The peak value Pd1 and the order Fd1 are numeric values representing the aerodynamic characteristic during rotation about the first axis Ax1. In the present embodiment, the peak value Pd1 is 270.2 mm, and the order Fd1 is 33.

FIG. 11 also shows the phantom sphere 14 of the golf ball 2. FIG. 11 shows the equator Eq and the longitude line Loa having a longitude ϕ of zero. In FIG. 11, the point (0, 0) is located in the front. In FIG. 11, reference character Ax2 represents a second axis. The second axis Ax2 passes through a point Pn2 and a point Ps2. The point Pn2 and the point Ps2 are present on the surface of the phantom sphere 14. The coordinates of the point Pn2 are (60, 270). The coordinates of the point Ps2 are (−60, 90). The second axis Ax2 is tilted relative to the earth axis. The angle of the tilt is 30°.

FIG. 11 shows a second great circle GC2 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the second axis Ax2 is orthogonal. The second great circle GC2 is tilted relative to the equator Eq. The angle of the tilt is 30°.

For rotation about the second axis Ax2, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the second axis Ax2, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the second great circle GC2 is 30°. The absolute value of the central angle between the small circle C2 and the second great circle GC2 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the second axis Ax2 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd2 of the maximum peak and the order Fd2 of the maximum peak are determined. The peak value Pd2 and the order Fd2 are numeric values representing the aerodynamic characteristic during rotation about the second axis Ax2. In the present embodiment, the peak value Pd2 is 177.9 mm, and the order Fd2 is 37.

FIG. 12 also shows the phantom sphere 14 of the golf ball 2. FIG. 12 shows the equator Eq and the longitude line Loa having a longitude ϕ of zero. In FIG. 12, the point (0, 0) is located in the front. In FIG. 12, reference character Ax3 represents a third axis. The third axis Ax3 passes through a point Pn3 and a point Ps3. The point Pn3 and the point Ps3 are present on the surface of the phantom sphere 14. The coordinates of the point Pn3 are (45, 270). The coordinates of the point Ps3 are (−45, 90). The third axis Ax3 is tilted relative to the earth axis. The angle of the tilt is 45°.

FIG. 12 shows a third great circle GC3 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the third axis Ax3 is orthogonal. The third great circle GC3 is tilted relative to the equator Eq. The angle of the tilt is 45°.

For rotation about the third axis Ax3, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the third axis Ax3, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the third great circle GC3 is 30°. The absolute value of the central angle between the small circle C2 and the third great circle GC3 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the third axis Ax3 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd3 of the maximum peak and the order Fd3 of the maximum peak are determined. The peak value Pd3 and the order Fd3 are numeric values representing the aerodynamic characteristic during rotation about the third axis Ax3. In the present embodiment, the peak value Pd3 is 150.2 mm, and the order Fd3 is 37.

FIG. 13 also shows the phantom sphere 14 of the golf ball 2. FIG. 13 shows the equator Eq and the longitude line Loa having a longitude ϕ of zero. In FIG. 13, the point (0, 0) is located in the front. In FIG. 13, reference character Ax4 represents a fourth axis. The fourth axis Ax4 passes through a point Pn4 and a point Ps4. The point Pn4 and the point Ps4 are present on the surface of the phantom sphere 14. The coordinates of the point Pn4 are (30, 270). The coordinates of the point Ps4 are (−30, 90). The fourth axis Ax4 is tilted relative to the earth axis. The angle of the tilt is 60°.

FIG. 13 shows a fourth great circle GC4 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the fourth axis Ax4 is orthogonal. The fourth great circle GC4 is tilted relative to the equator Eq. The angle of the tilt is 60°.

For rotation about the fourth axis Ax4, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the fourth axis Ax4, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the fourth great circle GC4 is 30°. The absolute value of the central angle between the small circle C2 and the fourth great circle GC4 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the fourth axis Ax4 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd4 of the maximum peak and the order Fd4 of the maximum peak are determined. The peak value Pd4 and the order Fd4 are numeric values representing the aerodynamic characteristic during rotation about the fourth axis Ax4. In the present embodiment, the peak value Pd4 is 316.4 mm, and the order Fd4 is 34.

FIG. 14 also shows the phantom sphere 14 of the golf ball 2. FIG. 14 shows the equator Eq and the longitude line Loa having a longitude ϕ of zero. In FIG. 14, the point (0, 0) is located in the front. In FIG. 14, reference character Ax5 represents a fifth axis. The fifth axis Ax5 passes through a point Pn5 and a point Ps5. The point Pn5 and the point Ps5 are present on the surface of the phantom sphere 14. The coordinates of the point Pn5 are (15, 270). The coordinates of the point Ps5 are (−15, 90). The fifth axis Ax5 is tilted relative to the earth axis. The angle of the tilt is 75°.

