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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: 2451
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 # 196.

#33. To: Jhoffa_ (#0)

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).

Neil McIver  posted on  2005-12-01   16:14:23 ET  Reply   Untrace   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.

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

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.

Moving forward generates the lift required to climb, of course.

Since the plane is not thrusting against the belt, but against the gases being expelled by the engine, it would accelerate.

On further thought, though, the only way the plane could move forward is if the wheels turned fasted than the conveyor belt, and the operation of the belt would make that impossible.

Ergo, as soon as thrust was applied, both the belt and the wheels would accelerate to an infinite speed, at which time the wheels, and probably the belt would both instantly explode, killing everyone and making the question moot. At that point the question would need to be redefined.

Neil McIver  posted on  2005-12-02   12:09:27 ET  Reply   Untrace   Trace   Private Reply  

the only way the plane could move forward is if the wheels turned fasted than the conveyor belt

nope, the wheels and conveyer belt are none issues

wakeup  posted on  2005-12-02   20:01:15 ET  Reply   Untrace   Trace   Private Reply  

nope, the wheels and conveyer belt are none issues

For the sake if this question, yes they are. It is mathematically impossible that the plane could move forward while in contact with cvbelt, the landing gear wheels are in fact solidly attached to the airframe, and are only moving forward to compensate for the rearward movement of conveyor belt. It says so right at the top! :)

Dakmar  posted on  2005-12-02   20:11:00 ET  Reply   Untrace   Trace   Private Reply  

For the sake if this question, yes they are. It is mathematically impossible that the plane could move forward while in contact with cvbelt, the landing gear wheels are in fact solidly attached to the airframe, and are only moving forward to compensate for the rearward movement of conveyor belt. It says so right at the top! :)

in a car, true

in a plane, nope

wakeup  posted on  2005-12-02   21:53:23 ET  Reply   Untrace   Trace   Private Reply  

in a plane, nope

then where are the extra spins of the landing gear wheels going, mister smartguy? Assuming solid construction and a magical fuel supply that plane is stuck on that conveyor belt forever.

Dakmar  posted on  2005-12-02   21:59:33 ET  Reply   Untrace   Trace   Private Reply  

then where are the extra spins of the landing gear wheels going, mister smartguy? Assuming solid construction and a magical fuel supply that plane is stuck on that conveyor belt forever.

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

As the plane reaches 1 mph relative to the ground (not the belt), let's say its tires are spinning at 2 mph (the outside edge). The conveyor belt must therefore be spinning at 2 mph (the upper edge) to match. All conditions are met.

As the plane reaches 100 mph relative to the ground (not the belt), let's say its tires are spinning at 200 mph (the outside edge). The conveyor belt must therefore be spinning at 200 mph (the upper edge) to match. All conditions are met.

Why the need for infinite rotational speed of the tires? There is no need whatsoever for the speed the tires spin at to be related in any way to the speed the plane is moving. You've got a skateboard sitting on a conveyor belt. The speed that the wheels spin has nothing to do with the speed of the skateboard. Further, the skateboard has a fan sitting on top of it. Nothing is going to counter that force. Picture the inside of the skateboard's ball bearing axles. Picture me accidentally stepping on a skateboard without knowing it is there. You may before it is over, lol. Perhaps you see me at the top of a tall flight of stairs. Now picture how frictionless I picture those wheels once I've reached the bottom. Ouch! Can't say I blame you but I'm not changing my opinion on this.

markm0722  posted on  2005-12-02   22:51:01 ET  Reply   Untrace   Trace   Private Reply  

As the plane reaches 1 mph relative to the ground

It wouldn't. It couldn't:

Thread Rule #1: The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

Dakmar  posted on  2005-12-02   22:57:25 ET  Reply   Untrace   Trace   Private Reply  

As the plane reaches 1 mph relative to the ground

It wouldn't. It couldn't:

Thread Rule #1: 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 nothing stopping the plane from moving forward. As the wheels begin to turn, the conveyor belt "exactly" matches the speed of the wheels, whatever that speed ends up being. There is no inconsistency here.

markm0722  posted on  2005-12-02   23:03:24 ET  Reply   Untrace   Trace   Private Reply  

The wheels could never move from their their original stop position, any movement they make is counteracted by The Belt. That's the rules, man.

Dakmar  posted on  2005-12-02   23:12:32 ET  Reply   Untrace   Trace   Private Reply  

The wheels could never move from their their original stop position, any movement they make is counteracted by The Belt. That's the rules, man.

You really have simply answered the question.

And the more I think about the wheels and the conveyor belt stipulation, the only way for this jet to take off would be vertically.

wbales  posted on  2005-12-03   7:55:10 ET  Reply   Untrace   Trace   Private Reply  

The wheels could never move from their their original stop position, any movement they make is counteracted by The Belt. That's the rules, man.

You really have simply answered the question.

And the more I think about the wheels and the conveyor belt stipulation, the only way for this jet to take off would be vertically.

It is not the correct answer in my opinion.

