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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: 1211
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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"Can the plane take off? Absolutely.

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."

wakeup  posted on  2005-12-01   3:28:35 ET  Reply   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 :)

(The Gospel of Jesus Christ is the only true good news)

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

"....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."

wakeup  posted on  2005-12-01   4:13:04 ET  Reply   Trace   Private Reply  

Can the plane take off?

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

Mr Nuke Buzzcut  posted on  2005-12-01   16:03:45 ET  Reply   Trace   Private Reply  

Can the plane take off?

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).

Pinguinite for Pinguins

Neil McIver  posted on  2005-12-01   16:14:23 ET  Reply   Trace   Private Reply  

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

wbales  posted on  2005-12-01   16:16:23 ET  Reply   Trace   Private Reply  

Here's another one, a bit harder.

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?

Pinguinite for Pinguins

Neil McIver  posted on  2005-12-01   16:24:50 ET  Reply   Trace   Private Reply  

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

Dakmar  posted on  2005-12-01   16:32:49 ET  Reply   Trace   Private Reply  

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

Mr Nuke Buzzcut  posted on  2005-12-01   18:22:04 ET  Reply   Trace   Private Reply  

this hurts my brain. ;)

christine  posted on  2005-12-01   18:36:25 ET  Reply   Trace   Private Reply  

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

Dakmar  posted on  2005-12-01   18:56:29 ET  Reply   Trace   Private Reply  

Where's this runway at. I gotta see it.

That thy beloved may be delivered; save with thy right hand, and hear me.

A K A Stone  posted on  2005-12-01   19:04:47 ET  Reply   Trace   Private Reply  

The plane would have forward motion thanks to the thrust caused by the engines.

Not if it was sitting on a conveyor belt. When taking off, the thrust from the engines propel the plane down the runway overcoming the friction between the wheels and the runway. As speed increases and the plane attains take off speed, lift on the wings pulls the plane up off the ground.

Think of running on ice--there is no traction--no friction to create forward movement despite a lot of thrust. Or think of a car wheel spinning on ice-- lots of thrust--no forward motion.

In this hypothetical, increasing thrust of the engines would only translate into higher wheel and conveyor belt counter rotation. The plane would sit spinning its wheels and the conveyor belt no matter how much thrust was being produced by the engines. The plane would not move. The wheels and the conveyor belt would be doing all the moving--the work and energy of the engines being realized there. The plane would remain stationary and would not, therefore, be able to attain lift rquired for 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

wbales  posted on  2005-12-01   19:14:02 ET  Reply   Trace   Private Reply  

The conveyer belt is magical in this exercise, it neutralizes and thrust from the jet engines by spinning the landing gear wheels. The plane wouldn't care about little spinny wheels and would shoot off into the air much as a similar plane on a concrete runway would do.

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

Dakmar  posted on  2005-12-01   19:26:35 ET  Reply   Trace   Private Reply  

Another example:

Suppose I am on a treadmill going at at snails pace. I have no forward motion. There is ZERO relative wind speed on my face as I am stationary.

Now, I turn the treadmill up to 1000 mph and I am running at 1000 mph with it. I still have no forward motion. I would still be stationary and there is ZERO relative wind speed on my face as I remain stationary.

All the energy I am expending is between my feet and the treadmill. If I had wings in this situation, they would be useless.

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

wbales  posted on  2005-12-01   19:28:18 ET  Reply   Trace   Private Reply  

Not if it was sitting on a conveyor belt. When taking off, the thrust from the engines propel the plane down the runway overcoming the friction between the wheels and the runway.

There are too many unaccounted-for factors for this to be a classic brain teaser.

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

Dakmar  posted on  2005-12-01   19:28:32 ET  Reply   Trace   Private Reply  

I'm thinking of organizing a Shopping Cart Hockey League, we have millions of acres of abandoned retail around here.

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

Dakmar  posted on  2005-12-01   19:30:41 ET  Reply   Trace   Private Reply  

The plane would have forward motion thanks to the thrust caused by the engines.

That is, BTW, very true ONCE AND ONLY AFTER a plane is airborne.

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

wbales  posted on  2005-12-01   19:39:35 ET  Reply   Trace   Private Reply  

I'm thinking of organizing a Shopping Cart Hockey League, we have millions of acres of abandoned retail around here.

I trust no jet engines would be involved.

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

wbales  posted on  2005-12-01   19:43:28 ET  Reply   Trace   Private Reply  

No, but we're having a charity drive for estes rocket motors. They contain chemicals that might just save your life some day.

