9-pin no-tap is a modified format: nine or ten on the first ball at a full rack
clears the rack and scores as a strike. USBC certifies modified formats under Rule 3, but only
standard American Tenpin scores qualify for its awards.
Nobody repeats a delivery exactly. The one published figure is that the best
professionals hold their initial angle to about 0.1 degrees; "Human" is that, "Loose" is three
and a half times it, and "Steady" turns it off and makes this a pure simulator. The wobble
comes from the game's own seeded stream, so a game is still reproducible from its seed, and
the line you actually threw is shown under the lane.
Bowling - how this works
An independent implementation of ten-pin bowling, built to the published specification rather
than to a guess. It runs entirely in your browser: no account, no model, no credits, and
nothing is sent anywhere.
The lane, at its published dimensions
60 ft from the lane side of the foul line to the centre of the No. 1 pin spot,
plus or minus half an inch.
41.5 in wide, plus or minus half an inch - 39 boards of
1.0641 in each, numbered 1 to 39 from the right for a right-handed
release, with marker arrows on boards 5, 10, 15, 20, 25, 30 and 35.
62 ft 10-3/16 in overall to the rear edge of the pin deck, of which
34-3/16 in is behind the head pin.
Channels 9-1/4 in wide and at least 1-7/8 in deep, from the foul line to
the pit. The approach behind the line is not less than 15 ft.
Targets sit 12 to 16 ft beyond the foul line, no more than 1-1/4 in wide and 6 in
long; the range guides sit 6 to 8 ft out.
The pins
Ten pins on 12 in centres in an equilateral triangle, plus or minus 1/16 in and
non-accumulative. The 7 and 10 spots sit 2-3/4 in from the edge of the deck and
3 in from the pit.
Each pin is 15 in tall and weighs 3 lb 8 oz, with its centre of gravity
5-25/32 in above the base and a coefficient of restitution of 0.670.
The pin in this app is lathed from the fourteen published diameters, widest at
4.766 in at 4.5 in above the base.
That belly is why the game is not simple geometry: 12 in centres less a 4.766 in belly
leave 7.234 in between two standing pins, and the smallest legal ball is
8.500 in across. The ball cannot fit between them - it has to
deflect, and most of the ten are taken by other pins.
The ball, and why it hooks
Every ball is 8.5 in across whatever it weighs, and no more than 16 lb.
That is the published reason a light ball deflects more: the same geometry, less momentum.
The ball here is integrated from a published system of five coupled differential
equations - Euler's equations for a rigid body with friction acting at a single contact
point. Nothing about the path is scripted.
While the contact point is still moving the ball skids and friction turns it;
once the contact point stops it is in pure roll and runs straight. The hook is
entirely a product of the oil pattern and your release.
Friction is about 0.04 on fully oiled lane and about 0.2 on dry. Set the
revs to zero on a flat pattern and the ball travels exactly straight.
USBC's testing puts the best entry angle at six degrees with the centre of the
ball on board 17.5. Aim for that.
Scoring, from the rulebook
Ten frames. Two deliveries in each of the first nine unless a strike is scored; three in
the tenth if a strike or spare is scored.
A strike counts 10 plus the next two deliveries. A spare counts 10 plus the
next one. An open counts the two deliveries themselves.
Twelve strikes in succession is the maximum, 300. An exhaustive check of every
reachable game confirms that 300 is the maximum and that exactly one game reaches it.
A split is a leave with the head pin down and at least one pin down between two or
more standing pins, or immediately ahead of two or more standing pins. The app applies that
test on the pin lattice - which is why the side-by-side leaves 2-3, 4-5, 5-6, 7-8, 8-9 and
9-10 are all splits, and why no leave that still has the head pin ever is.
A ball that leaves the lane before reaching the pins scores no pinfall, and a ball in the
channel cannot come back onto the lane.
The oil
Lanes are conditioned, and the pattern is why the ball skids and then hooks. Pattern lengths
here are the published ones - Wolf 34 ft, Cheetah 35, Bat 37, Viper 37, Bear 38, Chameleon 39,
Scorpion 43, Dragon 47, Shark 48, Badger 50 - and a modern pattern sheet publishes a total
volume in millilitres and a load in microlitres per board. A typical house shot's centre-to-
outside ratio can exceed 10 to 1; a USBC sport condition is limited to 3 to 1 or less, which
is why a sport pattern gives you no help finding the pocket.
The old "three units of dressing" rule is often quoted as current. It is not:
USBC suspended it indefinitely on 1 August 2019. A "unit" was a depth, not a volume - about
0.0167 cubic centimetres spread over a square foot, a film seven millionths of an inch thick.
What is reconstructed, and said so
The lane, the pins, the ball and the rules above are all published, and the app's constants
are the specification's constants. These are not published anywhere, and are the app's own:
The cross-lane shape of each oil pattern. Lengths and volumes are published; the
board-by-board load table on a pattern sheet is a graphic. Each pattern here is built from
its published length plus a documented shape family, inside the published ratios.
The typical house shot itself. No governing body publishes one; only its ratio is
described.
The collision model. The pin's mass, height, centre of gravity, radius of gyration
and restitution are published; how a struck pin topples and tumbles is not. The tipping
threshold of 9.96 degrees is derived from two published numbers, but the impulse model
around it is the app's own, and it is planar - a real pin flies. Its one calibration target
was published: the strike percentage peaks with the ball on board 17.5.
The computer bowler's accuracy. Its aim error is anchored on the one published
figure - the best professionals hold their initial angle to about 0.1 degrees - and the
four levels fan out from there.
Carry is simulated, not measured. USBC's pin-carry tables are not published as
data. In this model a pocket hit strikes about three times in four and the pocket is a few
boards wide; a real lane's is wider. That is a limitation, not a feature.
Sources
USBC, Equipment Specifications and Certifications Manual - the lane, the pin deck,
the pins, the ball, the channels, lane dressing.
USBC, Playing Rules, Chapter 2 - the game, strikes, spares, splits, fouls, legal
and illegal pinfall, dead balls, modified formats.
PBA oil pattern library - pattern names and lengths. A Kegel pattern sheet for a published
distance, reverse brush drop and volume.
Ji, Yang, Dominguez and Bester, Using Physics Simulations to Find Targeting Strategies
in Competitive Bowling (arXiv:2210.06753) - the equations of motion and the friction
endpoints.
Neil Stremmel (USBC) on entry angle - six degrees, board 17.5.
This is an independent implementation. It is not affiliated with, endorsed by or
connected to the United States Bowling Congress, the Professional Bowlers Association or any
bowling equipment manufacturer. CREDITS.txt carries the full list of sources and every
reconstruction.
Controls
Left and right move your target board; up and down move your
release board; space or Enter throws. H suggests a line. N starts
a new game. Escape closes a panel.