WO2019140090A1 - Balle de golf polyédrique à coefficient de traînée inférieur - Google Patents

Balle de golf polyédrique à coefficient de traînée inférieur Download PDF

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Publication number
WO2019140090A1
WO2019140090A1 PCT/US2019/013052 US2019013052W WO2019140090A1 WO 2019140090 A1 WO2019140090 A1 WO 2019140090A1 US 2019013052 W US2019013052 W US 2019013052W WO 2019140090 A1 WO2019140090 A1 WO 2019140090A1
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Prior art keywords
faces
golf ball
polyhedron
sphere
edges
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PCT/US2019/013052
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English (en)
Inventor
Nikolaos Beratlis
Elias Balaras
Kyle Squires
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Nikolaos Beratlis
Elias Balaras
Kyle Squires
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Application filed by Nikolaos Beratlis, Elias Balaras, Kyle Squires filed Critical Nikolaos Beratlis
Priority to JP2020538965A priority Critical patent/JP2021510578A/ja
Priority to US16/771,676 priority patent/US20210197029A1/en
Publication of WO2019140090A1 publication Critical patent/WO2019140090A1/fr

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Classifications

    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/007—Characteristics of the ball as a whole
    • A63B37/0077—Physical properties
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/0004—Surface depressions or protrusions
    • A63B37/0006—Arrangement or layout of dimples
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/0004—Surface depressions or protrusions
    • A63B37/0007—Non-circular dimples
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/0004—Surface depressions or protrusions
    • A63B37/0018—Specified number of dimples
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/007—Characteristics of the ball as a whole
    • A63B37/0077—Physical properties
    • A63B37/008—Diameter
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/007—Characteristics of the ball as a whole
    • A63B37/0077—Physical properties
    • A63B37/0089—Coefficient of drag
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/0004—Surface depressions or protrusions
    • A63B37/0007—Non-circular dimples
    • A63B37/0009—Polygonal
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/0004—Surface depressions or protrusions
    • A63B37/00215—Volume ratio
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63B—APPARATUS FOR PHYSICAL TRAINING, GYMNASTICS, SWIMMING, CLIMBING, OR FENCING; BALL GAMES; TRAINING EQUIPMENT
    • A63B37/00—Solid balls; Rigid hollow balls; Marbles
    • A63B37/0003—Golf balls
    • A63B37/007—Characteristics of the ball as a whole
    • A63B37/0072—Characteristics of the ball as a whole with a specified number of layers
    • A63B37/0074—Two piece balls, i.e. cover and core

