>>>So why did the problem statement specify a conveyor "as long as a runway."? It was obviously allowing for the possibility that the plane would move forward no matter how fast speed the conveyor runs.

Methinks you're reading too much into that. It was specified to be "as wide and long as a runway" to make sure the length of the belt didn't artificially limit the experiment.

The long and short of it is: Those who said 'no fly' were and are wrong, for precisely the reasons the rest of us said they were. Nanner, nanner.

>>>So why did the problem statement specify a conveyor "as long as a runway."? It was obviously allowing for the possibility that the plane would move forward no matter how fast speed the conveyor runs.

Methinks you're reading too much into that. It was specified to be "as wide and long as a runway" to make sure the length of the belt didn't artificially limit the experiment.

The long and short of it is: Those who said 'no fly' were and are wrong, for precisely the reasons the rest of us said they were. Nanner, nanner.

>>>Turn this around. You are flying in a plane, jet or prop. Place the wheels down on a conveyor belt. Is there any circumstance, ever (in theory -- catastrophic failure of wheels and resulting mess or other practical considerations), in which the movement of the belt in any way would reduce (or increase) the speed of the plane.

Say you are landing a plane in still air with an airspeed (and thus groundspeed (still air)) of 100 mph. You touch down on a conveyor belt moving backward at 50 mph. Assuming you don't hit the breaks, except for a slight slowing due to friction in your wheel bearings, you'll have a speed relative to the air and ground around the belt of 100 mph until you start decelerating. The instant you touch down, your wheels will start spinning 50% faster than your groundspeed would suggest they should.

@Anonymous #88:

>>The problem states that the conveyor belt matches the speed of the wheels, only in reverse. It doesn't say whether this is practical, it just states it. Since the wheels can't move forward, and the wheels are attached to the plane, then the plane can't move forward. If the plane can't move forward, then it can't take off. I don't know of any plane that can take off with zero forward movement. If there is one, then for that specific plane the answer is the "The plane takes off". For all other planes, which I believe is all of them, the answer is "The plane does not take off".

The wheels /can/ move forward. They are free-wheeling. They move as fast as the difference between the backward motion of the treadmill and the forward motion of the plane.

You are on the wrong side of this argument.

@72-Noen:

>>>Case closed

Well geez, that settles it then. Someone with no grasp of the mechanics and physics of what's going on has declared the debate over. LOL.

Once again, what does the wheels' interaction with the treadmill have to do with how fast it is moving in relation to the ground and/or the air? The answer is nothing. The wheels spin freely and do not impede the aircraft's forward motion through the air.

Dangerous, the original question (as I found it) was posed thusly:

“Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"

The belt matches the speed of the wheels. This makes sense as long as they are in contact with each other. The real question is: What do the wheels have to do with how fast the plane is moving through the air? The answer is: precisely nothing.

>>>reminiscent of "what do rockets push against in a vacuum?"

Nothing. But that's not how rockets work (by pushing against something). It is simple Newtonian physics (mass ejected from the back of the rocket * the mass' velocity) causes an equal but opposite reaction from the rocket.

But we digress...

>>>If the aircraft has any airspeed at all, this becomes nonsensical because the spinning of the wheels *cannot* be the same as the movement rate of the conveyor belt.

As long as the wheels are in contact with the belt, their speed will be /exactly/ that of the belt. You can speed the belt up as much as you like and the negligible friction in the wheel bearings won't really slow the plane down with respect to the airmass it is moving through.

Guysmiley is correct. Some friends and I have debated this over and over on another (aviation-related) board. The airplane will take off and its wheels will be rotating at slightly less than twice their normal speed. Its groundspeed will also be slightly slower than normal (owing to friction). Bonzo - if you put the plane on a treadmill with engine off, it will move with the treadmill because there is just enough friction for that to happen. You could literally hold the airplane still with one hand though, and in that case its wheels would spin.