formula.expert

Wind Correction Angle

Also known as wind correction angle · crab angle · drift angle · wind drift correction · heading correction for wind · how much to crab

WCA=arcsin⁡(Wsin⁡θV)\mathrm{WCA} = \arcsin\left(\frac{W\sin\theta}{V}\right)

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

See also
Wind Triangle Ground Speed — The other half of the same triangle — what the wind does to the speed rather than the heading.Compass to True Heading (Variation and Deviation) — This correction is applied to a TRUE track; variation and deviation come after it.Cross Track Error — What accumulates when the correction is wrong or is not applied at all.

Learning zone

To make good a track across a wind you have to point the aircraft partly into it, and the angle you point off by is the wind correction angle — the crab angle, or in older texts the drift correction. Once you are established, the aircraft is pointing one way and travelling another, permanently, and that is not a problem to be fixed. It is the solution working. The visible confirmation is the view down final approach in a crosswind, where the runway sits off to one side of the nose the whole way down.

Only the crosswind component appears in the formula. Wsin⁡θW\sin\theta is the part of the wind trying to push you off the track, and the correction is whatever heading change generates an equal and opposite push. The along-track part of the wind does not appear at all, because a pure headwind or tailwind cannot move you sideways however hard it blows. That is why a 40-knot wind straight on the nose needs no correction while a 20-knot beam wind needs a large one — the total wind speed is the wrong number to reason from.

Two vocabulary distinctions are worth being pedantic about, because the accident reports are not. HEADING is where the nose points; TRACK is the path over the ground; COURSE is the track you intended. The wind correction angle is the difference between heading and course, and the whole exercise is making track equal course. In marine work the same idea appears twice under different names: leeway is the sideways slip from wind pressure on the hull and rigging, and the current correction is the same construction done for the tidal stream, but the triangle is identical in all three cases.

The formula has a limit built into it. If the crosswind component exceeds the true airspeed, Wsin⁡θ>VW\sin\theta > V, there is no arcsine to take and no heading holds the track — the aircraft simply cannot out-point the wind. That is a real condition for a light aircraft or a slow vessel in strong weather, and the honest answer is not a bigger correction but a different track. The other place to be careful is the sequence of corrections: the wind correction is applied to the TRUE track first, and variation and deviation are applied to the result. Applying them in the other order is a favourite exam trap and it does not give the same answer.

Wind Correction Angle
WCA=arcsin⁡(Wsin⁡θV)\mathrm{WCA} = \arcsin\left(\frac{W\sin\theta}{V}\right)
VWWCAθ
Where
  • WCA\mathrm{WCA}= Wind correction angle (°)
  • WW= Wind speed (kn)
  • VV= True airspeed (kn)
  • θ\theta= Wind angle off the track (°)
Missing one of these? Work it out first, then come back