Dead Reckoning: Triangle of Velocities, Track, Heading, Wind and Ground Speed
The triangle of velocities
Dead reckoning combines the aircraft’s air vector (heading and TAS) with the wind vector (direction and speed) to give the ground vector (track and ground speed). Wind direction is always the direction from which the wind blows. Drift is the angle between heading and track: track = heading + drift (right drift positive). The wind correction angle (WCA) is applied into wind: if the wind is from the left, heading is left of track. Ground speed is the air vector plus the along-track wind component.
Components
For a wind at angle θ from the track, headwind component = wind speed × cos θ; crosswind component = wind speed × sin θ. A positive headwind reduces GS; a tailwind increases it. Approximate WCA = arcsin(crosswind/TAS), valid for moderate angles. Exact GS = TAS × cos(WCA) ± headwind component, or solve the vector triangle. For quick mental work, use the 1-in-60 rule: an off-track angle of 1° gives 1 NM drift in 60 NM.
Worked example
TAS 180 kt, required track 270°, wind 240°/30 kt. The wind is 30° off track from the left. Headwind component = 30 cos 30° ≈ 26 kt; crosswind = 30 sin 30° = 15 kt. GS ≈ 180 − 26 = 154 kt. WCA = arcsin(15/180) ≈ 4.8°, so heading ≈ 275° (turn right into the wind). Check: the wind from 240° blows toward 060°, producing right drift on a westerly track.
Traps
Adding the wind direction instead of the direction the wind blows toward is the classic error. Keep drift signs consistent: wind from the left gives right drift. Use GS, not TAS, for time and fuel. Apply magnetic variation only after the true track/heading triangle if the triangle is worked in true; do not mix true and magnetic vectors. Wind at flight level differs from surface wind.