Flight and the Conveyor Belt

[doggstar]

@1920s Style "Death Ray"

What if we covered the treadmill and left just enough of it exposed to allow it to contact the aircraft’s wheels? What if, instead of a treadmill, we had threads sets of undercarriage identical to the aircraft’s but upside down. The aircraft sits on them and they accelerate at what ever speed is necessary to keep the aircraft from moving forwards.

I agree with everything else you say (and I thought your people whistling analogy was hilariously accurate.)

It will drive off of the treadmill then. If the friction gets too great, then the plane will move backwards off of the treadmill.

There is nothing that can accelerate fast enough for the plane to remain stationary. But if it could, then the plane wouldn’t take off. But then again, the wind entrained by the treadmill would give the plane enough lift take off (just like a kite).

Its like the old story, if you are travelling .999% the speed of light in your mustang, what happens when you turn on your headlights?

[John_W.Kennedy]

Its like the old story, if you are travelling .999% the speed of light in your mustang, what happens when you turn on your headlights?

The light from your headlights will be emitted at c, relative to you. No matter how fast you’re moving, light will always travel c faster than that.

[enipla]

The question as asked that Cecil answered -

The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).

Bolding mine. So if the plane is moving forward at 70 mph, the conveyer is moving backwark at 70 mph. The wheels are turning like mad (140mph), but not to much for the engines to overcome. The plane is still moving forward at 70mph.

As the question is asked, the plane takes off. It moves. It’d be hell to control the plane on the ground with the wheels turning at twice the normal speed(sort of like driving 140 mph down a freeway).

It says nothing about wheel speed, it talks about plane speed.

I believe that just about any plane could over come the additional friction imparted on the landing gear at twice the normal take off speed. Not to be recommended though.

It says nothing about wheel speed, it talks about plane speed.

[cylon]

@Some guy in Ohio

I’m going to have to chalk this one up to the poor wording of the original question, by my reading - “conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same” - means that the plane will have no forward motion and hence no wing lift. Granted it is 1AM here and I’ve been up for about 32 hours, am I missing something obvious? The plane remains stationary - no forward motion, no wing lift, no flight.

Yes you are missing something obvious, the fact that no treadmill could keep the plane stationary. There is still fwd motion. But the wheels just spin twice as fast.
The falacy lies in assuming that the plane would remain stationary.

[zut]

@Christi7df

No, Cecil said this about stating the question that way, “The question thus stated asks the impossible – simply put, that A = A + 5 – and so cannot be framed in this way.”

I agree with Cecil.

So do you agree with Cecil’s interpretation of the question or not? First you say “no,” then you say “I agree with Cecil.” In the same post, even. Or, better yet, what does “the conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation” mean, in your own words? Last I knew, you were thinking it meant the belt matched the speed of the contact patch, measured with respect to the ground.

And Cecil is simply wrong that the question “cannot be framed that way.” Post 106.

@enipla

As the question is asked, the plane takes off. It moves. It’d be hell to control the plane on the ground with the wheels turning at twice the normal speed(sort of like driving 140 mph down a freeway).

It says nothing about wheel speed, it talks about plane speed.

Agreed, but I doubt too many people dispute that. However, Cecil also talks about an alternate wording of the question in the last paragraph. Which there does seem to be some argument over.

[Christi7df]

@zut

And Cecil is simply wrong that the question “cannot be framed that way.” Post 106.

I disagree.

[enipla]

The question that Cecil answered. Correctly.

“A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?”

And Cecil is simply wrong that the question “cannot be framed that way.” Post 106.

If you want to re-frame the question that the conveyer can accelerate to such a rate to impart enough force against the landing gear, than I and many others believe that you have completely changed the intent of the question.

If you ride a treadmill on roller skates, and have a rope attached to a wall, and pull your self towards that wall at 1mph how fast are you going relative to the ground and airspeed?

[zut]

@Christi7df

I disagree.

Got a reason? Did you read my earlier post? Do you agree with Cecil’s interpretation of the question or not?

@enipla

If you want to re-frame the question that the conveyer can accelerate to such a rate to impart enough force against the landing gear, than I and many others believe that you have completely changed the intent of the question.

Well, of course the question has changed. That’s kind of the point. But the alternate wording comes from Cecil’s column, so it’s not as if I’ve made it up from whole cloth.

@enipla

If you ride a treadmill on roller skates, and have a rope attached to a wall, and pull your self towards that wall at 1mph how fast are you going relative to the ground and airspeed?

One mph. What would this question be apropos of?

