Uploaded August 2026 | Updated September 2026, 2 hours ago
One continuous CFD simulation of a sail, upwind at 60° to the true wind, with the
sail angle fixed at 20° to the keel. The only thing that changes is the camber:
the outhaul is eased from dead flat to 28 % camber, slowly at first — the first
1 % of cloth slack takes the first 30 seconds — while the boat, the flow and the
cloth all keep running. Nothing is reset between settings.
The green curve draws itself: VMG upwind against camber.
What you're looking at
• Dots are tracer particles carried by the flow, coloured by pressure —
blue = suction, orange/red = higher pressure than the free stream.
• Green arrow = lift, red = drag, white = their sum, all in coefficient form.
• Bottom right: stern view, showing heel.
• The wind triangle: true wind (blue) = apparent wind (white) + boat velocity (green).
As the boat speeds up, the apparent wind swings forward — the sail is re-trimmed
to it automatically.
Result
0.1 % camber VMG 0.198 73 % of the best (a flat sail simply doesn't work)
0.5 % VMG 0.228 84 %
1 % VMG 0.265 98 %
2.9 % VMG 0.270 100 % ← best, at 10 % camber
5 % VMG 0.256 95 %
12 % VMG 0.249 92 %
20 % VMG 0.241 89 % (28 % camber, most heel)
The lesson: the first bit of camber does nearly all the work, the top is broad and
forgiving, and over-easing costs far less than over-flattening. Speeds are given as
fractions of true wind speed.
How it's simulated
• Flow: 2-D lattice-Boltzmann (D2Q9), BGK collision with a Smagorinsky LES model,
450 × 300 cells, 100 cells per chord, Reynolds number 5 000 — high enough that
the flow separates and the sail can stall.
• Sail: immersed boundary (multi-direct forcing), so the fluid feels the cloth and
the cloth feels the fluid.
• Cloth: position-based dynamics — an inextensible chain solved exactly, with
bending stiffness, anchored at the mast and trimmed at the clew.
• Boat: driven along its keel by the sail force projected on the course, against
quadratic hull drag, heeling against a righting moment; heel reduces the drive by
cos²(heel). Boat speed changes the apparent wind, which changes the trim — a
closed loop.
• 175 seconds of simulated flow, 17 minutes of compute, played at real time.
Caveats, honestly
• 2-D: no tip vortices, no twist, no mast interference, and 2-D flows shed stronger
vortices than real 3-D ones, so the instantaneous forces swing much more than the
displayed averages.
• The boat model has no leeway and no rudder — it can only move along its keel.
• Reynolds 5 000 is well below a real sail's ~10⁶; the trends are right, the absolute
numbers are not a polar diagram.
0:00 Flat sail — 0 % camber
0:15 First half percent of slack
0:30 1 % slack — already 98 % of best speed
1:12 Best: 2.9 % slack, 10 % camber
1:34 Past the peak — 5 %
2:10 Getting too full — 12 %
2:30 Over-eased — 20 % slack, 28 % camber
One continuous CFD simulation of a sail, upwind at 60° to the true wind, with the
sail angle fixed at 20° to the keel. The only thing that changes is the camber:
the outhaul is eased from dead flat to 28 % camber, slowly at first — the first
1 % of cloth slack takes the first 30 seconds — while the boat, the flow and the
cloth all keep running. Nothing is reset between settings.
The green curve draws itself: VMG upwind against camber.
What you're looking at
• Dots are tracer particles carried by the flow, coloured by pressure —
blue = suction, orange/red = higher pressure than the free stream.
• Green arrow = lift, red = drag, white = their sum, all in coefficient form.
• Bottom right: stern view, showing heel.
• The wind triangle: true wind (blue) = apparent wind (white) + boat velocity (green).
As the boat speeds up, the apparent wind swings forward — the sail is re-trimmed
to it automatically.
Result
0.1 % camber VMG 0.198 73 % of the best (a flat sail simply doesn't work)
0.5 % VMG 0.228 84 %
1 % VMG 0.265 98 %
2.9 % VMG 0.270 100 % ← best, at 10 % camber
5 % VMG 0.256 95 %
12 % VMG 0.249 92 %
20 % VMG 0.241 89 % (28 % camber, most heel)
The lesson: the first bit of camber does nearly all the work, the top is broad and
forgiving, and over-easing costs far less than over-flattening. Speeds are given as
fractions of true wind speed.
How it's simulated
• Flow: 2-D lattice-Boltzmann (D2Q9), BGK collision with a Smagorinsky LES model,
450 × 300 cells, 100 cells per chord, Reynolds number 5 000 — high enough that
the flow separates and the sail can stall.
• Sail: immersed boundary (multi-direct forcing), so the fluid feels the cloth and
the cloth feels the fluid.
• Cloth: position-based dynamics — an inextensible chain solved exactly, with
bending stiffness, anchored at the mast and trimmed at the clew.
• Boat: driven along its keel by the sail force projected on the course, against
quadratic hull drag, heeling against a righting moment; heel reduces the drive by
cos²(heel). Boat speed changes the apparent wind, which changes the trim — a
closed loop.
• 175 seconds of simulated flow, 17 minutes of compute, played at real time.
Caveats, honestly
• 2-D: no tip vortices, no twist, no mast interference, and 2-D flows shed stronger
vortices than real 3-D ones, so the instantaneous forces swing much more than the
displayed averages.
• The boat model has no leeway and no rudder — it can only move along its keel.
• Reynolds 5 000 is well below a real sail's ~10⁶; the trends are right, the absolute
numbers are not a polar diagram.
0:00 Flat sail — 0 % camber
0:15 First half percent of slack
0:30 1 % slack — already 98 % of best speed
1:12 Best: 2.9 % slack, 10 % camber
1:34 Past the peak — 5 %
2:10 Getting too full — 12 %
2:30 Over-eased — 20 % slack, 28 % camber
