Expert: Paul Soderman - 7/4/2009

Question
The pilot of a small plan is flying downwind and realizes that he needs to gain altitude quickly to reach an altitude sufficient to clear a mountain.  Will the pilot reach the desired altitude in a faster distance if he turns the airplane into the wind to gain altitude?  If so, what elements are at work?

Answer
Brent
There are two coordinate systems at work here - one fixed to the ground and one moving at the wind speed.  If an airplane is flying at 100 knots relative to the moving coordinate system in a 100 knot wind in the same direction, his ground speed is 200 knots.  If his climb rate is 1 to 10 in still air (he climbs one meter for every 10 meters forward), he will travel 20 meters over the ground flying downwind for every 1 meter of climb.  If he turns around and flies upwind, he will travel 0 meters over the ground for every 1 meter of climb.  So, he better turn around to avoid the mountain.
Paul