[1010011010]

@UncleRojelio

If there is any friction in the wheel bearings, then there then magical treadmill can accelerate fast enough so that the force from that friction equals the thrust from the engines.

If we posit frictionless bearings, then the belt must accelerate to generate force on the axles by exploiting the wheel’s resistance to changes in rotation. If there’s friction in the bearings then some steady state can be reached and constant acceleration is not required.

@hblask

this thought experiment contradicts itself, in a way. The notion of a plane on a treadmill assumes the tires are spinning freely and fully functional. In that case, the plane takes off.

Which is the point of embarking on the thought experiment of trying to figure out what conditions would be necessary to prevent the plane from taking off… it’s entertainment.

Invoking weird materials (E.G. frictionless bearings) is just a way to spice up the physics.

@cylon

Yes you are missing something obvious, the fact that no treadmill could keep the plane stationary. There is still fwd motion. But the wheels just spin twice as fast. The fallacy lies in assuming that the plane would remain stationary.

That would be a condition of (one interpretation of) the question, not a fallacy.
A plane is on a conveyor that moves backwards in some manner sufficient to keep the fuselage of the plane stationary. Does the plane take off? No. Easy. The interesting part if figuring out what that treadmill would have to do to keep the plane from moving.

@Christi7df

I disagree.

With what? Post #106 is kinda long.

[Christi7df]

@zut

Got a reason? Did you read my earlier post? Do you agree with Cecil’s interpretation of the question or not?

Did you read mine? If you did you totally missed the point.

You do not even understand Cecil. It is no wonder that you do not understand me.

At this point it appears that you are only baiting for an argument.

I will just go along with Cecil and say that that interpretation is nonsense.

[robby]

@Christi7df

That is fine as long as you are just playing make believe.

But the problem as I see it is when you are playing make believe, you can make believe anything.

Are we children just playing make believe?

We can just discuss all kind of impossible things then. I thought this board was supposed to be science related.

Christi7df, do you truly not understand the concept of “thought experiment”?

As I noted way back in our previous thread on this topic, Einstein never actually got on a rocket traveling near the speed of light, either. However, by thinking scientifically about what would happen if he were on a rocket traveling near the speed of light, he came up with the theory of relativity.

You seem to be using the concept of “impossibility” extremely pedantically. A treadmill capable of large accelerations is theoretically possible. Traveling in a rocket near the speed of light is also theoretically possible. Treadmills or rockets that exceed the speed of light in a vacuum are examples of truly impossible things.

Finally, while things like massless pulleys and frictionless bearings are indeed also not possible, they serve as useful simplifications for a first approximation of a solution to a given problem. Often, such an approximate solution is adequate.

Someone could just as well argue that you have not fully considered the problem because you didn’t take into consideration Coriolis forces, turbulence from the treadmill (or a butterfly a continent away), or the gravitational effect of the Moon on the plane. It could be pedantically argued that not considering the Moon is just playing “make-believe.”

[Christi7df]

@robby

Christi7df, do you truly not understand the concept of “thought experiment”?

As I noted way back in our previous thread on this topic, Einstein never actually got on a rocket traveling near the speed of light, either. However, by thinking scientifically about what would happen if he were on a rocket traveling near the speed of light, he came up with the theory of relativity.

You seem to be using the concept of “impossibility” extremely pedantically. A treadmill capable of large accelerations is theoretically possible. Traveling in a rocket near the speed of light is also theoretically possible. Treadmills or rockets that exceed the speed of light in a vacuum are examples of truly impossible things.

Finally, while things like massless pulleys and frictionless bearings are indeed also not possible, they serve as useful simplifications for a first approximation of a solution to a given problem. Often, such an approximate solution is adequate.

Someone could just as well argue that you have not fully considered the problem because you didn’t take into consideration Coriolis forces, turbulence from the treadmill (or a butterfly a continent away), or the gravitational effect of the Moon on the plane. It could be pedantically argued that not considering the Moon is just playing “make-believe.”

Playing theoretical make believe is fine as long as there is no practical way to accomplish the task posited in the real world.

In order to stop the airplane from moving forward, all you need to do is attach a cable to the back of it and anchor it to something that it cannot break free from. This would actually work in the real world.

Save theoretical for things that cannot be practically accomplished in the real world.

You have a paradox if you say that you have a treadmill that can accelerate to infinity and beyond and you also have an airplane that can overcome any force that can be applied to the airplane through the wheels from a treadmill.

As Cecil said, “Nonsense.”

[CantConfirmOrDeny]

People! Simmer down! This is not an engineering problem. We all agree that a plane won’t fly unless its wings are moving through the air. Correct? Good.

