Final Answers
© 2000-2020 Gérard P. Michon, Ph.D.

Pool and Billiards

It is impossible to imagine Goethe or
Beethoven being good at billiards or golf.

Henry Louis Mencken (1880-1956)

Is it, really? Mozart owned 12 cues and Linus Pauling played bottle pool.

Michon
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See also:

Related Links (Outside this Site)

Billiards With a Bottle. And This Game Is Dying? by Harry Hurt III.
Billiards and Snooker from England and the Commonwealth by J. Masters

The Physics of Billiard by Jim Loy.
IlliPool: The Math and Physics of Billiards by Brian Townsend.
BCA Equipment Specifications (Warning: Wrong weight for snooker balls)
Physical Properties of Pool Equipment by Dave Alciatore & Tom Ross.
Amateur Physics for the Amateur Pool Player by Ron Shepard of Chicago.
The Physics of Pool by Franco Normani.
Samm Diep / Vidal "Cherry Bomb" : Tip Jar | Samm's Side Pocket | Blog
Improving Your Carom Shot | Jim Loy's Billiards/Pool Page

Glossary of cue sports terms (Wikipedia).
In French: Billard | Règles | Théorie des effets | Vocabulaire | Blog

Regulating Bodies & Other Billiard Associations:

Coat-of-arns of Gaspard Gustave de Coriolis
  • Théorie mathématique des effets du jeu de billard (1835)
    by Gaspard Gustave de Coriolis (1792-1843; X1808).
    English translation (2005) by David Nadler.
  • Advanced Technique in Pool and Billiards (1990) by Robert Byrne.
  • The Science of Pocket Billiards (1989, 1995) by Jack H. Koehler.
  • The Illustrated Principles of Pool and Billiards (2004, Sterling Publishing) by David Alciatore, Ph.D. (Dr. Dave) with video illustrations, including:
    • NV B.41: Coriolis massé shot aiming method, with large curve.

Spotlight on Billiards | Le Billard. Français, Américain, Snooker et Pool

Movies : The Hustler (1961) | Trailer
The Color of Money (1991) | Trailer | Ending
Poolhall Junkies (2002) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
9-Ball, the Movie (2011) | Promo | Trailer

Science : Amazing Billiards in Super Slow Motion by Colin Colenso.
The Double-Kiss Zone by David Alciatore (DrDaveBilliards) | Bob Jewett
Digitally Assisted Billiards by Matthew Straub & Justin Needham.
Deep Green & Augmented Reality Pool (ARPool) RCVLab (Sammy Jordan).

Product Demos : The Pro Shop (UK) | Cue Clean | Pocket Lathe
Magic Ball Rack | Just-A-Bridge by Larry Keller | Flexi-Rest (The Big Idea)
Gravity Cue

Pocket Billiards (Pool, Snooker, Pyramid, Bumper Pool)
[9-Ball] 3-Foul Rule (Dong) | 2005 US Open (Ismael Paez vs. Mika Immonen)
[8-ball] Stripes & Solids (US) | Blackball cassé-fermé (runout) by Craig Marsh
Efren Reyes vs. Francisco Bustamante [ 1 | 2 ] (2001 8-Ball Invitational)
[Straight Pool = 14.1] 15 Balls to Thorsten Hohmann's Championship (2006)
[One-Pocket] Efren Reyes vs. Jose Parica (Galveston) | Max Eberle
[Bank Pool, Banks] Derby City Classic 1 | 2 | 3 | 4 (Daulton vs. Gregg)
[Rotation Pool, 61] Rules | Honduran Pool | rotation runout (playing the ghost)
[Ten-ball] 2009 Women's World Championship Yu-Ram Cha vs. Shin-Mai Liu
[Seven-ball] Luther "Wimpy" Lassiter vs. Willie Mosconi (1980) 1 | 2 | 3 | 4
[Cutthroat Pool, 3 players] Scratch? by Michael Lamendola | Bikini Pool
[Three-ball, several players] Carnie Ball by Michael Lamendola | Break Trick
[Snooker] Line of Aim by Jack Karnehm | Showmanship of Steve Davis
First televised 147 maximum break (1982) | Epic loss to Dennis Taylor (1985)
Stephen Hendry at the Crucible Theater in 1995 and 2009.
Ronnie "The Rocket" O'Sullivan's ninth 147 (2008) and his fastest one (2006).
Snooker Coaching by Steve Davis 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
Pot of the century by "Big" Bill Werbeniuk (miscue and rebound over a ball).
[Russian pyramid] Kremlin Tournament | Evgeny Stalev | Tricks
[Kaisa] Finnish Billiards (2 white cue balls, 2 reds & 1 yellow kaisa) | Trailer
[Bumper Pool, Arms of Thomas Jefferson T. Jefferson, 1805] Shots by Snoodges. | Tito's tutorial

Trick Shots (performed on pocket tables)
Oliver Whitehouse | Jeanette Lee "The Black Widow" sinks 12 balls at once.
Mike Massey "Tennessee Tarzan" : Trick Shot Collection | Finger Pool
Florian "Venom" Kohler of Kingersheim, Alsace (France) with Mike Massey
Pavel Poledno (www.trickshot.ic.cz) | Tommy Vancraybeek
Yoshikazu Kimura of Osaka, Japan | Yoshikazu Kimura & Mike Massey
Eric "The Preacher" Yow : Massé Insanity | Eric Yow and Andy Segal
Andy "Magic Man" Segal : Medley | Barthelette, Yow, McPhail, Segal
Willie Mosconi (1987) | Steve Mizerak (2000) | Tom "Dr. Cue" Rossman
Unbelievable Pool Trickshots & Impossible Pool Trickshots (2012) compilations from InsidePOOL, Florian "Venom" Kohler & Rick "PrayingMantis" McAvay.