FIG. 14 shows a fifth great circle GC5 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the fifth axis Ax5 is orthogonal. The fifth great circle GC5 is tilted relative to the equator Eq. The angle of the tilt is 75°.

For rotation about the fifth axis Ax5, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the fifth axis Ax5, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the fifth great circle GC5 is 30°. The absolute value of the central angle between the small circle C2 and the fifth great circle GC5 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the fifth axis Ax5 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd5 of the maximum peak and the order Fd5 of the maximum peak are determined. The peak value Pd5 and the order Fd5 are numeric values representing the aerodynamic characteristic during rotation about the fifth axis Ax5. In the present embodiment, the peak value Pd5 is 190.0 mm, and the order Fd5 is 27.

FIG. 15 also shows the phantom sphere 14 of the golf ball 2. FIG. 15 shows the equator Eq and a longitude line Lob having a longitude ϕ of 90°. In FIG. 15, a point (0, 90) is located in the front. In FIG. 15, reference character Ax6 represents a sixth axis. The sixth axis Ax6 passes through a point Pn6 and a point Ps6. The point Pn6 and the point Ps6 are present on the surface of the phantom sphere 14. The coordinates of the point Pn6 are (75, 0). The coordinates of the point Ps6 are (−75, 180). The sixth axis Ax6 is tilted relative to the earth axis. The angle of the tilt is 15°.

FIG. 15 shows a sixth great circle GC6 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the sixth axis Ax6 is orthogonal. The sixth great circle GC6 is tilted relative to the equator Eq. The angle of the tilt is 15°.

For rotation about the sixth axis Ax6, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the sixth axis Ax6, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the sixth great circle GC6 is 30°. The absolute value of the central angle between the small circle C2 and the sixth great circle GC6 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the sixth axis Ax6 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd6 of the maximum peak and the order Fd6 of the maximum peak are determined. The peak value Pd6 and the order Fd6 are numeric values representing the aerodynamic characteristic during rotation about the sixth axis Ax6. In the present embodiment, the peak value Pd6 is 270.2 mm, and the order Fd6 is 33.

FIG. 16 also shows the phantom sphere 14 of the golf ball 2. FIG. 16 shows the equator Eq and the longitude line Lob having a longitude ϕ of 90°. In FIG. 16, the point (0, 90) is located in the front. In FIG. 16, reference character Ax7 represents a seventh axis. The seventh axis Ax7 passes through a point Pn7 and a point Ps7. The point Pn7 and the point Ps7 are present on the surface of the phantom sphere 14. The coordinates of the point Pn7 are (60, 0). The coordinates of the point Ps7 are (−60, 180). The seventh axis Ax7 is tilted relative to the earth axis. The angle of the tilt is 30°.

FIG. 16 shows a seventh great circle GC7 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the seventh axis Ax7 is orthogonal. The seventh great circle GC7 is tilted relative to the equator Eq. The angle of the tilt is 30°.

For rotation about the seventh axis Ax7, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the seventh axis Ax7, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the seventh great circle GC7 is 30°. The absolute value of the central angle between the small circle C2 and the seventh great circle GC7 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the seventh axis Ax7 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd7 of the maximum peak and the order Fd7 of the maximum peak are determined. The peak value Pd7 and the order Fd7 are numeric values representing the aerodynamic characteristic during rotation about the seventh axis Ax1. In the present embodiment, the peak value Pd7 is 177.9 mm, and the order Fd7 is 37.

FIG. 17 also shows the phantom sphere 14 of the golf ball 2. FIG. 17 shows the equator Eq and the longitude line Lob having a longitude ϕ of 90°. In FIG. 17, the point (0, 90) is located in the front. In FIG. 17, reference character Ax8 represents an eighth axis. The eighth axis Ax8 passes through a point Pn8 and a point Ps8. The point Pn8 and the point Ps8 are present on the surface of the phantom sphere 14. The coordinates of the point Pn8 are (45, 0). The coordinates of the point Ps8 are (−45, 180). The eighth axis Ax8 is tilted relative to the earth axis. The angle of the tilt is 45°.

FIG. 17 shows an eighth great circle GC8 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the eighth axis Ax8 is orthogonal. The eighth great circle GC8 is tilted relative to the equator Eq. The angle of the tilt is 45°.

