This application claims priority on Patent Application No. 2010-148473 filed in JAPAN on Jun. 30, 2010. The entire contents of this Japanese Patent Application are hereby incorporated by reference.
1. Field of the Invention
The present invention relates to golf balls. Specifically, the present invention relates to designing methods for dimple patterns of golf balls.
2. Description of the Related Art
Golf balls have a large number of dimples on the surface thereof. The dimples disturb the air flow around the golf ball during flight to cause turbulent flow separation. By causing the turbulent flow separation, separation points of the air from the golf ball shift backwards leading to a reduction of drag. The turbulent flow separation promotes the displacement between the separation point on the upper side and the separation point on the lower side of the golfball, 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”.
Generally, a golf ball is formed by a mold having upper and lower mold halves. Since a molding material (e.g. a synthetic resin) leaks out from the parting face between the upper and lower mold halves, a flash is generated along the equator portion on the surface of the golf ball. The flash is generated along the parting line. The flash is ground and removed with a whetstone or the like. Removal of a flash generated inside the dimple is difficult. In order to facilitate the removal of the flash, no dimple is formed on the equator. In other words, no pimple is provided on the parting face of the mold. A great circle path is formed on the seam of a golf ball obtained by using this mold. The great circle path agrees with the equator. When a flash is removed, the land near the equator may be removed together with the flash. Due to this removal, dimples are deformed. In addition, the dimples near the equator tend to be orderly arranged.
Thus, the equator has the following characteristics:
(1) a great circle path exists;
(2) the dimples near the equator may be deformed; and
(3) the dimples near the equator tend to be orderly arranged.
On the surface of the golf ball, the region near the equator is a unique region.
Rotation in which the rotational axis of backspin passes through both poles is referred to as PH rotation. Meanwhile, rotation of which the rotational axis is orthogonal to the rotational axis of PH rotation is referred to as POP rotation. As described above, the region near the equator is a unique region. During PH rotation, a part where the greatest circumferential speed of the backspin is attained agrees with the equator. Thus, a sufficient dimple effect is not obtained. The dimple effect during PH rotation is less than the dimple effect during POP rotation. The difference between these dimple effects impairs the aerodynamic symmetry of a golf ball. Other than a shot at a teeing ground, golf players cannot decide a hitting place of a golf ball. Thus, the flight distance of a golf ball with inferior aerodynamic symmetry is variable. Golf players have difficulty in landing this golf ball at an intended point.
The United States Golf Association (USGA) has established the rules about aerodynamic symmetries of golf balls. A golf ball having a large difference between the trajectory during PH rotation and the trajectory during POP rotation does not conform to the rules. The golf ball cannot be used in golf tournaments.
JP-S61-284264 discloses a golf ball in which the dimples near the seam are greater in volume than the dimples near the poles. This volume difference contributes to eliminating the aerodynamic asymmetry caused by the uniqueness of the region near the equator. A similar golf ball is also disclosed in JP2000-93556.
JP-H9-164223 discloses a method in which a large number of dimples are randomly arranged by a computer. A golf ball having randomly arranged dimples has excellent aerodynamic symmetry. A similar method is also disclosed in JP2000-189542.
The golf ball disclosed in JP-S61-284264 eliminates, by the volume difference of dimples, the disadvantage caused by the dimple pattern. The disadvantage caused by the dimple pattern is eliminated not by modification of the dimple pattern. In the golf ball, the potential of the dimple pattern is sacrificed. The flight distance of the golf ball is insufficient. Similarly, the flight distance of the golf ball disclosed in JP2000-93556 is also insufficient.
In the method disclosed in JP-H9-164223, trials and errors are required for deciding a pattern, and it takes a long period of time for this decision. In this method, since the pattern depends on the computer, an intention of a designer is unlikely to be reflected in the pattern. In addition, the pattern obtained by this method has a wide variety of dimples. Thus, time and labor are required for producing a mold. The method disclosed in JP2000-189542 also has similar problems.
An object of the present invention is to provide a designing method by which a pattern having excellent aerodynamic symmetry can be easily obtained.
