Dead Reckoning: Triangle of Velocities, Drift and Ground Speed
The triangle of velocities
Dead reckoning combines heading, true airspeed, wind velocity and time to predict position. The triangle of velocities has three vectors: true heading/true airspeed (the aircraft through the air), wind velocity (direction from which the wind blows, at the altitude flown), and the resultant true track/ground speed. Draw it to scale or solve with trigonometry. The drift angle is the angle between heading and track; it is to the right (positive) with a wind from the left, and left (negative) with a wind from the right.
Key relationships
Track = heading + drift (right positive). Ground speed = TAS ± wind component along track. Wind correction angle (WCA) ≈ (wind speed / TAS) × sin(wind angle) × 57.3 degrees for small angles. The along-track wind component = wind speed × cos(wind angle), where the wind angle is measured from the nose. Headwind reduces ground speed and increases time; tailwind does the reverse.
Traps
Wind direction is given as the direction from which the wind blows; using it as a "to" direction reverses the triangle. Confusing track with heading, or drift with wind correction angle, is common. Also watch units: minutes versus hours in time calculations (time = distance / groundspeed × 60 for minutes).
Worked example
TAS 120 kt, heading 090°T, wind 180°/30 kt (from the south). Wind angle from nose = 90°. Along-track component = 30 × cos 90° = 0. Crosswind = 30 kt. WCA ≈ (30/120) × sin 90° × 57.3 ≈ 14° (to the right, since wind from the south pushes the aircraft north). Track ≈ 104°T. Ground speed ≈ √(120² + 0²) ≈ 120 kt (approximately, ignoring the small along-track effect of the drift).
Rule of thumb
"Wind from the left, drift right; wind from the right, drift left." Always sketch the triangle before computing.