Geez, I go to sleep for a few hours and this is what happens? People don't grasp this problem, it's no wonder that general relativity is so mind-blowing to many. Then, time itself starts to change as a function of velocity, but the fun part is, velocity is a value in terms of time - meters per second.
I broke it down before, here it is again:
There have been multiple definitions of the problem presented.
1) The treadmill/conveyor belt's velocity matches the plane's takeoff speed from an otherwise immobile surface, like a runway. Here, the plane can easily take off, as was just shown on Mythbusters. That scenario isn't an issue.
2) The belt's velocity is a function of the wheels' rotational velocity. Here, unless it's an inverse exponential, or fraction of the belt velocity, the velocity of the wheels and belt will quickly approach infinity. Think of a looped relationship in Excel, where one cell's answer winds up referring back to itself.
3) The belt's velocity is carefully set so that it can speed up to any speed, so as to keep the plane stationary, as a result of the rotational inertia of the wheels, as well as bearing/rolling resistance. In theory this is possible, as the rotational inertia and rolling resistance are finite, measurable values. The problem is that the conveyor belt, and thus the plane's wheels, would likely have to move so quickly that the bearings would sustain damage.
If I had some numbers, such as wheel mass, wheel diameter, rolling resistance, engine thrust, and the overall mass of the plane, I think I could solve this problem (that is, determine how fast the wheels would need to rotate) using what was covered in my Dynamics class.