A designing method for a dimple pattern of a golf ball according to the present invention includes the steps of:
(1) dividing a surface of a phantom sphere of the golf ball into a plurality of units by division lines obtained by projecting edge lines of a regular polyhedron inscribed in the phantom sphere, on the surface of the phantom sphere;
(2) obtaining a base pattern by randomly arranging a plurality of dimples in one unit such that the dimples do not overlap each other; and
(3) developing the base pattern over other units such that patterns of two adjacent units are not mirror-symmetrical to each other. By the method, a dimple pattern can be easily designed. A golf ball having the dimple pattern has excellent aerodynamic symmetry.
Preferably, the designing method further comprises the step of
(4-1) correcting a position of a dimple in the vicinity of a boundary between two adjacent units such that a distance between two adjacent dimples is reduced.
Preferably, the designing method further comprises the step of
(4-2) correcting a position of a dimple in the vicinity of a boundary between two adjacent units such that three or more dimples are not arranged along a line.
Preferably, the regular polyhedron is a regular dodecahedron, and each unit is a spherical regular pentagon. The spherical regular pentagon is obtained by dividing the surface of the phantom sphere by division lines obtained by projecting edge lines of the regular dodecahedron on the surface of the phantom sphere.
The regular polyhedron may be a regular icosahedron, and each unit may be a pair of two adjacent spherical regular triangles. Each spherical regular triangle is obtained by dividing the surface of the phantom sphere by division lines obtained by projecting edge lines of the regular icosahedron on the surface of the phantom sphere.
In a golf ball having a dimple pattern designed by the method according to the present invention, a ratio of a total area of all dimples to a surface area of a phantom sphere of the golf ball is preferably equal to or greater than 75% but equal to or less than 85%. Preferably, the golf ball does not have any great circle that does not intersect any dimple.
Hereinafter, the present invention will be described in detail based on preferred embodiments with reference to the accompanying drawings.
A golf ball 2 shown in
The golf ball 2 has a diameter of 40 mm or greater but 45 mm or less. From the standpoint of conformity to the rules established by the United States Golf Association (USGA), the diameter is more preferably equal to or greater than 42.67 mm. In light of suppression of air resistance, the diameter is more preferably equal to or less than 44 mm and particularly preferably equal to or less than 42.80 mm. The golf ball 2 has a weight of 40 g or greater but 50 g or less. In light of attainment of great inertia, the weight is more preferably equal to or greater than 44 g and particularly preferably equal to or greater than 45.00 g. From the standpoint of conformity to the rules established by the USGA, the weight is more preferably equal to or less than 45.93 g.
The core 4 is formed by crosslinking a rubber composition. Examples of base rubbers for use in the rubber composition include polybutadienes, polyisoprenes, styrene-butadiene copolymers, ethylene-propylene-diene copolymers and natural rubbers. Two or more of these rubbers may be used in combination. In light of resilience performance, polybutadienes are preferred, and in particular, high-cis polybutadienes are preferred.
In order to crosslink the core 4, a co-crosslinking agent can be used. Examples of preferable co-crosslinking agents in light of resilience performance include zinc acrylate, magnesium acrylate, zinc methacrylate and magnesium methacrylate. The rubber composition includes an organic peroxide together with a co-crosslinking agent. Examples of suitable organic peroxides include dicumyl peroxide, 1,1-bis(t-butylperoxy)-3,3,5-trimethylcyclohexane, 2,5-dimethyl-2,5-di(t-butylperoxy)hexane and di-t-butyl peroxide.
According to need, various additives such as a sulfur compound, a filler, an anti-aging agent, a coloring agent, a plasticizer, a dispersant and the like are included in the rubber composition of the core 4 in an adequate amount. Crosslinked rubber powder or synthetic resin powder may be also included in the rubber composition.
The diameter of the core 4 is equal to or greater than 30.0 mm and particularly equal to or greater than 38.0 mm. The diameter of the core 4 is equal to or less than 42.0 mm and particularly equal to or less than 41.5 mm. The core 4 may be formed with two or more layers.
A suitable polymer for the cover 6 is an ionomer resin. Examples of preferable ionomer resins include binary copolymers formed with an α-olefin and an α,β-unsaturated carboxylic acid having 3 to 8 carbon atoms. Examples of other preferable ionomer resins include ternary copolymers formed with: an α-olefin; an α,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.
