Thursday, January 31, 2008

Airplane on a treadmill


I created this blog specifically to make this post. It may be the only post I ever write, but since human ignorance is seemingly unbounded, perhaps it won't be.

I thought that today would be a monumental day for this topic. Today, the Mythbusters debuted their long-awaited "Airplane on a treadmill" episode. For years, physics teachers around the world have cringed in horror at heated internet debates concerning a ludicrous thought experiment. Sadly, half of them recoiled in disgust at the correct arguments. Forum posters signed their names with such epithets as "Ph.D. Aerospace Engineer" and "20-year pilot." Somewhat tellingly, these ego-boosters were most often employed by those delivering the wrong answers. Mythbusters finally attempted to end the insanity by performing the experiment themselves.

AND YET...

The debate rages on. Even after being shown seemingly conclusive evidence of the other side's argument, forum-goers from near and far continued to staunchly defend their own theories.

Here and now, the debate will end. I intend this long-winded article to be the definitive answer to the great AOAT conundrum. No further debate is necessary - simply direct the ignorant people to this page, tell them to read it, and let's all get on with answering more intriguing questions, like does P = NP?

For those of you just joining us, "Airplane On A Treadmill," also known as "Airplane on a Conveyor Belt," is a thought experiment in physics. Some consider it a litmus test for assessing one's knowledge of airplane physics. In its most basic form, the experiment is worded thusly:

A plane is standing on a large treadmill or conveyor belt. The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?

The question suffers from many rewordings that muddle much of the debate about the thought experiment. The basic idea is that there's a plane, on a treadmill, and we're going to run the treadmill backwards in an attempt to stop the plane from taking off. And here, at the very beginning of this explanation, is the definitive answer. There are in fact two correct answers to this question:

-No, the plane can't take off.
-Yes, the plane can take off.


Fooled you! But that's just the point. The experiment is meaningless, and the passionate internet debates more so, if we cannot agree on what is truly meant by the question. But don't worry, I won't pull a Lost on you - I do intend to give a truly airtight answer later on. For now though, we need to debate semantics.

Really, we do.

You see, the AOAT confusion all arises from misses - misconceptions, misinterpretations, and misunderstandings. Consider three rewordings of the question:

1) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I begin to attempt to take flight in the plane, and you attempt to match my speed to try to keep me stationary. Will the plane take off?

2) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I throttle up the airplane and you turn on the treadmill, and we conspire by our joint effort to try to keep the plane stationary relative to the ground. Will the plane take off?

3) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I attempt to take flight in the plane, but you match my speed with the treadmill and keep me stationary relative to the ground. Will the plane take off?

Here are the absolute, 100%, bet-your-life-on-it answers to these rewordings:

Yes.
No.
Whoever asked this question is an idiot.

And that's about all this debate comes down to, folks. If we could all agree on one set of rules for the thought experiment, then we ought to be able to make the explanation of the answer clear. As it stands, normally one side has interpretation (1) in mind, and argues vehemently with someone else who has interpretation (2) in mind, and the whole thing blows up into a senseless squabble.

Here are the three core facts that are rock-solid:

A) If the plane remains stationary relative to the ground, it will not take off.
B) If the plane moves relative to the ground, it will take off.
C) The person operating the conveyor belt cannot by himself make the plane remain stationary relative to the ground.

(EDIT: Really, you should substitute the word "air" for ground in the above facts. I use "ground" throughout this post because of a consistent mistake made by "no-flys" in their assumption that the plane remains stationary. It doesn't remain stationary, relative to the ground or the air. The important point is that it moves relative to the air, not the ground, but I'm assuming throughout this post that there is no significant tailwind or headwind. I discuss the implications of this briefly in the section about windtunnels.)

That's about all you need to know to argue whichever interpretation is appropriate. I'll discuss why these facts are true in a moment. In the meantime, look back at the three re-wordings of the question above.

In (1), the key phrase is "you attempt to match my speed to try to keep me stationary." Since we know from fact (C) that you cannot keep me stationary, it follows from (B) that I will take off successfully.

In (2), we conspire together to keep the plane stationary. This is possible, albeit stupid. We know from fact (A) that I will not take off.

In (3) - and this is the important part - the actions being described are impossible. We know from (C) that the conveyor operator cannot keep the plane stationary. The most powerful conveyor belt in the world couldn't do it. David Copperfield couldn't do it. It can't be done. Only if the pilot "plays along" can the plane be made to remain stationary.

Unfortunately, most of the "no-flys" - the label given to those who argue that the plane won't take off - are assuming that interpretation (3) is what is being asked. They accept that the plane remains stationary, and say it won't take off. The "will-flys" know that the plane can't remain stationary, and say it will take off. Add to the mix a few people who see that in one way, the plane could be forced to be stationary by some pilot-conveyor cooperation, and you've got a deadly internet forum explosion cocktail.

Let's examine the physics behind the three key facts, so that there will be no doubt as to their validity. The first two are pretty easy to follow. Airplanes create lift by causing air to flow over their wings. This airflow is caused by the motion of the wings relative to the air - that can happen in two ways. The first way is to move the plane forward through the air. The second is to blow air against the plane and over the wings. As far as the plane is concerned, these two scenarios are equivalent. So you could put a plane in a very powerful wind tunnel, blow air over its wings, and have it fly stationary relative to the ground. But that's another question.

In our treadmill scenario, the air is stationary relative to the ground, so the plane has to move relative to the ground in order to gain flight. If it doesn't move, it simply won't fly. There will be no airflow over the wings, and there will be no lift. A lot of people get confused here, and think that the original thought experiment is some sort of trick question, and that the propeller of the airplane, or possibly the jet engines, will be blowing air backwards over the wings, which will create lift. While there will be a certain amount of airflow created by the propeller or engines, it is not enough to create flight. I promise you, that's not what the question is asking.

Really, I promise. Please, please stop talking about airflow created by the prop. It isn't part of the question.

So we have facts (A) and (B) well taken care of. If the plane moves, it flies. If it doesn't move, it doesn't fly. The real question is, will it move? Again, the answer is unambiguous - if the pilot doesn't try to make the plane stay still, it won't. If he does, it will. This is always, always the part that confuses people, so stick with me for a few more paragraphs.

When a plane is sitting on a runway, it moves by using its engines. It does not move by any sort of motorized wheel. The propellers or jets create thrust that pushes against the surrounding air and causes the plane to move forward. A plane wouldn't move at all in a vacuum chamber. Compare this to a car, which moves by applying torque to the wheels. A car would drive just fine in a vacuum chamber - at least, as long as the driver could survive (and technically, it would need some sort of air reservoir to provide something to mix with the fuel. An electric car wouldn't have this problem.) However, a car could not drive on a frictionless surface - imagine, for example, that you had your car on a super slippery frozen lake. As you hit the gas, the wheels would simply spin and spin in place, and the car wouldn't move forward. You may even have firsthand experience with this situation if you've ever gotten stuck in a snow bank. In contrast, a plane would have no trouble moving on a frictionless surface. The jet engines or propeller would still push against the air, and the plane would still move forward. If it were on a truly frictionless surface, then you would see the wheels sliding along the ground, not rotating.

