Wind correction angle

The wind correction angle is the difference between the aircraft heading and the desired ground track needed to compensate for a crosswind. A heading points the vehicle; a track describes horizontal travel over the ground. In the horizontal model here, the air-relative velocity is aligned with the heading. Wind-direction statements below specify where the air moves, not the meteorological direction it comes from.^[ref]

Let $V$ be true airspeed, let $w_{\parallel }$ be wind along the desired track, and let $w_{\perp }$ be wind to its right. Define a positive correction $\delta$ as heading right of the track. Cancelling cross-track velocity and projecting along the track givesFor the branch with a nonnegative along-track air-relative component,The condition $|w_{\perp }|\le V$ permits crosswind cancellation, but forward progress also requires $V_g>0$.

In an original example, take $V=40m/s$, wind $8m/s$ rightward and $12m/s$ opposite the intended track. Then $\delta \simeq -11.54{}^{\circ }$ and $V_g\simeq 27.19m/s$. A constant-condition $100\mathrm{km}$ ground leg takes about $61.29\min$. With the same headwind, a rightward component of $39m/s$ can still be cancelled, but $\sqrt{40^2-39^2}-12\simeq -3.11m/s$: the resulting track-line motion is backward.

The calculation assumes a uniform horizontal wind and a steady true airspeed. Ground-position measurements can test the resulting groundspeed; they cannot determine the correction from air-relative speed alone without wind information. Wind variation and a difference between heading and air-relative velocity require a fuller vector model.