Definitions

  • the present invention relates to golf balls having a polyhedra design that can yield lower drag coefficient than a dimpled sphere.
  • the drag reduction is applicable to other sports equipment in general having a bluff body, such as the head of a golf club or a bike helmet.
  • a dimple generally refers to any curved or spherical depression in the face or outer surface of the ball.
  • the traditional golf ball as readily accepted by the consuming public, is spherical with a plurality of dimples, where the dimples are generally depressions on the outer surface of a sphere.
  • the vast majority of commercial golf balls use dimples that have a substantially spherical shape.
  • FIG. 1 shows the variation of the drag coefficient, CD, as a function of Reynolds number, Re, for smooth and dimpled spheres.
  • the data were obtained by performing wind tunnel experiments of non-spinning spheres.
  • the drag coefficient shown by the solid black line
  • CD remains constant (CD ⁇ 0.5) until the Reynolds number approaches a critical value (Re Cr ⁇ 300,000).
  • CD decreases rapidly and hits a minimum, which is an order of magnitude lower CD ⁇ 0.08.
  • the flow enters the post-critical regime characterized by turbulent boundary layers on the surface of the sphere. In this regime the drag coefficient rises slowly with increasing Reynolds number.
  • the critical Reynolds is increased and the drag coefficient in the post-critical regime increases.
  • Drag is one of the two forces (the other being lift) that influence the aerodynamic performance of a golf ball.
  • the dimple design is a balance between achieving the lowest critical Reynolds number and the lowest drag coefficient in the post-critical regime.
  • dimples are the only configuration known to provide a golf ball having a reduced drag coefficient.
  • the golf ball has a plurality of flat faces with sharp edges and points that collectively form a polyhedron.
  • FIG. 1 shows a plot of the drag coefficient CD VS Reynolds number Re for smooth and dimpled spheres.
  • the solid black line represents a smooth sphere (Achenbach, 1972); the double-dashed lines represent a dimpled sphere (J. Choi, 2006); and the dash-dot lines represent a dimpled sphere (Harvey, 1976).
  • the shaded area represents the typical range of Reynolds experience by a golf ball in flight during a driver shot (50,000 - 200,000).
  • FIG. 2(a) shows a golf ball in accordance with one embodiment of the invention.
  • FIG. 2(b) shows an outline of a golf ball.
  • FIG. 2(c) shows an outline of a golf ball with non-sharp rounded edges.
  • FIG. 2(d) shows an icosahedron, a well-known Platonic solid used to derive the golf ball 100.
  • FIG. 2(e) shows an example of splitting a hexagonal face into 6 triangular faces.
  • FIG. 3 shows the Goldberg polyhedron with 192 faces.
  • FIG. 4 is a graph of the drag coefficient versus Reynolds for the Goldberg polyhedra with 162 faces and 192 faces.
  • FIG. 5 is a graph showing the CD versus Reynolds for a Goldberg polyhedron with 192 faces and a dimpled sphere.
  • FIG. 6 is a graph showing the CD versus Reynolds for a Goldberg polyhedron with 162 faces and a dimpled sphere.
  • FIG. 7 shows a geodesic polyhedron made from 320 triangles.
  • FIG. 8 shows a geodesic cube with 174 faces.
  • FIG. 9 shows a polyhedron with 162 faces and 162 dimples.
  • FIG. 10 is a graph showing the drag coefficient CD versus Reynolds number Re for a Goldberg polyhedron with 162 faces and a Goldberg polyhedron with 162 faces and 162 dimples.
  • FIG. 11 is a comparison of drag coefficient CD versus Reynolds number for one of the embodiments of the present invention shown in FIG. 9 against a commercial ball Callaway Superhot.
  • FIG. 12 is an alternative embodiment of a golf ball based on an icosahedron with 312 faces and 312 spherical dimples.
  • FIG. 13 is a comparison of drag coefficient CD versus Reynolds number Re for one of the embodiments of the present invention based on a polyhedron with 312 faces and 312 spherical dimples of FIG. 12 against a commercial golf ball Bridgestone Tour.
  • the present invention is directed to a golf ball design based on polyhedra that can have reduced drag coefficient compared to a dimpled sphere.
  • a family of golf ball designs are made up of convex polyhedra whose vertices he on a sphere.
  • a polyhedron is a solid in three dimensions with flat polygonal faces, straight sharp edges and sharp comers or vertices.
  • FIG. 2(a) shows a golf ball 100 in accordance with one embodiment of the present invention.
  • the golf ball 100 has a body 110 with an inner core and an outer shell with an outer surface 112.
  • a plurality of faces 120 are formed in the outer surface, creating a pattern 116. All the faces are formed in the outer surface and each of such faces is flat and lies in a plane. The faces are bound by straight or linear edges 124.
  • the golf ball 100 is a polyhedron with 162 polygons.
  • the body 110 defines a circumscribed sphere 102, which is the smallest sphere containing the polyhedron, and is shown with a dashed line about the outermost points 104 of the body 110.
  • the sphere and the diameter provide a reference for the size of the golf ball.