For rotation about the eighth axis Ax8, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the eighth axis Ax8, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the eighth great circle GC8 is 30°. The absolute value of the central angle between the small circle C2 and the eighth great circle GC8 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the eighth axis Ax8 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd8 of the maximum peak and the order Fd8 of the maximum peak are determined. The peak value Pd8 and the order Fd8 are numeric values representing the aerodynamic characteristic during rotation about the eighth axis Ax8. In the present embodiment, the peak value Pd8 is 150.2 mm, and the order Fd8 is 37.

FIG. 18 also shows the phantom sphere 14 of the golf ball 2. FIG. 18 shows the equator Eq and the longitude line Lob having a longitude ϕ of 90°. In FIG. 18, the point (0, 90) is located in the front. In FIG. 18, reference character Ax9 represents a ninth axis. The ninth axis Ax9 passes through a point Pn9 and a point Ps9. The point Pn9 and the point Ps9 are present on the surface of the phantom sphere 14. The coordinates of the point Pn9 are (30, 0). The coordinates of the point Ps9 are (−30, 180). The ninth axis Ax9 is tilted relative to the earth axis. The angle of the tilt is 60°.

FIG. 18 shows a ninth great circle GC9 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the ninth axis Ax9 is orthogonal. The ninth great circle GC9 is tilted relative to the equator Eq. The angle of the tilt is 60°.

For rotation about the ninth axis Ax9, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the ninth axis Ax9, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the ninth great circle GC9 is 30°. The absolute value of the central angle between the small circle C2 and the ninth great circle GC9 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the ninth axis Ax9 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd9 of the maximum peak and the order Fd9 of the maximum peak are determined. The peak value Pd9 and the order Fd9 are numeric values representing the aerodynamic characteristic during rotation about the ninth axis Ax9. In the present embodiment, the peak value Pd9 is 316.4 mm, and the order Fd9 is 34.

FIG. 19 also shows the phantom sphere 14 of the golf ball 2. FIG. 19 shows the equator Eq and the longitude line Lob having a longitude ϕ of 90°. In FIG. 19, the point (0, 90) is located in the front. In FIG. 19, reference character Ax10 represents a tenth axis. The tenth axis Ax10 passes through a point Pn10 and a point Ps10. The point Pn10 and the point Ps10 are present on the surface of the phantom sphere 14. The coordinates of the point Pn10 are (15, 0). The coordinates of the point Ps10 are (−15, 180). The tenth axis Ax10 is tilted relative to the earth axis. The angle of the tilt is 75°.

FIG. 19 shows a tenth great circle GC10 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the tenth axis Ax10 is orthogonal. The tenth great circle GC10 is tilted relative to the equator Eq. The angle of the tilt is 75°.

For rotation about the tenth axis Ax10, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the tenth axis Ax10, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the tenth great circle GC10 is 30°. The absolute value of the central angle between the small circle C2 and the tenth great circle GC10 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the tenth axis Ax10 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd10 of the maximum peak and the order Fd10 of the maximum peak are determined. The peak value Pd10 and the order Fd10 are numeric values representing the aerodynamic characteristic during rotation about the tenth axis Ax10. In the present embodiment, the peak value Pd10 is 190.0 mm, and the order Fd10 is 27.

FIG. 20 also shows the phantom sphere 14 of the golf ball 2. FIG. 20 shows the equator Eq and a longitude line Loc having a longitude ϕ of 180°. In FIG. 20, a point (0, 180) is located in the front. In FIG. 20, reference character Ax11 represents an eleventh axis. The eleventh axis Ax11 passes through a point Pn11 and a point Ps11. The point Pn11 and the point Ps11 are present on the surface of the phantom sphere 14. The coordinates of the point Pn11 are (75, 90). The coordinates of the point Ps11 are (−75, 270). The eleventh axis Ax11 is tilted relative to the earth axis. The angle of the tilt is 15°.

FIG. 20 shows an eleventh great circle GC11 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the eleventh axis Ax11 is orthogonal. The eleventh great circle GC11 is tilted relative to the equator Eq. The angle of the tilt is 15°.

For rotation about the eleventh axis Ax11, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the eleventh axis Ax11, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the eleventh great circle GC11 is 30°. The absolute value of the central angle between the small circle C2 and the eleventh great circle GC11 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the eleventh axis Ax11 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd11 of the maximum peak and the order Fd11 of the maximum peak are determined. The peak value Pd11 and the order Fd11 are numeric values representing the aerodynamic characteristic during rotation about the eleventh axis Ax11. In the present embodiment, the peak value Pd11 is 270.2 mm, and the order Fd11 is 33.