Other polymers may be used instead of or together with an ionomer resin. Examples of the other polymers include thermoplastic polyurethane elastomers, styrene block-containing thermoplastic elastomers, thermoplastic polyamide elastomers, thermoplastic polyester elastomers and thermoplastic polyolefin elastomers.
According to need, a coloring agent such as titanium dioxide, a filler such as barium sulfate, a dispersant, an antioxidant, an ultraviolet absorber, a light stabilizer, a fluorescent material, a fluorescent brightener and the like are included in the cover 6 at an adequate amount. For the purpose of adjusting specific gravity, powder of a metal with a high specific gravity such as tungsten, molybdenum and the like may be included in the cover 6.
The thickness of the cover 6 is equal to or greater than 0.3 mm and particularly equal to or greater than 0.5 mm. The thickness of the cover 6 is equal to or less than 2.5 mm and particularly equal to or less than 2.2 mm. The specific gravity of the cover 6 is equal to or greater than 0.90 and particularly equal to or greater than 0.95. The specific gravity of the cover 6 is equal to or less than 1.10 and particularly equal to or less than 1.05. The cover 6 may be formed with two or more layers.
In
By these division lines 14, the surface of the phantom sphere 12 is divided into 12 units U. Each unit U is a spherical regular pentagon. In the present specification, the spherical regular pentagon is a curved surface existing on the surface of the phantom sphere 12. The edges of the spherical regular pentagon are five circular arcs.
In a designing method according to the present invention, a base pattern is designed in one unit U.
Since the dimples 8 are randomly arranged, the base pattern does not have line symmetry in a plan view. In other words, the pattern does not have an axis of line symmetry. Since the dimples 8 are randomly arranged, the base pattern does not have rotational symmetry. The rotational symmetry means a state where when the pattern is rotated about the center of gravity of the unit U by a rotation angle less than 360°, the pattern overlaps the pattern before the rotation.
The base pattern is developed over the other units U. When developed, the base pattern may be transferred to the other units U without changing the base pattern. When developed, a pattern obtained by mirror-inverting the base pattern may be transferred to the other units U. The pattern obtained by mirror-inverting the base pattern is mirror-symmetrical to the base pattern. Even in the pattern obtained by mirror-inverting the base pattern, the dimples 8 are randomly arranged. In
In light of aerodynamic symmetry of the golf ball 2, it is not preferred if the patterns of adjacent units U are mirror-symmetrical to each other. When the patterns of adjacent units U are mirror-symmetrical to each other, correction is performed for either one of the units U.
Such development is also performed on the other units U. A pattern obtained by repeating the mirror inversion two or more times may be transferred to the other units U. As a result of completion of the transfer to all the units U, a pattern having 240 dimples A and 84 dimples B is obtained.
The dimples 8 are randomly arranged in each unit U, and the pattern of one unit U and the pattern of another unit U are not mirror-symmetrical to each other. Thus, the golf ball 2 has excellent aerodynamic symmetry. In the designing method, a pattern having excellent aerodynamic symmetry can be obtained easily in a short time. In the designing method, the designer decides the diameter and the number of the types of the dimples 8. Thus, a dimple pattern in which an intention of the designer is reflected can be obtained.
In the golf ball 2, the number of pairs of adjacent units is 30. Ideally, a state where the pattern of one unit U and the pattern of the other unit U are not mirror-symmetrical to each other is achieved in all the pairs of the adjacent units. In some of the pairs of the adjacent units, the pattern of one unit U and the pattern of the other unit U may be mirror-symmetrical to each other. In light of aerodynamic symmetry of the golf ball 2, the ratio Pn of the number of pairs of adjacent units that are not mirror-symmetrical to each other, to the total number of the pairs of the adjacent units is preferably equal to or greater than 50%, more preferably equal to or greater than 65%, and particularly preferably equal to or greater than 80%. In the dimple pattern shown in
The number of the units U in one golf ball 2 is preferably equal to or greater than 8 and more preferably equal to or greater than 10. The number of the units U is preferably equal to or less than 12.