  • the Rules of Golf jointly governed by the R&A and the USGA, state that the diameter of a "conforming" golf ball cannot be any smaller than 1.680 inches.
  • the diameter of the circumscribed sphere is at least l.68in.
  • the vertices l22a, l22b of the polyhedron are the only points 104 on the polyhedron that lie on the sphere. Any point along the edges l24a, l24b or on the faces l20a, l20b of the polygons lies below the surface of the circumscribed sphere.
  • the golf ball body 110 is a polyhedron that is made from first faces l20a and second faces l20b.
  • the first faces l20a have a first shape, namely pentagons
  • the second faces l20b have a second shape different than the first shape, namely hexagons. All of the faces are flat and each such face forms a single plane.
  • pentagons l20a and hexagons l20b can be used.
  • the number of polygons and the angle between them determine when the drag coefficient will start to drop and how low it will become. In general, as the number of faces is increased the drag crisis occurs at higher Reynolds number and the drag coefficient decreases.
  • the first and second faces l20a, l20b form the pattern 116.
  • edges 124 are sharp, in that the faces are at an angle with respect to one another.
  • FIG. 2(b) shows a cross sectional cut through the body 110 of ball 100 of FIG. 2(a) along the line 150.
  • the edges 124 are sharp, in that the radius of curvature 140 of an edge is less than 0.001D, where D is the diameter of the circumscribed sphere. Ideally all edges should be the sharpest possible. A radius of curvature of 0 is the case with the sharpest possible edges, though golf ball edges might become a little rounded during manufacture or follow use.
  • FIG. 2(c) shows a cross section cut of two faces with rounded edges, whose radius of curvature is more than 0.001D.
  • the resulting edge is not sharp and the reduction in drag is not maximized, which can be detrimental to the aerodynamic performance of the golf ball as the shape would approach that of a smooth sphere.
  • Both a sharp edge and a non-sharp edge is shown in that embodiment for illustrative purposes.
  • the angle Q formed between two adjacent flat / planar faces 120 is always smaller than 180 degrees.
  • the geometric shape of the embodiment illustrated in FIG. 2(a) falls into the class of convex polyhedral where the angle between any pair of adjacent faces is always less than 180 degrees. In this
  • the angle between a pentagon face l20a and an adjacent hexagonal face l20b is 166.215 degrees.
  • the angle between two adjacent hexagon faces l20b varies from 161.5 degrees to 162.0 degrees.
  • Each face 120 is immediately adjacent and touching a neighboring face 120, such that each edge 124 forms a border between two neighboring faces 120 and each point 122 is at the intersection of three neighboring faces 120. And, each point 122 is at an opposite end of each linear edge 124 and is at the intersection of three linear edges 124. Accordingly, there is no gap or space between adjacent neighboring faces 120, and the faces 120 are contiguous and form a single integral, continuous outer surface 112 of the ball 100.
  • a golf ball usually has a rubber core and at least one more layer surrounding the core.
  • the pattern 116 is formed on the outermost layer.
  • the pattern is based on an icosahedron shown in FIG. 2(d).
  • the icosahedron 170 is a well-known convex polyhedron made up of 20 equilateral triangle faces 180, 12 vertices 182 and 30 edges 184.
  • An icosahedron is one of the five regular Platonic solids, the other four being the cube, the tetrahedron, the octahedron and the dodecahedron (see https://en.wikipedia.org/wiki/Platonic_solid).
  • Table 1 lists the coordinates of all the vertices and how each face is formed, which defines the geometry of the golf ball.
  • Table 1 lists the coordinates x, y, and z of all of the vertices 122 of golf ball 100. Faces are constructed by connecting the vertices with straight lines. The coordinates x, y, z are normalized by the diameter D of the circumscribed sphere 104 and are with respect to the center of the sphere.
  • the golf ball 100 contains 320 vertices 122, 480 straight edges 120 and 162 polygonal faces 120.
  • the particular polyhedron can be any suitable configuration, and in one embodiment is a class of solids called Goldberg polyhedra that comprises convex polyhedra that are made entirely from a combination of rectangles, pentagons and hexagons.
  • Goldberg polyhedra are derived from either an icosahedron (a convex polyhedron made from 12 pentagons), or an octahedron (a convex polyhedron made from 8 triangles) or a tetrahedron (a convex polyhedron made from 4 triangles).
  • the invention can utilize any convex polyhedron (that is, a polyhedron made up of polygons whose angle is less than 180 degrees), though in one embodiment on such polyhedron is a convex polyhedron with sharp edges, flat faces forming a single plane, and adjacent faces having an angle of less than 180 degrees between them.
  • the particular configuration Goldberg polyhedral 162 faces and icosahedral symmetry
  • other geometries with around 162 faces may be possible to do using only pentagons or only hexagons.
  • Other embodiments of the invention can include a pattern with various geometric configurations.