I hope those two scenarios clearly illustrate the difference in motive force between cars and planes. Cars create their forward movement from torque applied to the wheels, which push against the ground and create forward motion from friction. Planes create their forward movement from thrust applied to the air, which pushes the plane forward regardless of the surface it is on.

Imagine a plane without wheels. The fuselage would sit on the runway, and as you fired up the engines, it would skid spectacularly along the runway, possibly spewing sparks in its wake and doing quite a number on the body of the aircraft. No matter how fast it was going, the frictional force against the airplane would be constant; friction does not depend on speed! If the engines were strong enough to get the plane up to the critical take-off speed, then it would still take off. The only reason planes have wheels is to reduce this sliding friction. The wheels roll along the runway instead of sliding, and the only friction that the plane feels is in the bearings of the wheels. This is substantially less than the friction that a sliding fuselage would create, and it's a much smoother ride for the passengers as well.

(Edit: Technically, there are some factors that would make the friction change with speed. The classic idealized model called "coulomb friction" doesn't really apply to bearings. As the bearings spun faster and faster, they would generate heat, which would increase the friction slightly on the wheels. However, it would never be enough force to prevent take-off. The only time this would prevent take-off is if the wheels locked up or broke off, and then we'd have a much bigger problem and catastrophic failure.)

So what does this all have to do with treadmills? Well, now let's place our plane on that treadmill and see what happens. If the wheels were perfect - that is, there is no friction in the bearings (and no deformation of the wheels as they spin) - then something interesting happens. When we turn on the treadmill, the plane stays stationary on its own. The wheels simply spin along the track, and impart no force to the plane. If you had a car with frictionless axles, and you disconnected the whole drive train, the same thing would happen to your car.

The only reason that a plane or a car moves backwards on a treadmill is that the wheels are somehow partially locked to the axles. In a plane, this is because of minor friction in the bearings. In a car, it's because of the drive train. If you want the car to stay still, you have to turn the drive train at the proper speed. If you want the plane to stay still, you have to overcome the minor bearing friction. And again, since friction does not change with speed, you don't have to exert any more force at higher speeds. If you run the treadmill at 5mph and turn on the plane's engines just slightly, they will provide enough thrust, pushing against the air, to keep the plane still. If you then increase the treadmill speed to 500 mph, you won't need to adjust the throttle on the airplane - it will remain stationary. That's because it's seeing the same frictional force that it was at 5mph. Thus, it doesn't matter how fast the treadmill is moving - if the pilot does not want to remain stationary, then he won't. It only uses the very first bit of power from the engines to keep the plane stationary. As the throttle is increased from that point, it moves forward just as it would on any other runway. It's pushing against the stationary air!

If you don't believe me, imagine this (or even try it at home): you're standing on a skateboard on a treadmill. You hold onto the handrails of the treadmill and turn it on. Of course, you'll remain stationary (relative to the ground). In fact, you only need to use a very light touch to stay stationary - perhaps a few fingers pressed against the handrails. Crank up the treadmill speed as high as you like. You'll still only need the same light touch to remain stationary. At any time you like, you can move forward - closer to the treadmill console - by simple pulling on the handrails. If you had a jet engine, or super-strong hairdryer, you could use this to propel yourself forward instead of holding onto the handrails. In fact, if you're really careful, you might be able to do this at home with a skateboard and a leafbower, but I doubt you'll have a sensitive enough control of your leafblower thrust to get yourself to remain stationary.

So you see (oh please tell me you see), the conveyor operator cannot force the plane to remain stationary. And if the plane isn't stationary, it can take off.

And yes, if we interpret the question in a different way, and assume that for some reason the pilot is colluding with the conveyor operator and keeping the plane stationary, then the plane can't take off.

But what is the question really getting at, anyway? There are really two "spirits" of the question. In the first, we're asking "can a plane take off with no runway, if I replace the runway with a treadmill?" The answer, as we know now, is no. The plane must move relative to the ground in order to take off. In another deep-meaning of the question, we're asking "is it possible to prevent a plane from taking off, by moving the runway backwards under it?" The answer again is no, you can't prevent it from taking off.

The interesting thing about all this is that in both scenarios, you'd wind up with a plane moving relative to the ground. In the first scenario, you might think you're being clever by allowing a plane to take off from a very small field, by using a treadmill runway. If you actually tried it, you'd be attempting to take off, so the plane would move, and would likely crash into something, or fall off a cliff, or suffer some other catastrophe that you were trying to avoid with questionable physics. In the second scenario, you'd give the plane plenty of room and safety to take off, but attempt to play a practical joke on the pilot by moving the runway backwards, and you'd wind up with a plane in flight, much to your chagrin.

When the "no-flys" saw the Mythbusters episode, they all complained that it wasn't done properly, because the plane didn't remain stationary. But think about it for a moment. No, really think about it, don't just spout about Bernoulli's principle and airflow and all that. In what possible scenario would the plane actually stay still? The only way this can happen is if the pilot is trying to stay still, and this only happens if he just barely applies the throttle, making no attempt to take off. This makes no sense. Either you're trying to prevent him from taking off with your clever and misinformed use of a conveyor belt, or he's trying to defy physics by taking off in a too-small area. There is no scenario in which the plane would realistically stay still. We know what would happen if it did - it would sit on the runway, not taking off, and we'd all stare at each other in an all-too-short silence punctuated by loud exclamations of "I told you so!". But that's not really what the thought experiment is getting at, no matter how you reasonably interpret it. Luckily for all of us, if we agree on the interpretation, reasonable or not, we should all agree on the answer.

So let's get back to the next great internet debate, shall we?



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211 comments:

1 – 200 of 211   Newer›   Newest»
ShrinkingMudball said...

"Whoever asked this question is an idiot."

LOL. I just about dropped out of my chair in a fit of joy after reading this. Thanks for this article... perhaps there is hope for humanity afterall.

Anonymous said...

"On some signal, I throttle up the airplane and you turn on the treadmill, and we conspire by our joint effort to try to keep the plane stationary relative to the ground. Will the plane take off? No."

No amount of collaboration will prevent the plane from taking off. Given the existence of a free wheel between the treadmill and the plane, the treadmill is incapable of applying any horizontal force to the plane. It cannot slow the plane down.

ShrinkingMudball said...

"No amount of collaboration will prevent the plane from taking off. Given the existence of a free wheel between the treadmill and the plane, the treadmill is incapable of applying any horizontal force to the plane. It cannot slow the plane down."

