Wind and Airspeed

Trigonometry · Axiom Academy

LESSON Wind and Airspeed: Navigation Learn how pilots use trigonometry to navigate crosswinds and maintain their desired flight path. You're piloting an aircraft from City A to City B, 200 miles due east. Your aircraft can fly at 150 mph in still air. But there's a problem: a 30 mph wind is blowing from the north! Problem: If you point the aircraft east, the wind will push you south of your destination! To compensate for the crosswind, you need to point the aircraft slightly into the wind (towards the north). Adjust the heading angle to keep the aircraft on track! Airspeed + Wind = Ground Speed To solve this navigation problem, we use vector addition and trigonometry . The aircraft's motion is the vector sum of its airspeed and the wind. Desired Ground Track: Due East (0°) We want the resultant ground velocity vector to point exactly east, even though the wind is pushing south. Unknown: Heading angle θ to compensate for wind Break each vector into components, then solve: For due east ground track, north component must = 0: Now let's solve this problem! Given: Wind: 30 mph from the north (blowing south) What heading should the pilot use to fly due east? (Remember: Positive angles are north of east, negative are south) Vector Addition in Navigation Aircraft motion = Airspeed vector + Wind vector. The resultant is the ground track. Trigonometry Solves Real Problems Use sin and cos to break vectors into components, then solve algebraically.

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