  • the pattern can be comprised of more or fewer of hexagons and pentagons than shown. Or it can comprise all hexagons, all pentagons, or no hexagons or pentagons but instead one or more other shapes or polyhedrals having flat faces and sharp edges.
  • One other shape can be formed, for example, by splitting each hexagon into 6 triangles or each pentagon into 5 triangles, which provides a similar drag coefficient.
  • One embodiment can include any of the Goldberg polyhedra with a combination of pentagons and hexagons or even a convex polyhedral made of triangles or squares.
  • flat faces give lower drag and have the uniqueness of not being dimples (curved indentations).
  • the flat faces only provide points of the faces that he on the circumscribed sphere.
  • the sharp edges are defined by the angle between two adjacent faces.
  • the edges forming the boundaries between the two adjacent faces are flat and not excessively rounded.
  • An example of a non-sharp edge is shown in FIG. 2(c). The angle between the two edges is the same as is in FIG. 2(b) but it is rounded such that the edge is not sharp.
  • the ratio of pentagons to hexagons is 12: 150, though any suitable ratio can be provided.
  • one of the hexagons can be split into 6 triangles and a have a polyhedron with 12 pentagons, 149 hexagons and 6 triangles and obtain substantially the same drag coefficient.
  • FIG. 2(e) illustrates how such a splitting can be performed on one of the hexagonal faces 120.
  • a vertex 140 can be chose anywhere inside the hexagon 120.
  • the vertex 140 is near the center of the hexagon although any other location can be used.
  • Six new edges 142 can be formed by connecting the each of the vertices 122 with the new vertex 140.
  • a triangular face 144 is formed by one edge 124 of the hexagon and two adjacent edges 142.
  • the exact shape of the faces making up the polyhedral can vary but one important feature of the polyhedral pahem is the angle between faces.
  • FIG. 3 shows an example of a golf ball in accordance with another embodiment of the invention.
  • the golf ball 200 has a body 210 with an inner core and an outer shell with an outer surface 212.
  • a plurality of faces 220 are formed in the outer surface, creating a pahem 216. All the faces are formed in the outer surface and each of such faces is flat and lies in a plane. The faces are bound by straight or linear edges 224.
  • the golf ball 200 is a polyhedron with 192 polygons.
  • the body 210 defines a circumscribed sphere 202, which is the smallest sphere containing the polyhedron, and is shown with a dashed line about the outermost points 204 of the body 210.
  • the vertices 222a, 222b of the polyhedron are the only points 204 on the polyhedron that lie on the sphere. Any point along the edges 224a, 224b or on the face of the polygons lies below the surface of the circumscribed sphere.
  • the golf ball body 210 is a polyhedron that is made from first faces 220a and second faces 220b.
  • the first faces 220a have a first shape, namely pentagons
  • the second faces 220b have a second shape different than the first shape, namely hexagons. All of the faces are flat and each such face forms a single plane.
  • other quantities and/or ratios of such pentagons 220a and hexagons 220b can be used.
  • the first and second faces 220a, 220b form the pattern 216.
  • edges 224 are sharp, in that the radius of curvature of an edge is less than 0.001D, where D is the diameter of the circumscribed sphere. Ideally all edges should be the sharpest possible. A radius of curvature of 0 is the case with the sharpest possible edges, though golf ball edges might become a little rounded during manufacture or follow use.
  • the geometric shape of the embodiment illustrated in FIG. 3 falls into the class of convex polyhedral where the angle between any pair of adjacent faces is always less than 180 degrees.
  • the angle between a pentagon face 220a and an adjacent hexagonal face 220b is 167.6 degrees.
  • the angle between two adjacent hexagon faces l20b varies from 163.4 degrees to 164.2 degrees.
  • Each face 220 is immediately adjacent and touching a neighboring face 220, such that each edge 224 forms a border between two neighboring faces 220 and each point 222 is at the intersection of three neighboring faces 220. And, each point 222 is at an opposite end of each linear edge 224 and is at the intersection of three linear edges 224. Accordingly, there is no gap or space between adjacent neighboring faces 220, and the faces 220 are contiguous and form a single integral, continuous outer surface 212 of the ball 200.
  • the patern is based on an icosahedron shown in FIG. 2(c). In the icosahedron 170 five equilateral triangles 180 meet at each of its twelve vertices 182. The 12 pentagons 220a of the golf ball 200 shown in FIG. 3 are centered on the vertices of an icosahedron.
  • any pair of 3 pentagons 220a form an equilateral triangle 280.
  • the pentagons 220a are all equilateral, that is the 5 edges 224a all have the same length equal to 0.136D, where D is the diameter of the circumscribed sphere.
  • the hexagons 220b are not equilateral and the lengths of the edges 224b vary from 0.136D to 0.168D.
  • Table 2 lists the coordinates of all the vertices and how each face is formed, which defines the geometry of the golf ball.