French Billiards or "three-ball carom" is played on a pocketless table with a red object ball (bille de but) and two distinct cue balls (billes de choc, yellow or white, spotted or not). Each shot must be a carambole where a cue ball hits the other two balls under the conditions imposed by the rules of the discipline (for artistic billiards those rules are different for each shot). The 7 currently practiced disciplines of French billiards are listed below in order of increasing difficulty, starting with the 5 so-called classic disciplines (jeux de série) which involve mostly low-speed action over short distances. Among those, each of the three modern flavors of Balkline (jeu de cadre) is denoted by a pair of numbers; the first one is the width of the cadre (in cm) and the second one is the maximum number of consecutive shots allowed within the same rectangle (71 cm is half the width of a full-size table, 47.4 cm is one third). Unrestricted straight-rail allows poussette (nursing) tactics that can make championships uninteresting (the so-called serie à l'Américaine was invented in Canada by the brothers Cyrille and Joseph Dion around 1870). Maurice Vignaux (-1916) still holds the straight-rail record for the run of 1531 points he made in Paris in 1880, on April 10-14, against George F. Slosson. The precursor of the many variants of modern balkline was the short-lived Champion's Game (1879-1883) which merely barred corner play using 18'' by 38'' lines (Slosson held the record for this, with a run of 398 points achieved in 1882 during a match against Vignaux).
- Straight rail : (Partie libre) taught by Thierry de Marchi [1,2] in French.
- 47/2 : Georges Bourezg [1,2,3] by Louis-Emile Galey | Laurent Guénet [blog]
- 47/1 : Arnim Kahofer | Xavier Gretillat | P. Soumagne vs. W. Gerimoni | 2
- 71/2 : Marek Faus | Esteve Mata vs. Raul Cuenca | 2 | 3 | 4 | ... | 16 | 17
- Cushion caroms ("One-cushion") Raymond Ceulemans (1984)
- 3-Cushion : 15 ways to start | Frédéric Caudron (1996) | Run of 15 by Sang Lee vs. Hank Habraken (1999) | Daniel Sanchez (2005) | Torbjörn Blomdahl (2006) | Marco Zanetti (2009) | Dick Jaspers (2009) | Carom
- Artistic billiards : Raymond Ceulemans | Semih Sayginer | Jean Reverchon Haci Arap Yaman vs. Xavier Fonellosa | Florian Kohler | Martin van Rhee | Thomas Ahrens | Sander Jonen |

Pentathlon is a form of international billiard competition combining straight-rail to 200 points, 47/1 and 71/2 to 150 points, cushion-caroms to 100 points and 3-cushion to 30 points. Biathlon involves 3-cushion French billiards and 5-pin Italian billiards.

[5-pin Italian billiards & 9-pin goriziana] Brigitte Nielsen (Bye Bye Baby, 1988)
19 Opening Shots | 11 Opening Safety Shots | Biliardo 5 Birilli | Uneven Tricks
[4-ball carom] Yotsudama or Sa Gu (Korean billiards) | Czech 10-carom, etc.
Boccette is digital billiards (no cues) on a carom table, with 5 skittles & 9 balls.
Pétanque is played with a 38 mm jack, between 4 players. Each one has 4 cue balls (48 mm) of a specific color and plays bank shots to get nearest to the jack.

Training : Instructional Videos by Mike Page (FargoBilliards) BCA instructor. Fargo Billiards & Gastropub, in Fargo, North Dakota.

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The Physics of Pool and Billiards

This page (which is still a work in progress) will neither teach you the rules of the many extant billiard games, nor is it intended to improve your skills (I am not qualified to do that, but I recommend exploring some of the many encyclopedic and video links provided here).

One limited aim is to provide a rational introduction to all billiard games by describing their common history and characteristics as well as some basic differences in their implements.

Because Numericana is a mathematical site, the main emphasis is to explain why billiard balls (and cues) move the way they do. Many people share a fascination for the physics involved and rightly celebrate billiard masters as practitioners of a true form of art.


(2010年12月31日) Size of the playing area (playbed) in a billiard table.
The nominal size of a pool table is 8'' more than its playing length.
(Traditionally, that nominal size was the length of the slate slab.)

The width of the playbed in a billiard table must be half its length. The width and the length are measured between the tips of opposing rail cushions.

The nominal size of a table (expressed in feet) is 8'' more than the length of its playing area. The advertised size (or quoted size) of a standard pool table is exactly equal to its nominal size, except in two cases:

  • A standard 7' table has a true nominal size of 7' 2'' corresponding to a playbed length of 78'' (not 76'' ).
  • An 8½' table has a nominal size of 8' 4'' corresponding to a playing area 92'' long (not 94'' ). Tables of that unusual size are also referred to as oversize 8 foot tables (or even 8 foot tables, which they're not).

The actual outside length of a pool table is almost always a few inches longer than its nominal size, but that's irrelevant to the calculation of the clearance space needed around a given table (which depends only on its cushion-to-cushion dimensions and on the length of the longest cue you wish to use). The traditional length of the playbed in carom tables used to be specified as 8 pieds & 9 pouces in terms of the royal foot (pied de roi) used in France (and elsewhere, for scientific purposes) before the metric system. The legal conversion factor for this obsolete unit is effectively determined by Canada, which still uses an exact multiple of it for surveying purposes (the arpent). The pied de roi should thus be considered to be exactly 12.789'' or 0.3248406 m. With ludicrous precision, this makes the nominal length of a traditional carom playing surface exactly equal to 2.84235525 m. This piece of trivia is now all but forgotten. Instead, modern regulators have chosen to round the above number to the nearest centimeter (2.84 m) and allow a tolerance of 5 mm. A manufacturer mindful of tradition could still aim for the above bed length rounded to the nearest millimeter (2.842 mm) and enjoy a comfortable manufacturing tolerance of 3 mm. Following the above pattern, the nominal size of a traditional carom table is 8'' longer than its playing area (9.984' ). Such pocketless tables are advertised as 10 foot tables. Converting a pool table to a carom table...