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

Dakmar  posted on  2005-12-01   19:47:03 ET  Reply   Trace   Private Reply  

If the plane is a prop, it might be able to take off. It would be an unusual plane for certain. The propeller air wash over the lifting surfaces could concievably generate enough lift to get the plane airborne, even as the plane had zero velocity.

If it used a high bypass turbo fan jet for it's propulsion, as is typical for jetliners, the answer is never, assumeing there is no headwind at all.

These engines are produce very little thrust, by their basic nature, until foreward velocity begins to cram air for combustion into the nacelle, where the air is slowed down, and hence increased in pressure for the first stage of the compressors to throw into the burners. When stationary, the compressors pull a vacuum in the nacelle and very little combustion can take place.

Then, and only then do you get the massive thrust these engines are renowned for.

BTW it is easy to tell what the design speed of a jet is. If the nacelle (Front intake of the engine) is 90 degrees to the air flow, it is a subsonic design. If the nacelle if angled, supersonic, with the angle matching the sonic shock wave angle generated by the speed of the plane. In other words, the greater the angle of the nacelle, the greater the design speed of the plane.

tom007  posted on  2005-12-01   19:48:04 ET  Reply   Trace   Private Reply  

A jet would throttle up and not give a damn about what the tires were thinking.

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

Dakmar  posted on  2005-12-01   19:51:13 ET  Reply   Trace   Private Reply  

Yet another reason this plane wouldn't take off--the jet fan engine.

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

wbales  posted on  2005-12-01   20:02:28 ET  Reply   Trace   Private Reply  

get some bottlerockets and visit your local supermarkey, see if bottle rockets care how fast conveyer belt is turning.

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

Dakmar  posted on  2005-12-01   20:08:35 ET  Reply   Trace   Private Reply  

Yes, the engine could care less what the tires are doing, but the fan jets must have O2 to perform . At zero air intake velocity, ie. no foreward motion of the plane, the engine is starved for O2. Remember the nacelle actually slows down the air intake velocity and thus increases the air pressure so the compressor blades can get ahold of it.

One of my Aerospace engineering professors stated that you could stand in front of a fighter jet and keep it from moving with your hands - but is it got a little foreward motion..... you are flying.

He did not mean this literally, but was trying to demonstrate how these engines work. - they are designed to have plenty of high velocity air entering the nacelle.

tom007  posted on  2005-12-01   20:10:39 ET  Reply   Trace   Private Reply  

some bottlerockets and visit

The bottle rockets would fly, no matter what the conveyor was doing. They are a self contained control system. The propellent contains an oxident. Thrust here is independent of external conditions.

tom007  posted on  2005-12-01   20:13:25 ET  Reply   Trace   Private Reply  

How would sitting on conveter belt with wheels spinning be different from idling on tarmac, they still sucking in air. I know I've been on jets that were able to utilise their engines for taxiing, don't tell me they are helpless if they come to a complete stop, I know better.

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

Dakmar  posted on  2005-12-01   20:17:16 ET  Reply   Trace   Private Reply  

I know I've been on jets that were able to utilise their engines for taxiing, don't tell me they are helpless if they come to a complete stop, I know better.

They are rendered helpless if sitting on a conveyor belt. That is why so few modern airports have conveyor belt runways.

And anyway, back to the question: if this plane could take off on a moving conveyor belt, we shouldn't need runways at all.

Nope, runways are required for a jet to attain take off speed--that critical moment when airspeed produces enough lift to get the plane off the ground.

On a conveyor belt, the plane would not move. An observer in the control tower would just be watching a stationary jet revving its engines. No forward movement = no lift = 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

wbales  posted on  2005-12-01   20:47:48 ET  Reply   Trace   Private Reply  

On a conveyor belt, the plane would not move.

Bull, you should watch me take a airboat up a particularly wide escalator sometime. It's all about horsepower vs weight. Don't cheap out on landing gear too, I guess.

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

Dakmar  posted on  2005-12-01   20:52:19 ET  Reply   Trace   Private Reply  

On a conveyor belt, the plane would not move. An observer in the control tower would just be watching a stationary jet revving its engines. No forward movement = no lift = no take off.

blast up those jets and unless the conveyer belt is physically restraining the airplane wheels with chains or something the airplane is gonna scoot across a scrolling hanna-barbara inspired runway like it was some sort of joke, it all makes perfect sense now.