The plane can always not take off, if the pilot doesn't want it to. If its forward thrust matches the force of friction it will remain stationary. If by "free wheel" you mean frictionless then the pilot doesn't apply any thrust at all and the plain remains stationary.

Anonymous said...

Ok, I can agree to that. As long as we're clear that in #2 you're arguing a deep corner case. That is, the pilot purposely fails to overcome the (relatively) small friction in the axles of his wheels with the engines, in some cases by keeping them shut off. Of course, you can say the same thing about a runway without a treadmill.

If the pilot wanted to take off, he could.

ShrinkingMudball said...

"If the pilot wanted to take off, he could."

Agreed.

Anonymous said...

I once saw a UFO take off from a treadmill. I've never been the same.

NewtonHatesYou said...

Simplest way for me to think about it is Newton's laws. You apply a force, F, to the plane with the prop. Its mass, m, relative to the ground, must accelerate, since F is the only force acting along the horizontal axis. F=ma, so eventually it must reach takeoff speed because it is accelerating relative to ground.

nex said...

I fully agree with the people who said that in situation #2 the pilot would have to keep the engines on stand-by or even shut off, in which case the presence or absence of a conveyor belt doesn't even begin to enter into the equation, at least not for practical purposes.

In the discussion over on kottke.org, I explained it like this:

> "and we conspire by our joint effort to try to keep the plane stationary relative to the ground. Will the plane take off? No."
The conclusion would be correct assuming that premise, but the premise is surreal. In order to keep the plane stationary relative to the ground, the pilot wouldn't be allowed to turn on the engines in the first place. Once they're running and generating thrust, the c-belt operator can't do anything to hold the plane in place. (Except in those situations, already mentioned by many posters, in which the belt would accelerate beyond light speed in a microsecond and the universe violently implodes, or something like that. Which obviously neither works in a thought experiment with ideal, friction-less wheels, nor in the real world.) Note that you can 'prove' anything when you start out from a wrong premise. Consider the following statement: "If the circumference of a circle equals its radius, then the pope is a Protestant." Think about it. It's true, literally!

Anonymous said...

"In the first, we're asking "can a plane take off with no runway, if I replace the runway with a treadmill?" The answer, as we know now, is no. The plane must move relative to the ground in order to take off."
Not in a good enough headwind!!

Anonymous said...

Being an MD, PhD, and a Scientologist, I consider myself an expert on everything.

1) The very idea that this Chris character decided to spend so much time on the subject makes me violently angry. It is obvious that the plane will take off, lest the pilot match the applied force of the engines to friction force from the ground. If you needed to read this entire post to get that, you might want to forget how to breath.

2) Find me a perfect frictionless bearing that will allow the plane to remain stationary on a treadmill, and I will pull a leprechaun out of my rear end. Frictionless is a concept used to make physics problems simpler. It is near impossible to create frictionless conditions in the really real world.

73|<|\|05145|-|3|P\ said...

The biggest problem with this thought experiment, is that many of the wordings make the assumption that the plane does, in fact, remain stationary. Since this is worded as a part of the statement, and not the question, people do not question it, and assume the statement is correct. Therefore, the plane would not take off, because it's stationary. This assumption is further assisted by images such as this one, when posing the question "will it take off?" http://farm1.static.flickr.com/134/336644021_adf0c4a276_m.jpg

Since the plane is shown on a treadmill only as long as the fuselage, and there is a barrier to keep it from rolling -off- the treadmill, it seems a valid enough assumption that the plane must not be moving, and this assumption is translated to the question, "Will it take off?"
In this case, it couldn't because the wings would hang on the treadmill - but that's just an interpretation of the image.

Chris said...

"The biggest problem with this thought experiment, is that many of the wordings make the assumption that the plane does, in fact, remain stationary."

That would be interpretation (3) in the original post, answered by the authoritative "Whoever asked this question is an idiot."

duff said...

Simplify. There are 2 interpretations to this question:

1. If you keep the plane from moving, will it be able to take off?

Clearly, the answer is "NO". Movement is necessary to generate airflow and thus lift.

2. Will the treadmill be able to keep the plane from moving, and thus prevent it from taking off?

The answer to number 2 is also "NO". This seems to be the question that most people fail to understand, but the proofs have been posted so I will not repeat them.

The treadmill cannot prevent the plane from moving. It will gain airspeed and thus generate lift, and will fly.

A good quote I came across somewhere:

"The plane is not magically levitating while standing still. It is moving forwards as usual, and ignoring what the ground underneath it is doing. Which is the entire point of having a plane, really."

Mesa Mike said...

Is it really true that an airplane moves forward by "pushing against the surrounding air"?

Isn't it really that the forward thrust is generated by the "equal and opposite reaction" of the action of throwing stuff backwards (like air or spent fuel)?

An airplane in a vacuum chamber couldn't move forward, because there is no air to throw backwards.
Unless it was rocket propelled. No air needed in that case.

duff said...


Is it really true that an airplane moves forward by "pushing against the surrounding air"?

That is a simplification, but yes it's true.


Isn't it really that the forward thrust is generated by the "equal and opposite reaction" of the action of throwing stuff backwards (like air or spent fuel)?

Yes, that's correct. But what is an airplane engine pushing backwards? You said it yourself - air! It's pulling the surrounding air into the engine, and then pushing that air backwards to generate thrust. The fact that there is "spent fuel", or exhaust, in that air now is of little to no consequence.


An airplane in a vacuum chamber couldn't move forward, because there is no air to throw backwards.
Unless it was rocket propelled. No air needed in that case.


True, but no air also means no combustion, so the engine couldn't run anyway. And rockets, believe it or not, actually carry their own "air" with them, in the form of an oxidizer, so they are still pushing air backwards in order to generate thrust forwards.

Anonymous said...

thank you thank you thank you. now lets see jamie and adam fly a plane in a wind tunnel.

Anonymous said...

...we conspire by our joint effort to try to keep the plane stationary...

#2 is a specious argument. The only way the plane can remain grounded is to have the pilot purposely powering down his engine, or even never turning the engines on. If this is the case, why even get the pilot out of bed for the experiment? Why use a plane with working engines?

Anonymous said...

The simplest way to bust this "myth" is to look at the implications of the original question.

It says that the conveyor belt must match the speed of the plane.

What speed? If the plane stays stationary, there is no speed.

To have speed, the plane must already be moving and thus it cannot stay stationary.

Brian said...

Yeah, if you could add a slight edit in your post it would be perfect. Where you mention a vacuum preventing a plane from taking off, a rocket engine could take off even in a vacuum. (I just don't want anyone to be able to poke holes in your explanation ;)

Some figures would be nice but I'm having trouble trying to think of any. I'll send some if I can.

pkasting said...

It turns out it _is_ possible for the conveyor operator to keep the plane stationary, but not by matching "speed"; and to do it indefinitely you need a conveyor that can accelerate indefinitely.

