RE: Airplane on a Treadmill
In an idealized setting where the plane and conveyor have maximum traction between them [for the sake of argument consider a cogged conveyor and matching gears for the planes' wheels]......then take this scenario a step further and imagine a conveyor drive that can instantaneously and infinitely match whatever the plane is trying to do. In this idealized setting, I can not see how the plane can attain any airspeed for lift off.