@phoenyx: yes, I read the link, and the most plausible explanation I found from there was:
“Basically, the question assumes that moving the runway backward under the plane while it is accelerating forward will cancel out its forward motion. But that’s not necessarily true. The degree to which this is possible is the degree to which there’s friction between the wheels and their axles. In a frictionless environment, it doesn’t matter what the runway is doing.
Looking at it from the opposite extreme, if the runway can push back on the plane exactly as much as the engines are pushing forward, the plane will stand still. Rather than needing any fancy conveyor belt system, you could just put big blocks in front of the wheels. :)
Does this mean that the plane won’t take off? Well, probably. You might want to think that the engines, as they push the air over the wings, will produce some lift, and I guess that this is true at least minimally, but the real lift generated by the wings is the relative motion between them and the air through which they move. Without forward motion, you don’t have that lift. I doubt the engines could run fast enough to even generate enough lift to bring it off the runway at all.
So, the bottom line is that this isn’t a hard problem if you understand that a plane flies because the wings generate lift as they move through the air, not merely because the engines push air over the wings. The engines push air over the wings in some cases just because it’s a convenient design. The purpose of the engines to propel the plane forward. They can be anywhere in relation to the wings (well, excepting worrying about turbulence and stuff).
A more complete answer is that if you attempted this experiment, what would happen is that only at first would the conveyor belt cancel out the engines push forward. But very quickly, that small friction of the wheels wouldn’t matter. The plane will move forward regardless of how fast the conveyor belt is moving backward. So the plane will just be slightly slow to start moving, then once it does, it will quickly act like any other plane taking off.
Alternatively, assuming you really could apply a backward motion equal to the forward propulsion of the engines, then the plane wouldn’t take off. It’d sit there as the engines ran faster and faster because the engines aren’t what generate lift. And the fancy backward-moving conveyor belt is a distraction, because you can get the same effect by just locking the plane against forward motion.”
It is amazing though that once the plane’s wheels overcome the friction of the conveyor belt, they’ll move faster (as johnpowell and the mythbuster team points out), and the plane will move forward. But that’s where the question gets a bit complicated. Perhaps the question could be worded more effectively as: “Can a plane’s thrust overcome a conveyor belt moving under it in the opposite direction?” The answer would be yes, as it would take a minimal thrust force to overcome the force of the belt against the tires.
But in any case, no forward air current, no lift. If instead of some monstrosity of a conveyor belt, as the poster indicated above, the wheels were just blocked up (creating a similar state of “infinite” frictionless force against the tires), then if the tires were not the issue, the plane would just sit still on the tarmac.