the plane is on a giant treadmill....
I run on treadmills three times a week. Usually my average speed is measure as 1 mile per 7 minutes. I usually run for 21 minutes or 3 miles. My body is sweating and I'm out of breath because I did run 3 miles. However my displacement is equal to 0 miles.
For a plane to achieve vertical lift it MUST achieve horizontal displacement, acceleration, and something called wind under wing speed.
Hence, runways are measured and designed carefully so that a plane can acheive appropiate displacement, acceleration and final wind under wing speed.
speed = distance / time. So on the giant threadmill the plane will acheive a certain speed, and the wheels have rotated for a certain distance during a certian time.
velocity = displacement / time. On the giant threadmill the planes velocity will always equal 0 regardless of how fast the wheels are turning. Simply because the plane is not moving from a to b.
the key difference between the plane being on a threadmill and being on a runway is the displacement. and Displacement is NOT the same as the measured Distance travelled.
oh and if your airplane has no displacement there is no air UNDER the wings to provide lift.
BTW can everyone please stop saying "air over the wings"....
air over the wings will not allow the plane to fly. The air that is flowing under the wings is actually air trapped in pressurized stream of air. It is the difference between the high pressure under the wings and the low pressure above the wings that provide lift.
it's not the same as saying air is lifting the plane. It's more about the pressure variance (same technology is used for submarines under water)...okay.