See http://www.straightdope.com/columns/060303.html for the details.

So, the thrust of your post is correct w.r.t. the original (silly) question, but your supporting assertion that it is fundamentally impossible for _any_ action on the conveyor's part to prevent the plane from moving is not correct.

duff said...

you need a conveyor that can accelerate indefinitely.

The original question required the speed of the belt to match the speed of the plane. Accelerating the belt to infinity breaks this condition.

Anonymous said...

"to do it indefinitely you need a conveyor that can accelerate indefinitely."

In other words, no. You can't keep the plane from taking off.

You can't accelerate the conveyor belt past the speed of light, which means you can't stop the plane from taking off.

What a silly argument.

Anonymous said...

DUFF has it right... there's two different understandings of the problem:

1) can a plane achieve flight from a stationary position relative to earth, but in motion relative to the treadmill?

2) can the force of the plane overcome the force of the treadmill?

the treadmill is intended as a device that keeps the plane from moving forward, assuming that the plane behaves on the treadmill the same as a car would. but it doesn't. and that sets up problem number 2.

the 1st understanding of the problem is a question about what generates lift. the 2nd understanding of the problem is a question about the origin of force and the influence of friction.

Mesa Mike said...

My analysis:

Plane on a Conveyor Belt Takes Off!

As predicted, of course. The Mythbusters proved it in last night's show.

There has been lots of discussion on the internet about whether an airplane on a conveyor belt could take off, if the conveyor belt moved in the opposite direction at the same speed as the airplane. The problem is usually stated something like this:

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


The people who say no, typically reason that for an airplane to take off, it needs airflow over the wings (more than just the amount the propeller blows), but since the airplane can't move forward, there is no airflow over the wings, therefore the airplane can't take off.

But this begs the question. Of course the airplane needs to move forward at a speed great enough to supply the lift in order to take off. That's kind of integral to the idea of "taking off." Whether the airplane can do so is exactly the question we are being asked, I think.

The faulty assumption is that the contraption is designed to prevent the airplane from gaining forward speed. That, however, is not stated in the problem. People make this assumption, I guess, by analogy to walking on a tread mill where one does not go forward, but stays in one spot as the treadmill goes backward at the same speed one is walking forward.

But airplanes don't propel themselves forward by pushing against the ground (or the treadmill in this case) like walking people or cars do. Airplanes' forward thrust comes from the "equal and opposite reaction" of the action of throwing stuff backwards (air, in the case of a propeller plane, or the hot expanding gases of spent fuel in the case of a rocket).

It amazes me that so many people just don't get it, even after having it explained and demonstrated. Many of them claim that the Mythbusters experiment was flawed, because "the plane actually did move forward!" For some reason, they thought that the "wheel speed" of the plane was to match the conveyor belt speed. But the original question only says that the speed of the conveyor belt matches the speed of the plane.

The assumption that the "speed of the plane" means it's wheel speed relative to the belt is an unwarranted assumption, in my opinion. Unwarranted, because it makes the original question illogical. The only way for the wheel speed to match the belt speed is for neither the plane nor the belt to be moving at all; or for the plane's engines to be providing just enough thrust to match the very minimal force of the wheel friction in order to keep it from being dragged backwards. But the question is, "can the plane take off?" This implies that the plane is trying to take off, which means full thrust, not just minimal or no thrust. So it must be that the "speed of the plane" must be relative to the ground.

Jeremiah Halonie said...

Wow

I'd never even heard of this debate until now, and i have to say at first, i was on the stupid end of the stick but your explanation was very to the point, and it cleared it right up for me.

and while i felt kind of stupid for getting it wrong at first: (no it can't take off! durrr!) I have to say this is a really elegant thought puzzle. unless you realise where the actuall force is comming from and being applied, your stuck in your own stupidity. good post

Anonymous said...

"Here are the three core facts that are rock-solid:
...
C) The person operating the conveyor belt cannot by himself make the plane remain stationary relative to the ground."


This is true for planes with wheels and achievable speeds on conveyor belts. The friction with the ground is very small.

However, if the plane has skis or pontoons (on the ground) or you allow the conveyor speed to be unbounded then friction can increase to a degree where it is possible for the conveyor operator to keep the plane grounded.

ShrinkingMudball said...

"or you allow the conveyor speed to be unbounded then friction can increase to a degree where it is possible for the conveyor operator to keep the plane grounded."

In theory, the speed at which the wheels are turning should not increase the force of friction. That is, an ideal wheel would not be affected by the speed. Of course, in the real world, the mechanics of the wheel would break down at high enough speeds and the friction would increase to the point where either the plane would slow down and stop, or the wheels would snap off. Of course, these speeds would be pretty astronomical, and I doubt any treadmill in the real world would be able to withstand those speeds itself.

However, even if we allow an 'ideal wheel' there is still a purely hypothetical scenario where the treadmill could keep the plane stationary. If the treadmill is allowed to have unbounded speed and unbounded acceleration, then I believe the rotational inertia would also be unbounded, because it can be expressed as a function of the acceleraion of the treadmill. And if the rotational inertia is unbounded then the force it exerts on the plane is also unbounded, and the plane could be forced to remain stationary.

....Aaactually, now that I think about it, the friction between the wheel and the treadmill would probably not be great enough, and when the rotational inertia started to build against the turning of the wheel, the wheel would just start to slide along the treadmill.. and the plane would still move forward.

Eoin said...

I have FAITH that it won't take off...you're persecuting my religion!!1!11

Seriously though, well done. You've gathered a coherant collection of arguments (none of which should really have been required if you ask me...). There's still gonna be people complaining though. Some people simply can't admit that they are wrong (I think the largest source of confusion is people mistaking the wheels on a car [driven] with the wheels on a plane [freewheeling]).

GMontag said...

"So what does this all have to do with treadmills? Well, now let's place our plane on that treadmill and see what happens. If the wheels were perfect - that is, there is no friction in the bearings (and no deformation of the wheels as they spin) - then something interesting happens. When we turn on the treadmill, the plane stays stationary on its own. The wheels simply spin along the track, and impart no force to the plane. If you had a car with frictionless axles, and you disconnected the whole drive train, the same thing would happen to your car."

This part is not true unless you are talking about massless as well as frictionless wheels. The wheels' rotational inertia will resist the treadmill and will apply a backward force on the airplane as the treadmill is accelerating.

Anonymous said...

Oh, if I could only sage, I would sage you to deletion and beyond.

RAAAAAAAAAAAAAAAAAAGE

siztem said...

Alright, so we've got a 747 sitting at rest on a hypothetical uber-treadmill. the engines fire up, and the plane starts to roll forward.

then the treadmill starts rolling backwards at an equal amount to keep the plane geographically stationary.

guess what guys - the whole reason a plane has engines is so it can move the damn wings through the air, as its the movement of the air over the wings that provides lift.

if there's not sufficient wind flowing over the wings..

