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The Callaway
Big Bertha Dimple
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The
Dimple-Error ProblemThis diagram from the Bald Eagle putting ball website indicates the nature of the dimple-error problem. The putter should impact the ball flush to the directional orientation of the face, but sometimes the edge of a dimple gets in the way, with the result that the direction the ball starts off is slightly different than the intended line (the line that is perpendicular to the putter face at impact). The REAL issues are 1) HOWBIG of a problem is this -- when or how often does it occur, under what conditions, and what difference does it make, and 2) WHAT TO DO about it in terms of choices for ball design, putter design, and putting technique.
The
Callaway DimpleOVERVIEW: The Callaway Big Bertha dimple is the same design as used on the earlier Callaway HX ("Hex") ball. It features a large, shallow dimple with tube-shaped rims. The design covers nearly 100% of the ball surface, which is an aerodynamic advantage over most patterns, which usually cover only around 80%.
Callaway's HEX aerodynamic pattern is one of crisscrossing "tubes" that form a series of hexagons and pentagons. That, according to Callaway, is a more efficient configuration than traditional dimple patterns that often leave a little space between dimples. Callaway says Big Bertha Golf Balls achieve 100 percent surface coverage, which reduces drag at takeoff and increases lift at the end of the ball's flight. The result, Callaway says, is a high, strong trajectory with the potential for increased distance. Each Big Bertha Golf Ball features a proprietary ionomer blend for a softer cover that is just as durable as that on a standard two-piece distance ball. The Big Bertha Golf Balls also have relatively soft, low-compression cores. The Big Bertha Red Golf Ball is a soft-feel distance ball, while the Big Bertha Blue Golf Ball is a combination of distance feel and spin, with higher compression and a softer cover.
The Rule 35 ball had more surface area, about 86 percent, covered by dimples than previous balls. Dimples reduce the drag on a golf ball when it is in the air. "The design of a golf ball is a balance between minimizing drag at high speed and maximizing lift at low speeds," Ogg explained. "When you don't have enough surface-area coverage, it is very difficult to do that. You have to make the dimples very deep to get lift at low speeds, and those dimples create a lot of drag at high speeds." Ogg's idea for what became the HX ball was to replace the dimples with a tubular lattice network of 332 hexagons and 12 pentagons with rounded edges, which eliminated the flat areas between dimples. Those flat areas create distance-robbing drag. Uniroyal first made a ball with hexagon-shaped dimples in 1971. Ogg has one, called a Plus Six, on his desk. But that design didn't eliminate the flat areas. Ogg's ball also eliminates the seam -- found on all other golf balls -- where the two halves are joined. Hitting a golf ball on the seam can produce inconsistent results. "I wanted to come up with a way to have the same geometry at the seam as away from the seam."
Each Big Bertha Golf Ball features a proprietary ionomer blend for a softer cover that is just as durable as that on a standard two-piece distance ball. The softer cover also provides better feel and performance around the green while still producing distance-enhancing ball speed and trajectory off the driver. The Big Bertha Golf Balls also have relatively soft, low-compression cores. This large rubber core is very resilient, which helps transfer energy more efficiently from club to ball. The Big Bertha Red Golf Ball is a soft-feel distance ball, designed with a cover and core composition calibrated for more distance while still delivering responsive feel. Meanwhile, the Big Bertha Blue Golf Ball is a combination of distance feel and spin, with higher compression and a softer cover fine-tuned to deliver complete performance.