FIG. 21 also shows the phantom sphere 14 of the golf ball 2. FIG. 21 shows the equator Eq and the longitude line Loc having a longitude ϕ of 180°. In FIG. 21, the point (0, 180) is located in the front. In FIG. 21, reference character Ax12 represents a twelfth axis. The twelfth axis Ax12 passes through a point Pn12 and a point Ps12. The point Pn12 and the point Ps12 are present on the surface of the phantom sphere 14. The coordinates of the point Pn12 are (60, 90). The coordinates of the point Ps12 are (−60, 270). The twelfth axis Ax12 is tilted relative to the earth axis. The angle of the tilt is 30°.

FIG. 21 shows a twelfth great circle GC12 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the twelfth axis Ax12 is orthogonal. The twelfth great circle GC12 is tilted relative to the equator Eq. The angle of the tilt is 30°.

For rotation about the twelfth axis Ax12, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the twelfth axis Ax12, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the twelfth great circle GC12 is 30°. The absolute value of the central angle between the small circle C2 and the twelfth great circle GC12 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the twelfth axis Ax12 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd12 of the maximum peak and the order Fd12 of the maximum peak are determined. The peak value Pd12 and the order Fd12 are numeric values representing the aerodynamic characteristic during rotation about the twelfth axis Ax12. In the present embodiment, the peak value Pd12 is 177.9 mm, and the order Fd12 is 37.

FIG. 22 also shows the phantom sphere 14 of the golf ball 2. FIG. 22 shows the equator Eq and the longitude line Loc having a longitude ϕ of 180°. In FIG. 22, the point (0, 180) is located in the front. In FIG. 22, reference character Ax13 represents a thirteenth axis. The thirteenth axis Ax13 passes through a point Pn13 and a point Ps13. The point Pn13 and the point Ps13 are present on the surface of the phantom sphere 14. The coordinates of the point Pn13 are (45, 90). The coordinates of the point Ps13 are (−45, 270). The thirteenth axis Ax13 is tilted relative to the earth axis. The angle of the tilt is 45°.

FIG. 22 shows a thirteenth great circle GC13 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the thirteenth axis Ax13 is orthogonal. The thirteenth great circle GC13 is tilted relative to the equator Eq. The angle of the tilt is 45°.

For rotation about the thirteenth axis Ax13, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the thirteenth axis Ax13, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the thirteenth great circle GC13 is 30°. The absolute value of the central angle between the small circle C2 and the thirteenth great circle GC13 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the thirteenth axis Ax13 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd13 of the maximum peak and the order Fd13 of the maximum peak are determined. The peak value Pd13 and the order Fd13 are numeric values representing the aerodynamic characteristic during rotation about the thirteenth axis Ax13. In the present embodiment, the peak value Pd13 is 150.2 mm, and the order Fd13 is 37.

FIG. 23 also shows the phantom sphere 14 of the golf ball 2. FIG. 23 shows the equator Eq and the longitude line Loc having a longitude ϕ of 180°. In FIG. 23, the point (0, 180) is located in the front. In FIG. 23, reference character Ax14 represents a fourteenth axis. The fourteenth axis Ax14 passes through a point Pn14 and a point Ps14. The point Pn14 and the point Ps14 are present on the surface of the phantom sphere 14. The coordinates of the point Pn14 are (30, 90). The coordinates of the point Ps14 are (−30, 270). The fourteenth axis Ax14 is tilted relative to the earth axis. The angle of the tilt is 60°.

FIG. 23 shows a fourteenth great circle GC14 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the fourteenth axis Ax14 is orthogonal. The fourteenth great circle GC14 is tilted relative to the equator Eq. The angle of the tilt is 60°.

For rotation about the fourteenth axis Ax14, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the fourteenth axis Ax14, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the fourteenth great circle GC14 is 30°. The absolute value of the central angle between the small circle C2 and the fourteenth great circle GC14 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the fourteenth axis Ax14 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd14 of the maximum peak and the order Fd14 of the maximum peak are determined. The peak value Pd14 and the order Fd14 are numeric values representing the aerodynamic characteristic during rotation about the fourteenth axis Ax14. In the present embodiment, the peak value Pd14 is 316.4 mm, and the order Fd14 is 34.

FIG. 24 also shows the phantom sphere 14 of the golf ball 2. FIG. 24 shows the equator Eq and the longitude line Loc having a longitude ϕ of 180°. In FIG. 24, the point (0, 180) is located in the front. In FIG. 24, reference character Ax15 represents a fifteenth axis. The fifteenth axis Ax15 passes through a point Pn15 and a point Ps15. The point Pn15 and the point Ps15 are present on the surface of the phantom sphere 14. The coordinates of the point Pn15 are (15, 90). The coordinates of the point Ps15 are (−15, 270). The fifteenth axis Ax15 is tilted relative to the earth axis. The angle of the tilt is 75°.