....guess what...

IT WONT FLY.

Anonymous said...

then the treadmill starts rolling backwards at an equal amount to keep the plane geographically stationary.
siztem, did you even READ the webpage? The whole point is that the plane doesn't remain geographically stationary. It doesn't matter how uber your uber treadmill is.

...guess what...

IT WILL FLY.

grahame said...

A 747 taxies to the threshold and lines up, ready for take-off. Each set of wheels sits on a conveyor belt which is free-moving (i.e. not driven and, for the sake of this hypothetical, completely friction-less). Light the fires. Accelerate to take-off thrust. Forward thrust is created but the heavy body doesn't move - just spins its wheels. Just like an engine test bed situation, except the engine isn't tethered down. The thrust has instead been converted into spinning a conveyor belt.

What's happening inside the cockpit? OttoPilot has pushed his thrust levers fully forward. He hears the scream of the engines, but the world outside isn't moving. What does the ASI read? Zip. Because there's no movement through the air.

No airspeed? No lift.

That 747 isn't going anywhere. Least of all up.

Grahame said...

Same 747 at the threshold, mains are sitting on the conveyor belts. Engines are off. This time OttoPilot is staring at a whacking great big fan sitting on the runway in front of the nose. The fan starts up with a whirr. Faster and faster it spins, pushing air at OttoPilot and his 747. The heavy bird would move backwards because of the force of the air pressure, but instead the wheels spin backwards on the free-moving belt. Otto looks out of his window, but no movement is discernable. He looks at his ASI. Wow! The needle moves! As the fan speeds up even more, the ASI creeps upwards until - lo and behold! - takeoff speed is reached. With a slight judder, the wings produce enough lift to raise the wheels off the belt. Flying! No engines! WTF?

Eoin said...

Grahame said: "... the heavy body doesn't move - just spins its wheels...."

It doesn't spin its wheels. A CAR would spin its wheels, because a CARs engine drives the wheels. A planes engines, however, DO NOT DRIVE THE FUCKING WHEELS. A plane, effectively, pushs itself off from the air behind it. It takes off.

grahame said...

Eoin, yes...engine thrust does not directly power the wheels. Agreed.

1. We know that the engine produces thrust. Undisputed.

2. Engine is attached to plane. Engine thrust directed rearwards. Because of equal and opposite reaction, plane wants to move forward.

3. Thrust develops until it overcomes inertia of the body. As it overcomes that inertia, thrust is then greater than all the forces holding the body to the ground. Something must happen. If the plane's wheels were on concrete, the wheels would enable it to move forward, acting as bearings between two solid bodies, the plane and the ground, converting engine thrust into movement. But now instead of the ground, we have a free-wheeling conveyor belt.

Thrust is therefore converted into movement of the belt (which can be connected via an axle to a belt-driven generator to supplement Eskom's deficiencies - a jumbo electricity supply. Probably still cheaper than accepting quotes from all the power station smouse now flocking to the scene of the disaster).

Plane can't fly. So where is my layman's logic wrong. Help please.

Grahame said...

Sorry, please ignore comments about Eskom - this is a reference to a South African power supply issue.

Chris said...

A 747 taxies to the threshold and lines up, ready for take-off. Each set of wheels sits on a conveyor belt which is free-moving (i.e. not driven and, for the sake of this hypothetical, completely friction-less). Light the fires. Accelerate to take-off thrust. Forward thrust is created but the heavy body doesn't move - just spins its wheels.

INCORRECT!!

If the belt is unpowered, it won't move at all. The plane will roll along the belt just as well as along the ground. Now, if the belt is truly frictionless, as you say, and the wheels have any amount of friction in the bearings, the belt will actually move forwards (ie, in the same direction as the plane), but very slowly (since it's only being accelerated by a very minor frictional force in the wheel bearings), and the wheels will roll faster along the belt, causing forward motion of the plane.

Same analogy with the home treadmill and skateboard again - if you stand on a skateboard (or rollerskates) on a treadmill, and pull yourself forward by using the handrails, it doesn't make the belt spin under you, does it? Even if the belt was completely frictionless, surely, surely, you would move. Do you believe that you would be pulling on the handrails as hard as you could, and magically the belt would be spinning underneath you? Of course not! As soon as you pull on the handrails, you will move, regardless of what the belt under you is doing. The plane is doing exactly the same thing, but its handrails are made of stationary air.

The plane will move. I promise.

grahame said...

Chris, I see the light! Hallelujah! Why, though, isn't yet clear. But the analogy of the roller skates on the treadmill made intuitive sense.

Eoin said...

Grahame: "...Thrust is therefore converted into movement of the belt..." is where your laymans logic went wrong. The statement is false.

Glad you've seen the light...although the skateboard analogy in the original post really should have made it clear for you...

Alex said...

Graham, the easiest way to picture it for me is if you consider the plane to have super-slick near-frictionless skiis on the bottom, instead of wheels. The wheels thing messes people up because they are used to cars. When you compare the wheels on a plane to skiis, its easy to see that they both serve the same purpose... simply that of reducing friction.

If a plane with super-slick skiis is on a fast-moving treadmill, as long as the thrust of the engine is enough to overcome the friction between the skiis and the treadmill, the plane will accelerate forward to take-off speed. The same is true of a plane with wheels. Wheels are just better at reducing friction than skiis.

Anonymous said...

All 3 of his interpretations are incorrect because he is measuring the plane speed relative to the conveyor belt, then measuring the conveyor belt speed relative to the ground, then comparing the two speeds measured in different reference frames.

The question does not specify how speeds are measured. But there is no common speed dial on a plane that measures speed by the rotation of the wheel, and the general rule for every situation is to measure speed relative to the Earth (the ground).

Christopher said...

Chris,

This site is great! You finally disassemble each side of the argument in a well-thought out article. And yes, I know that the plane takes off (given the original wording of the question).

A long time ago, I was thinking of explaining this whole question in different terms (on the ebaumsworld forum, of course). I'd explain what was meant by "speed of the airplane" and "speed of the treadmill" (as an anonymous poster mentioned above). That is, I'd explain what effects each of the 9 different cases of reference points (or 4 if you consider air and the stationary ground to be equivalent frames of reference) had on the interpretation and the potential answers to the original question.

So let's break it down to just 4 cases for the sake of brevity. The 3 reference points I'm using are airplane, treadmill, and ground (== air). Because an object has 0 speed relative to itself, I won't consider those cases.
1. The airplane's speed is relative to the ground, and the treadmill's speed is relative to the ground.
2. The airplane's speed is relative to the ground, and the treadmill's speed is relative to the airplane.
3. The airplane's speed is relative to the treadmill, and the treadmill's speed is relative to the ground.
4. The airplane's speed is relative to the treadmill, and the treadmill's speed is relative to the airplane.

