Wind correction angle and ground speed

The wind triangle

The wind triangle links three vectors: the aircraft through the air (true heading, TAS), the wind (direction from, speed) and the resulting track over the ground (true course, ground speed). Given course, TAS and wind, we solve for heading and ground speed.

WCA = asin( Vw · sin(Wd − TC) / TAS )
GS  = TAS · cos(WCA) − Vw · cos(Wd − TC)
TH  = TC + WCA

Worked example

Convert true heading to magnetic heading with the local variation (magnetic = true − easterly variation).

TC 338°T, TAS 110 kt, wind 270°/13 kt
WCA = −6.3° (correct left) → TH ≈ 332°T
GS ≈ 104.5 kt  (headwind 4.9 kt, crosswind 12.1 kt from the left)

Limits

If the crosswind component exceeds TAS, no heading can hold the course. If the headwind component equals or exceeds TAS, there is no forward ground speed. OIBK reports these cases instead of producing a number.