  • Table 1 lists the coordinates x, y, and z of all of the vertices 220 of polyhedron of golf ball 200. Faces are constructed by connecting the vertices with straight lines. The coordinates x, y, z are normalized by the diameter D of the circumscribed sphere 204 and are with respect to the center of the sphere.
  • the golf ball 200 contains 380 vertices 222, 570 straight edges 220 and 192 polygonal faces 220.
  • FIG. 4 shows a graph of the drag coefficient, CD, versus the Reynolds number, Re, for the polyhedron with 162 and 192 faces.
  • the drag coefficient was obtained by wind tunnel experiments of non-spinning models.
  • For the polyhedron with 192 faces CD reaches a minimum value of 0.14 at Re l l0,000 and remains almost constant as the Reynolds increases.
  • the graph reveals that as the number of faces increases the drag crisis shifts towards a higher Reynolds number and the CD in the post-critical regime decreases.
  • This feature can be taken into advantage when designing a golf ball to tailor the needs of a golfer.
  • a golf ball in flight during a driver shot can experience a Reynolds number ranging from 180,000 at the beginning of the flight to 60,000 at the end of the flight.
  • a golf ball in flight during a driver shot can experience a Reynolds number ranging from 220,000 at the beginning of the flight to 80,000 at the end of the flight.
  • the range of Reynolds number experienced by a golf ball for an amateur golfer is lower than that for a professional golfer.
  • a golf ball with more polygon faces might suit the needs of a professional golfer while a golf ball with less polygon faces might suit the needs of an amateur golfer.
  • the dimpled sphere has 322 spherical dimples and is representative of a commercial golf ball.
  • a lower drag coefficient is important because it plays an important role in achieving more carry distance during a driver shot.
  • FIG. 6 A comparison of the drag curve of the golf ball 100 against the same dimpled sphere is shown in FIG. 6. While CD in the post-critical regime is almost identical for the two balls, the drag crisis for the golf ball 200 occurs at a lower Reynolds number. As a result, CD for Re ⁇ l 10,000 is consistently lower for the polyhedron with 192 faces than for the dimpled sphere. Thus, the embodiment of FIG. 2(a) has a lower drag coefficient than a dimpled sphere. A lower drag coefficient is important because it plays an important role in achieving more carry distance during a driver shot.
  • FIGS. 7, 8 are additional non-limiting embodiments of the invention.
  • Those golf balls 300, 400 have similar structure as the embodiments of FIGS. 2, 3, and those structures have similar purpose.
  • Those structures have been assigned a similar reference numeral and similar structure with the differences noted below.
  • FIG. 7 shows an example of a golf ball 300 with a body 310 with an inner core and an outer shell with an outer surface 312.
  • a plurality of faces 320 are formed in the outer surface, creating a pattern 316. All the faces are formed in the outer surface 312 and each of such faces is flat and lies in a plane.
  • the faces are bound by straight or linear edges 324 and comers vertices 322.
  • the body 310 defines a circumscribed sphere 302, which is the smallest sphere containing the polyhedron, and is shown with a dashed line about the outermost points 304 of the body 310.
  • FIG. 8 shows an example of a golf ball 400 with a body 410 with an inner core and an outer shell with an outer surface 412.
  • a plurality of faces 420 are formed in the outer surface, creating a pattern 416. All the faces are formed in the outer surface 412 and each of such faces is flat and lies in a plane.
  • the faces are bound by straight or linear edges 424 and comers or vertices 422.
  • the body 410 defines a circumscribed sphere 402, which is the smallest sphere containing the polyhedron, and is shown with a dashed line about the outermost points 404 of the body 410.
  • FIGS. 7, 8 are included for illustrative purposes as examples of convex polyhedral that are not made from pentagons or hexagons. Other convex polyhedra not made up of pentagons or hexagons can also be used for the design of a golf ball.
  • a convex polyhedron is shown in FIG.
  • the polyhedron belongs to a class of solids called Geodesic polyhedron which are derived from an icosahedron by subdividing each face into smaller faces using a triangular grid, and then applying a canonicalization algorithm to make the result more spherical (see https://en.wikipedia.org/wiki/Geodesic_polyhedron).
  • the vertices of the polyhedron are the only points on the polyhedron that he on a sphere. Any point along the edges or on the face of the triangles lies below the surface of a circumscribed sphere.
  • the polyhedron in FIG. 7 is made from 320 triangles but any geodesic polyhedron with an arbitrary number of triangles can be used as the design of a golf ball.
  • a convex polyhedron is shown in FIG. 8.
  • the polyhedron belongs to a class of solids called Geodesic cubes which are made from rectangular faces.
  • a geodesic cube is a polyhedron derived from a cube by subdividing each face into smaller faces using a square grid, and then applying a canonicalization algorithm to make the result more spherical (see http://dmccooey.com/polyhedra/GeodesicCubes.html).