FIG. 24 shows a fifteenth great circle GC15 that is present on the surface of the phantom sphere 14 of the golf ball 2 and to which the fifteenth axis Ax15 is orthogonal. The fifteenth great circle GC15 is tilted relative to the equator Eq. The angle of the tilt is 75°.

For rotation about the fifteenth axis Ax15, an aerodynamic characteristic is evaluated by the same method as that for rotation about the first axis Ax1. Specifically, for rotation about the fifteenth axis Ax15, two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the fifteenth great circle GC15 is 30°. The absolute value of the central angle between the small circle C2 and the fifteenth great circle GC15 is also 30°. In the region, of the surface of the golf ball 2, sandwiched between these small circles, 1440 total lengths L2 are calculated. In other words, a data constellation for the fifteenth axis Ax15 is calculated. Fourier transformation is performed on this data constellation, thereby obtaining a transformed data constellation. From a graph plotting the transformed data constellation, the peak value Pd15 of the maximum peak and the order Fd15 of the maximum peak are determined. The peak value Pd15 and the order Fd15 are numeric values representing the aerodynamic characteristic during rotation about the fifteenth axis Ax15. In the present embodiment, the peak value Pd15 is 190.0 mm, and the order Fd15 is 27.

In this evaluation method, the steps (a) to (h) are executed for each of 15 axes Ax that are

(1) the first axis Ax1 passing through the point Pn1 the coordinates of which are (75, 270) and the point Ps1 the coordinates of which are (−75, 90),

(2) the second axis Ax2 passing through the point Pn2 the coordinates of which are (60, 270) and the point Ps2 the coordinates of which are (−60, 90),

(3) the third axis Ax3 passing through the point Pn3 the coordinates of which are (45, 270) and the point Ps3 the coordinates of which are (−45, 90),

(4) the fourth axis Ax4 passing through the point Pn4 the coordinates of which are (30, 270) and the point Ps4 the coordinates of which are (−30, 90),

(5) the fifth axis Ax5 passing through the point Pn5 the coordinates of which are (15, 270) and the point Ps5 the coordinates of which are (−15, 90),

(6) the sixth axis Ax6 passing through the point Pn6 the coordinates of which are (75, 0) and the point Ps6 the coordinates of which are (−75, 180),

(7) the seventh axis Ax1 passing through the point Pn7 the coordinates of which are (60, 0) and the point Ps7 the coordinates of which are (−60, 180),

(8) the eighth axis Ax8 passing through the point Pn8 the coordinates of which are (45, 0) and the point Ps8 the coordinates of which are (−45, 180),

(9) the ninth axis Ax9 passing through the point Pn9 the coordinates of which are (30, 0) and the point Ps9 the coordinates of which are (−30, 180),

(10) the tenth axis Ax10 passing through the point Pn10 the coordinates of which are (15, 0) and the point Ps10 the coordinates of which are (−15, 180),

(11) the eleventh axis Ax11 passing through the point Pn11 the coordinates of which are (75, 90) and the point Ps11 the coordinates of which are (−75, 270),

(12) the twelfth axis Ax12 passing through the point Pn12 the coordinates of which are (60, 90) and the point Ps12 the coordinates of which are (−60, 270),

(13) the thirteenth axis Ax13 passing through the point Pn13 the coordinates of which are (45, 90) and the point Ps13 the coordinates of which are (−45, 270),

(14) the fourteenth axis Ax14 passing through the point Pn14 the coordinates of which are (30, 90) and the point Ps14 the coordinates of which are (−30, 270), and

(15) the fifteenth axis Ax15 passing through the point Pn15 the coordinates of which are (15, 90) and the point Ps15 the coordinates of which are (−15, 270). Accordingly, 15 peak values (Pd1 to Pd15) and 15 orders (Fd1 to Fd15) are calculated.

The minimums among the 15 peak values (Pd1 to Pd15) are Pd3, Pd8, and Pd13. The minimum value of the peak value Pd is 150.2 mm. According to the findings by the present inventor, the minimum value is preferably not less than 95 mm. In the golf ball 2 in which the minimum value is not less than 95 mm, a sufficient dimple effect can be achieved even during rotation about any axis Ax. The flight distance of the golf ball 2 is large. In this respect, the minimum value of the peak value Pd is more preferably not less than 120 mm and particularly preferably not less than 140 mm.