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

Dakmar  posted on  2005-12-01   20:57:21 ET  Reply   Trace   Private Reply  

blast up those jets and unless the conveyer belt is physically restraining the airplane wheels with chains or something the airplane is gonna scoot across a scrolling hanna-barbara inspired runway like it was some sort of joke, it all makes perfect sense now.

Do not--I repeat--DO NOT--try this at home.

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

wbales  posted on  2005-12-01   21:06:37 ET  Reply   Trace   Private Reply  

I should have stopped at shooting bottle rockets at grocery clerks, but what do I know?

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

Dakmar  posted on  2005-12-01   21:09:54 ET  Reply   Trace   Private Reply  

In my opinion, the plane will move forward and can take off. If I'm wrong I'm going to have to think twice about the worth of a physics degree, lol. Here's my reasoning.

There is a force applied by the thrust of the engines to propel the plane forward. Where is the opposite force to counter it and hold the plane motionless? There is only one possible source in this brainteaser: the wheels, or more specifically the axles the wheels are mounted on. How are the "as frictionless as we can engineer them" axles going to stop the plane from moving forward if they are allowed to freely spin? Yes, there is friction between the wheels and the ground, but where's the friction in the axles? Without that it does not matter what the wheels are doing. Without friction in the axles none of the "conveyer counter force" can be transferred to the plane.

One more attempt to explain the importance of the axle. When you apply brakes in your car, in an attempt to stop, you are forcing the axle to stop spinning. Unfortunately, your wheels also get a vote. On ice, they often choose to disagree. However, if you don't apply the brakes, at least as far as going forwards is concerned, your car is on a near frictionless surface no matter what surface you are on: pavement, ice, or conveyer belts. If the axle is allowed to freely spin you can pretty much rule out the wheels.

And lastly, why the conveyer belt? Just find a plane that can take off with the brakes fully applied (leaving long black skid marks until it gets airborne). Put a coyote in the cockpit, put a roadrunner at the end of the runway, and make sure the manufacturer of the engine is Acme! Beep! Beep! Hehehe :)

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-01   21:24:23 ET  Reply   Trace   Private Reply  

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

You might want to rethink that. The key part you are overlooking is highlighted in bold.

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

God is always good!
"It was an interesting day." - President Bush, recalling 9/11 [White House, 1/5/02]

RickyJ  posted on  2005-12-01   22:24:30 ET  Reply   Trace   Private Reply  

Just find a plane that can take off with the brakes fully applied

Well if there are such planes then of course it would fly, but since there aren't, it's a mute point.

God is always good!
"It was an interesting day." - President Bush, recalling 9/11 [White House, 1/5/02]

RickyJ  posted on  2005-12-01   22:37:59 ET  Reply   Trace   Private Reply  

If I'm wrong I'm going to have to think twice about the worth of a physics degree, lol.

Wow, you are putting a lot on the line there aren't you? I would have kept that info to myself.

God is always good!
"It was an interesting day." - President Bush, recalling 9/11 [White House, 1/5/02]

RickyJ  posted on  2005-12-01   22:39:31 ET  Reply   Trace   Private Reply  

Just find a plane that can take off with the brakes fully applied

Well if there are such planes then of course it would fly, but since there aren't, it's a mute point.

That was the joke part of my post by the way. Hence the reference to the Wile E. Coyote and Road Runner.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-01   22:42:19 ET  Reply   Trace   Private Reply  

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).

The only way the plane could take off is if it actually did move forward or up. Since the force of the engines is basically parallel with the ground then the only option is moving forward to become airborne. How does a multi-ton object become air born when it has no upward force being applied? The only way it could move forward is if it skidded down the runway and took off that way. I don't think they make planes capable of doing that, so it wouldn't take off. But if they had jet engines powerful enough and planes able to withstand the skidding, then it would take off.

God is always good!
"It was an interesting day." - President Bush, recalling 9/11 [White House, 1/5/02]

RickyJ  posted on  2005-12-01   22:55:42 ET  Reply   Trace   Private Reply  

The only way it could move forward is if it skidded down the runway and took off that way.

Why would it skid? The axle is freely rotating. The wheels are free to turn. The brakes aren't being applied.

When prosperity comes, do not use all of it. - Confucious
The nation is prosperous on the whole, but how much prosperity is there in a hole? - Will Rogers
There are 9,000 hedge funds out there. There aren't that many smart people in the world. - Michael Driscoll, a trader at Bear Stearns & Co. in New York
Some days you just want to pull out the Bonehead Stick and beat people senseless. - mirage

markm0722  posted on  2005-12-01   22:57:38 ET  Reply   Trace   Private Reply  

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