  • the vertices of the polyhedron are the only points on the polyhedron that he on a sphere. Any point along the edges or on the face of the rectangular faces lies below the surface of a circumscribed sphere.
  • the polyhedron in FIG. 8 is made from 174 rectangular flat faces but any geodesic cube with an arbitrary number of faces can be used as the design of a golf ball.
  • the polyhedra do not contain any dimples (i.e., curved or spherical depressions or indents), but instead have flat surfaces that he in a plane.
  • the polyhedra provide enhanced aerodynamic characteristics, drag coefficient being one of them, that can help increase the carry distance of the golf ball.
  • golf ball geometries that are based on any convex polyhedra and either include or omit dimples are contemplated.
  • at least one of the faces may include one or more dimples.
  • FIG. 9 shows an example
  • a golf ball 500 that is based on a convex polyhedron with a plurality of polygonal faces 520.
  • the convex polyhedron is identical to the one shown in FIG. 2, and includes a body 510 with an inner core and an outer shell with an outer surface 512.
  • a plurality of faces 520 are formed in the outer surface, creating a pattern 516. All the faces are formed in the outer surface 512 and each of such faces is flat and lies in a plane.
  • the faces are bound by straight or linear edges 524 and comers or vertices 522.
  • the body 510 defines a circumscribed sphere 502, which is the smallest sphere containing the polyhedron, and is shown with a dashed line about the outermost points 504 of the body 510.
  • each face 520 of the polyhedron contains one dimple 560.
  • the dimples 560 have a substantially spherical shape and are created by subtracting spheres 570 from each of the faces 510 of the polyhedron 500.
  • Table 3 lists the coordinates x, y and z of the center of the spheres 570 along with the diameter d of the spheres 570.
  • the coordinates x, y, z and the diameter of the spheres d are normalized by the diameter D of the circumscribed sphere 504.
  • the coordinates x, y, and z are with respect to the center of the circumscribed sphere.
  • the total dimple volume ratio defined as the aggregate volume removed from the surface of the polyhedron divided by the volume of the polyhedron, is 0.317%.
  • the dimples 560 are each located at the center of each 510. However, the dimples 560 can be positioned at another location such as offset within each face 510, or overlapping two or more faces 510. In addition, while spherical dimples 560 are shown, the dimples 560 can have any suitable size and shape. For example, non-spherical depressions can be utilized, such as triangles, hexagons, pentagons. And the dimples need not all have the same size and shape, for example there can be dimples with more than one size and more than one shape.
  • FIG. 10 A comparison of the drag curve of this embodiment against that of golf ball 100 is shown in FIG. 10.
  • the drag crisis occurs at a lower Reynolds number range. That is, the drag coefficient starts to drop at a lower Reynolds number.
  • the total dimple volume approaches zero the drag curve of golf ball 500 would approach that of golf ball 100. Therefore, one can fine tune the exact behavior of the drag curve by adjusting the total dimple volume.
  • Each dimple is formed by subtracting a sphere for the face of the polyhedron as explained above.
  • the dimple volume is the amount of volume that each sphere subtracts from the volume of the polyhedron.
  • FIG. 11 compares the drag curve of the golf ball 500 shown in FIG. 9 against a commercial golf ball, namely the Callaway SuperHot, which is a dimpled ball marketed as having a low drag coefficient and shown in U.S. Patent No. 6,290,615.
  • the drag coefficient for both balls were obtained by performing wind tunnel experiments using the actual commercial golf ball and a 3D printed prototype of the golf ball 500.
  • the drag crisis for the golf ball 500 happens earlier, that is the drag coefficient starts to drop at lower Reynolds number.
  • Clearly CD for golf ball 500 is consistently lower than that of the commercial golf ball for the range of Reynolds numbers 60,000-160,000.
  • a lower drag coefficient can help a golf ball achieve longer carry distances.
  • the golf ball 500 is the exact same polyhedron of golf ball 100, however the golf ball 500 has a dimple on each face.
  • the polyhedron which golf ball 500 is based on is identical to the polyhedron of golf ball 100 in FIG. 2.
  • FIG. 12 shows an example of a golf ball based on a convex polyhedron with dimples in accordance with another embodiment of the invention.
  • the golf ball 600 has a body 610 with an inner core and an outer shell with an outer surface 612.
  • a plurality of faces 620 are formed in the outer surface, creating a pattern 616. All the faces are formed in the outer surface and each of such faces is flat and lies in a plane. The faces are bound by straight or linear edges 624.
  • the golf ball 600 is based on a polyhedron with 312 polygons.
  • the body 610 defines a circumscribed sphere 602, which is the smallest sphere containing the polyhedron, and is shown with a dashed line about the outermost points 604 of the body 610.
