The Triangle of Velocities and Wind Problems
The three vectors
Every wind problem closes three vectors: heading and TAS (the air vector), the wind vector, and track and groundspeed (the ground vector). Two of the three must be known to solve the third. Examiners test solving for drift and groundspeed, solving for the heading needed to make good a track, and deriving an unknown wind from two observed headings and ground tracks.
Rules to apply
- Wind is always quoted as the direction it blows FROM, so the plotted arrow points to the reciprocal.
- Wind angle is the smaller angle (0 to 180 degrees) between track and wind direction.
- Head or tail component = wind speed x cos(wind angle); crosswind component = wind speed x sin(wind angle).
- Max drift = (wind speed / TAS) x 60, occurring with the wind fully across track. Approximate drift = max drift x sin(wind angle).
- Exact solution via the sine rule: sin(drift) / wind speed = sin(wind angle) / TAS.
- To find wind from two runs: compare the two drift angles and groundspeeds at the same TAS; the change in drift gives the crosswind, the change in groundspeed gives the head/tail component.
Worked example
TAS 180 kt, track 060T, wind 300/40. Wind angle = 120 degrees. Head component = 40 cos 120 = minus 20 kt, a 20 kt tailwind. Crosswind = 40 sin 120 = 34.6 kt from the left, so drift is to the right. sin(drift) = 34.6 / 180 = 0.192, drift 11 degrees right, heading 049T. Groundspeed = 180 cos 11 + 20 = 197 kt.
Traps
Using the TO direction of the wind; using sin for the head component; reversing the drift sign so the heading is applied the wrong side of track; and forgetting that drift must be applied to track to obtain heading, never the reverse.