How to Find the Wind Correction Angle and Ground Speed

A crosswind pushes an airplane sideways, so to fly a straight course over the ground the pilot points the nose a little into the wind. That small turn is the wind correction angle (WCA). The wind also changes the ground speed.

For learning only. This lesson is for studying and ground-school work, not for planning a real flight. Use official weather, charts and flight-planning tools, and the numbers in your aircraft’s handbook (POH).

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The steps

Write down the true course (TC), the true airspeed (TAS) and the wind: the direction it blows from and its speed. Winds-aloft forecasts give true directions.
Find the wind angle: wind direction − course. Plus means the wind is from the right, minus from the left.
Find the crosswind part: wind speed × sin(wind angle). Then sin WCA = crosswind ÷ TAS, so WCA = sin⁻¹(crosswind ÷ TAS).
Turn into the wind: true heading = course + WCA for a wind from the right, course − WCA for a wind from the left.
Ground speed = TAS × cos(WCA) − wind × cos(wind angle). A headwind makes it less than the TAS, a tailwind more.

A worked example

You want a true course of 090° at a true airspeed of 120 knots. The wind is from 040° at 20 knots. Find the WCA, the true heading and the ground speed.

Wind angle: 040° − 090° = −50°. The wind is 50° to the left of the course, from ahead.
Crosswind part: 20 × sin 50° = 20 × 0.766 = 15.32 kt.
sin WCA = 15.32 ÷ 120 = 0.1277, so WCA = sin⁻¹ 0.1277 ≈ 7.34°, about 7°.
The wind is from the left, so turn left: true heading = 090° − 7° = 083°.
Ground speed: 120 × cos 7.34° − 20 × cos 50° = 119.02 − 12.86 = 106.16, about 106 kt.

Fly a true heading of 083° (a WCA of 7° left), and expect a ground speed of about 106 knots.

Why it works

Think of the airplane’s motion as two arrows added together: its heading at the true airspeed, and the wind’s drift. For the sum to point exactly along the course, the sideways parts must cancel, so the airplane’s sideways part, TAS × sin WCA, has to match the wind’s crosswind part. That is where sin WCA = crosswind ÷ TAS comes from. The parts along the course then add up to the ground speed.

Try it with your own problem

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Common mistakes

Reading the wind as where it blows to. Winds are reported by where they come from. A wind from 040° blows toward 220°.
Turning the wrong way. Turn the nose into the wind: a wind from the left means a heading less than the course.
Mixing true and magnetic. Winds aloft are true, so work with the true course, then apply the variation to get the magnetic heading.
Using the TAS as the ground speed. With a headwind part you cover less ground than the airspeed says, so the time and fuel go up.

Questions people ask

Is there a quick rule of thumb for the WCA?

The most the wind can push you is about 60 × wind ÷ TAS degrees: 60 × 20 ÷ 120 = 10° here. A wind 50° off the course gives about 50/60 of that, roughly 8°, close to the 7° worked out.

How do I get the magnetic heading?

Apply the variation from the chart: east is least (subtract), west is best (add). With 10° east variation, a true heading of 083° is a magnetic heading of 073°.

Why is the ground speed less than the airspeed here?

The wind comes from ahead of the wing, so part of it, 20 × cos 50° ≈ 12.9 kt, is a headwind.

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