Learning hub · General Navigation · Lesson 1
The wind triangle: heading and groundspeed
An aeroplane does not fly through the ground, it flies through the air, and the air is moving. The wind triangle is how you work out where to point the nose so that you end up where you meant to go, and how long it will take.
About 12 minutes, plus the quiz. Part of General Navigation.
1. Five words to get straight
- Course (or desired track) is the line over the ground you want to follow, measured from north.
- Heading is the direction the nose points. With a crosswind it is different from your course.
- True airspeed (TAS) is your speed through the air.
- Groundspeed (GS) is your speed over the ground. It is TAS corrected for wind.
- Wind is always given as the direction it blows from, and a speed in knots.
The angle you add to or subtract from the course to hold the track is the wind correction angle (WCA). If the wind comes from your right you point to the right of the course, and if it comes from your left you point to the left. You always aim into the wind.
2. The triangle
Draw three arrows. The first is your heading and TAS, the second is the wind, and the third, which joins them, is your track and groundspeed. Heading plus wind equals track. Because you know the course and the wind, and you choose the TAS, you can solve for the heading and the groundspeed with a flight computer, a plotter or a little arithmetic.
To do it with arithmetic, split the wind in two parts relative to your course:
- the crosswind pushes you sideways and decides the correction angle;
- the headwind or tailwind speeds you up or slows you down.
The part of the wind that is across or along your course depends on the angle between the wind and the course:
- wind 30° off the nose: about half the wind is crosswind;
- 45° off: about 70 per cent is crosswind and 70 per cent is headwind;
- 60° off: about 90 per cent is crosswind, and the headwind is only half. At 90° all of it is crosswind.
3. The one-in-sixty shortcut
A small angle in degrees is roughly the sideways distance divided by the distance along, times sixty. For the wind correction angle:
WCA ≈ crosswind ÷ TAS × 60
A 20 kt crosswind at 120 kt TAS needs about 10° (20 ÷ 120 × 60). This is good for flying and for sense-checking an answer, and it works well up to about 20°.
4. A worked example
Course 090° true, TAS 100 kt, wind from 150° at 20 kt.
- The wind is 60° to the right of the course (150 − 090). Crosswind is about 90 per cent of 20, so 17 kt from the right. Headwind is about half, so 10 kt.
- WCA ≈ 17 ÷ 100 × 60 ≈ 10° right. The heading is 090 + 10 = 100°.
- Groundspeed is about the TAS minus the headwind, a little less for the angle: about 88 kt.
Check it in the wind triangle calculator: it gives 100° and 88 kt.
5. From true to what the compass reads
Courses measured on a chart are true (from true north). Your magnetic compass points to magnetic north, which is somewhere else. The difference is the variation, printed on the chart and different in each place. A further small error, deviation, comes from the aircraft itself and is shown on a card near the compass.
True → (variation) → Magnetic → (deviation) → Compass
The memory aid is east is least, west is best: going from true to magnetic, subtract easterly variation and add westerly variation. In the example, with variation 5° east, the magnetic heading is 100 − 5 = 095°. Take care: under ICAO rules the wind in a METAR or TAF is a true direction, while the wind from ATIS or the tower is magnetic.
Do the sum on every leg and check it against what the ground tells you. A map, a river or a road should agree with the track you expect. If they do not, check the numbers before you trust the plan.
6. Try it yourself
Work each one out on paper first, then open the answer to compare. The numbers are invented.
- Course 180° true, TAS 90 kt, wind from 225° at 20 kt (all invented). Work out the wind correction angle, the heading and the approximate groundspeed.
Show the answer
The wind is 45° to the right of the course (225 − 180). At 45°, about 70 per cent of the wind is crosswind and 70 per cent is headwind, so both are about 14 kt (70 per cent of 20).
WCA ≈ crosswind ÷ TAS × 60 = 14 ÷ 90 × 60 ≈ 9°. The wind is from the right, so you point right of the course: heading 180 + 9 = 189°.
Groundspeed is about TAS minus the headwind, a little less for the angle: 90 − 14 = 76, so about 75 kt.
- Course 270° true, TAS 150 kt, wind from 240° at 30 kt (invented). The variation is 4° east. What true heading and what magnetic heading do you fly?
Show the answer
The wind is 30° to the left of the course (240 is 30° less than 270). At 30° off the nose about half the wind is crosswind: 15 kt.
WCA ≈ 15 ÷ 150 × 60 = 6°. The wind comes from the left, so you point left: true heading 270 − 6 = 264°.
East is least: going from true to magnetic you subtract easterly variation, 264 − 4 = 260° magnetic.
- The METAR for your departure gives the wind as 240° at 15 kt. The variation is 6° west. What direction would you expect the tower or ATIS to give? Why is it different?
Show the answer
A METAR or TAF wind is a true direction. The wind from ATIS or the tower is magnetic. Going from true to magnetic you add westerly variation (west is best): 240 + 6 = 246° magnetic, at the same 15 kt.
The wind has not changed. Only the north it is measured from has. Never mix the two in one calculation: use the true wind with true courses, and the magnetic wind with magnetic runway headings.
7. Watch
Seeing the triangle drawn helps. This video builds it up step by step.
Open on YouTube if the player does not load. Not made by VectorEFB; check what you learn against your flying school’s material and your instructor.
More to watch
A worked walk-through of wind correction angle, groundspeed and magnetic heading on the flight computer, which is a good way to check the arithmetic in this lesson. This video is American, so wording and some rules differ from European (ICAO/EASA) practice.
Open on YouTube if the player does not load. Not made by VectorEFB.
8. Check yourself
Five original practice questions. Answer them, press Check answers and read each explanation.
Next: lift, angle of attack and the stall. Back to the learning hub.