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Title: Brainteaser: There's an airplane on the runway..
Source: Elsewhere
URL Source: http://www.someplaceelse.com
Published: Dec 1, 2005
Author: I have no idea
Post Date: 2005-12-01 01:10:02 by Jhoffa_
Keywords: Brainteaser:, airplane, runway..
Views: 2378
Comments: 202

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. There is no wind.

Can the plane take off?

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Begin Trace Mode for Comment # 30.

#2. To: Jhoffa_ (#0)

No.

The plane much reach takeoff "air speed", a certain speed of air flowing over the wings at which lift is generated by the wings. The plane must move forward, relative to the air flow over the wings. Merely rotating the wheels via the conveyer while the plane is otherwise motionless relative to the air won't get it done.

Now, a wind tunnel instead of a conveyor....

Starwind  posted on  2005-12-01   1:16:01 ET  Reply   Untrace   Trace   Private Reply  

True.. can I change my answer ?? :P

Zipporah  posted on  2005-12-01   1:19:31 ET  Reply   Untrace   Trace   Private Reply  

Are you sure you want to?

Jhoffa_  posted on  2005-12-01   1:21:09 ET  Reply   Untrace   Trace   Private Reply  

Are you sure you want to?

LOL! I was wrong.

The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

That is another way to say, the conveyor moves forward at the exact same speed of the plane, but the wheels never actually rotate.

So the plane would gather speed, the conveyor keeps pace, the wheels never rotate, lift is produced as the air flows over the wings, plane takes off.

See, Zipporah, you were right the first time :)

Starwind  posted on  2005-12-01   1:41:45 ET  Reply   Untrace   Trace   Private Reply  

"That is another way to say, the conveyor moves forward at the exact same speed of the plane, but the wheels never actually rotate."

I believe you misunderstand the question.

"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation."

The wheels roll or "rotate" forward as the conveyer belt moves the "opposite direction."

Try to imagine God holding the plane from moving forward and someone turns on the conveyer belt. The wheels spin, the conveyer belt moves along in the opposite direction yet, the plane is stationary. Now, God lets go and the plane, which was at full throttle, starts to push against the air and begins to move forward. It is irrelevant what the tires or the conveyer belt are doing.

wakeup  posted on  2005-12-01   2:34:09 ET  Reply   Untrace   Trace   Private Reply  

The wheels roll or "rotate" forward as the conveyer belt moves the "opposite direction."

That's actually a physical impossibility, or at least it would indicate the wheels skidding on the conveyer. The plane moves forward (under its thrust, weight resting on the wheels), but no, the wheels don't rotate because the forward motion of the conveyer (keeping pace with the accelerating plane) negates their rotation.

The wheels can't be in physical contact with the conveyor moving forward while the wheels also rotate opposite - two objects in contact moving in opposite directions with shear forces - the wheels would be "peeling out" like a drag racer. But the wheels aren't driven and they don't need to rotate, since the conveyor is pacing the plane's velocity.

It is irrelevant what the tires or the conveyer belt are doing.

From a standpoint of the plane developing lift on its own, yes. The wheels and conveyer were a "red herring". I missed it earlier.

Starwind  posted on  2005-12-01   2:50:50 ET  Reply   Untrace   Trace   Private Reply  

"the wheels don't rotate because the forward motion of the conveyer (keeping pace with the accelerating plane) negates their rotation."

Read this again. "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation."

Note that the conveyer belt matches the speed of the wheels, NOT THE PLANE. The wheels roll forward and the conveyer belt moves the opposite directions. No friction, imagine a bike on a treadmill. Tires rolling one way... forward, and the treadmill going the other. Perfectly logical.

Obviously, the question was designed to make you think the plane would spin it's tires in place and go nowhere, like a car on the conveyer belt would do. Cars push against the ground, planes push against the air.

The answer would be too obvious if the conveyer belt moved along with the plane.

wakeup  posted on  2005-12-01   3:04:53 ET  Reply   Untrace   Trace   Private Reply  

Note that the conveyer belt matches the speed of the wheels, NOT THE PLANE

The wheels have two speeds in this. A rotational speed which if in contact with the conveyor belt, must be matched and a translational velocity as the plane to which they are attached moves forward.

And there are two directions. The rotational direction of the wheels at the tangential point of contact with the conveyeor (bottom of tire rotates rearward ), in which case the opposite direction of the conveyor would be forward, and consequently shear forces and 'skiding' would exist, if the wheels were driven (but they're not); and the other direction is the translational direction of the wheels (and the plane) - forward, in which case the opposite direction of the conveyor would be rearward.

I 'overanalyzed and overempahsized' the rotational aspects.

The answer would be too obvious if the conveyer belt moved along with the plane.

Oh, idunno, it made a fine red herring as-is, for me anyway :)

Starwind  posted on  2005-12-01   3:31:58 ET  Reply   Untrace   Trace   Private Reply  

#31. To: Starwind (#30)

"....conveyer belt.......moving in the opposite direction of rotation..."

You speak of a stationary tire. The question speaks of a rotating tire. You misunderstand the question.

I clearly see a tire rolling on a conveyer belt. The tire rolls forward the belt moves in the opposite direction, just as a bike tire on a treadmil would behave.

You're tired. We're done.

wakeup  posted on  2005-12-01 04:13:04 ET  Reply   Untrace   Trace   Private Reply  

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