13:40 04 JanuaryÊ02
A golf ball covered with hexagonal and pentagonal dimples, rather than the traditional circular ones, will be available from March. Its creators say it could improve player performance by travelling through the air more aerodynamically. The angular dimples of the HX ball remove the areas of flat surface that are normally found between the circular dimples of a golf ball. These smooth regions actually increase the drag that a ball experiences as it travels through the air. The HX ball's dimples cover virtually the entire surface of the ball, reducing drag and making it travel further and straighter through the air, according to experts at Callaway. The company also says their new ball is more susceptible to spin, which can curve its flight. Turbulent layer Joaquim Peiro, of the aeronautics department at Imperial College London, says that the new design should, in principle, improve the flight of the golf ball. "With a hexagonal arrangement you can cover more of the ball than with dimples," Peiro says. "Probably you can affect a wider area of the flow past the ball." Dimples create a turbulent boundary layer as air flows past a golf ball. This allows air to "hug" the surface further round the ball as it passes, reducing the size of its wake and, consequently, its drag. For this reason a ball with dimples of the right depth is more aerodynamic than a smooth ball. Cross winds According to Callaway, the HX ball was less affected by cross winds than round-dimpled balls in testing. "Every touring pro that tested our ball told us the same thing: into the wind, downwind, through crosswinds, the HX is more stable than any ball they've ever played," says Richard C. Helmstetter, senior executive vice president of research and development at Callaway. Each HX ball has a lattice network of 332 hexagons and 12 pentagons. The bottom of each dimple is flat and the edges curved, which Callaway says achieves the right aerodynamic balance between a small turbulent layer and drag. The ball was designed by ex-Boeing aircraft aerodynamics expert Steve Ogg, who now works for Callaway. It has been approved for competitive play by the US Golf Association. Another company, Uniroyal, proposed hexagonal dimples in 1971, but its design did not prove a success. -- Will Knight Ê
Aerodynamic
Function of DimplesOVERVIEW: Spheres are not a good shape for aerodynamics. A blade or fin or wing works much better at controlling air flow for flight by maximizing lift and minimizing drag forces. Dimples on a ball help reduce drag, while spin mostly promotes lift. Without dimples, golf balls wouldn't fly half as far as they do.
To return to the dimpled golf ball: the sheath of air traveling viscously with the moving ball is called the boundary layer. It is an advantage, for fast travel, for the boundary layer to cling as long as possible to the surface of the ball. In an undimpled ball the boundary layer separates from the surface typically when the air has gone about halfway from the front to the back of the ball.7 True streamlining would enable the boundary layer to cling much longer, but a golfball shaped like the wing of a 747, even in miniature, would putt badly. In lieu of that, dimples serve much the same purpose, enabling the boundary layer to cling all the way around nearly to the rear of the ball. The Navier-Stokes equations for this situation have never been solved, so it's not completely clear just how the local pockets of turbulence around the dimples help the boundary layer to cling longer, but one explanation is as follows: when the boundary layer "fits like a glove" around the ball, the layer slows down rapidly and separates quickly. But turbulence provides coupling to the "outside" airstream and enables the boundary layer to continue receiving momentum from the outside air. This lets it "stay on the ball" longer, makes the overall wake of the dimpled ball narrower, and the pressure differential between the front and the rear of the dimpled ball is not as great as that of a smooth ball. This treatment follows Jearl Walker's excellent discussion in Scientific American, April 1979.
Two California scientists named Holmstrom and Nepela have patented a ball (U.S. Pat. 3,819,190) with only half as many dimples, but the dimples are confined to an equatorial band; the "poles" are smooth. This ball doesn't fly as far as fully dimpled models, but reduces hooking and slicing as much as 80%.9
9 Science, March 14, 1975, p. 941
The air streaming over a golf ball forms a "boundary layer" of relatively slow moving air. It's distinct. Right at the surface, the air is stuck. A millimeter away from the surface, the air is going full blast. In between -- in the boundary layer -- it's just slurping along. So here's the deal. That slow moving air in the boundary layer is a drag. Uh, I mean, it's a source of drag. It lets the air stick to the surface and tumble behind the ball in wild whipping whirlpools. The energy in the boundary layer is lost energy. The tumbling air behind the ball allows a large (relatively large, it's just a golf ball) region of low pressure to form, creating a partial vacuum that would suck the ball back toward the tee. So, the thinner we can make the boundary layer, the less slurpy drag we'll have, and the sooner the air behind the ball can get back up to the "free stream" speed (at least from your micro entity point of view). The less drag, the farther the ball will be driven. Here's where the dimples do their job. Dimples make the molecules in the layer tumble. They start roiling against one another. We say the boundary layer becomes "turbulent." The molecules in the layer are no longer just sliding across the surface gently jostling. Now, they're rolling and bouncing and bumping each other along. When the molecules are in a turbulent boundary layer, they're moving closer to the free-stream speed. There is less of a difference between the speed of the tumbling molecules and the speed of the ball. It turns out that the air flow in a turbulent boundary layer on a dimpled golf ball is thinner than a smooth or "laminar" flow on, say, a ping-pong ball. Boundary layers are laminar or turbulent, or somewhere in between. We say they're in "transition." Dimples make the transition quick-- not a smooth transition, a turbulent one, ha! (A little fluid dynamics gag there...) When the layer is turbulent and thin, the ball loses less energy to the free stream air. And, drag is lower. Isn't that weird? The dimples make the ball develop less drag. Weird, huh?
