Cecil,
I am new to this airplane on a treadmill conundrum (and straightdope.com), but I think your column on this issue from March 3, 2006 more scientifically addresses this thought experiment than any other I have read. However, that being said, I feel there is one key piece of information that many people (even you) have overlooked in the scenario below.
In your column you say in BR#2 if it were possible to accelerate a treadmill to a high enough speed to counteract the force of the plane’s thrust that the plane would stay in place. Now, I understand why you say that and you explain your reasoning quite eloquently, but here is why I believe the infinitely accelerating treadmill will still fail to keep the plane from achieving lift.
It is because air has mass and there is a lot of air resting on that treadmill. This can be proven by a simple experiment. Simply turn on a small treadmill at its highest rate of speed you can easily feel the slight breeze generated by holding your hand just above the surface of the treadmill.
If this mythical treadmill is now exponentially increased in both size and speed, it will also exponentially increase the rate of airflow generated by the treadmill. As the treadmill reaches several hundred miles per hour, I theorize that it will be generating enough wind speed on its own to give the plane lift effectually allowing the plane to still takeoff with minimal difficulty.
Does this theory hold any water or am I just thinking too hard on this? Anyway, thanks for fighting ignorance!! Someday I hope we all win that battle!!