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But what if the treadmill continues to accelerate? Different story. In principle it's possible to accelerate the treadmill at a rate that will exactly counteract any forward force you care to apply. (This is a departure from the original question, which said the conveyor belt compensated for the plane's speed,, not its force.) The only mathematics needed to demonstrate this is the well-known physics axiom F = ma--that is, force equals mass times acceleration. Given that the conveyor exerts some backward force F on the plane, we simply crank up the acceleration as much as necessary to equal any forward force F generated by its engines. Result: The plane stands still and doesn't take off. Welcome to BR #2.

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I'll stand down - This is exactly how I was coming at it. Although I am still not convinced it would need to accelerate to infinity in this case. If this opposite force is applied at the instant from static rest neither the plane nor treadmill will barely move. You could think of it as happening in pulses. Cancelled out before it starts.

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Ya know...I'm thinking here about rescinding my acknowledgement. He is only talking about speed of the wheel - and that was never my understanding and the basis from my argument which I clearly state. Of course it would take off then. I'm talking speed of say, the nose of the plane in relation to the fixed ground (Ground Speed)

Yes....thinking this through...

I STAND BY MY ORIGINAL CLAIMS!!!!!!!!!!!! And I will even go so far as to repeat that neither (in a perfect environment) - will barely move

Why? Because in my case of it being in relation to True Ground Speed - That number is "a" in the formula. It will not move - ever.

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