The maximums among the 15 peak values (Pd1 to Pd15) are Pd4, Pd9, and Pd14. The maximum value of the peak value Pd is 316.4 mm. According to the findings by the present inventor, the maximum value is preferably not greater than 500 mm. The golf ball 2 in which the maximum value is not greater than 500 mm has an excellent aerodynamic characteristic. The flight distance of the golf ball 2 is large. In this respect, the maximum value of the peak value Pd is more preferably not greater than 400 mm and particularly preferably not greater than 330 mm.

The average of the 15 peak values (Pd1 to Pd15) is preferably not less than 200 mm. The golf ball 2 in which the average is not less than 200 mm has an excellent aerodynamic characteristic. The flight distance of the golf ball 2 is large. In this respect, the average is more preferably not less than 210 mm and particularly preferably not less than 220 mm. The average is preferably not greater than 300 mm and particularly preferably not greater than 230 mm. In the present embodiment, the average is 220.9 mm.

The minimums among the 15 orders (Fd1 to Fd15) are Fd5, Fd10, and Fd15. The minimum value of the order Fd is 27. According to the findings by the present inventor, the minimum value is preferably not less than 27. The golf ball 2 in which the minimum value is not less than 27 has an excellent aerodynamic characteristic. The flight distance of the golf ball 2 is large.

The maximums among the 15 orders (Fd1 to Fd15) are Fd2, Fd3, Fd7, Fd8, Fd12, and Fd13. The maximum value of the order Fd is 37. According to the findings by the present inventor, the maximum value is preferably not greater than 37. The golf ball 2 in which the maximum value is not greater than 37 has an excellent aerodynamic characteristic. The flight distance of the golf ball 2 is large.

The average of the 15 orders (Fd1 to Fd15) is preferably not less than 30 and not greater than 34. The golf ball 2 in which the average falls within this range has an excellent aerodynamic characteristic. The flight distance of the golf ball 2 is large. In the present embodiment, the average is 33.6.

In this method, the golf ball 2 is evaluated by the 15 peak values Pd and the 15 orders Fd based on the 15 axes Ax. By this method, the aerodynamic characteristic of the golf ball 2 can be objectively evaluated.

EXAMPLES
Example 1

A rubber composition was obtained by kneading 100 parts by weight of a high-cis polybutadiene (trade name “BR-730”, manufactured by JSR Corporation), 22.5 parts by weight of zinc diacrylate, 5 parts by weight of zinc oxide, 5 parts by weight of barium sulfate, 0.5 parts by weight of diphenyl disulfide, and 0.6 parts by weight of dicumyl peroxide. This rubber composition was placed into a mold including upper and lower mold halves each having a hemispherical cavity, and heated at 170° C. for 18 minutes to obtain a core with a diameter of 38.5 mm.

A resin composition was obtained by kneading 50 parts by weight of an ionomer resin (trade name “Himilan 1605”, manufactured by Du Pont-MITSUI POLYCHEMICALS Co., Ltd.), 50 parts by weight of another ionomer resin (trade name “Himilan AM7329”, manufactured by Du Pont-MITSUI POLYCHEMICALS Co., Ltd.), and 4 parts by weight of titanium dioxide with a twin-screw kneading extruder. The core was covered with this resin composition by injection molding to form a mid layer with a thickness of 1.6 mm.

A paint composition (trade name “POLIN 750LE”, manufactured by SHINTO PAINT CO., LTD.) including a two-component curing type epoxy resin as a base polymer was prepared. The base material liquid of this paint composition includes 30 parts by weight of a bisphenol A type solid epoxy resin and 70 parts by weight of a solvent. The curing agent liquid of this paint composition includes 40 parts by weight of a modified polyamide amine, 55 parts by weight of a solvent, and 5 parts by weight of titanium dioxide. The weight ratio of the base material liquid to the curing agent liquid is 1/1. This paint composition was applied to the surface of the mid layer with a spray gun, and kept at 23° C. for 6 hours to obtain a reinforcing layer with a thickness of 10 μm.

A resin composition was obtained by kneading 100 parts by weight of a thermoplastic polyurethane elastomer (trade name “Elastollan XNY85A”, manufactured by BASF Japan Ltd.) and 4 parts by weight of titanium dioxide with a twin-screw kneading extruder. Half shells were obtained from this resin composition by compression molding. The sphere consisting of the core, the mid layer, and the reinforcing layer was covered with two of these half shells. These half shells and the sphere were placed into a final mold that includes upper and lower mold halves each having a hemispherical cavity and having a large number of pimples on its cavity face, and a cover was obtained by compression molding. The thickness of the cover was 0.5 mm. Dimples having a shape that is the inverted shape of the pimples were formed on the cover. A clear paint including a two-component curing type polyurethane as a base material was applied to this cover to obtain a golf ball of Example 1 with a diameter of about 42.7 mm and a weight of about 45.6 g. The dimple pattern of the golf ball is shown in FIGS. 2 and 3. The specifications of the dimples of the golf ball are shown in Table 1 below. The peak values (Pd1 to Pd15) and the orders (Fd1 to Fd15) of the golf ball are shown in Table 3 below.

