What heading and ground speed do I need with this wind?

How it works

An aircraft moves through the air, and the air itself moves with the wind. To travel along the line on the chart, the pilot points the nose a little into the wind, so the aircraft crabs along the line. The wind triangle has three sides: the air vector (heading and true airspeed), the wind, and the ground vector (track and ground speed). This is the wind side of the E6B flight computer.

If the course is CRS, the wind blows from WD at W and the true airspeed is TAS, the wind correction angle is WCA = asin(W × sin(WD − CRS) / TAS), the heading is CRS + WCA, and the ground speed is GS = TAS × cos WCA − W × cos(WD − CRS). Example: course 090°, TAS 110 kt, wind from 040° at 20 kt. WCA = asin(20 × sin(−50°) / 110) ≈ −8°, so fly 082°, and GS = 110 × cos 8° − 20 × cos 50° ≈ 96 kt. A 60 nmi leg then takes 60 / 96 h ≈ 38 minutes. Sources: FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 16; Ed Williams, Aviation Formulary.

Forecast winds are true, so the course and heading here are true too; subtract an east variation (add a west one) for the magnetic heading on the compass. The answer is only as good as the forecast wind, and the fuel figure has no taxi, climb or reserve fuel. For learning, simulators and curiosity, not for flight planning or navigation.