The 9-foot tournament pool table has exactly the same playing field (100'' by 50'' ) as the so-called small carom table (which has no pockets). The diagonal of a small carom bed is nearly the length of a full-sized one (111.8'' = 2.84 m).

Some manufacturers provide kits ("plugs") to convert a pool table into a small carom table with add-on rails that plug the six pockets (see picture at right).

Inexplicably, the current regulations for snooker specify a width and a length for the playing area which are not in a 1:2 ratio, although this was clearly not the intend of the regulators. Nevertheless, the large tolerance of 13 mm allows the construction of correctly proportioned playbeds, including three that have a whole number of millimeters per diamond unit, namely:

  • Width = 1788 mm. Length = 3576 mm. Tolerance = 2.7 mm
  • Width = 1784 mm. Length = 3568 mm. Tolerance = 7 mm
  • Width = 1780 mm. Length = 3560 mm. Tolerance = 4 mm

If the snooker regulators wanted to fix their mistake, they could choose one of these three specifications, ideally adopting a grandfather clause allowing an extended tolerance for tables built before a certain date (in order not to rule out equipment that was compliant when it was built). The last possibility listed has the superficial advantage of dimensions involving a whole number of centimeters (playbed dimensions of 3.56 m by 1.78 m) but it would entail a fairly large grandfather tolerance (22 mm in length and 15 mm in width).

To avoid numerical inconsistencies in the present article, I chose the middle specifications (3568 mm by 1784 mm) which has the best compatibility with the published (flawed) standards. If adopted (with a simplified grandfather tolerance of 19 mm in either dimension) those new specifications would entail manufacturing tolerances of 7 mm on 12' tables, which would be directly comparable to what's currently required for carom tables (namely, 5 mm on 10' tables). Every table made to the new specifications would comply with the former standards.

Physical Dimensions of the Basic Equipment Used in Cue Sports
Length of playbed is indicated between parentheses. It's exactly twice the width, measured between cushions.
Mini Pool (UK) Pool (US) Carom Snooker
Full-Size Table 5' 7' (78'' ) 9' (100'' ) 10' (2.84 m) 12' (3.57 m)
Smaller Size(s) 4' 6' (64'' ) 7', 8' (88'' ) 9' (100'' ) 8', 9', 10'
Ball Diameter 44.45 mm 50.8 mm 57.15 mm 61.5 mm 52.4 mm
Cue Length 36-48'' 52-57'' 56-58'' 56-58'' 57-63''
Tip Diameter
[ most common ] (8 mm)
8-10.5 mm
[ 8.5 mm ] 9-14 mm
[ 12.75 mm ] (12.25 mm)
[ 12 mm ] 8.5-11 mm
[ 10 mm ]
The unofficial format listed as mini is found in folding tables for casual family use. Smaller tabletop billiard boards are used with marble-like balls (1¼'' = 31.75 mm or smaller) barely playable with tiny cuesticks.

At the other end of the spectrum, tournaments of Russian billiards (Pyramid) are played on regulation snooker tables using large balls (68 mm diameter) which are barely 5 mm smaller than the corner pockets. Some amateurs play that game with slightly smaller balls (60.3 mm) on less massive tables (e.g., 9', 8' or 7').

The space around a pool table must allow shots where the cue ball is against the cushion and the cue stick is perpendicular to the edge. So, the distance between the wall and the edge of the playing area (cushion nose) must be at least one cue length, plus six inches of draw (backstroke).

So, with 58'' cues, a minimum distance of 64'' (1.63 m) is required between the nose of a cushion and the wall behind it. The wall-to-wall distance required to play a given table with a full cue is thus 128'' (3.25 m) longer than either dimension of the table's playing surface (the size of the rails is irrelevant). For a full-size (9-ft) pool table, this works out to be 228'' by 178'' (5.79 m by 4.52 m). A 7-ft table (playing length 78'') fits in a 5.23 m x 4.24 m room. A table can be used in an undersized room by playing the aforementioned critical shots with a "shorty" cue (whose maximum length is 6'' less than the smallest cushion-to-obstacle distance). According to regulations, a pool cue must be at least 40'' in length but shorter cues (down to 30'' or so) are available which can accomodate severe space limitations (they're also great for younger players).

Carom tables have no pockets. The other tables listed above have 6 pockets (at the 4 corners and in the middle of the long sides). The width of each pocket is such that two balls of the tabulated diameter will barely fit side by side between the slanted rails (watch: How to Measure a Pocket).

Diamond Sights & Diamond Unit :

The conventional unit of length in billiards is called the diamond and it's equal to the center-to-center distance between the adjacent diamond marks that all billiard tables have (or should have) on their rails. One diamond is equal to one fourth of the width of the playing area (or one eighth of the length). Pocketless (carom) tables thus feature 9 diamond marks on the long rails and 5 diamond marks on the short ones, including extreme marks (which are sometimes omitted) that indicate the positions of the noses of the cushions perpendicular to the rail. On pool tables, the presence of pockets eliminates the four pairs of corner marks and the two marks in the middle of the long sides. This only leaves six sets of three actual diamond markers between adjacent pockets. Nevertheless, the underlying diamond grid is exactly the same for pool tables and pocketless tables.

The value of the diamond unit varies with the size of the table
Quoted Size Nominal Size Playing Length Diamond Unit
12' Snooker 12''' 3.568 m 446 mm
10' Carom 9' + 30 cm 2.84 m 355 mm
9' 9' 100'' 12.5'' = 317.5 mm
' 8' 4'' = 100'' 92'' 11.5'' = 292.1 mm
8' 8' 88'' 11'' = 279.4 mm
7' Bar box / Pub 7' 2'' 78'' 9.75'' = 247.65 mm
6' 6' 64'' 8'' = 203.2 mm
5' Mini 5' 2'' 54'' 6.75'' = 171.45 mm
L + 8'' L L / 8

For traditional tables, the actual length of the table would typically be L+11½'' which is slightly larger than the nominal size.