Examples 2 and 3 and Comparative Examples 1 to 4

Golf balls of Examples 2 and 3 and Comparative Examples 1 to 4 were obtained in the same manner as Example 1, except the specifications of the dimples were as shown in Tables 1 and 2 below. The peak values (Pd1 to Pd15) and the orders (Fd1 to Fd15) of each golf ball are shown in Table 3 or 4 below.

[Flight Test]

A driver with a head made of a titanium alloy (trade name “SRIXON Z-TX”, manufactured by DUNLOP SPORTS CO. LTD., shaft hardness: X, loft angle: 8.5°) was attached to a swing machine manufactured by Golf Laboratories, Inc. A golf ball was put on a tee. The golf ball was hit under the conditions of a head speed of 50 m/sec, a launch angle of about 10°, and a backspin rate of about 2500 rpm, and the distance from the launch point to the stop point was measured. During the test, the weather was almost windless. The average value of data obtained by 100 measurements is shown in Tables 5 and 6 below. The orientation of the golf ball when the golf ball was put on the tee was randomly determined. Therefore, the axis for the backspin was randomly selected.

TABLE 1

Specifications of Dimples

Dm
Dp2
Dp1
CR
V

Number
(mm)
(mm)
(mm)
(mm)
(mm³)

Ex.
A
60
4.40
0.138
0.2506
17.61
1.051

1
B
158
4.30
0.137
0.2445
16.94
0.996

C
72
4.15
0.134
0.2341
16.13
0.908

D
36
3.90
0.123
0.2114
15.52
0.736

E
12
3.00
0.122
0.1743
9.28
0.432

Ex.
A
30
4.60
0.135
0.2581
19.66
1.123

2
B
66
4.50
0.135
0.2528
18.82
1.075

C
84
4.40
0.135
0.2476
17.99
1.028

D
30
4.30
0.135
0.2425
17.19
0.982

E
48
4.20
0.135
0.2376
16.40
0.936

F
60
4.00
0.135
0.2280
14.88
0.850

G
6
2.70
0.135
0.1773
6.82
0.388

Ex.
A
6
4.70
0.135
0.2635
20.52
1.172

3
B
126
4.40
0.135
0.2476
17.99
1.028

C
122
4.30
0.135
0.2425
17.19
0.982

D
6
4.15
0.135
0.2351
16.01
0.914

E
66
3.90
0.135
0.2234
14.15
0.808

F
12
3.00
0.135
0.1873
8.40
0.478

TABLE 2

Specifications of Dimples

Dm
Dp2
Dp1
CR
V

Number
(mm)
(mm)
(mm)
(mm)
(mm³)