  • the vertices 622a, 622b of the polyhedron are the only points 604 on the polyhedron that he on the sphere. Any point along the edges 624 or on the face of the polygons lies below the surface of the circumscribed sphere.
  • the golf ball body 610 is a polyhedron that is made from first faces 620a and second faces 620b.
  • the first faces 620a have a first shape, namely pentagons
  • the second faces 620b have a second shape different than the first shape, namely hexagons. All of the faces are flat and each such face forms a single plane.
  • the first and second faces 620a, 620b form the pattern 616.
  • edges 624 are sharp, in that the radius of curvature of an edge is less than 0.001D, where D is the diameter of the circumscribed sphere. Ideally all edges should be the sharpest possible. A radius of curvature of 0 is the case with the sharpest possible edges, though golf ball edges might become a little rounded during manufacture or follow use.
  • the geometric shape of the embodiment illustrated in FIG. 12 falls into the class of convex polyhedral where the angle between any pair of adjacent faces is always less than 180 degrees.
  • the angle between a pentagon face 620a and an adjacent hexagonal face 620b is 170.2 degrees.
  • the angle between two adjacent hexagon faces 620b varies from 167.1 degrees to 168.2 degrees.
  • Each face 620 is immediately adjacent and touching a neighboring face 620, such that each edge 624 forms a border between two neighboring faces 620 and each point 622 is at the intersection of three neighboring faces 620. And, each point 622 is at an opposite end of each linear edge 624 and is at the intersection of three linear edges 624. Accordingly, there is no gap or space between adjacent neighboring faces 620, and the faces 620 are contiguous and form a single integral, continuous outer surface 612 of the ball 600.
  • the pattern is based on an icosahedron shown in FIG. 2(c).
  • the icosahedron 170 five equilateral triangles 180 meet at each of its twelve vertices 182.
  • the 12 pentagons 620a of the golf ball 600 shown in FIG. 12 are centered on the vertices of an icosahedron.
  • any pair of 3 pentagons 620a form an equilateral triangle 680 shown with dashed line in FIG. 12.
  • the pentagons 620a are all equilateral, that is the 5 edges 624a all have the same length equal to 0.102D, where D is the diameter of the circumscribed sphere.
  • the hexagons 620b are not equilateral and the lengths of the edges 624b vary from 0.102D to 0.132D.
  • Table 4 lists the coordinates of all the vertices and how each face is formed, which defines the geometry of the polyhedron.
  • Table 4 lists the coordinates x, y, and z of all of the vertices 622 of polyhedron of golf ball 600. Faces are constructed by connecting the group of vertices with straight lines. The coordinates x, y, z are normalized by the diameter D of the circumscribed sphere 604 and are with respect to the center of the sphere.
  • the golf ball 600 contains 620 vertices 622, 930 straight edges 624 and 312 polygonal faces 620.
  • Each of the face 620 of the polyhedron contains one dimple 690.
  • the dimples 690 have a substantially spherical shape and are created by subtracting spheres 670 from the face 620 of the polyhedron.
  • Table 5 lists the coordinates x, y and z of the center of the spheres 670 along with the diameter d of the spheres 670.
  • the coordinates x, y, z and the diameter of the spheres d are normalized by the diameter D of the circumscribed sphere 604.
  • the coordinates x, y, and z are with respect to the center of the circumscribed sphere.
  • the graphs shows the invention having a lower drag coefficient.
  • the drag coefficient for both balls were obtained by performing wind tunnel experiments using the actual commercial golf ball and a 3D printed prototype of the embodiment.
  • At Reynolds number of 100,000 CD for the Bridgestone Tour ball is 0.195 while CD for the current embodiment is 0.162, a drag reduction of 17%.
  • Overall CD for the current embodiment is consistently lower than that of the commercial golf ball for the range of Reynolds numbers 80,000-160,000.
  • a lower drag coefficient can help a golf ball achieve longer carry distances.
  • FIGS. 9, 12 are revisions to the Goldberg principle in that each face of the polyhedron contains a dimple.
  • edges may not be exactly linear, hexagonal, pentagonal or spherical, but still be considered to be substantially linear, hexagonal, pentagonal or spherical, and faces may not be exactly flat or planar but still be considered to be substantially flat or planar because of, for example, roughness of surfaces, tolerances allowed in manufacturing, etc.
  • the boundaries need not be sharped, but can be curved. And other suitable shapes can be utilized for the faces. And, while the invention has been described with a certain number of faces and/or dimples, other suitable numbers of faces and/or dimples, more or fewer, can also be provided within the spirit and scope of the invention. Within this specification, the various sizes, shapes and dimensions are approximate and exemplary to illustrate the scope of the invention and are not limiting. The faces need not all be the same shape and/or size, and there can be multiple sizes and shapes of faces.

