Regulating Bodies & Other Billiard Associations:

• The WorldConfederation of Billiard Sports  is the umbrella organization  (recognized by theIOC)  advocating cue sports as Olympic events.
• The International Billiards & Snooker Federation is the governing body for non-professional snooker & English billiards worldwide. 
• Union Mondiale de Billard: Carom billiards  governing body.
• Condédération Européennede Billard (CEB)  in Lausanne, Switzerland. 
• United States Billiard Association (USBA). Carom billiards in the US.
• English Association of Snooker and Billiards (EASB).
• English Amateur Billiards Association (EABA).
• WorldProfessional Billiards and Snooker Association (WPBSA). Players participating in professional tournaments (World Snooker).
• Billiard Congress of America:  BCA (est. 1948). Billiard industry trade.
• Women's Professional Billiard Association: WPBA (est. 1976).
• American Poolplayer Association: APA (est. 1981).  266000 members.
• North American Poolshooters Association: NAPA (est. 2009).
• Fédération Belge de Billard à Bouchon: FBBB (Bumper Pool).

(2010-12-31) 
The nominal  size of a pool tableis  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 intwo 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 thanits nominal size,  but that's irrelevant to thecalculation of the clearance space needed around a given table (which depends only on its cushion-to-cushion dimensions and on the length of thelongest cue you wish to use).

The traditional length of the playbed in carom  tables used to bespecified 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 effectivelydetermined 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 abovenumber to the nearest centimeter (2.84 m)  and allow a tolerance of  5 mm. A manufacturer mindful of tradition could still aim forthe 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 tableis  8''  longer than its playing area (9.984' ).  Such pocketless  tables are advertised as 10 foot tables.

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

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

Inexplicably, thecurrent regulationsfor snooker specify a widthand 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  allowsthe construction of correctly proportioned playbeds, including three that havea whole number of millimeters perdiamond 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 couldchoose one of these three specifications, ideally adoptinga grandfather clause allowing an extended tolerance for tablesbuilt before a certain date (in order not to rule out equipmentthat was compliant when it was built). The last possibility listed has the superficial advantage of dimensionsinvolving a whole number of centimeters(playbed dimensions of 3.56 m by 1.78 m)  but it wouldentail 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 requiredfor carom tables  (namely, 5 mm  on10' tables).  Every table made to the new specificationswould comply with the former standards.

The space  around a pool table must allow shots where the cue ball isagainst 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).

Carom tables have no pockets.  The other tables listed above have 6 pockets (at the 4 corners and in the middle of the longsides).  The width of each pocket is such that twoballs 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 adjacentdiamond marks that all billiard tables have (or should have)  on their rails. One diamond  is equal to one fourth of the widthof the playing area  (or one eighth of the length).Pocketless  (carom)  tables thusfeature 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 ofthe noses of the cushions perpendicular to the rail. On pool tables, the presence of pockets eliminatesthe 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 markersbetween adjacent pockets.  Nevertheless, the underlyingdiamond grid is exactly the same for pool tables and pocketless tables.

For traditional tables, the actual length of the tablewould 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 thetable is constructed. The size of that is thus  L+8''  by   L/2+8''  with athickness of 1''  (thickness may vary, seebelow). Thedensity of solid slate rock is  2.691 g/cc. Neglecting the pocket cutouts, this makes the slate slabfor a 7' table weigh  178 kg. The slab of a 9-foot table weighs 262 kg and is normallydivided into 3 pieces of 92 kg each. A full-sized snooker table features about 512 kg of rock, divided into5 pieces of 102 kg each.

(2011-04-07)  

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),

(2011-02-24)  

(2011-02-24)  

K66 profile.

(2010-12-31)  
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 ballswere 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 the4th Duke of Norfolk (Thomas Howard, 1536-1572)  who kept atHoward 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 obtainedfrom a single tusk of a female elephant. In fact, this wasn't so, sinceballs made from the same tooth could vary considerably. Instead, the matching was done by selecting from a large numberof finished balls.  Only  4%  of those matched sets wereconsidered 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 workersso that the central nerve in the tusk appearedon 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.

Thousands of elephants were slaughtered yearly to provide for the needs of thebilliard industry.  Well before the current ecological mindset, therewere concerns that the supply of ivory was dwindling too rapidly and that human liveswere put at risk in the hunts. A  $10,000  prizefor 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 startedwith the first man-made plastic, invented in 1856 byAlexander 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 ofcelluloid (the name was duly registered in 1873, but it's nowgenericized).

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

The nominal density of modern billiard balls is  1700 kg/m³ . That's close to the mean density of ivory [1.70]  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...

The most praised modern billiard balls are made with phenolic resin,  which is a thermosetting bonding compound obtainedby polymerizing  C₆ H₅ OH  (phenolor carbolic acid)  with  HCHO  (formol or methanal). That synthetic material was invented by the Belgian chemistLeo Baekeland(1863-1944) in 1907.  It became popular in the 1920'sunder the name ofBakelite®. 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.

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

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

The Belgian companySaluc S.A.  (founded in 1923 andowned 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 ofCallenelle,they supply 80% of the billiard balls worldwide.

The largest billiard company in the World, Brunswick Billiards, an American manufacturerof 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 specificationsas the finest Aramith balls (a 16-ball set of either brand retails for about $250).

Other brands offer more affordable balls,  made fromunsaturated polyesterresins,  which do not quite matchthe performance or durability of real "Belgian phenolic balls". Simpson's decorative Elephant Beautiful Balls (about $180 a set)  have based their reputation ongood looks,not durability.

