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Plane

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Can you not see that you're suggesting that the 747 does the same impossible thing in reverse at takeoff?
How do you envisage the takeoff? Does it instantaneously achieve that 180mph to become and remain airborne or does it somehow manage to hover with minimal airspeed as it leaves the ground.
Where does the "instantaneous" bit come from?

Once the pilot starts up the engines, it will start to accelerate forwards the plane from rest. The fact it stands on a treadmill that is programmed to speed up is irrelevant, as the drive is not generated through the wheels.

The plane will continue to thrust forwards until it reaches take off speed, then take off.
 
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This question is at the best, ambiguous. There can be both yes and no answers based on what is being done with the aircraft and treadmill. The point is that for an airplane to lift off, there should be sufficient airspeed. If there is no wind, there airspeed is equal to the ground speed

Assuming that there is no wind (into or against the aircraft), there are two possible solutions.

  • If the airplane is stationary relative to the ground, it won't take off (as wind speed is zero).
  • If the airplane moves relative to the ground (with sufficient speed), it will take off.
Assume that we have a jet airplane (just for sake of argument) and some one pushes the throttle and it begins to move forward. Now, as the treadmill has an infinitely adjustable speed, we can have three conditions:

  • If the treadmill speed is zero, the airplane will eventually generate sufficient lift and take off.
  • If the treadmill speed is adjusted such that the airplane is kept stationary relative to the treadmill, the airplane will take off (as it is moving with respect to ground, and so has some airspeed).
  • If the treadmill speed is adjusted so that the airplane is kept stationary relative to the ground, the airplane cannot takeoff, as the ground and air speeds are both zero. Note that in this case, the aircraft speed relative to the treadmill is twice that of the speed at which the treadmill is being operated.
If there is a wind, the required ground speed can be adjusted accordingly, but the principle remains the same. For example, if the wind speed is equal to the airspeed required for take off, the airplane will lift off even though it is stationary with respect to the ground.

Again, the important concept here is airspeed. It does not matter if the aircraft is on a treadmill, train track or runway.
The image was, perhaps, a little misleading.
Maybe the thread would have taken a different course if the conveyor belt pictured had been full runway length.
And the choice of the word "counteracting" the wheels' rotation. The wheels are not "acting" so can not be counteracted. Deliberately misleading, maybe.
The wheels are passively responding not actively acting.
 
Where does the "instantaneous" bit come from?

Once the pilot starts up the engines, it will start to accelerate forwards the plane from rest. The fact it stands on a treadmill that is programmed to speed up is irrelevant, as the drive is not generated through the wheels.

The plane will continue to thrust forwards until it reaches take off speed, then take off.
Are you suggesting that the plane is moving forwards down the treadmill or that it is stationary relative to the Earth?
 
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