philip wrote:To imply from this that the plane is stationary even when the engines are going is wrong, as said by many people above.
I believe that we are interpereting the problem in two different ways. I am imagining that the plane is being held in a specific horizontal position by the conveyor belt.
I suppose one thing to consider is whether or not the wheels themselves have friction. If they are assumed to be massless, frictionless wheels, no thrust would be needed to keep the plane in the same position and it would be trivial, as any thrust added could not be countered by the belt.
If the wheels had mass (and hence rotational inertia) they would initially resist the motion by the belt, but once an equalibrium was reached, no thrust would be required to maintain the initial conditions (plane stationary).
If we had friction, the plane would have to generate some thrust by moving air in order to maintain the conditions of the experiment. This is assuming we are not dealing in the trivial case of all of the velocities being zero.
With the final case, the thrust must be generated by air being drawn in, which must be expelled in order to produce a thrust. To continue to draw in air, it must be replaced from in front of the plane. The air above and in front will be replaced more readily than that above and below (more steradians of available influx), so there would be a tendancy for the turbine to "pull" in that direction. After this, it is just a matter of providing enough thrust to equalize the gravitational attaction of the plane.
Once that is done, as soon as the wheels leave the ground, the plane will recieve quite a large acceleration (no more friction on the wheels).
After that, it may or may not be able to maintain any altitude, as the pressure imbalance will be corrected by the plane moving to a new position forward. I could envision a situation where the plane was in a somewhat harmonic motion, bouncing off the belt.
Edit: Fixed the quote.