| epsilon72 said: Huh? If the conveyor belt is moving this way ---> and the plane is trying to move this way <--- (at the same speed - one of the original problem's stipulations) it'll be stationary. If the atmosphere surrounding the plane does not move at the same speed+direction as the conveyor belt, the plane ain't takin' off. What they're trying to do in essence is have a stationary plane lift off of the ground - which would only happen if you had something that could do vertical takeoff and landing... @drkohler - a stationary 'normal' plane won't take off. |
Once _again_, a stationary plane WILL take off if its engines create airflow along its wings, provided the following conditions are fullfilled:
1. The plane's engines are strong enough that they can accelerate the plane to the equal and opposite speed of the conveyor belt underneath the plane (keeping the plane stationary to someone standing at the belt). It is completely irrelevant what is holding the plane on the belt, be it wheels, sleds, skis, whatever. As long as the plane can match the speed of the belt by overcoming the sum of the resistive forces, we are ok.
2. The engine(s) must be mounted horizontally, otherwise we can cheat and actually build a rocket...
3. The engine(s) must move air along its wings to create momentum directed upwards.
4. The speed of the conveyor belt can be increased to a critical speed. The critical speed is defined as the speed at which the momentum generated by the engine(s) on its wings overcome the weight of the plane. At this point, the plane will lift off the belt and jolt.
What most people here seem to misunderstand is that even though the plane is stationary to someone standing at the belt (and the air surrounding her/him), the air is not stationary in the engine(s)/wing system. In order to match the conveyor belt movement backwards, the plane has to move/roll/scratch/ski/whatever forward at the same speed with momentum mass(plane) x velocity(plane), the engines have to create the backward momentum m(air) x velocity(air). Now velocity(air) is _a lot_ higher than velocity(plane/belt), therefore there is considerable airflow around the engine(s).
Now a plane takes off if the airflow on its wings is high enough so that the upward force created is higher than the weight of the plane. If we attach the engine(s) to the plane at a place so that the airflow does not flow along its wings, there will be no upward force created and the plane does nothing. If we mount propellers to the wings, the airflow by the propellers _will_ create uplift, and given the critical speed can be achieved, uplift will cancel weight and the thing takes off.
Whether this theoretical situation can actually be performed is a completely different matter and depends on fullfilling all the conditions above. I'm certainly not going to stand next to the plane if somebody tries it, I still value my life somewhat.
So for the final time: Yes, at least in theory the plane _will_ take off the conveyor belt.