Let's picture 3 scenarios.

Scenario #1: A billiard ball is sitting on the runway. There is no conveyor belt. I hit the billiard ball so that it moves 10 mph up the runway. The billiard ball moves up the runway and also spins around its center of mass (its axle so to speak) so that the outside edge is moving at 10 mph.

Scenario #2: A billiard ball is sitting on the conveyor belt. I turn the belt on and it is immediately sliding at 10 mph underneath the ball AWAY from the end of the runway. What does the ball do? It does not move. It merely spins so that its outside edge moves at 10 mph. You can verify this for yourself by putting a tennis ball on a piece of typing paper. Pull the typing paper out from under the ball. You will see that for the most part, your efforts only go into spinning the ball and do not go into actually moving the ball towards you.

Scenario #3: Combine both forces. Hit the ball and at the EXACT same time (no lag) turn on the conveyor belt. In order to see what happens physics allows us to merely combine the outcomes. The ball WILL move up the runway at 10 mph and spin at 10 mph on its outside edge from hitting it. The BALL will also spin an additional 10 mph on its outside edge from the conveyor belt moving underneath it. Therefore, the ball will move up the runway at 10 mph AND its outside edge will be rotating at 20 mph relative to its center of mass while on the moving conveyor belt. However, as seen from a stationary observer, the bottom part of the ball is moving at the exact same speed as the top of the conveyor belt. There is no slippage.

We measure the speed of the plane relative to the stationary observer in the control tower.

We have chosen to measure the speed of the conveyor belt relative to the stationary observer in the control tower. Further, we were forced to pick a particular point on the conveyor belt in order for the braintwister to make sense and we chose the point where it touches the wheels.

We have chosen to measure the speed of the wheels relative to the stationary observer in the control tower. Further, we were forced to pick a particular point on the wheels in order for the braintwister to make sense and we chose the point where they touch the conveyor belt.

The plane, as seen from the control tower, is moving up the runway at 10 mph. The top of the conveyor belt, as seen from the control tower, is moving the opposite direction down the runway at 10 mph. The bottom of the wheels, as seen from the control tower, are also moving down the runway at 10 mph perfectly matching the speed of the conveyor belt. However, the wheels are spinning at a speed high enough to allow the plane to move forward without its wheels slipping. All of these conditions are consistent with what the brainteaser asked of us.

I therefore say that upon takeoff the plane's wheels will be spinning exactly twice as fast because of the conveyor belt.

markm0722  posted on  2005-12-03   14:37:58 ET  Reply   Untrace   Trace   Private Reply  

If assume that "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation" refers exlusively to the relationship between the wheels and the conveyor belt, you are correct. However, if we assume that we are referring to a fixed point, the plane cannot move relative to that. If two cars are travelling side-by-side at the exact same speed neither is moving in relation to the other, yet they still are moving if observed from a fixed point, so it's basically a matter of which assumptions we are to make.

Dakmar  posted on  2005-12-03   16:37:05 ET  Reply   Untrace   Trace   Private Reply  

If assume that "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation" refers exlusively to the relationship between the wheels and the conveyor belt, you are correct. However, if we assume that we are referring to a fixed point, the plane cannot move relative to that. If two cars are travelling side-by-side at the exact same speed neither is moving in relation to the other, yet they still are moving if observed from a fixed point, so it's basically a matter of which assumptions we are to make.

Since "speed" in this brainteaser is left relatively (pardon the pun ;)) vague, there are many ways one could read it unfortunately. If one chooses an assumption which forces the tires to rotate to infinite speeds, as other posters have commented, the plane will not take off simply because the landing gear must fall apart. Further, all sorts of other odd effects would happen. The sheer speed of the conveyor belt would certainly create some headwinds. That would be good for lift in the short-term (for the same reason carriers head into the wind before launching fighters), but would the plane potentially stall out as it gained altitude and therefore removed itself from those headwinds?

In fact, one might even argue that the landing gear using my assumptions might fall apart. Are the plane's tires able to rotate at double their usual rate without incident? The rotational energy goes up as the square of the rotational speed. The tires on my car may handle 100 mph, but do I really want to try 200 mph?

Other people might choose assumptions which form paradoxes. That does not necessarily mean they are wrong. It is a brainteaser after all. It wouldn't be the first time paradoxes were intentionally inserted to make people think.

It is too bad the brainteaser isn't more clear. It seems to me that more than an average amount of assumptions must be made.

markm0722  posted on  2005-12-03   18:12:46 ET  Reply   Untrace   Trace   Private Reply  

#197. To: markm0722 (#196)

It is too bad the brainteaser isn't more clear. It seems to me that more than an average amount of assumptions must be made.

Live and learn, that's what I say.

Not all the time, but now, for instance.

Dakmar  posted on  2005-12-03 18:17:21 ET  Reply   Untrace   Trace   Private Reply  

Am I saying "now" in real time, or on this thread?

Dakmar  posted on  2005-12-03 18:18:28 ET  Reply   Untrace   Trace   Private Reply  

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