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:793 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.
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....
(The Gospel of Jesus Christ is the only true good news)
Unlike a car, thrust is not generated through the wheels.
The craft was manned by a crew that had been frozen to death. The heating equipment of the ship had been destroyed and the unimaginable cold of outer space had done the rest. The result was instant death for the men who were the last of the Trigans, all that were left of a once-mighty civilization, pride of the planet Elekton.
Yes, and it's easy to explain. Unlike a car or individual walking on slippery ice or a conveyer belt, a plane is propelled by thrust against air resistance and does not require surface friction of whatever may be under it. The plane is pushing itself against the air resistance, not the ground.
Clever question.
Adolf Hitler... "What luck for rulers that men do not think."
John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."
"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.
Adolf Hitler... "What luck for rulers that men do not think."
John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."
"Hmm I'd say.. yes.. because it's about lift and whether there is wind or not there would be airflow under and over the wings?"
The plane would fly but, not for the reasons you imply. You left out a crucial factor. The plane must be propelled forward at a substantial speed in order to lift off the ground.
Your answer seems to imply that the plane would hover like a chopper and depends only on the airflow caused by the engine. The engine propels the plane forward until sufficient airspeed is reached causing the lift factor on the wings you describe.
Adolf Hitler... "What luck for rulers that men do not think."
John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."
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.
(The Gospel of Jesus Christ is the only true good news)
"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.
Adolf Hitler... "What luck for rulers that men do not think."
John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."
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.
Unlike a car, thrust is not generated through the wheels."
Correct.
The wheel and conveyer belt issue was included to confuse. The author knew most folks would think of how a car would react and not consider why planes fly.
Adolf Hitler... "What luck for rulers that men do not think."
John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."
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 oppositedirection 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 oppositedirection 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 :)
(The Gospel of Jesus Christ is the only true good news)
"....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.
Adolf Hitler... "What luck for rulers that men do not think."
John F. Kennedy... "Those who make peaceful revolution impossible will make violent revolution inevitable."
Of course! It doesn't matter what the ground is doing with respect to the wheels, because the wheels don't propel the craft down the runway. The propellor or jet engine cause the plane to move forward and they work just fine even if the ground is moving in the wrong direction. It will just cause the tires to rotate at twice the speed they would normally.
Now I'm going to read the thread and see what everyone else said and whether I've missed something. hehehe
"Liberty is the solution of all social and economic questions." ~~Joseph A. Labadie
Without reading too many of the responses so far, if I understand right, at whatever speed the plane begins to move forward, the conveyer belt moves backwards.
Assuming the plane is propelled forward by jet or prop engines and not through a drive transmission to the wheels (which would not be a particularly well designed aircraft), then it won't stop the plane from going airborne. The only difference it would make is that the wheels would be spinning twice as fast at the airspeed when it takes off (which I'm assuming won't cause them to blow out, causing the plane to crash).
I disagree. Forward motion is what provides the wing lift required for a plane to leave the ground. Forward motion keeps a plane aloft. All engine power would be merely transferred to the conveyor belt through the wheels and there would be no forward motion by the plane and its wings, ergo, no take off.
Why should we hear about body bags and deaths. Oh, I mean, it's not relevant. So why should I waste my beautiful mind on something like that? -- Big Mama Bush
A plane is flying and inside the plane's cabin is a fly which is flying. As we know, the wings of an aircraft are supporting the total weight of the the plane and it's contents.
So... if the fly is flying inside the plane, does the weight of the fly count in the total weight of the aircraft?
Yes, it's wings are displacing air, which exert downward force on the floor of the plane.
If a shipping company charges by weight, would they have to pay you if you sent some helium?
As for the original problem, is the plane stationary or moving with the conveyor belt? It would need to reach takeoff speed relative to the ground in order to ahieve flight. Even if it's moving, the conveyor belt may be moving enough air that there is insufficient lift (relative speed of air passing over/under wing), but I doubt that would be much of a factor.
And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush
I disagree. Forward motion is what provides the wing lift required for a plane to leave the ground. Forward motion keeps a plane aloft. All engine power would be merely transferred to the conveyor belt through the wheels and there would be no forward motion by the plane and its wings, ergo, no take off.
You are wrong on two counts, one of which is significant to the question.
1) Wing lift is created by the pressure differential created by the air passing over the airfoil surface - the top of which is longer, causing the air to move move swiftly than it does across the bottom.
2) The plane would have forward motion thanks to the thrust caused by the engines. The wheels are irrelevant, neutral, just along for the ride. The conveyor could be run at a speed 100 times that of the forward motion of the aircraft and all it would accomplish is making the wheels spin faster before takeoff. Forward motion and thereby wind speed would in no way be affected.
"Liberty is the solution of all social and economic questions." ~~Joseph A. Labadie
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.
I misread that earlier, the plane would be stationary, so barring a steam catapult or some other b-movie trick, no the plane would not take off. Maybe if the conveyer belt/plane is at a steep angle to the ground and the plane has enough space to pick up the required airspeed for the aerodynamics to kick in.
There is no giant fan?
And I'm optimistic. See, I think you can be realistic and optimistic at the same time. I'm optimistic we'll achieve -- I know we won't achieve if we send mixed signals. I know we're not going to achieve our objective if we send mixed signals - gwbush