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  • Health & Medical Sciences (AREA)
  • General Health & Medical Sciences (AREA)
  • Physical Education & Sports Medicine (AREA)
  • Professional, Industrial, Or Sporting Protective Garments (AREA)

Abstract

L'invention concerne une balle de golf présentant une surface externe comportant un motif formant un polyèdre. Le motif peut être des faces plates formant des arêtes vives et des points aigus entre celles-ci. Dans un mode de réalisation, le polyèdre est un polyèdre de Goldberg.
PCT/US2019/013052 2018-01-12 2019-01-10 Balle de golf polyédrique à coefficient de traînée inférieur WO2019140090A1 (fr)

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JP2020538965A JP2021510578A (ja) 2018-01-12 2019-01-10 より低い抗力係数を有する多面体ゴルフボール
US16/771,676 US20210197029A1 (en) 2018-01-12 2019-01-10 Polyhedra golf ball with lower drag coefficient

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US201862616861P 2018-01-12 2018-01-12
US62/616,861 2018-01-12

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Publication number Priority date Publication date Assignee Title
JP7238382B2 (ja) * 2018-12-19 2023-03-14 住友ゴム工業株式会社 ゴルフボール

Citations (5)

* Cited by examiner, † Cited by third party
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US2861810A (en) * 1954-12-10 1958-11-25 Veatch Franklin Golf ball
US4765626A (en) * 1987-06-04 1988-08-23 Acushnet Company Golf ball
US20030158002A1 (en) * 2002-02-15 2003-08-21 Morgan William E. Golf ball with spherical polygonal dimples
US20030224878A1 (en) * 2002-05-29 2003-12-04 Sullivan Michael J. Golf ball with varying land surfaces
US20050014579A1 (en) * 2003-07-14 2005-01-20 Takeshi Asakura Golf ball

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Publication number Priority date Publication date Assignee Title
JP4129625B2 (ja) * 2002-10-17 2008-08-06 ブリヂストンスポーツ株式会社 ゴルフボール
JP4626146B2 (ja) * 2003-12-24 2011-02-02 横浜ゴム株式会社 ゴルフボール、ゴルフボールの設計方法およびゴルフボール製造用金型
JP5082806B2 (ja) * 2006-11-29 2012-11-28 横浜ゴム株式会社 ゴルフボールおよびゴルフボールの製造方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2861810A (en) * 1954-12-10 1958-11-25 Veatch Franklin Golf ball
US4765626A (en) * 1987-06-04 1988-08-23 Acushnet Company Golf ball
US20030158002A1 (en) * 2002-02-15 2003-08-21 Morgan William E. Golf ball with spherical polygonal dimples
US20030224878A1 (en) * 2002-05-29 2003-12-04 Sullivan Michael J. Golf ball with varying land surfaces
US20050014579A1 (en) * 2003-07-14 2005-01-20 Takeshi Asakura Golf ball

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