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

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

(2010-12-31)  

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

Nowadays, the finest cues are meant to travel with their owner and comein 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 cuesalways 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 saythat the buttpiece is about  16'' and the shaft is  42''  (a foot longer than incenter-joint design).  The traditional design for a one-piecesnooker cue calls for a butt of ebony to be spliced into a shaft of ashup to a distance of about  22''  from the rear. That distance is typically respected in jointed cues but the splicing is limitedto 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 theconical joint.

(2011-03-29)  

Only once in my adult life did I travel to a remote location for the solepurpose of having fun: In the Summer of 1976,  I spentseveral weeks on the Island of Mauritius at the Club Méditerranée  resort, where I learned towater-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, froma British TV broadcast:  Unwittingly, I had learned snooker !

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.

(2010-12-31)  

CaptainFrançois Mingaud(1771-1847) was one of the most famous billiard player of his day, in his native Franceand elsewhere. He had designed a very popular cue in 1790 which he perfected in 1807 by inventingrounded leather tips  (while imprisoned in theBastille). Captain Mingaud also inspired the first complete analysis of the gameby the physicistGaspard Coriolis, in 1835.

Modern leather tips come in several grades, according to theirmechanical 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 typeof hard resin used in modern billiardballs; they are commonlyknown 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 onjump 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...

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-centUS 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:

• Willard's Cue Tip Shapers (1985)by James Willard.
• etc.

(2011-03-14)  
One reduces  hand friction, the other increases  tip friction.

Modern billiard cue chalk is different fromcommon chalk (limestone, composed of calcium carbonate)  which billiard playerswere using on their leather cue tips before 1897. It's also entirely unrelated to what's variously calledblackboard chalk,artist's chalk orsidewalk chalk which consists mostly  of compressed calcium sulfate  powder, obtained fromgypsum.

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

Billiard Powder Decreases Friction :

To most chemists, billiard chalk  means magnesium carbonate (MgCO).  This stuff is thepowdery substance that gymnasts and other athletes put on their hands,or other body parts, to reducefriction withvarious sport implements, includingbarbell andhigh bar. (The effect is opposite  to that ofrosin, which is usedto improve  grip on ashot put,baseball or bowling ball.)   In pool halls, this type of "chalk" (improperly known as talc ) is called cone chalk  as it's usually availablein the form of solid cones mounted on walls or furniture. Some billiard players apply thaton their bridge hand to reduce shaft friction.

Other players choose to bring their own powder to the scene, which isusually some form of real talc in the finely powdered form otherwiseknown 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 touse 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 respiratoryproblems associated with the repeated inhalation of talc by babies.

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 undesirablephenomenon known as a miscue.

The use of cue chalk  to prevent miscues predates the invention byMingaud of the leather tip (in 1807). At first, players were simply scratching the tip of their wooden sticks directly on theplaster finish of surrounding walls (plaster is calcium sulfate). Pieces of chalk for specific use in billiards had already been in use for some timewhen oneJack Carrhad the idea of marketing them as "twisting chalk" to stress the idea thathis 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 1896by the American chemist William Hoskins  (1862-1934, also remembered for invented thenichrome alloy used in electric heating) and the professional billiard playerWilliam 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:

The stuff was marketed by Wm. A. Spinks & Co.  early in the20^th century. The original cakes of Spinks  chalk were cylinders. Now, virtually all cakes of cue chalk  are manufactured as cubes with asmall spherical indentation that grows with actual use.

Most brands of chalk are now discontinued  (see table below for today'sdominant brands).  Former favorites becamecollectibles,including:

• Spinks.
• Manhattan Club  (by the Brunswick-Callender-Blake Company).
• Clik  (by the Brunswick-Callender-Blake Company).
• Etc.

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 sphericalindentation  12 mm  in diameter)  and weighs about  17.2 g.

(2011-04-01)  
A magic lubricant used by some trickshot artists.

To perform critical trickshots, friction with the cloth can be drastically reducedby 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).

HTCburton17  (Yahoo!2011-02-08) 
A puck collides with an identical one at rest.  They emerge at anglesof  33°  and  46° from the incoming line.  Was the collision elastic?

Let's call the oriented  angles ofemergence   and . 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   and   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 theconservation of linear momentumin Cartesian coordinates:

M u

1 0

=   M v

cos sin

+  M w

cos sin

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

v   =   u  sin / sin()        and        w   =   u  sin / sin()

(2011-01-30)  
The trajectory of a ball is a parabola followed by a straight line.

The eldest son of Leonhard Eulerwas 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 planein the presence ofNewtonian friction. His main result would be rediscovered independently by Gaspard Coriolis  as part of his authoritative theoreticalwork 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).

(2011-03-19)  
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 thatthe spin can wear off with distance and vanish precisely at the time ofimpact with the object ball.

(2011-04-27)  
Backspin is imparted by hitting the cue ball below center.

(2011-04-27)  
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 denotesa rolling motion where the point of contact has zero speed (solling without sliding).

(2011-02-23)  
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.

(2011-03-26)  
The cue ball may spin for a long time after stopping.

(2011-02-23)  
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.

(2011-01-30)  

In outer space, when a spinless ball collides with an object ball at rest, thelatter is ejected at an angle which is at most  90° from the directionof 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 resultin some extra deflection which allows the angle toreach or exceed  90°.

Ray Higley,PE (2011-01-30. NE,Georgia) 
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 fromthe 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.

(2011-03-24) 
Legal and illegal ways to send the cue ball up in the air.

(2016-02-16) 
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 inascending 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.

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

The mythical maximum break  of 147 is obtained when a playerpots 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 thefinalof the UK Snooker Championship 2015, Neil Robertson achieved that maximum break of 147 after a foul from his opponent ( 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.