Worked Examples — Wind Correction

The concept lesson Wind Triangle lays out the theory. Here are four worked wind-correction exercises.

Exercise 1: Simple headwind

TT = 180°, TAS = 100 kt
Wind: 180°/20 kt (direct headwind)

Solution:

Wind angle to TT: 0° (directly opposing)
HW/TW = 20 × cos(0°) = +20 kt headwind
XW = 20 × sin(0°) = 0 kt
WCA = 0° (no offset needed)
TH = TT = 180°
GS = TAS − HW = 100 − 20 = 80 kt

Exercise 2: Pure crosswind

TT = 270°, TAS = 120 kt
Wind: 180°/30 kt (wind from 180°, exactly cross from the left)

Solution:

Wind angle to TT: 270° − 180° = 90° (pure cross from left)
HW/TW = 30 × cos(90°) = 0 kt (no component)
XW = 30 × sin(90°) = 30 kt from the left
WCA: sin(WCA) = 30/120 = 0.25 → WCA ≈ 14.5° (offset left, so TH < TT)

But: wind comes from the left → aircraft drifts right → heading must be offset left.

TH = TT − WCA = 270° − 14.5° = 255.5°
GS = TAS × cos(WCA) = 120 × cos(14.5°) ≈ 120 × 0.968 ≈ 116 kt

Exercise 3: Quartering headwind from the right

TT = 045°, TAS = 110 kt
Wind: 090°/25 kt (wind from 090°, due east; track is NE)

Solution:

Wind angle to TT: 090° − 045° = 45° (from right front)
HW/TW = 25 × cos(45°) = 25 × 0.707 ≈ 17.7 kt headwind
XW = 25 × sin(45°) = 25 × 0.707 ≈ 17.7 kt from right
WCA: sin(WCA) = 17.7/110 = 0.161 → WCA ≈ 9.3° (to the right, because wind pushes left)

Since wind from right → aircraft drifts left → offset heading right.

TH = TT + WCA = 045° + 9.3° = 054°
GS = TAS × cos(WCA) − HW = 110 × cos(9.3°) − 17.7 ≈ 108.5 − 17.7 ≈ 91 kt

Exercise 4: Wind exactly behind the track (test case)

TT = 360° (north), TAS = 80 kt
Wind: 180°/15 kt (direct tailwind)

Solution:

Wind angle to TT: 180° − 360° = −180° = 180° (opposite, tailwind)
HW/TW = 15 × cos(180°) = −15 → +15 kt tailwind
XW = 15 × sin(180°) = 0
WCA = 0°, TH = TT = 360°
GS = TAS + TW = 80 + 15 = 95 kt

Mental cross-check

Wind from 30° to track: HW/TW ≈ 87 %, XW ≈ 50 %.
Wind from 45°: both ≈ 71 %.
Wind from 60°: HW/TW ≈ 50 %, XW ≈ 87 %.
Useful for cockpit estimation before reaching for the E6B.

Crosswind limit

On approach, the crosswind limit of the aircraft (in the POH) must be observed. Example C172: max demonstrated crosswind = 15 kt. Wind 60°/30 kt to runway → XW ≈ 25 kt → outside limit, approach not permitted.