Final answer to the airplane on a long treadmill problem ...

[speedminded]

The treadmill matches the SPEED of the plane, not the thrust. The tread mill can be moving at 100,000knots while the plane is going at 100knots. It WOULD NOT matter. It would ONLY make the wheels spin at 100,100knots. NOTHING MORE. Guys, the wheels would spin faster, but that would not change the thrust up the engines.

The treadmill in NO way can counteract the THRUST of the engines.

lemme help you out with the porsche on the dyno analogy....imagine a vehicle on the dyno in neutral...the wheels are free spinning just as a planes wheels are. Now imagine if that car was not strapped down on the dyno, it should remain free wheeling on top of the rollers even if power were applied to the dyno (like a treadmill) in turn causing the wheels to spin. Ok so now you would have a car sitting there with wheels spinning but not going anywhere (ever seen anyone spin 2 basketballs on top of each other or a man running on a floating barrel or log in the water?) Same idea, one causes the other to spin but since the bottom one is stationary neither go anywhere.

Anyways, back to the car on the dyno...it's not strapped down and no power is being supplied to the wheels. Now imagine if you had 4 people or even just one person run and push the back of the vehicle...is the car still going to go forward? yes. Now if you turn on the engines of the plane is it going to go anywhere? yes.