The area S of the dimple 8 is the area of a region surrounded by the contour line when the center of the golf ball 2 is viewed at infinity. In the case of a circular dimple 8, the area S is calculated by the following mathematical formula.
S=(Di/2)2*π
In the golf ball 2 shown in
In the present invention, the ratio of the sum of the areas S of all the dimples 8 to the surface area of the phantom sphere 12 is referred to as an occupation ratio. From the standpoint that a sufficient dimple effect is achieved, the occupation ratio is preferably equal to or greater than 75%, more preferably equal to or greater than 78%, and particularly preferably equal to or greater than 80%. The occupation ratio is preferably equal to or less than 85%. In the golf ball 2 shown in
In light of suppression of rising of the golf ball 2 during flight, the depth of the dimple 8 is preferably equal to or greater than 0.05 mm, more preferably equal to or greater than 0.08 mm, and particularly preferably equal to or greater than 0.10 mm. In light of suppression of dropping of the golf ball 2 during flight, the depth of the dimple 8 is preferably equal to or less than 0.60 mm, more preferably equal to or less than 0.45 mm, and particularly preferably equal to or less than 0.40 mm. The depth is the distance between the tangent line TA and the deepest part of the dimple 8.
In the present invention, the term “dimple volume” means the volume of a part surrounded by the surface of the dimple 8 and a plane that includes the contour of the dimple 8. In light of suppression of rising of the golf ball 2 during flight, the sum of the volumes (total volume) of all the dimples 8 is preferably equal to or greater than 240 mm3, more preferably equal to or greater than 260 mm3, and particularly preferably equal to or greater than 280 mm3. In light of suppression of dropping of the golf ball 2 during flight, the total volume is preferably equal to or less than 400 mm3, more preferably equal to or less than 380 mm3, and particularly preferably equal to or less than 360 mm3.
From the standpoint that a sufficient occupation ratio can be achieved, the total number of the dimples 8 is preferably equal to or greater than 200, more preferably equal to or greater than 250, and particularly preferably equal to or greater than 300. From the standpoint that the individual dimples 8 can have a sufficient diameter, the total number is preferably equal to or less than 500, more preferably equal to or less than 450, and particularly preferably equal to or less than 400.
The golf ball 2 does not have any great circle that does not intersect any dimple 8. The golf ball 2 does not have any great circle path. The golf ball 2 has excellent aerodynamic symmetry.
Hereinafter, an evaluation method for the aerodynamic characteristic of the golf ball 2 will be described.
There is assumed a great circle GC that exists on the surface of the phantom sphere 12 of the golf ball 2 and is orthogonal to the first rotation axis Ax1. The circumferential speed of the great circle GC is faster than any other part of the golf ball 2 during rotation of the golf ball 2. In addition, there are assumed two small circles C1 and C2 that exist on the surface of the phantom sphere 12 of the golf ball 2 and are orthogonal to the first rotation axis Ax1.
In
The above mathematical formula is a combination of two trigonometric functions having different periods. In the above mathematical formula, an and bn are Fourier coefficients. The magnitude of each component synthesized is determined depending on these Fourier coefficients. The coefficients are represented by the following mathematical formulas, respectively.
In these mathematical formulas, N is the total number of pieces of data of the first data constellation, and Fk is the kth value in the first data constellation. The spectrum is represented by the following mathematical formula.
P
n=√{square root over (an2+bn2)}
By the Fourier transformation, a first transformed data constellation is obtained.
Moreover, a second rotation axis Ax2 orthogonal to the first rotation axis Ax1 is determined. Rotation of the golf ball 2 about the second rotation axis Ax2 is referred to as POP rotation. Similarly as for PH rotation, for POP rotation, a great circle GC and two small circles C1 and C2 are assumed. The absolute value of the central angle between the small circle C1 and the great circle GC is 30°. The absolute value of the central angle between the small circle C2 and the great circle GC is also 30°. For a region, sandwiched between the small circles C1 and C2, of the surface of the golf ball 2, 1440 total lengths L2 are calculated. In other words, a second data constellation regarding a parameter dependent on a surface shape appearing at a predetermined point moment by moment during one rotation of the golf ball 2, is calculated.