Aerodynamics is largely based upon fluid flow, since air and water are both media that consist of molecules more or less uniformly distributed in space with a consistent density. The same equations govern the physics.
Navier-Stokes Equation for fluid-flow dynamics
Heinrich Hertz
Laminar vs Turbulent Flow -- turbulence from dimples reduces "Drag" (low pressure area behind ball)
The Reynolds Number is a dimensionless number that expresses the tendency of the flow to be laminar or turbulent.
If you could hit a ball with a velocity to impart a high enough Reynolds Number, the drag drops way down -- even for a smooth ball. Tiger Woods may be able to achieve this on occasion.
Reynolds Number Calculator -- indicating character of flow as laminar or turbulent
Bob Thurman
Geodesic
GeometryOVERVIEW: The hexagonal pattern is common in nature -- in crystal lattices, in bee hives, and elsewhere -- due to its facility for relating rectilinear shapes and volumes to spherical shapes and volumes. A hexagon is six equilateral triangles, so it is really taking advantage of the way the triangle mediates between the square and the circle. The pentagon is five equilateral triangles. The Callaway pattern has 332 hexagons and 12 pentagons, and this pattern is a result of fitting a web of hexagons onto a sphere to maximize coverage of the sphere.
A regulation golf ball is spherical and has 384 dimples, arranged in a triangular pattern. Most of the dimples are surrounded by six other dimples, but some are surrounded by only five. How many dimples have only five neighbors? Give a mathematical proof if possible. Explain steps and reasoning.Ê
Solution: (From Nick McGrath, persistent and industrious entrant; sorry about my e-mail!) "Since we are told the dimples are surrounded by either 5 or 6 neighbors we can consider the problem as one of tiling a sphere with a combination of hexagons and pentagons. In the case of the golf ball each of the "faces" (hexagonal or pentagonal) has a dimple at its center as well as one at each of the vertices. Since it is important that the ball has a symmetrical pattern for consistency of flight the "faces" must be symmetrically oriented relative to the center of the ball. In addition, we can assume regular pentagons and hexagons. [Dan's note: In practice, actual regular hexagons won't provide the proper gradual curvature necessary for a spherical shape.] Ê First question: Why not all hexagons? [ ... Nick provides a proof by contradiction.] Second question: If we have a combination of hexagons and pentagons, how many pentagons are there? Counting ends of edges we have 3V=2E. Also, F=P+H (P is the # of pentagons and H is the # of hexagons). Counting sides of edges we have 2E=5P+6H so 3V=5P+6H. Substituting ito Euler's formula: V+F-E=2 gives us (5P+6H)/3 + (P+H) - (5P+6H)/2 = 2 => 10P+12H+6P+6H-15P-18H = 12 => P=12. We must have12 pentagons; so of the 384 dimples on the golf ball, exactly 12 have only 5 neighbors. (In fact the planes of the 12 pentagons, if extended, would form a regular dodecahedron. See my geometry page for more info and pictures of tessellations and Polyhedra. - Dan)
Disney World's Epcot Center
Paper model of geodesic dome for astronomy showing equilateral-triangle-based relation between hexagons (six such triangles) and pentagons (five such triangles)
Icosahedron -- usual form of geodesic
Nike Geo soccer ball geometry:
Puma soccer ball with patches in hexagonal-pentagonal pattern, also has small dimples for improved flight
Top competition ball with "Dimple CW" -Puma claims the "Dimple CW System is for unbeatable control and straight trajectory. The dimples cause less drag and more lift than a regular surface which provides further, higher and faster shooting speed". "The FIFA-approved, patented ball ensures maximum trajectory, precision, and increased shooting speed by adapting the physics designed for golf balls. The dimpled surface area gives the ball the positive flight characteristics of a golf ball: consistency and length of trajectory. The dimples create an air pocket of Òpositive turbulenceÓ around the ball in flight, which translates to superior distance, maximum speed and unparalleled accuracy."
