Wind triangle (heading & groundspeed)
Terms:
- Groundspeed (GS): speed over ground. TAS adjusted for wind (PHAK glossary).
- Wind velocity: direction wind blows from + speed in knots (AWH: wind named by direction it blows from; TP 1102: "100 KT TAS into a 20 KT head wind").
Wind split against true course (hold track = correct for wind):
| Component | Direction | Sets | Formula |
|---|---|---|---|
| Crosswind | Across track | Wind correction angle | WCA = asin(windSpeed · sin WA / TAS) |
| Along-track | Along track | Groundspeed | GS = TAS · cos WCA − windSpeed · cos WA |
- WA: wind direction (measured from) relative to course. TAS: true airspeed.
- Crosswind pushes off track: crab into it by WCA.
cos WCAfactor: speed lost to crabbing.
Heading conversions:
- True heading = true course + WCA.
| Result | Given | Operation | Ref |
|---|---|---|---|
| True heading | Wind from right | Add WCA (crab right) | PHAK ch.16 |
| True heading | Wind from left | Subtract WCA | PHAK ch.16 |
| Magnetic heading | East variation | Subtract from true heading | TP 1102; PHAK ch.16 |
| Magnetic heading | West variation | Add to true heading | TP 1102; PHAK ch.16 |
- TP 1102 variation example: MB 330 + 15°E = TB 345.
Sign of cos WA:
cos WA |
Wind | GS effect |
|---|---|---|
| > 0 | Headwind | Slows |
| < 0 | Tailwind | Speeds up |
- Always subtract the term. Tailwind:
cos WAnegative, so subtracting adds speed. Never add a tailwind by hand.
Special cases (TP 1102, Estimate Ground Speed; PHAK ch.16):
- Direct head/tailwind (WA = 0° or 180°): crosswind term drops out, WCA = 0. GS = TAS minus/plus wind speed.
- No wind: GS = TAS.
Quick estimate, no formula (TP 1102, Estimate Ground Speed):
| Wind from | Assumed effect on GS |
|---|---|
| Wing tip position | No appreciable effect |
| About 45° to flight direction | Head/tailwind component about two-thirds wind speed |
Diagram: completed wind triangle, GS = length of true course (TC) line (PHAK ch.16).
Trap: swapping head/cross components, or reading GS as TAS.
References
- TP 1102, Pilot Navigation (Setting Heading, Drift Compensation, Estimate Ground Speed)
- FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25), ch.16
- FAA Aviation Weather Handbook (FAA-H-8083-28), wind direction convention