An aircraft has a demonstrated maximum crosswind capability of 17 kt. If the actual wind speed is 19 kt, what is the greatest angular difference between the wind direction and the runway heading before the crosswind component reaches 17 kt?
The crosswind component is the part of the wind that’s perpendicular to the runway. If the wind makes an angle θ from the runway heading, then:
- Crosswind (XWC) = Wind speed x sin (θ)
- Headwind (HWC) = Wind speed x cos (θ)
In this case, we are given a wind speed of 20 kt and a maximum XWC of 17 kt:
Crosswind (XWC) = Wind speed x sin (θ)
17 kt = 19 kt x sin (θ)
sin (θ) = 17 ÷ 19
θ = sin-1 (17 ÷ 19) = 63.4°
Quick mental checks (why the other answers don’t fit):
- 45°: 19 sin (45°) ≈ 19 × 0.707 = 13.4 kt (too low)
- 60°: 19 sin (60°) ≈ 19 × 0.866 = 16.4 kt (very close)
- 75°: 19 sin (75°) ≈ 19 × 0.966 = 18.3 kt (too high)
- 80°: 19 sin (80°) ≈ 19 × 0.985 = 18.7 kt (too high)
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