The Buckminster Soccer Ball
Early footballs were sewn up with laces. These days, footballs are made from synthetic leather patches sewn together in a design based on the 'Buckminster Ball' or known as the Buckyball. The American architect Richard Buckminster Fuller came up with the design when he was trying to find a way for constructing buildings using a minimum of materials. The shape is a series of hexagons, pentagons and triangles, which can be fitted together to make a round surface. The modern soccer ball is essentially a Buckminster Ball consisting of 20 hexagonal and 12 pentagonal surfaces. When they are sewn together and inflated they make a near perfect sphere.
Keep dirt out of the dimples or suffer the aerodynamic consequences -- it's the inside of the dimple that stirs the air -- or more properly, it's the edges of the dimples that knock the nearest air molecules about as the ball slips thru the sky.
Dimples
in Nature -- Buckyballs and Pollen SporesThe 60 carbon atoms form what is called a truncated icosahedron, which literally looks like a soccer ball. It consists of 12 regular pentagons and 20 regular hexagons. The C60 molecule does not bond readily to other atoms or molecules, as all bonds are to another carbon atom. The buckyball is the only molecule of a single atom to form a hollow spheroid, and it spins at over one hundred million times per second. According to John R.D. Copley, physicist at the National Institute of Standards and Technology, "there are 174 ways that [the buckyball] can vibrate." One of the principal researchers of the buckyball is Richard E. Smalley, professor of physics and chemistry at Rice University, Houston. Smalley asserts that it is the largest possible symmetric molecule, saying: Sixty is the largest number of proper rotations in the icosahedral group. That, in turn, is the largest point group-the largest group where symmetry operations, rotations, reflections, etc. leave one point unmoved. This makes C-60 the most symmetric possible molecule.
Gravity Map of asteroid crater off Yucatan 65 Million Years ago
Hollow Buckyball / Fullerene containing captured extraterrestrial gas from a distant star brought to earth in an asteroid -- the gas is still inside the buckyballs after 65 million years
Palynology -- the Science of Pollen -- Periporate pollen -- Pollen dimples
Niklas, K. J. (1987). "Aerodynamics of wind pollination." Scientific American 257: 90-95.
Salicornia virginica -- Pickleweed pollen of Class Periporate
Various pollens -- note hexagonal dimples in 26A-C
Australian swamp pollen with hexagonally arranged dimples
Golf
Ball Dimple History -- from Scuffs, the Brambles, to DimplesInitially, "featherie" balls were smooth. Caddies noticed that scufffed-up featheries flew further and started deliberately scuffing them. Later, balls were deliberately scored and hammered by hand to get better flight performance. Gutta percha (rubber) balls were more easily scored and hammered by hand.
After 1880, gutties were produced with patterns on their surface in an attempt to reproduce the distance characteristics of a scored Featherie. With the Victorians came industrialisation and mechanisation, and by 1890 Gutties were being made in moulds which further increased their affordability, consistency and quality. The most notable pattern of the period was the 'Bramble' - raised spherical bumps across the surface of the ball. Many of the rubber companies including Dunlop began mass-producing balls which killed off the handcrafted ball business.
BRAMBLE PATTERN COVER GOLF BALLS
In 1898, Coburn Haskell introduced the one-piece rubber cored ball which was universally adopted by 1901 after it proved so effective in the British and US Opens. These balls looked just like Gutties but gave the average golfer an extra 20 yards from the tee. These balls were constructed from a solid rubber core wrapped in rubber thread encased in a gutta percha sphere. Once W. Millison developed a thread winding machine, Haskell balls were mass-produced and therefore more affordable.
Throughout this period there was a lot of experimentation with the patterns on golf balls - one of the reasons why golf collecting is so interesting. When William Taylor first applied the dimple pattern to a Haskell ball in 1905, golf balls took on their modern form. The dimple pattern maximises lift while minimising drag.
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