Case 1 is the most likely interpretation of "speed" for the airplane and treadmill. The reference point is the same for both, so the answer must be "yes", the plane takes off (with little difference from a normal runway takeoff, even).
Case 2 doesn't seem like a good interpretation of "speed" for the treadmill; who would measure the treadmill's speed relative to the airplane? If you did, you would see that it's impossible to keep the speeds the same but opposite except at a speed of 0. But as the original question stated, the plane does in fact move. This case is not possible, and fortunately it's not a popular interpretation of "speed".
Case 3 is similar to case 2, in that the plane must not move for the condition that the speeds must match for the treadmill to do its job. Besides, nobody measures the speed of an airplane by its wheels, and normally an airplane doesn't use the runway below it to measure its speed; an airplane's speed is measured by the air flowing past it, which (I think) can be assumed to be the same as the speed over the stationary ground.
Case 4 is always true by law, as two objects' speeds relative to each other are always equal but opposite. That's a given. Of course, as in case 3, nobody measures the plane's speed with its wheels (which is its speed relative to the treadmill); as in case 2, nobody would measure the treadmill's speed relative to the airplane. So case 4 is right out. (The plane can take off as normal in this case—the runway could move at any speed w.r.t. the ground and the airplane moves as normal, alse w.r.t. the ground/air—but it should be obvious that this interpretation is a silly one).

I think most people use case 3 to argue that the plane does not take off, and in fact you (Chris) don't make it clear that this is not a good set of reference points to use. Case 1 seems the better interpretation of the two, and it's easy to explain that it takes off if a common reference point (the stationary ground) is used to measure the two speeds.

Anonymous said...

"If the plane remains stationary relative to the ground, it will not take off."

If you want to bury every shred of the no-fly argument, you can counter that statement. It is possible to design a plane that will take off with its brakes on, just from propwash alone. Just give it freakishly huge flaps. It won't fly very well, but on takeoff, it can pop itself straight upward. Nobody's built a physical plane that does it, but there have been a few designs that work in X-plane, a very accurate flight simulator.

Of course, there are many real-life examples of VTOL, but I'm sure the no-fly folks won't accept VTOL as an answer to the question.

caltel said...

Thanks...

Caltel
Article

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flotson said...

I think your model is missing a force: you mention the friction of the wheel bearings, but omit the rolling resistance force created by friction between the wheel and the ground.

Doesn't change the fact that the plane will take off, though.

However, I'm interested in the hypothetical case in which the conveyor belt speed is unlimited (and the wheels are indestructible). . .trying to figure out the math required to compute the conveyor belt acceleration (and the energy input) required. . .

PS-- I'm thinking that a rocket doesn't generate thrust by pushing "air," if you're referring to the oxidizing agent. . .it pushes whatever the byproduct of combustion is, the exhaust (thrust = exhaust mass * rate at which it's expelled). . .

duff said...

It doesn't have to be air int he 79%N/21%O sense of earth's atmosphere. It is a mass of various gasses, including CO2 and other waste products. As I said in my original post, rockets carry their own oxygen with them for combustion, so in a sense it is still air that they exhaust.

cosmicnomad said...

Well, I've enjoyed this blog immensely. I especially liked Grahame's 747 comments. LOL

I've always explained this problem to people who don't get it by using a swimming pool as the example.... If I put a treadmill on the bottom of a pool that rotates along at a speed equal to the speed i swim, will the treadmill be able to keep me from moving forward.... Of course not, because I'm not walking on the treadmill, I'm pushing myself through the water.

I can't wait to hear the "no swim" answers.... :-)

Great blog man!

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Anonymous said...

To all those who still don't get it - this is a really dull thought experiment to get worked up about. There are far more interesting ones.

meowsqueak said...
This comment has been removed by the author.
Phlip said...

Yes! Thank you!

I've used the same skateboard analogy for other people, and it always seems to help... though, I use rollerskates and a rope, rather than a skateboard and handlebars, but the principle's the same.

Incidentally, two different versions of this puzzle came up in a forum I frequent at the same time... one of them was worded "the treadmill spins at the same speed that the plane would move if the treadmill was absent"... that is, a certain amount of thrust is applied to the plane that'd normally make it move at v(t), then the same amount of thrust is applied to the plane on the treadmill, and the treadmill moves at -v(t). I personally think this is the best wording for the puzzle, because it takes out the human factor which you have in your wordings, but still has the "puzzle" interpretation, as the same treadmill setup would hold a person running stationary (and is, indeed, the way that the speed is chosen for most treadmills). Of course, with a plane, it just spins the wheels at twice the speed, and the plane takes off.

The other one was worded ambiguously, but in a way that (from a literal interpretation) meant that the plane had to be stationary (to be specific: it said that the speed of the treadmill at all times matched the speed of the wheels. Since the speed of the wheels is the speed of the treadmill plus the speed of the plane, this implied the speed of the plane was always 0). Clearly this fell into your #3, and the thread quickly split into (a) people saying basically "it's stationary, therefore it won't take off", (b) people trying to explain how the plane could possibly be stationary (with an absurdly-accelerating treadmill, and friction/rotational inertia), and (c) people claiming that this wording of the question is stupid, and trying to drag the conversation over to the sane wording, where the plane takes off. All three groups were pretty much constantly arguing with each other.

I found the discussion of the first wording to be more civil, the solution more satisfying, and the question more deserving of the title of "puzzle"... and would recommend that wording to anyone considering sharing the puzzle.

Anonymous said...

Yeah but what about the moon landing thing... as if that could really happen. Also what would happen if you put a ship on a giant treadmill, i reckon you could get it to take off.

Anonymous said...

To stop the plane from flying, the generated force by turning the engines on will have to equal or be less than the force driving the plane backwards... perhaps they should glue the plane to the belt.. although I think that defites the object of having a belt in the first place.

Sentinel said...

Brilliant. An excellent and clearly reasoned explanation. I hadn't actually heard of the debate before, but it's an interesting concept. Thanks for taking the time to put this together.

Anonymous said...

Nice try. You your self have done exactly what the you were complaining about. Misinterpreted the question. It does not ask 'if I set a treadmill to a really high speed, can the plane still take off?' it asks, 'if by some complex control system a treadmill runs at the exact same magnitude of velocity, but opposite direction, of the wheels, can the plane take off?'. For the plane to take off, it must still move through the air, and as the plane starts stationary, and does not provide lift, the plane can only move through the air if it moves relative to the ground (it is not like a swimming pool where external lift is provided, the mass of the plane is being supported by the ground, therefore you must move relative to the ground), and therefore the wheels must spin faster. It does not matter where the force comes from to provide this acceleration, it must still spin the wheels faster relative to the runway. As the treadmill is under the control of some system to maintain the exact speed of the wheels (not the force imparted on the wheels by a drive shaft, but the absolute velocity of the wheels) then the plane can never move faster than the treadmill, can never travel forwards relative to the ground or air. This is of course ignoring friction in the barrings and assuming no head or tail wind. These things would make it harder to take off, as the net force will be backwards relative to the plane, and the wings on aircraft rely on the curvature of the airfoil on the front of the wing, its is not reversible.