Is Cecil Correct? Yes. Good.

Is Cecil playing with us, purposely obfuscating and declarifying simple, obvious situations for the purpose of providing entertainment to all? Yes. Good.

Imagine you’re in an airplane already in the air, flying towards the airport. All seems normal, you’re descending smoothly, everything’s cool. Of course, you’re landing at a special airport with a moving runway. In fact, the stupid runway is moving backwards at 150 knots, exactly your landing speed, coincidentally. Now - what happens the moment you touch down on this runway? Do you stop instantaneously? I think not. Is there an unusual noise as the wheels spin up to twice their normal speed? Yup. Do you roll out and stop pretty much normally after that? Yah - more or less. Tough to make the first turnoff, though, that’s a problem for another day.

The engineering question is settled. The plane takes off and flies, just like Cecil said. Now, how do we settle this semantic question regarding what was implied by the “original” question, then the “rephrased” question? The question I read clearly stated “the plane moves” - implying there’s nothing holding it stationary - the reverse of the landing scenario described above. (Don’t go all entropy on me here…) The rephrased question, as far as I can tell, simply dwells more on the obfuscatory yet irrelevant description of how the runway decides how fast to go. There is still nothing to imply that the plane is somehow being held stationary w.r.t. the Earth - the only unfamiliar thing about this situation is the moving runway, which under no normal circumstances could appreciably affect the takeoff performance of the airplane. Appreciably.

If you don’t buy this explanation, my next post will go into free body diagrams and basic engineering analysis methodologies. 'Course, i could just hit my head with a hammer and achieve the same result. But this is more fun.

Cheers,
-CCoD-

[Richard_Pearse]

@Christi7df

In order to stop the airplane from moving forward, all you need to do is attach a cable to the back of it and anchor it to something that it cannot break free from. This would actually work in the real world.

That’s a little like someone asking “how fast does this chair lift need to go to take me up the top of the mountain in two seconds?” Your response is “if you want to be there in two seconds then leave 30 minutes early and take a helicopter.”

Do you get the fact that there are a couple of people here who are, or were, interested in just what a treadmill would need to do to keep an aircraft stationary? Do you get that saying “tie the aircraft to a poll” is of absolutely no relevance at all and that you may as well discontinue the discussion? Do you realise that the interpretation of the question that sparked the discussion on the incredible accelerating treadmill was the logical interpretation from the question as phrased in the original GQ forum thread before Cecil tackled it?

Do you understand that for the last few pages of this thread some people have been discussing whether it’s Tuesday or Wednesday and you keep piping up and saying “it’s blue!”

Save theoretical for things that cannot be practically accomplished in the real world.

A treadmill that can hold an aircraft stationary is just such a theoretical thing. A reminder, we don’t just want the aircraft to remain still, we want to use a treadmill to do it.

You have a paradox if you say that you have a treadmill that can accelerate to infinity and beyond and you also have an airplane that can overcome any force that can be applied to the airplane through the wheels from a treadmill.

Sure, but no one, aside from you, is trying to give the aircraft any powers to overcome the force from the magic treadmill. Everyone is happy leaving the aircraft as stock, and then figuring out what the treadmill has to do to keep it still.

[Lockseer]

Here is my understanding of the problem, and forgive me if it’s been framed like this in the prior 300+ posts:

The real question is, to me, is it possible for a treadmill to prevent a plane from achieving forward momentum from it’s jet engines? If no, then the plane can move forward, and can achieve lift.

I liked Cecil’s roller-blade/treadmill/rope analogy. But let’s look at it this way, as I this analogy came up while arguing about this with a co-worker today:

I’m on a treadmill on a skateboard. I have a buddy standing behind me, off the treadmill, with his hands on my back, arms bent (so they aren’t extended all the way). As the treadmill picks up speed, I pretty much remain motionless, as the wheels roll underneath me, and my friend is providing a force behind. Indeed, once the treadmill reaches a constant speed of, say 90 mph, my friend could even remove his hands and I’d be fine…my wheels are spinning at 90mph and I’m for all intents and purposes motionless…but I’d slowly drift back to the rear of the treadmill as friction set in.

Now…put my friend back in place. I’m coasting along at 90mph. And now…my friend extends his arms to the full length in front of him, pushing me forward along the treadmill. He meets no resistance, despite the speed the treadmill is going. Indeed, he could take me by elbow, walk alongside the treadmill, and I’d move with him…and no matter how fast the treadmill was spinning, I would have no choice but to move forward.

The engines acting on the air have the same effect on the plane as my friend walking forward and tugging me by the elbow.