The nominal size (L+8'') is the length of the slate slab around which the table is constructed. The size of that is thus L+8'' by L/2+8'' with a thickness of 1'' (thickness may vary, see below). The density of solid slate rock is 2.691 g/cc. Neglecting the pocket cutouts, this makes the slate slab for a 7' table weigh 178 kg. The slab of a 9-foot table weighs 262 kg and is normally divided into 3 pieces of 92 kg each. A full-sized snooker table features about 512 kg of rock, divided into 5 pieces of 102 kg each.

Do it yourself: Pool Table Plans | "How it's made" Video : Pool Tables
Novelty Tables: Modern (Mars Made) | Glass (Nottage Design) | Round | Gyroscopic | 3D-Miniature


(2011年04月07日) Slate Slab

The density of slate rock is 2.691 g/cc. Thickness vary from a minimum of 3/4'' (19 mm) to 7/8'', 1'' (Pool tournament) 30 mm or even 45 mmm (Carom tournament),

[画像: Come back later, we're still working on this one... ]

Do it yourself or repair: Billiard Slate for Sale ( Lakeside Billiard Supply )


(2011年02月24日) Billiard Cloth

[画像: Come back later, we're still working on this one... ]

Championship Fabrics | Simonis Cloth

k66 profile (pool cushion)
(2011年02月24日) Cushions

K66 profile.

[画像: Come back later, we're still working on this one... ]

Championship Cushions | Brunswick Superspeed Rubber Rails


(2010年12月31日) Billiard Balls
From wood or clay to ivory, to celluloid, to Belgian phenolic balls.

Early billiard balls were made out of wood. They wore out quickly and developed bruises and flat spots... Clay balls were also used as late as the 1960's. They were fairly inexpensive but broke too easily.

The exact time when ivory billiard balls (ivories) were introduced isn't well documented. Ivory balls are mentioned in the first edition of The Compleat Gamester (1674) by Charles Cotton. The oldest extant reference to ivory balls is in the 1588 inventory of the 4th Duke of Norfolk (Thomas Howard, 1536-1572) who kept at Howard House "a billyard bord covered with a greene cloth [...] three billyard sticks and 11 balls of yvery".

Legend had it that the best matched three-ball sets were obtained from a single tusk of a female elephant. In fact, this wasn't so, since balls made from the same tooth could vary considerably. Instead, the matching was done by selecting from a large number of finished balls. Only 4% of those matched sets were considered good enough for tournament play (according to an interview of one James Burroughes published in the New York Times on December 1, 1889). Balls were turned by highly-qualified workers so that the central nerve in the tusk appeared on opposite points in the ball. Like wood, ivory swells across the grain in a damp atmosphere. So, a spherical shape can only be maintained at constant humidity.

Changes in humidity also promotes cracking, which is what motivated the invention of heated billiard tables. Such tables remain mandatory today in international carom tournaments, because maintaining the surface a few degrees above ambient temperature prevents dampness of the cloth and ensures the consistency of the playing surface.

Thousands of elephants were slaughtered yearly to provide for the needs of the billiard industry. Well before the current ecological mindset, there were concerns that the supply of ivory was dwindling too rapidly and that human lives were put at risk in the hunts. A 10,000ドル prize for an artificial substitute to ivory billiard balls. was offered by the Phelan & Collender billiard manufacturer (which merged with Brunswick Billiards in 1884).

The development of the modern substitutes for ivory started with the first man-made plastic, invented in 1856 by Alexander Parkes (1813-1890) who plasticized nitrocellulose with camphor (the stuff was dubbed Parkesine at first). In 1868, John Wesley Hyatt (1837-1920) investigated a high-pressure manufacturing process for that same substance, which he would popularize with his older brother, Isaiah Smith Hyatt, under the name of celluloid (the name was duly registered in 1873, but it's now genericized).

Celluloid was used to make the so-called composition balls which used a denser substance in their cores to achieve the correct density. Such balls didn't quite play like regular balls, partly because they didn't have the same moment of inertia as homogeneous spheres. That desirable characteristic would only be achieved with the advent of the synthetic resins that allow an homogeneous mix with dense powders (like calcium carbonate).

Modern celluloid (used for ping-pong balls and guitar picks) is made with acetic acid instead of nitric acid. It's much safer than the original flammable celluloid that could reportedly explode during manufacture.

The nominal density of modern billiard balls is 1700 kg/m3 . That's close to the mean density of ivory [1.70(2)] the former substance of reference. The maximal density of 1740.40 kg/m3 , would give a 2¼'' ball (57.15 mm) its maximal regulation mass of 6 oz (about 170 g). Incidentally, a ball with a volume of 100 cc (0.1 L) would have a diameter of 57.59 mm...

A 2¼'' ball (57.15 mm) must weigh between 5½ oz (156 g) and 6 oz (170 g). At the nominal density of 1700 g/L, a 2¼'' ball would weigh 166.15 g.

The most praised modern billiard balls are made with phenolic resin, which is a thermosetting bonding compound obtained by polymerizing C6 H5 OH (phenol or carbolic acid) with HCHO (formol or methanal). That synthetic material was invented by the Belgian chemist Leo Baekeland (1863-1944) in 1907. It became popular in the 1920's under the name of Bakelite®. Its uses have included telephone casings, electrical insulators, kitchenware, toys and even jewelry... Due to high manufacturing costs, this material has now been supplanted by other mouldable plastics, except in top-quality billiard balls and a few other critical products.

Inert countertops (in the lab or at home) are currently made from phenolic resin, with a filler consisting of up to 70% of cellulose fibers (e.g., Richlite®). Phenolic resin is also commonly applied as a thin layer on both faces of a wood product known as phenolic plywood.

Since pure phenolic resin has a fairly low density of 1215 g/L, heavier filling materials (colored or not) must be used to reach the aforementioned nominal density of modern billiard balls (1700 g/L).

