Hold the buttons above, or use the keys: A/D or ←→ shove the pebble across
Space bail Enter launch H help.
Bailing and trimming are the same pair of hands: you cannot do both at once.
The two pictures that decide everything
Righting lever against heel. The dashed line is the textbook
GZ = GM sinθ; it parts company with the truth the moment the windward
bilge lifts clear of the water.Energy the boat can absorb before it fails, across every fold of this sheet.
The shaded band is every fold within 1% of the best one.
Help, sources and what was actually measured
How to play
Fold the boat with the sliders, then launch it. Gusts arrive at random and roll it. Shove the
pebble to windward to hold the boat up, or bail out whatever has come aboard — but not both at
once, because you only have two hands. Reach the end of the gutter and you have landed.
What the numbers mean
KB
how high the centre of buoyancy sits above the keel.
BM
the metacentric radius, I/V: the second moment of the waterplane divided
by the displaced volume. It exists only because the centre of buoyancy moves as the
hull heels.
GM
KB + BM − KG. Positive and the boat rights itself; negative and it
lolls onto its side and stays there. Big GM means stiff and jerky, small means tender and slow.
Energy to failure
the work a gust has to do to push the boat to whichever comes
first — the deck edge going under, or the righting lever running out. This, not GM, is what a
gust actually has to beat.
The finding
A wider boat is stiffer: over the whole range in which these boats float upright, GM
rises with beam, the roll period falls with it, and the deck-edge angle falls with it too. All
three are strictly monotone. But the safest fold is not the widest — it is the one that maximises
the energy the hull can absorb before water starts coming in, and that is an interior optimum.
Past it, the freeboard you sold to buy stiffness is exactly what sinks you.
The failure mode is swamping, not capsize, and the reason is exact: for a
box-section hull the free surface of shipped water is as wide as the waterplane, so
i/V and BM are the same number. Water aboard cancels the entire metacentric
radius and leaves you with KB − KG. That is why bailing saves a wide boat and does
nothing at all for a narrow one.
Measured, not asserted
Every figure below was produced by the project's own test harness and written into this page by
it. Nothing here was typed in by hand. 0 assertions passed.
Where each number comes from
tag
fact
source
Constants this page runs on, read straight off the engine:
g = -- m/s², fresh water -- kg/m³,
weir coefficient --, girth = -- of the sheet
width, hull length = -- of the sheet height, and the small-angle
landmark the closed form produces, --.
The paper
paper
grammage
caliper
implied density
soak time
Grammage and caliper are documented. Soak time is not. No source
was found for how long an untreated sheet takes to lose its stiffness in water; those four
numbers are a calibration and nothing more.
sheet
size
area
Credits
The traditional paper boat has no known author, no year and no publisher. The earliest evidence
of paperfolding in Europe is a picture of a small paper boat in the 1498 French edition of
Johannes de Sacrobosco's Tractatus de Sphaera Mundi. A Japanese court has held that
"the method to folding origami is in the public domain". There is no Wikipedia article titled
"Paper boat" at all.
This is an independent reimplementation in the sense that it reimplements nothing: there is no
original piece of software. What differs from a real paper boat is stated plainly — the hull is
prismatic, the fold is one slider, the splay is calibrated rather than documented, and how fast
paper goes limp is a guess. The full list is in
CREDITS.txt, alongside the sources.
Trade marks
A trade-mark register was reachable. TMview returned 65 marks matching "paper boat" on
2026‑09‑20, and PAPER BOAT is a live registered word mark in class 9
(software, CA 2045187‑00), class 41 (entertainment, BR 932796710 and IN 1762035) and
class 28 (games, CO 93401981), among others. Those classes are squarely on point for a
browser game of this name.
No clearance is claimed and none was sought. This page uses the words as the
ordinary English name of a folded sheet of paper. It is free, carries no advertising, sells
nothing, collects nothing, and is not affiliated with or endorsed by any proprietor. The full
register extract is in CREDITS.txt.
Nothing you do here leaves your browser. The only thing stored is your last fold
and your best distance, in this browser's own local storage.