>>1191627You're correct at the beginning, that the plane needs to throttle up to stay stationary. What you're missing is that regardless of how much the treadmill accelerates, the plane wouldn't use all of it's thrust to stay there. Even while taxiing planes really only throttle up to start moving, then use near idle to maintain speed. Once the wheels are turning, it's easier to keep them turning. The excess thrust is then used to accelerate relative to the observer, and takeoff normally.
The important thing here is that the wheels rotate freely. There IS some friction there, obviously, but as long as the brakes are released, it won't hold the plane back enough to counter the much greater amount of thrust the engine(s) produce.
>There must be a point where the plane can no longer throttle up to counter the backward motion of the treadmill, right?It's actually the opposite, there's a point where the friction can no longer overpower the engines, which happens at a very low speed, hence taxiing on idle. To overpower the engines through friction like that, the treadmill would need to be moving impossibly fast - so much so, that it would tear itself and the tires apart.