I don't know what filler is actually employed in phenolic balls, but I am tempted to investigate calcite (density 2.71) to mimic the high-calcium content of natural ivory, in which case 51.7% of calcite (by mass) would be needed (about 32.44% by volume). That works out to be 15 parts of finely powdered calcium carbonate for 14 parts of resin. Recall that the average density of a mix is a harmonic mean:

15 / 2.71 + 14 / 1.215 = (15+14) / 1.700113...

Sizes of Billiard Balls Used in Modern Games (nominal density: 1.7 g/cc)
"Grapefruit" and "rock" are calibers for cueballs in automatic tables that detect and return oversized or heavy balls.
Game FormatDiameter VolumeNominal
MassRegulation Mass
Min.Max.
? 72.00 mm 195.43 cc 332.23 g
Pyramid - full 68.00 mm 164.64 cc 279.88 g
Carom 61.50 mm 121.79 cc 207.05 g 205.00 g 220.00 g
Pyramid - small 60.50 mm 115.95 cc 197.11 g
Grapefruit ( 23/8'' ) 60.33 mm 114.95 cc 195.41 g 205 g (measured)
Rock ( 2¼'' ) 57.15 mm 97.73 cc 195.41 g Heavier Density
US Pool - 2¼'' 57.15 mm 97.73 cc 166.15 g 155.92 g 170.10 g
Bumper ( 21/8'' ) 53.98 mm 82.33 cc 139.97 g
Snooker ( 21/16'' ) 52.39 mm 75.28 cc 127.98 g
UK Pool - 2'' 50.80 mm 68.64 cc 116.69 g
Pétanque - cue 48.00 mm 57.91 cc 98.44 g
Pétanque - jack 38.00 mm 28.73 cc 48.84 g
Mini - 1¼'' 31.75 mm 16.76 cc 28.49 g
Half-scale ( 11/8'' ) 28.58 mm 12.22 cc 20.77 g

The Belgian company Saluc S.A. (founded in 1923 and owned by Armand Capital Group of Chicago) dominates the manufacture of phenolic billiard balls, which it sells under the Aramith brand, in several grades. From the Belgian village of Callenelle, they supply 80% of the billiard balls worldwide.

The largest billiard company in the World, Brunswick Billiards, an American manufacturer of pool tables founded in 1845, started making phenolic billiard balls in 1945. Now, they sell only the Brunswick Centennial prestige brand, which is actually manufactured by Saluc to the same specifications as the finest Aramith balls (a 16-ball set of either brand retails for about 250ドル).

Other brands offer more affordable balls, made from unsaturated polyester resins, which do not quite match the performance or durability of real "Belgian phenolic balls". Simpson's decorative Elephant Beautiful Balls (about 180ドル a set) have based their reputation on good looks, not durability.

The manufacture of "Elephant Balls" is now commissioned by Sterling Gaming, a billiard wholesaler from Matthews (North Carolina) retailing as CueSight Technologies. Under the Sterling brand, they sell other styles of balls, in different grades, based on the same technology.

Bargain brands like Action are offering decent 16-ball sets for 30ドル or so.

Unbranded cheap acrylic billiard balls are apparently off the market...

Videos on sphere-making: Bowling Balls | Marbles | Ball Bearings


(2010年12月31日) Cue Sticks, Butts & Shafts (Queues, Talons & Flèches)

A pool stick should have about 3 times the mass of the ball it's intended for. Snooker cues have longer and thinner shafts with shorter butts featuring a flat section which can accomodate a plate. Some snooker cues can be fitted with butt extensions which may or may not be associated with the use of a mechanical bridge or rest (the latter term used to be a slang term).

Because of the large size of snooker tables, rests are more commonly used in snooker than in other forms of billiards. They come in many shapes and designs: rake, cross, spider, swan (swan-neck spider) and extended rest. Lately, the versatile "Flexi-Rest" has been supplementing the traditional assortment and seems to be slowly replacing part of it.

Nowadays, the finest cues are meant to travel with their owner and come in two pieces which are screwed together at play time:

  • An ornate rear thick part, called butt (talon in French).
  • A plain thin part (½'' in diameter) called shaft (flèche in French).

For pool and carom billiards, two-piece cues always feature a center joint (i.e., the two pieces are roughly of the same length). On the other hand, snooker cues are almost always "3/4 jointed", which is to say that the buttpiece is about 16'' and the shaft is 42'' (a foot longer than in center-joint design). The traditional design for a one-piece snooker cue calls for a butt of ebony to be spliced into a shaft of ash up to a distance of about 22'' from the rear. That distance is typically respected in jointed cues but the splicing is limited to the front part of the cue; the rear part being solid ebony.

The joint between the two parts is mechanically critical. A superior solution, introduced by the Canadian cuemaker Thierry Layani, is the conical joint.

Selecting a snooker cue | "How it's made" Video : Pool Sticks
Thread : Are We All Using Low-Deflection Shafts, Now? (Pool.bz) | OB Cue Shafts

Novelties : Demo by Jason Lynch of Pneu-Power Cues (2010) 199ドル | Laser Cue by CueSight (1999) 149ドル


(2011年03月29日) Cue Case (French: étui de billard)
[画像: Brown Sonoran (Layani Cue) ]

Only once in my adult life did I travel to a remote location for the sole purpose of having fun: In the Summer of 1976, I spent several weeks on the Island of Mauritius at the Club Méditerranée resort, where I learned to water-ski and was initiated to a billiard game that I would only know as billard sud-africain until I learned its correct name, much later, from a British TV broadcast: Unwittingly, I had learned snooker !

Although snooker was invented around 1875 (possibly by Colonel Sir Neville Chamberlain of the British Army garrisons of India) its modern popularity is due to the advent of British color TV broadcasts (1969).
Layani Conical Joint

Today, on my 55-th birthday, I finally got my own state-of-the-art billiard gear... As an engineer, I could only go for the conical joint of Thierry Layani. Once you know about it, no other cue joint makes sense.