As is obvious from
There are numerous straight lines orthogonal to the first rotation axis Ax1. A straight line of which the corresponding great circle GC contains the most number of dimple 8 centers substantially located therein is set as the second rotation axis Ax2. When there are in reality a plurality of straight lines of which the corresponding great circles GC each contain the most number of dimple 8 centers substantially located therein, the peak value is calculated for each of the cases where these straight lines are set as second rotation axes Ax2. The maximum value of these peak values is the peak value Pd2.
In light of aerodynamic symmetry, the absolute value of the difference (Pd1−Pd2) is preferably equal to or less than 150 mm and particularly preferably equal to or less than 110 mm. Ideally, the difference is zero.
In light of aerodynamic symmetry, the absolute value of the difference (Fd1−Fd2) is preferably equal to or less than 10, more preferably equal to or less than 8, and particularly preferably equal to or less than 4. Ideally, the difference is zero.
By projecting the edge lines of the regular icosahedron on the surface of the phantom sphere, 20 spherical regular triangles are obtained. In the embodiment, one unit is assumed by combining two adjacent spherical regular triangles. The number of units is 10.
The base pattern is developed over the other units U. When developed, the base pattern may be transferred to the other units U without changing the base pattern. When developed, a pattern obtained by mirror-inverting the base pattern may be transferred to the other units U. A pattern obtained by repeating the mirror inversion two or more times may be transferred to the other units U. As a result of completion of the transfer to all the units U, a pattern having 240 dimples A, 50 dimples B, and 40 dimples C is obtained.
In the vicinity of the boundary between the two adjacent units U, the positions of the dimples 8 may be corrected such that three or more dimples 8 are not arranged along a line. By this correction as well, excellent flight performance of the golf ball 18 can be achieved.
The dimples 8 are randomly arranged in each unit U, and the pattern of one unit U and the pattern of another unit U are not mirror-symmetrical to each other. Thus, the golf ball 18 has excellent aerodynamic symmetry. In the designing method, a pattern having excellent aerodynamic symmetry can be obtained easily in a short time. In the designing method, the designer decides the diameter and the number of the types of the dimples 8. Thus, a dimple pattern in which an intention of the designer is reflected can be obtained.
In the golf ball 18, the number of pairs of adjacent units is 20. Ideally, a state where the pattern of one unit U and the pattern of the other unit U are not mirror-symmetrical to each other is achieved in all the pairs of the adjacent units. In some of the pairs of the adjacent units, the pattern of one unit U and the pattern of the other unit U may be mirror-symmetrical to each other. In light of aerodynamic symmetry of the golf ball 18, the ratio Pn of the number of pairs of adjacent units that are not mirror-symmetrical to each other, to the total number of the pairs of the adjacent units is preferably equal to or greater than 50%, more preferably equal to or greater than 65%, and particularly preferably equal to or greater than 80%. In the dimple pattern shown in
The units U may be obtained by projecting the edge lines of the regular octahedron inscribed in the phantom sphere, on the surface of the phantom sphere.
The base pattern of the golf ball 30 is the same as the base pattern according to Embodiment 1 shown in
The aerodynamic symmetries of golf balls according to Embodiments 1 to 3 and Comparative Examples 1 and 2 are evaluated. Prior to the evaluation, the specifications of dimples are determined as shown in Table 1 below.
umber
indicates data missing or illegible when filed
By the aforementioned method, Pd1, Pd2, Fd1 and Fd2 of each golf ball are calculated. The results are shown in Table 2 below.
As shown in Table 2, the absolute value of the difference (Pd1−Pd2) and the absolute value of the difference (Fd1−Fd2) are small in the golf balls according to Embodiments 1 to 3. This means that the golf balls according to Embodiments 1 to 3 have excellent aerodynamic symmetry.
The dimple pattern obtained by the method according to the present invention is applicable to a one-piece golf ball, a multi-piece golf ball and a thread-wound golf ball, in addition to a two-piece golf ball. The above description is merely for illustrative examples, and various modifications can be made without departing from the principles of the present invention.
Number | Date | Country | Kind |
---|---|---|---|
2010-148473 | Jun 2010 | JP | national |