In any normal sort of scenario the aeroplane gets airborne with the treadmill at any sort of finite speed. However consider the workings of the treadmill:
Wheel speed and treadmill speed start at zero.
Plane starts to accelerate, from 0 to deltaV. Wheels are spinning at deltaV. Ttreadmill speed is zero.
Treadmill reacts, by going from speed 0 to deltaV, as it must match the wheel speed. This means that wheels are now spinning at 2*deltaV. But now the treadmill must react by increasing it's speed to 2*deltaV as ist must match the wheel speed, which increases wheel speed to 3*deltaV.
This cycle would go on until infinity under idealised scenarios. It would all depend on the sampling rate of the treadmill. If deltaT (the inverse of the sampling rate) were very small, the tyres would explode and the plane would get sent backwards and crash.
(I think)
Wheel speed and treadmill speed start at zero.
Plane starts to accelerate, from 0 to deltaV. Wheels are spinning at deltaV. Ttreadmill speed is zero.
Treadmill reacts, by going from speed 0 to deltaV, as it must match the wheel speed. This means that wheels are now spinning at 2*deltaV. But now the treadmill must react by increasing it's speed to 2*deltaV as ist must match the wheel speed, which increases wheel speed to 3*deltaV.
This cycle would go on until infinity under idealised scenarios. It would all depend on the sampling rate of the treadmill. If deltaT (the inverse of the sampling rate) were very small, the tyres would explode and the plane would get sent backwards and crash.
(I think)