Here is what's in my case, now:

  • The 29½'' (420 g) no-point Layani Brown Sonoran buttpiece pictured at left (nutmeg-stained curly maple with bloodwood, Brazilian wood and ebony inlays and rings) sporting a velvet grip of 32.5 cm (Renzline manchon weighing 15 g).
  • Predator 3142 shaft (no logo, 0.6'' ferrule, 114 g). Conical joint by Thierry Layani (thanks to Philippe Singer of Kozoom).
  • Layani pool shaft (12.75 mm tip / 29 inches = 73.66 cm / 123 g).
  • Layani 3-cushion shaft (12 mm tip / 69 cm / 105 g).
  • Layani 5-layer medium-hard cue tips (13.5 mm in diameter).
  • A 25 cm Layani extension tube (28.5 cm with joint) 112 g.
  • A weight kit (balancing bolts & key) 56 g, 36 g, 26 g, 16 g, 10 g.
  • 4 female Layani joint protectors (for shafts).
  • 2 male Layani joint protectors (for buttpieces).
  • Just-A-Bridge. Moosehead Bridge Head.
  • Willard's Tip Shapers (nickel and dime).
  • Blue Diamond chalk (blue). Silvercup chalk (green).
  • Aramith micro-fiber cloth, with backing.
  • Etc.

The Layani extension normally goes between butt and shaft. Happily, it doubles as an 11½'' buttpiece (with a joint protector in the rear) which is just long enough to form a legal jump cue, using any 29'' shaft.

The minimum length allowed for a pool cue is 40'' and the maximum weight is 25 oz. There's no set maximum length or minimum weight. The diameter of the tip must be between 9 and 14 mm.

What's in the pool cue case of...
Efren "Bata" Reyes | Johnny Archer (The Scorpion) | Ralf Souquet (The Kaiser) | Eric Frost
Earl Strickland (The Pearl) | Eric "Fatboy" Peterson | Max Eberle (Mad Max) | Eric Yow (The Preacher)
Ladies: Jasmin Ouschan | Samm Diep | Sarah Rousey | Kelly Fisher | Laetitia Dos Santos (in French)
Carom Players: Pierre Soumagne (in French) | Peter De Backer | Frédéric Caudron



(2010年12月31日) Cue Tip (French: procédé)

Captain François Mingaud (1771-1847) was one of the most famous billiard player of his day, in his native France and elsewhere. He had designed a very popular cue in 1790 which he perfected in 1807 by inventing rounded leather tips (while imprisoned in the Bastille). Captain Mingaud also inspired the first complete analysis of the game by the physicist Gaspard Coriolis, in 1835.

Modern leather tips come in several grades, according to their mechanical properties: soft (or slow) medium and hard. They may be layered or include additives to achieve the desired grade. The hardest tips forgo leather entirely, in favor of the type of hard resin used in modern billiard balls; they are commonly known as phenolic tips and are exceptionally durable (they hardly ever require shaping or replacement for many years). The misguided current trend is to ban phenolic tips on break cues (such tips will probably always remain legal on jump cues, where they are all but indispensable, and on playing cues, where there are all but useless). The advertised motivation of regulators is to increase the life expectancy of cueballs...

Curiously enough, the use of leather tips can be objectionable to some players for religious reasons, since "leather" is often pigskin (according to many manufacturer specifications).

The front end of a tip should have a spherical shape. Poolplayers can choose between only two sizes (named after the ten-cent and five-cent US coins) because only two gauges of shaping tools are available:

  • Dime: Nominal radius of 0.3532'' (8.9535 mm). About 9 mm.
  • Nickel: Nominal radius of 0.4175'' (10.6035 mm). About 10½ mm.

The most popular shaping tools (single or dual gauge) include:

Video Guide to Pool Cue Tips | Fitting a Snooker Cue Tip


(2011年03月14日) The two kinds of billiard chalk...
One reduces hand friction, the other increases tip friction.

Modern billiard cue chalk is different from common chalk (limestone, composed of calcium carbonate) which billiard players were using on their leather cue tips before 1897. It's also entirely unrelated to what's variously called blackboard chalk, artist's chalk or sidewalk chalk which consists mostly of compressed calcium sulfate powder, obtained from gypsum.

The term billiard chalk denotes ambiguously two different things which are better called, respectively, billiard powder and cue chalk :

Billiard Powder Decreases Friction :

Cone Chalk To most chemists, billiard chalk means magnesium carbonate (MgCO3). This stuff is the powdery substance that gymnasts and other athletes put on their hands, or other body parts, to reduce friction with various sport implements, including barbell and high bar. (The effect is opposite to that of rosin, which is used to improve grip on a shot put, baseball or bowling ball.)

In pool halls, this type of "chalk" (improperly known as talc ) is called cone chalk as it's usually available in the form of solid cones mounted on walls or furniture. Some billiard players apply that on their bridge hand to reduce shaft friction.

Other players choose to bring their own powder to the scene, which is usually some form of real talc in the finely powdered form otherwise known as baby powder or, more precisely, talcum powder. The solid form is known as taylor's chalk. Soapstone (steatite) consists mostly of pure talc or magnesium silicate hydroxide Mg3Si4O10(OH)2 [not MgSiO3 ].

Above a certain level of humidity, all billiard players need to use such stuff, unless they wear a billiard glove. Nowadays, corn starch is often substituted for talc in actual baby powder (watch the labels). Both work fine for billiard use but corn starch will not cause the respiratory problems associated with the repeated inhalation of talc by babies.

Because of its smoothness and ease of carving, soapstone (steatite) was chosen by the French sculptor Paul Landowski for the outer layer of the famous statue of O Cristo Redentor (Christ, the Redeemer) 710 m over Rio de Janeiro, Brazil.

The statue has a 30 m span. Its concrete core was designed by the local engineer Heitor da Silva Costa. It was built between 1922 and 1931 on top of the prominent Corcovado granite peak (whose name means hunchback in Portuguese). Christ the Redeemer, over Rio de Janeiro.
Cristo Redentor, Corcovado Peak Rio de Janeiro, Brazil
Martyn Poliakoff's means SiO3 (not 4) and granite (not marble). Slips of the tongue...