Martin said...

The internet thanks you for this pleasantly thorough treatment of what has been a highly tedious topic.

One potential improvement: there's no need to take a tangent about cars in a vacuum, just refer to the Moon Rover.

But then again, some of the idiots involved probably don't think that was real either...

Anonymous said...

First off, on the "no-swim" thing, the problem is that you aren't connected to the treadmill on the bottom of the pool. In this plane scenario, the wheels are connected to the plane. And the problem with the skateboard thing is that yes, you can pull yourself forward on the treadmill, but only if you don't increase the speed of the treadmill. If you leave it at the same speed, you can move up or down.

Think about running on a treadmill. You match the pace of the treadmill. If you increase the speed of the treadmill but keep running at the same speed you were before, you begin moving backwards. That's why you get all those wacky scenes in movies where people start running on a treadmill, it speeds up, they have to run faster and faster to keep up, and then eventually fall off the back.

The wheels do NOT generate any force on a plane, we get it. But the wheels ARE in contact with the ground, and if they aren't rolling across the ground (which they wouldn't be on a treadmill that exactly matches the speed/force/thrust generated by the plane, then the plane isn't moving relative to the ground, and no air is moving over the wings. It's not that hard.

Salubri said...

OK...

I think I have an example that will help people understand a bit better that the wheels have very little relevance...

Many people get hung up on the idea that increasing treadmill speed keeps up with the wheels... eg the last comment: "and if they aren't rolling across the ground [...] then the plane isn't moving relative to the ground"

Imagine the plane is on the runway and you turn on the wheel brakes and then hit full thrust... The plane WILL move forward! Thrust from the engines against the air is greater than can be compensated for by wheel brakes - now I don't know if the wheel brakes could cause enough friction to prevent the plane taking off but I'm pretty sure that just friction between un-braked wheels and the bearings / ground can't...

/me <> scientist but I understood the post and am convinced... It's not rocket science ;-)

CompSci Student said...

YOU SIR, ARE AN INTERNET SUPERHERO!

When I heard for the first time that people on the interwebs are actually debating this I could not believe it. I still don't believe it that some people lack the basic physical intuition or education, but now I can just redirect them to this site and end the argument.
Because frankly put, arguing on this topic is not an option. It's not a religion, it's simple facts.

So, THANK YOU for this site!

Anonymous said...

"In the first, we're asking "can a plane take off with no runway, if I replace the runway with a treadmill?" The answer, as we know now, is no. The plane must move relative to the ground in order to take off."
Not in a good enough headwind!!


not sure if anyone has already commented about this, but this would be in a wind tunnel (or a senario very similar to one), which is already explained in the artical as: "So you could put a plane in a very powerful wind tunnel, blow air over its wings, and have it fly stationary relative to the ground. But that's another question."

and, im probs wrong, but im sure that if there was a strong enough headwind for the plan to take off without the use of its engine (keeping still relative to the ground) surely the airport and a cow or two would be moving through the air aswell?

Anonymous said...

The simplest way to bust this "myth" is to look at the implications of the original question.

It says that the conveyor belt must match the speed of the plane.

What speed? If the plane stays stationary, there is no speed.

To have speed, the plane must already be moving and thus it cannot stay stationary.


Depends if the speed is its speed to air, or its speed to land. If treadmill ran at 10mph, and the planes air speed was 8.68976242knots (10mph) then yes, it would take off, (I know it needs to go faster than 9knots to take off). If in relative to the *moving* ground, it travelled at 10mph, it wouldnt take off

if that makes sense

Anonymous said...

While there will be a certain amount of airflow created by the propeller or engines, it is not enough to create flight.

Slight correction: it is not enough to create flight in a conventional aircraft. The Custer Channelwing manages quite nicely, though. But this doesn't affect the answer to the question, nor the validity of the argument.

Anonymous said...

Alright, so we've got a 747 sitting at rest on a hypothetical uber-treadmill. the engines fire up, and the plane starts to roll forward.

then the treadmill starts rolling backwards at an equal amount to keep the plane geographically stationary.

guess what guys - the whole reason a plane has engines is so it can move the damn wings through the air, as its the movement of the air over the wings that provides lift.

if there's not sufficient wind flowing over the wings..

....guess what...

IT WONT FLY.


Move the PLANE at 5mph, wheels move at 5mph! move the TREADMILL at 5mph also, the wheels will now move at 10mph! the plane is still moving at FIVE MILES PER HOUR relative to the air and though 10mph relative to the ground, which isnt important for a plane to fly

that it all =)

Anonymous said...

Move the PLANE at 5mph, wheels move at 5mph! move the TREADMILL at 5mph also, the wheels will now move at 10mph! the plane is still moving at FIVE MILES PER HOUR relative to the air and though 10mph relative to the ground, which isnt important for a plane to fly

edit: by "wheels move" i mean "wheels turn"..sorry

Anonymous said...

Actually, you voiced some of what I had thought, especially with the wheels. Great post; you seem quite informed.

Calion said...
This comment has been removed by the author.
Calion said...

Okay, forgive me if this is repeating something in an earlier comment, but I read about thirty and gave up.

You've made an error in your presentation. In the summary, you say, "In the first, we're asking 'can a plane take off with no runway, if I replace the runway with a treadmill?' The answer, as we know now, is no. The plane must move relative to the ground in order to take off."

The problem with this, and the thing that is probably going to cause a lot of grief, is that the plane is moving relative to the ground,, because the ground is moving! The treadmill is the ground. You really mean to say here that "the plane must move relative to the air to take off. I realize you caveated this out earlier, but the way this is worded in the summary is simply going to fuel the argument).

(I got directed here by the xkcd forums.)

Calion said...

"The wheels do NOT generate any force on a plane, we get it. But the wheels ARE in contact with the ground, and if they aren't rolling across the ground (which they wouldn't be on a treadmill that exactly matches the speed/force/thrust generated by the plane, then the plane isn't moving relative to the ground, and no air is moving over the wings. It's not that hard."

Oh...dear. You're trying to answer Question 3. There's a problem here. IT IS NOT THE CASE that "on a treadmill that exactly matches the speed/force/thrust generated by the plane, then the plane isn't moving relative to the ground." The plane basically ignores the ground when determining its speed. It doesn't much matter (except for friction, which the wheels make fairly negligible) whether the ground is stationary, moving, moving erratically, or moving in changing directions (so long as the wheels can swivel...or so long as you're willing to let the wheels get ripped off by the moving ground). THE WHEELS HAVE NOTHING WHATSOEVER TO DO WITH THE SPEED OF THE PLANE. Put the plane on skids. Move the treadmill at whatever (non-infinite) speed you choose. The plane's jet or prop engines will throw air behind it and move it through the air, essentially ignoring the treadmill. The ground basically has nothing at all to do with the whole thing, except that the goal of the plane is to get off it. This is why I thing the original poster should have used "relative to the air" all the way though. Speed relative to the ground is completely immaterial to the flight of an airplane.

