Quote:
Originally Posted by prhom
So you are arguing that the plane will not fly?
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Quote:
Originally Posted by prhom
Wait just a minute orange, pilots NEVER care about groundspeed! If you were to tie a model plane to a string in a very high wind it could fly even though it's not moving relative to the ground. You can't deny that would be true.
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Yes.
When you're on the ground, yes. In this problem, the plane never acquires any airspeed - because it never moves from it's starting point. It actually never acquires any groundspeed either - but its wheels are spinning. All of the energy from that spinning is being transferred to the treadmill which is spinning under the plane.
Suppose we had an airplane that could take off on a windless day at 100 mph (liftoff airspeed is 100 mph). We are at an airport with an east-west runway that is 1 mile long. The wind is blowing 20 mph towards the west and the airplane takes off going east. The wind is blowing towards the aircraft which we call a headwind. Since we have defined a positive velocity to be in the direction of the aircraft's motion, a headwind is a negative velocity. While the plane is sitting still on the runway, it has a ground speed of 0 and an airspeed of 20 mph:
Airspeed = Ground Speed (0) - Wind Speed (-20) = 20 mph
The airplane starts its take off roll and has a constant acceleration a. From Newton's second law of motion, the ground speed V at any time t is:
V = a * t
and the distance d down the runway at any time is:
d = 1/2 * a * t^2
For a fixed length runway, this specifies the time to be used in the velocity equation. Let's assume that at 5000 feet down the runway, the velocity is 80 mph. Then the airspeed is given by
Airspeed = Ground Speed (80) - Wind Speed (-20) = 100 mph
and the airplane begins to fly. Now another pilot, with exactly the same airplane decides to take off to the west. The wind is now in the same direction as the motion and this is called a tailwind. The sign on the wind speed is now positive, not negative as with the headwind. The acceleration along the ground is the same, so at 5000 feet down the runway, the ground speed is again 80 mph. The airspeed is then given by:
Airspeed = Ground Speed (80) - Wind Speed (20) = 60 mph
This airplane doesn't have enough airspeed to fly. It runs off the end of the runway!
http://www.grc.nasa.gov/WWW/K-12/airplane/move.html