posted on Feb, 14 2006 @ 09:48 PM
I haven't read the answer yet, but theoretically it would be possible for an aircraft to lift off under these circumstances. However, when you
actually start crunching the numbers, you realize that the scale of the required conditions is quite extreme.
As stated by previous posters, the only thing we need to consider is motion of air over the aircraft's wings, regardless of reference frame. Due to
the fact that there is a "no-slip" boundary condition at the runway surface, the moving runway will pull air along with it at its surface and over a
short vertical distance above the runway until the velocity of the air is once again zero. This can be seen as some kind of reverse boundary layer.
The thickness of this "boundary layer" will be determined by the speed of the runway movement, the length of the runway, the place on the runway at
which the aircraft is placed and the roughness of the runway.
The requirement for lift-off will be this:
- the properties and motion of the runway will need to be such that the air velocity at the wing height is equal to or greater than the take-off
velocity of the aircraft.
Once this threshold is met, the aircraft will lift off the runway but will immediately begin to be pushed backwards by the air from the runway (due to
drag) now that the wheels can no longer force the aircraft forwards. This would quickly reduce the relative velocity of the air across the wing,
dropping it below the required take off velocity.
The craft would then touch down on the runway again, and we start over as seen in this image:
Up to this point though, this is completely theoretical. Let's try putting in some numbers to test this out. The two equations that are of primary
These equations come from the One-Seventh Power Law for estimating the velocity profile of a turbulent boundary layer over a smooth flat plate, where
delta is the BL thickness, x is the horiz. distance from the right of the runway in this case and y is the vertical distance from the runway. If we
say that the vertical height of the wings from the ground is 3 m, and assume a lift-off speed of 50 m/s, then it turns out that we would need a
runway that is 2 km long and moving at 1000 m/s in order to generate enough lift to get the aircraft to lift off... not very practical. There is also
the problem that the wind velocity would be far greater closer to the runway so that when the craft lifts off, it is possible that the much stronger
winds acting on the landing gear would cause a large pitching moment which would cause the nose to come slamming down. An interesting question to