Cue Chalk Increases Friction :

The rest of this article deals with something else entirely, which is what almost all billiard players (who aren't chemists) think of as chalk, namely the stuff unambiguously known as billiard-cue chalk or cue chalk. It is applied to cue tips to increase friction with the cue ball during collision. With too little friction, some skidding between tip and ball might occur; an undesirable phenomenon known as a miscue.

The use of cue chalk to prevent miscues predates the invention by Mingaud of the leather tip (in 1807). At first, players were simply scratching the tip of their wooden sticks directly on the plaster finish of surrounding walls (plaster is calcium sulfate). Pieces of chalk for specific use in billiards had already been in use for some time when one Jack Carr had the idea of marketing them as "twisting chalk" to stress the idea that his own "brand" of chalk could help players mimic his own skill at imparting spin.

The dominant (cheap) type of cue chalk is still based on the recipe devised in 1896 by the American chemist William Hoskins (1862-1934, also remembered for invented the nichrome alloy used in electric heating) and the professional billiard player William A. Spinks (1865-1933), who was more commonly known as Billy Spinks. They were jointly issued US pat. 578514, dated March 9, 1897 [ 1, 2 ] which covers:

A substitute for billiard-chalk composed of [normally white] pulverized silica, corundum, a binding agent and a coloring agent such as chrome-green, the whole being compacted into cakes or blocks.

The stuff was marketed by Wm. A. Spinks & Co. early in the 20th century. The original cakes of Spinks chalk were cylinders. Now, virtually all cakes of cue chalk are manufactured as cubes with a small spherical indentation that grows with actual use.

Most brands of chalk are now discontinued (see table below for today's dominant brands). Former favorites became collectibles, including:

  • Spinks.
  • Manhattan Club (by the Brunswick-Callender-Blake Company).
  • Clik (by the Brunswick-Callender-Blake Company).
  • Etc.
Some Current Brands of Cue Chalk
Pack size is smallest number of pieces available at retail. Cost is from Internet offers (without tax & shipping).
Owned byBrand$ / packPieceColorsRecipe
Longoni
(est. 1945, Italy)
manufactured by Tweeten
for the Norditalia Company Blue
Diamond
$6.10 / 2 3ドル.05 Blue (c. 1980)
NIR Super
Professional $7.75 / 3 2ドル.58
undersized Blue (c. 2000)
Brunswick $5.52 / 12 0ドル.46 B,G
Silver Cup Chalk
(est. 1990)
Macon, GA National
Tournament
$3.25 / 12 0ドル.27
"NTC" B,G
red wrap US patent
578,514
(1897)
Silver Cup $2.75 / 12 0ドル.23 24
Tweeten Fibre Co.
Chicago, IL Master [thick] $2.75 / 12 0ドル.23 10
Triangle [thin] $2.75 / 12 0ドル.23 B,G,R

The density of billiard chalk is typically 1.62 g/cc. A standard cube of chalk is 22 mm on a side (with a shallow spherical indentation 12 mm in diameter) and weighs about 17.2 g.

Billiard Chalk | Best type of chalk? | What chalk is the best? (Snooker)
Why I pay 3ドル.50 instead of 25 cents for chalk by Michael McCafferty "FastMikie" (Diary of a Pool Shooter)

CRC Heavy-Duty Silicone
(2011年04月01日) The Controversial Use of Silicone Spray
A magic lubricant used by some trickshot artists.

To perform critical trickshots, friction with the cloth can be drastically reduced by spraying a ball with heavy-duty silicone.

Another possibility is to apply silicone sparingly to the cloth itself. To do so, one simple method is to mist the product over the table. For a more contolled application, the cloth is wiped with a towel sprayed with silicone (the cloth can be humidified first).

This use of silicone is messy. Ball treatment is only reliable for a single shot (after each use, either cleaning or re-coating is required).

The "secret" of Eric Yow (at 5:40)
Silicone Spray Effects [ Massé-draw | Coriolis massé aiming principle ] by Dave Alciatore


HTCburton17 (Yahoo! 2011年02月08日) Colliding Carroms
A puck collides with an identical one at rest. They emerge at angles of 33° and 46° from the incoming line. Was the collision elastic?

Let's call the oriented angles of emergence a and -b. They must be of opposite signs (or else the zero momentum perpendicular to the incoming direction couldn't possibly be conserved). So, WLG, we may assume that a and b are both positive. Let's call M the mass of each puck and u the speed of the incoming puck. Let v and w be the outgoing speeds. We express the conservation of linear momentum in Cartesian coordinates:

M u [ 1
0 ] = M v [ cos a
sin a ] + M w [ cos b
- sin b ]

This is a system of two simultaneous linear equations in two unknowns (v & w) of determinant sin(a+b). The solution is:

v = u sin b / sin(a+b) and w = u sin a / sin(a+b)

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Video : Lecture 16 MIT 8.01 (Physics 1) by Walter Lewin (Fall 1999)
How to Play Carroms | Carrom Fever |
Carrom White Slam by Steeve Collard (France) | Carrom White Slam by Karnal Abdin (UK)


Johann-Albert Euler (1734-1800) (2011年01月30日) The theorem of Johann-Albert Euler (1758)
The trajectory of a ball is a parabola followed by a straight line.

The eldest son of Leonhard Euler was a prominent geometer in his own right. In 1758, Johann-Albert Euler (1734-1800) published a study of the motion of a sphere on an horizontal plane in the presence of Newtonian friction. His main result would be rediscovered independently by Gaspard Coriolis as part of his authoritative theoretical work on the topic: Théorie mathématique des effets du jeu de billard (1835).

A billiard ball in contact with the cloth has 5 degrees of freedom (2 for position and 3 for spin).

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Crazy Spin Shots (1984) by Jimmy "Whirlwind" White.


