FAA Sport Pilot Airplane (SPA)Airspace and NavigationHard
An aircraft has a true airspeed of 100 knots and is flying a course of 360°. The wind is from 045° at 20 knots. Approximately what groundspeed should the pilot expect?
- A100 knots
- B94 knots
- C80 knots
- D86 knots
Show answer & explanationAnswer & explanation
Correct answer: D. 86 knots
The wind is 45° off the nose (from 045° relative to a course of 360°), so the headwind component is calculated as wind speed × cos(45°) = 20 × 0.707 ≈ 14 knots. Subtracting this headwind component from the true airspeed gives 100 − 14 ≈ 86 knots groundspeed.
Why the other options are wrong
- A. This assumes no headwind component at all, ignoring the angle between wind and course.
- B. This underestimates the headwind component, treating the angle as smaller than 45°.
- C. This would be correct only if the wind were a direct headwind (100% component), which it is not since it's 45° off the nose.
Wind Component Calculation
When wind is not directly aligned with the course, only a portion of the wind speed acts as a headwind or tailwind, calculated using the cosine of the angle between wind direction and course.
- Headwind/tailwind component = wind speed × cos(angle off nose/tail)
- Crosswind component = wind speed × sin(angle off nose/tail)
- At 45°, the headwind and crosswind components are roughly equal (≈0.707 × wind speed)
Memory trick: '45 degrees, split the difference' — headwind and crosswind share the wind speed roughly evenly.