Crabwise · Library
How should a heading calculation cross zero degrees?
A 005° course with wind from 300° at 25 kt and 110 kt TAS needs a −11.89° correction, so the heading wraps through north to about 353.11°.
Signed correction, normalised heading
Crabwise's wind triangle finds the wind angle θ = WD − TC and normalises it to the range −180° to 180°. The crosswind on the course is XW = WS × sin θ, the correction angle is WCA = asin(XW ÷ TAS), positive to the right and negative to the left, and the heading is TH = TC + WCA, brought back into 0° to 360°. Ground speed is TAS × cos WCA − WS × cos θ.
When the course is close to north, a left correction takes the raw sum below zero and the app adds 360°. The direction is the same; only its representation changes.
Worked example
A course of 355° plus approximately 7.335° gives a heading of approximately 2.335° after wrapping through north.
- Signed correction (degrees)
- 7.335207
- Normalized heading (degrees)
- 2.335207
Solve a course near north
- Enter TAS, the true course and the wind's FROM direction and speed, all directions referenced to true north.
- Read the signed correction: a minus sign means the heading is left of the course.
- Check that the heading equals course plus correction, modulo 360°.
- Convert to a magnetic heading separately with the local variation, as the app's note says.
A left correction across 360°
TAS 110 kt, true course 005°, wind from 300° at 25 kt. The wind angle is 300 − 5 = 295°, normalised to −65°. The crosswind is 25 × sin(−65°) ≈ −22.657695 kt, from the left. The correction is asin(−22.657695 ÷ 110) ≈ −11.886817°, and 5 − 11.886817 = −6.886817°, which normalises to 353.113183°. Ground speed is about 97.075748 kt.
- Wind angle θ (°)
- −65
- Wind correction angle (°)
- −11.886817
- True heading (°)
- 353.113183
- Ground speed (kt)
- 97.075748
Common mistakes
- Reading −6.89° as an error instead of the raw value before normalisation.
- Entering the direction the wind blows towards instead of where it comes from.
- Mixing a magnetic course with a true wind direction.
Scope
The triangle assumes one steady wind and true directions throughout. Magnetic variation and instrument errors are not applied. The FAA navigation chapter below describes the same wind-triangle construction.
Educational calculation only. Check current aircraft limits, weather, performance and reserve requirements with approved information.