(2011年03月19日) The Stop Shot (Stun Shot)
Making the cue ball stop after hitting the object ball.

In an elastic collision with an object ball of the same mass, the cue ball will stop only when it is aimed dead center (i.e., directly toward the center of the object ball) and has no spin at the time of impact.

This is achieved by giving the cue ball just enough initial backspin so that the spin can wear off with distance and vanish precisely at the time of impact with the object ball.

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Video Instruction: Cue Ball Control


(2011年04月27日) Draw Shots (Screw Shots)
Backspin is imparted by hitting the cue ball below center.

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Sense & Nonsense of Cue Ball Draw by Mike Page (FargoBilliards) | Snooker power draw (screw) shot
Draw shot by Joe Nichols (Breaktime Billiards, Wilmington, NC). | Extreme Draw by Mike Massey


(2011年04月27日) Force Follow Shots
Some forward spin (topspin) is needed to achieve natural roll.

What billiard players call natural roll is normally dubbed pure roll by physicists... Either term denotes a rolling motion where the point of contact has zero speed (solling without sliding).

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Is Maximum Topspin Overspin? by Mike Page (FargoBilliards)
APA Instruction by "Dr. Cue" (Tom Rossman): Force Follow Shots! Lesson 44 & Lesson 45
Draw shot by Joe Nichols (Breaktime Billiards, Wilmington, NC).


(2011年02月23日) The Stun Path of the Cue Ball (no sidespin)
Starts at a right angle from the line of the object ball.

Draw or follow spin will pull or push the cue ball away from the stun path.

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Video Clip by Jeanette Lee ("The Black Widow")


(2011年03月26日) Leftover Spin
The cue ball may spin for a long time after stopping.

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Claimed Records: Jason Lynch "The Michigan Kid" (2006, 26.2 s) | Dave (2007, 26.54 s)
Timothy White "The Australian Oyster" (2008, 26.7 s) | Colin Mazaika (2008, 28 s)
Drew Conner, 2009: 27.9 s & 38.5 s


(2011年02月23日) The Stun Path of the Cue Ball (no sidespin)
Starts at a right angle from the line of the object ball.

Draw or follow spin will pull or push the cue ball away from the stun path.

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Video Clip by Jeanette Lee ("The Black Widow")


(2011年01月30日) The not-so-impossible 90° shot.

In outer space, when a spinless ball collides with an object ball at rest, the latter is ejected at an angle which is at most 90° from the direction of the striking ball. The limiting angle of 90° corresponds to a grazing collision (where the object ball is imparted vanishing speed).

On a pool table, extreme english on the cue ball can result in some extra deflection which allows the angle to reach or exceed 90°.

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Video : 90-degree 'impossible' pool cut-shot by Bob Jewett to the tune of "Take Five" by Dave Brubeck.
Actual shot is at 2:02; at Shoreline Billiards, on Tuesday September 16, 2008 (using a Balabushka cue).

Video : Vernon Elliott's Impossible Bank Shot by Bob Jewett | >90° shots by Dave Alciatore


Ray Higley, PE (2011年01月30日. NE, Georgia) Squirt Effect
When a level cue induces a pure side-spin (about a vertical axis) how is the cue ball deflected away from the cue's central axis?

Squirt is the modern term for the tendency of the cue ball to be deflected away from the striking axis when it's imparted with lateral english (side spin). Pool gurus who have adopted that name include: Robert Byrne, Bob Jewett, Ron Shepard, Mike Page, Joe Tucker, etc.

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Everything You Always Wanted to Know About Cue Ball Squirt, but Were Afraid to Ask
by Ron Shepard (2001)

Videos: Using Left or Right English: What is Squirt in Pool?
Understanding Cue Ball Deflection by Dominic Esposito (predatorfan314)
Sidespin, squirt & swerve revisited by Mike Page (FargoBilliards).
3 lessons on "Cue Ball Side-Spin & Squirt" [ 1 | 2 | 3 ] by Joe Tucker (jt10ball)


(2011年03月24日) Jump Shots (with full cues or shorties)
Legal and illegal ways to send the cue ball up in the air.

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Using a jump cue or Jumping a ball with a full cue by Joe Nichols (Breaktime Billiards, Wilmington, NC).
Jerico's Stinger Cues : "Learn to Jump Balls" [ 1 | 2 ] by BCA Master Billiards Instructor Tom Simpson.
Overhanded Method | Bank Jump Shot | Close Jump Shot | Rocky Lane | Joonas Ohtonen


(2016年02月16日) Rules and Vocabulary of Snooker
Regulation snooker is significantly different from other cue sports.

White cue-ball. 15 red balls (1 point) and 6 "color" balls: Yellow (2 points, top-left spot), Green (3 points, top-right spot), Brown (4 points, top-center), Blue (5 point, middle), Pink (6 points) and black (7 points, bottom).

Reds and colors are alternatively "on" to be potted until the last red is potted. Once a color has been potted after the last red, the colors must be potted in ascending order of their point values.

The most common foul consists of hitting first a ball which isn't "on". When that happens, the other player is awarded 4 points

Black cushion, yellow pocket, green pocket.

Respotted black (tie-breaker).

4-point snooker.

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Each time a player pots a ball, the announcer calls how many points the player has scored on that particular visit, not the overall total which will be used to decide the frame (that total is obtained by adding all the balls potted on successive visits to the penalty points due to the opponent's fouls, if any).

The mythical maximum break of 147 is obtained when a player pots 15 times a red followed by the black and then all balls in ascending order:

147 = 15 (1+7) + 2 + 3 + 4 + 5 + 6 + 7

In the final of the UK Snooker Championship 2015, Neil Robertson achieved that maximum break of 147 after a foul from his opponent (LIANG Wembo) for a total score of 151.

Theoretically, the opponent could make an unlimited number of fouls, so there's no hard maximum to the total score a snooker player can achieve.

Video : The Rules of Snooker by Ninh Ly.

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