FAA Aircraft Dispatcher (ADX)Flight Planning and PerformanceMedium
An aircraft is flying with a true airspeed of 200 knots. The wind is 40 knots, striking the aircraft at an angle of 60° off the nose. What is the approximate ground speed?
- A200 knots
- B160 knots
- C180 knots
- D140 knots
Show answer & explanationAnswer & explanation
Correct answer: C. 180 knots
Headwind component = wind speed × cosine of angle off the nose = 40 × cos(60°) = 40 × 0.5 = 20 knots. Ground speed = TAS − headwind component = 200 − 20 = 180 knots.
Why the other options are wrong
- A. 200 knots would be correct only if the wind had no headwind component.
- B. 160 knots would require a 40-knot headwind component, ignoring the cosine reduction.
- D. 140 knots would require a headwind component of 60 knots, too large for this angle.
Wind Component Calculation
The headwind or tailwind component equals wind speed multiplied by the cosine of the angle between the wind and the aircraft's course.
- Headwind component = wind speed × cos(angle off nose)
- Ground speed = TAS − headwind (or + tailwind) component
- At 90° off the nose, wind is pure crosswind with no speed effect
Memory trick: 'Cosine cuts the wind down to size.'