think about this...

[d10]

Once we established the fact that lift requires forward airspeed (real aircraft take off at 0 KIAS btw, rotary wing >>>>>>>>>>> fixed wing), and that prop wash != airflow capable of producing lift, everyone seems to be on track, but it seems this argument will continue forever because the question posed can not ever occur, even in theory, once you assume that thrust from the engines will produce forward airspeed.

Group 1, led by OP and Patrick seem to be completely ignoring the fact that if the aircraft starts to move forward, the speed of the wheels will increase, which by definition means the speed of the treadmill must increase, which by definition means the speed of the wheels must increase, etc. It seems they're taking the situation as posted, then thinking about what would happen if you added thrust to the aircraft, and then not really caring about the fixed relationship between the wheels and the conveyor anymore. Basically these people are thinking of what would happen given the situation as posted as an initial state, and then thinking of what would happen in the real world based on physics, despite the fact that what would happen deviate from the rules of the OP.

Group 2 can't get around the fact that the OP states there is in fact a fixed relationship between the conveyor and the wheels of the aircraft. They realize that the only way to solve the equation of X=X+Y, where Y is the forward airspeed, is if Y=0. For this reason, they assume that the forward airspeed must in fact be 0, and therefore lift is impossible.

I have yet to see Patrick answer the question of how the forward airspeed can be anything but 0 while still maintaining the direct relationship of the wheels and the conveyor. I suspect that his ownage in the works will also ignore this.

This question is horrible, and probably designed to create confrontation just like we have here. The answer depends entirely on if you want to think in terms of the rules posted, or think in terms of what would be possible in the real world ignoring the rules (assuming that this set up is possible to begin with). Everybody realizes that if you take the OP as an initial state, and then accelerate the aircraft, allowing the wheels to spin faster than the conveyor, you could move the aircraft forward and take off. Everybody should also realize that moving the aircraft forward will move the wheels faster than the conveyor. Anyone who flames another party for not seeing the correct answer is really just ignorant themselves of what rules the other person is assuming. Although if I had to answer the OP, it states nothing about engines on the airplane, or anything else that would produce thrust, however it does state a relationship exists which forces the aircraft to maintain an airspeed of 0 KIAS. Therefore I would say lift is not possible, and before I get flamed, I fully understand what would happen if you added a thrust component to the aircraft. I'm assuming there is none because there was none stated, and if there was, the relationship between the wheels and the conveyor would not be possible.

Also, the Herrier picture is way off.

[Slow Play Ray]

[ QUOTE ]
Infinity +1 = infinity

[/ QUOTE ]

FYP [img]/images/graemlins/grin.gif[/img]

Again:

[ QUOTE ]
just because theres no solution for the rate at which the wheels should be rotating, doesnt mean there is some force impeding the plane.

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The whole point is IT DOESN'T MATTER WHAT THE WHEELS ARE DOING. Stop thinking about the wheels, and the problem is trivial.

The OP was worded the way it was to get you thinking about the wheels, essentially to cause what happened to happen. But you have to realize by now that you are (still) trying to solve an impossible problem (the wheel/conveyor interface) - a problem to which the solution has absolutely no bearing on the answer to the original question anyway!

[CrazyEyez]

[ QUOTE ]
Obviously the plane moves if you ignore the "runway moves in the opposite direction of the plane at the exact same speed as the plane's wheels" stipulation. The fact that we took the original post at face value rather than ignored this impossible stipulation doesn't make us "idiots".

[/ QUOTE ]
Thank you. That was perfectly stated.

[Slow Play Ray]

[ QUOTE ]
Which is why it was asked the way it was.

[/ QUOTE ]

exactly.

What this means is pretty obvious. In practical terms, it would be impossible to make the treadmill move fast enough to satisfy the conditions outlined by the OP.

[felson]

[ QUOTE ]
Stop thinking about the wheels, and the problem is trivial.

[/ QUOTE ]

See, here's the thing. I have a rule about brainteasers. They are supposed to make sense.

[Slow Play Ray]

[ QUOTE ]
What this means is pretty obvious. In practical terms, it would be impossible to make the treadmill move fast enough to satisfy the conditions outlined by the OP.

[/ QUOTE ]

I acknowledged this around page 2 or so:

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Clearly this whole scenario is probably not physically possible, but it's an interesting theory to discuss.

[/ QUOTE ]

[d10]

[ QUOTE ]
[ QUOTE ]
Infinity +1 = infinity

[/ QUOTE ]

FYP [img]/images/graemlins/grin.gif[/img]

Again:

[ QUOTE ]
just because theres no solution for the rate at which the wheels should be rotating, doesnt mean there is some force impeding the plane.

[/ QUOTE ]

The whole point is IT DOESN'T MATTER WHAT THE WHEELS ARE DOING. Stop thinking about the wheels, and the problem is trivial.

The OP was worded the way it was to get you thinking about the wheels, essentially to cause what happened to happen. But you have to realize by now that you are (still) trying to solve an impossible problem (the wheel/conveyor interface), a problem to which the solution has absolutely no bearing on the answer to the original question anyway!

[/ QUOTE ]

But the OP said there was a direct relationship between the wheels and the conveyor, so how do you say the wheels don't matter? The OP specifically states that it does matter.

I have read every post and switched sides a dozen times. I have come to the conclusion that the plane will take off. Here is how:

Imagine there was no ground. For all intents and purposes this is what the original scenario would be like. If there was no ground and the plane was somehow suspended in mid air would it be able to take off? Yes. The engines or prop would still propel the plane through the air.

Back to the original scenario, to an observer it would look like the plane was sliding along the conveyor propelled by the engines until take off. Wheels and conveyor moving in opposite directions at the same speed.

I lost it until I realized that the wheels are meaningless for moving the plane. All they do is keep it upright and off the ground until the plane can take off. Keep telling yourself that the wheels do not move the plane or have anything to do with its forward propulsion.

[CrazyEyez]

[ QUOTE ]
[ QUOTE ]
Infinity +1 = infinity

[/ QUOTE ]

FYP [img]/images/graemlins/grin.gif[/img]

Again:

[ QUOTE ]
just because theres no solution for the rate at which the wheels should be rotating, doesnt mean there is some force impeding the plane.

[/ QUOTE ]

The whole point is IT DOESN'T MATTER WHAT THE WHEELS ARE DOING. Stop thinking about the wheels, and the problem is trivial.

The OP was worded the way it was to get you thinking about the wheels, essentially to cause what happened to happen. But you have to realize by now that you are (still) trying to solve an impossible problem (the wheel/conveyor interface), a problem to which the solution has absolutely no bearing on the answer to the original question anyway!

[/ QUOTE ]
I admitted all of that pages and pages ago, and in fact then stated that I believed the problem to be semantical. To which a few replied that it was not. And it obviously is. So I'm not disagreeing with anything you said. I fully believe and understand that the wheels could be motionless or moving backwards and it doesn't matter.