Com.
A
30
4.60
0.135
0.2581
19.66
1.123

Ex.
B
68
4.50
0.135
0.2528
18.82
1.075

1
C
92
4.40
0.135
0.2476
17.99
1.028

D
74
4.30
0.135
0.2425
17.19
0.982

E
38
4.15
0.135
0.2351
16.01
0.914

F
14
3.85
0.135
0.2211
13.79
0.787

G
8
3.60
0.135
0.2103
12.07
0.688

Com.
A
156
4.91
0.135
0.2766
22.39
2.609

Ex.
B
98
4.65
0.135
0.2620
20.09
2.217

2
C
12
3.00
0.135
0.1878
8.40
0.663

Com.
A
70
4.10
0.135
0.2336
15.63
1.538

Ex.
B
30
3.90
0.135
0.2242
14.15
1.336

3
C
120
3.80
0.135
0.2197
13.44
1.243

D
170
3.70
0.135
0.2153
12.74
1.155

E
20
3.60
0.135
0.2110
12.07
1.072

F
12
2.50
0.135
0.1716
5.85
0.422

Com.
A
30
4.60
0.135
0.2581
19.66
1.123

Ex.
B
54
4.50
0.135
0.2528
18.82
1.075

4
C
72
4.30
0.135
0.2425
17.19
0.982

D
54
4.20
0.135
0.2376
16.40
0.936

E
108
4.00
0.135
0.2280
14.88
0.850

F
12
2.70
0.135
0.1773
6.82
0.388

TABLE 3

Aerodynamic Characteristic

Example 1
Example 2
Example 3

Peak
Pd1
270.2
143.5
195.1

value
Pd2
177.9
195.4
153.1

Pd3
150.2
147.0
147.8

Pd4
316.4
322.0
322.0

Pd5
190.0
152.2
152.2

Pd6
270.2
143.5
195.1

Pd7
177.9
195.4
153.1

Pd8
150.2
147.0
147.8

Pd9
316.4
322.0
322.0

Pd10
190.0
152.2
152.2

Pd11
270.2
143.5
195.1

Pd12
177.9
195.4
153.1

Pd13
150.2
147.0
147.8

Pd14
316.4
322.0
322.0

Pd15
190.0
152.2
152.2

Order
Fd1
33
31
31

Fd2
37
31
31

Fd3
37
33
33

Fd4
34
36
36

Fd5
27
29
29

Fd6
33
31
31

Fd7
37
31
31

Fd8
37
33
33

Fd9
34
36
36

Fd10
27
29
29

Fd11
33
31
31

Fd12
37
31
31

Fd13
37
33
33

Fd14
34
36
36

Fd15
27
29
29

TABLE 4

Aerodynamic Characteristic

Compa.
Compa.
Compa.
Compa.

Example 1
Example 2
Example 3
Example 4

Peak
Pd1
116.0
245.2
181.3
206.0

value
Pd2
93.2
204.6
117.2
302.6

Pd3
174.6
317.5
87.3
190.4

Pd4
440.9
336.5
296.0
420.1

Pd5
151.1
134.7
146.3
112.6

Pd6
207.7
147.7
225.3
196.5

Pd7
177.0
230.7
329.8
155.2

Pd8
165.9
458.1
347.1
281.5

Pd9
257.7
778.5
259.2
358.3

Pd10
157.5
244.8
165.7
89.7

Pd11
187.0
524.8
181.3
206.0

Pd12
146.3
284.0
117.2
302.6

Pd13
263.3
184.0
87.3
190.4

Pd14
383.1
282.7
296.0
420.1

Pd15
146.1
185.4
146.3
112.6

Order
Fd1
31
25
35
31

Fd2
33
29
37
33

Fd3
30
29
35
29

Fd4
34
31
41
31

Fd5
32
31
35
29

Fd6
30
33
39
35

Fd7
33
31
37
37

Fd8
34
29
39
31

Fd9
34
31
41
33

Fd10
30
29
35
33

Fd11
31
29
35
31

Fd12
32
23
37
33

Fd13
32
29
35
29

Fd14
34
31
41
31

Fd15
32
31
35
29

TABLE 5

Results of Evaluation

Example 1
Example 2
Example 3

Front view
FIG. 2
FIG. 25
FIG. 27

Plan view
FIG. 3
FIG. 26
FIG. 28

Total number N
338
324
338

Total volume
564.6
579.0
574.3

TV (mm³)

Peak value
Max
316.4
322.0
322.0

Pd
Min
150.2
143.5
147.8

Average
220.9
192.0
194.0

Order
Max
37
36
36

Fd
Min
27
29
29

Average
33.6
32.0
32.0

Flight
263.5
262.5
263.0

distance (m)

TABLE 6

Results of Evaluation

Compa.
Compa.
Compa.
Compa.

Example 1
Example 2
Example 3
Example 4

Front view
FIG. 29
FIG. 31
FIG. 33
FIG. 35

Plan view
FIG. 30
FIG. 32
FIG. 34
FIG. 36

Total number N
324
266
422
330

Total volume
589.7
632.2
519.8
571.3

TV (mm³)

Peak value
Max
440.9
778.5
347.1
420.1

Pd
Min
93.2
134.7
87.3
89.7

Average
204.5
304.0
198.9
236.3

Order
Max
34
33
41
37

Fd
Min
30
23
34
29

Average
32.1
29.4
37.1
31.7

Flight
261.4
261.2
261.0
261.0

distance (m)

As shown in Tables 5 and 6, the golf ball of each Example has excellent flight performance. From the results of evaluation, advantages of the present invention are clear.

The aforementioned dimple pattern is applicable to golf balls having various structures such as a one-piece golf ball, a two-piece golf ball, a four-piece golf ball, a five-piece golf ball, a six-piece golf ball, a thread-wound golf ball, and the like in addition to a three-piece golf ball. The above descriptions are merely illustrative examples, and various modifications can be made without departing from the principles of the present invention.

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Priority Claims (1)