It almost helps to think in terms of the wheels cancelling out the treadmill (rather than vice versa). Whatever speed the treadmill goes, the wheels will negate it. Any force from the engine (my friend, in the above analogy), will then push the plane forward.

[zut]

@Christi7df

Did you read mine? If you did you totally missed the point.

You do not even understand Cecil. It is no wonder that you do not understand me.

sigh I read your post. It said “I disagree.” That’s not exactly a complete and cogent argument, and there’s really nothing to misunderstand.

In order to figure what the answer to the question is, you have to first determine what the question is. The answer could be either “the plane takes off” or “the plane doesn’t take off” depending on your assumptions. I went over all the variations I could think of, in a fair amount of detail, in post #106. If you’d like to comment on any of that, I’d be happy to hear what you think.

I’ve asked you repeatedly what you think the interpretation of the question should be, since you’ve given conflicting statements on the subject. You’ve dodged each time, and I’m not really sure why. I’m at a loss as to how you can be so sure about the answer to a question when you can’t even define the question. So, one more time: Do you agree with Cecil’s interpretation of the question or not? What’s the interpretation, in your own words? Did you read my earlier post, number 106? Do you have something specific about the physics that you disagree with, or is this more of a faith-based argument?

@Christi7df

You have a paradox if you say that you have a treadmill that can accelerate to infinity and beyond and you also have an airplane that can overcome any force that can be applied to the airplane through the wheels from a treadmill.

Do you realize that you’re the only person in this thread that is actually arguing this?

[zut]

@CantConfirmOrDeny

The engineering question is settled. The plane takes off and flies, just like Cecil said.

Agreed.

@CantConfirmOrDeny

The rephrased question, as far as I can tell, simply dwells more on the obfuscatory yet irrelevant description of how the runway decides how fast to go. There is still nothing to imply that the plane is somehow being held stationary w.r.t. the Earth - the only unfamiliar thing about this situation is the moving runway, which under no normal circumstances could appreciably affect the takeoff performance of the airplane. Appreciably.

The question statement, for reference, is: “The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.” [my bold] Under what I think is the most reasonable interpretation of what “the speed of the wheels” means (which is the same interpretation that Cecil uses), the only way the speed of the wheels will match the speed of the conveyor is if the fuselage remains stationary. Even though it’s not stated specifically, the problem statement requires that to happpen.

If you don’t buy this explanation, my next post will go into free body diagrams and basic engineering analysis methodologies.

Please do. I would actually appreciate an argument from physics as opposed to an argument from semantics or faith. But please state your assumptions as to what the problem statement means up front, and please do me the favor of reading posts 106 and 161 in this thread.

[zut]

@Lockseer

It almost helps to think in terms of the wheels cancelling out the treadmill (rather than vice versa). Whatever speed the treadmill goes, the wheels will negate it. Any force from the engine (my friend, in the above analogy), will then push the plane forward.

And the reason this isn’t a very good analogy (bad Cecil!) is that this is a constant-speed conveyor, not one that is “designed to exactly match the speed of the wheels at any given time.” Everything you’ve stated above is true, but the problem statement leaves out the key “speed-matching” requirement.

Now, if you add that speed-matching requirment back in, then as soon as your buddy pushes forward, the treadmill will accelerate backwards to counteract the force, right? And what happens then depends on the other assumptions in the problem–friction, mass, and so forth. I’ve stuck every variation I can think of in post #106.

[UncleRojelio]

@Lockseer

Now…put my friend back in place. I’m coasting along at 90mph. And now…my friend extends his arms to the full length in front of him, pushing me forward along the treadmill. He meets no resistance, despite the speed the treadmill is going. Indeed, he could take me by elbow, walk alongside the treadmill, and I’d move with him…and no matter how fast the treadmill was spinning, I would have no choice but to move forward.

You said it yourself. There is friction in the system. What if the treadmill were turning (much) faster than 90mph and there was so much backwards force from that friction that your friend could not overcome? The theoretical treadmill has no upper speed limit, which means there is no upper bound on the amount of force generated by friction in the wheels.

[Lockseer]

@UncleRojelio

You said it yourself. There is friction in the system. What if the treadmill were turning (much) faster than 90mph and there was so much backwards force from that friction that your friend could not overcome? The theoretical treadmill has no upper speed limit, which means there is no upper bound on the amount of force generated by friction in the wheels.

My apologies. A theoretical treadmill with no upper speed also assumes theoretical wheels with no friction. Are you saying that the treadmill would reach a speed where it would no allow my friend to walk next to it, pulling me forward?