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.
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 practioners of a true form of art.
(2010-12-31) 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
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 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
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
as 10 foot tables.
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).
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
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.
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
(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
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
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
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
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.
(2010-12-31) 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 developped bruises and flat spots...
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 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 developement of the modern substitutes for ivory started
with the first man-made plastic, invented in 1856 by
(1813-1890) who plasticized nitrocellulose with camphor
(the stuff was dubbed Parkesine at first).
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
Celluloid was used to make the so-called composition balls
which used a denser substance in their cores to achieve the
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).
(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
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
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
(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
Phenolic resin is also
applied as a thin layer on both faces of a wood product known as
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
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
calcium carbonate for 14 parts of resin.
Recall that the average density of a mix is a
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.
Pyramid - full
Pyramid - small
Grapefruit ( 23/8'' )
205 g (measured)
Rock ( 2¼'' )
US Pool - 2¼''
Bumper ( 21/8'' )
Snooker ( 21/16'' )
UK Pool - 2''
Pétanque - cue
Pétanque - jack
Mini - 1¼''
Half-scale ( 11/8'' )
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
in several grades.
From the Belgian village of
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).
The manufacture of "Elephant Balls" is now
commissioned by Sterling Gaming,
a billiard wholesaler from
(North Carolina) retailing as
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
Unbranded cheap acrylic
billiard balls are apparently off the market...
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
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
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 !
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).
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).
0.6'' ferrule, 114 g). Conical joint by
Thierry Layani (thanks to Philippe Singer of
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.
Blue Diamond chalk (blue). Silvercup chalk (green).
Aramith micro-fiber cloth, with backing.
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.
Captain François Mingaud
(1771-1847) was one of the most famous billiard player of his day, in his native France
He had designed a very popular cue in 1790 which he perfected in 1807 by inventing
rounded leather tips (while imprisonned in the
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 indispensible, 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
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
because only two gauges of shaping tools are available:
Nominal radius of 0.3532'' (8.9535 mm). About 9 mm.
Nominal radius of 0.4175'' (10.6035 mm). About 10½ mm.
The most popular shaping tools (single or dual gauge) include:
(2011-03-14) The two kinds of billiard chalk...
One reduces hand friction, the other increases tip friction.
Modern billiard cue chalk is different from
(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
The term billiard chalk denotes ambiguously
two different things which are better called, respectively,
billiard powder and cue chalk :
Billiard Powder Decreases Friction :
To most chemists, billiard chalk means
(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
(The effect is opposite to that of
rosin, which is used
to improve grip on a
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 realtalc
in the finely powdered form otherwise
known as baby powder or, more precisely,
The solid form is known as taylor's chalk.
(steatite) consists mostly of pure talc
or magnesium silicate hydroxide
[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
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).
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
It is applied to cue tips to
increase friction with the cue ball
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
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
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
Manhattan Club (by the Brunswick-Callender-Blake Company).
Clik (by the Brunswick-Callender-Blake Company).
Some Current Brands of Cue Chalk
Pack size is smallest number of pieces available at retail. Cost is from Internet
offers (without tax & shipping).
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).
HTCburton17 (Yahoo! 2011-02-08)
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
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
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 [
] = M v [
cos a sin a
] + M w [
cos b - sin b
This is a system of two simultaneous linear equations in two unkwnowns
(v & w)
of determinant sin(a+b). The solution is:
(2011-01-30) 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.
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).
(2011-03-19) 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.
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°.
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?
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:
Mike Page, Joe Tucker, etc.