Angle of attack is the angle between a sail chord reference and the apparent-wind direction. This calculator reports only selected angular relationships; it does not predict drive, heel, stall, trim quality or sail performance.
Sail Chord and Apparent Wind · Selected Angle Ledger
Explore selected apparent-wind and sail-chord angular relationships without aerodynamic performance claims.
Equation Used
- Both inputs are bearings in one shared planar reference.
- Apparent-wind and chord arrows are directed references.
- The acute value treats each reference as an unoriented line.
- Orientation cosine is geometric and is not a force coefficient.
- Sail shape, wind speed, flow regime, forces, stall and vessel response are excluded.
The secondary figure shows the same selected direction rays; arrow length has no force meaning.
Selected angle ledger
Subtract the selected chord bearing from the selected apparent-wind bearing to obtain a signed separation. Wrapping that result to ±180° gives the signed directed separation; its magnitude is the selected angle between the directed references.
What the calculator determines
Use it to inspect selected wind and chord bearings, their signed separation, absolute directed separation, acute line separation and orientation cosine.
Exact selected relationships
delta=wrap180(beta_aw-beta_chord); alpha=|delta|; acute=min(alpha,180-alpha); orientation cosine=cos(delta).
Selected-input example
At apparent-wind bearing 15° and chord bearing 0°, delta=15°, alpha=15°, the acute line separation is 15° and cos(delta)=0.966.
Not an aerodynamic-performance model
Sail shape, camber, twist, area, aspect ratio, wind speed and gradient, vessel velocity, Reynolds number, rigging, hull and foil forces, sea state and measured aerodynamic coefficients are excluded.
Questions
Does 15° mean optimum trim?
No. The former universal optimum claim is removed.
Does this predict stall?
No. Stall depends on sail shape and flow conditions and requires suitable aerodynamic evidence.
Are drive and heel forces calculated?
No. Two bearings alone cannot determine them.
Technical references
- NASA Glenn, Angle of Attack — defines angle of attack between relative wind and chord line.
- MIT 2.972, How a Sail Boat Sails Into the Wind — identifies sail angle of attack between apparent wind and sail chord.
- NASA Glenn, Inclination Effects on Drag — notes that stall determination relies on matched wind-tunnel testing.
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