Anonymous said...

Ha.

Anonymous said...

so... if we got a really massive fan that could make the air around the plane match the planes speed it would remain on the ground then. however this not being the proposed method i aggree fully with the results shown here.

Anonymous said...

what if the pilot is determined to make the plane take off, but hes on crack, and is just balled up on the cock pit floor crying? technically, he meets the criteria of wanting to take off, but it's highly doubtful he'll be successful.

J.A.G. said...

Look, you elitist, college-educated, arugula-eating snob, I will say this once and only once: You are WRONG!

For the sake of clarity, let me repeat that: You are WRONG (the opposite of RIGHT)!

Everyone should know by know that if God had meant for us to fly, he would have given us wings. So, logically, any situation where a plane might not fly, it won't. As it says in Psalm 55:6,

"And I said, Oh that I had wings like a dove! for then would I fly away, and be at rest."

It should be clear to everyone that this means that since we do not have wings like a dove, we cannot simultaneously fly and be at rest, as we would be on a treadmill (assuming we also had wheels).

As for the "Mythbusters", everyone who trusts in God's Laws of Biblical Physics knows that the outcomes of their experiments are influenced by Lucifer and, as such, are highly suspect. So, once again, I say, you are WRONG...

http://meditativeentropy.blogspot.com/

Anonymous said...

"IS NOT THE CASE that "on a treadmill that exactly matches the speed/force/thrust generated by the plane, then the plane isn't moving relative to the ground."

I think the poster you're responding to meant that the wheels are always countered by the treadmill, in which case, yes, it IS the case that the plane would not be capable of moving relative to the ground.

This is a commonly held view of the problem, interpreting it to mean the treadmill ALWAYS counters the speed of the wheels in such as way as to make them spin in place no matter what changes are made to the thrust.

However this condition may be achieved (this is a thought experiment after all) isn't pertinent. In and of itself this premise dictates that the plane cannot go forward relative to the treadmill (and hence the ground).

Period.

There's really nothing else to consider in this (completely valid) interpretation--the will of the pilot, the frictional cooefficient of the treads, the mass of the wheels--all are irrelevent to the central concept of the wheels being matched by the treadmill.

So...in this version, how can the plane move forward relative to the treadmill? It can not.

ANY forward motion relative to the treadmill breaks the premise--the wheels would have to "skid" ahead, which isn't allowed since any rotational acceleration is countered, making skidding impossible.

The plane can't move, no flight takes place. Yes, it is a "Question 3" scenario, but it's a valid interpretation of the problem as it is often stated (ie, whenever the wheels (NOT the plane) is bound to the speed of the treadmill).

Kevin said...

The force of friction from the wheels on the planes is constant with speed, but the relevant value to consider is not the force to be overcome, but the dissipated. Energy is force*distance. Power is energy/time, or force*(distance/time). So the power dissipated by the friction in the wheels scales as force*speed. As the speed of the treadmill increases, the power necessary for the plane engine to overcome increases also. Since there is a limit on the power of the plane engine (and not necessarily a limit on the power of the treadmill), then the operator of the treadmill can force the plane to be stationary.

If you disagree (or even agree), please reply! Hopefully I can convince people to see the problem the right way!

xsjado said...

I really can't be bothered to read the comments because its always frustrating. Needless to say I always interepreted the oringinal scenario as the plane remaining stationary with respect to the ground (or air if you want to be really pedantic but it we are talking about any comercial or military plane then the windspeed at the groud would rarely ever be sufficient to make much difference). Lift is generated as a fluid medium (air in this case) passes over the wing. If the plane doesn't move forwards then it can never take off.

The interesting bit in reality is of course what happens at the wheels, but the way I see it, the scenario specifies that the plane remains stationary. So any arguments regarding the forces at play here are pointless.

I'm not claiming this to be the accurate real world answer, but I see the whole thing as a theoretical model. Models aren't always accurate and in this case it isn't. Nethertheless, if we follow the model specified in the question then the plane will not take off.

healingkid said...

Neither the explanation nor the "internet explosion" accurately take into account whether the plane is necessarily propelled by wheels, jets, or unladen swallows.

Unladen African Swallows FTW.
....QED

Jesse said...

Oohhhhhhhhhhhhhhhhhh.

I'd never actually heard of this debate before xkcd today, so I decided your article would be a fun read.

I wasn't quite sure I believed/understood it all until it got to the skateboard/treadmill analogy. Well-written, sir.

"Much to your chagrin"... lololol.

Anonymous said...

You are wrong. You are assuming that no matter how fast the treadmill turns, it cannot affect the airplane. This seems obvious... but isn't actually true.

How so? Well... once the wheels star moving at relativistic velocities, their effective mass increases. Increase their mass enough, and there is no way the plane can take off. Since the plane has a maximum forward velocity due to air friction, it must also have a maximum lift. If its weight becomes higher than the lift, it cannot leave the treadmill.

Kyle said...

Thanks for the light in this darkness, lol.

Also: Ø friction means that the air would not be able to lift the plane??
I'm only a junior in hs who hasn't taken physics, so pardon the potential for stupidity.

Atpaw said...

Nice site!

My only nitpick would be the factually-correct "friction force does not increase with speed" - The force itself does not change, true, but as the relative speed increases, the Power required to combat that rolling resistance/friction does increase; by P = F*V .

But since the friction of the wheelbearings and rolling resistance is relatively insignificant compared to the power of the aircraft's thrust, we can ignore that (as you did).

:)

Anonymous said...

I think a lot of the confusion is in the interpretation of the concept of "frictionless" and having "perfect" bearings, as well as the idea of a powerful enough treadmill to run at infinite speeds.
Let's replace the treadmill with magnets in the plane, and opposing electromagnets on the runway. Turn on the electromagnets and you can make the plane levitate, as with a Maglev train.
Now the plane is levitating in a stationary situation relative to the ground, it's easy to see that if the engines are turned on then there will be nothing to stop it moving forward unless a rearward force is actually applied to the plane. In the scenario of a "frictionless" treadmill and "freewheeling" wheels on the plane, then this is why the plane will take off.
If the electromagnetic fields were manipulated in such a way (as in a Maglev train) as to produce a rearward thrust counteracting the forward thrust of the engines, then it could be possible to make the plane stay in the same place, and therefore prevent takeoff. This is not the same as running the treadmill backwards at a higher speed with freewheeling wheels. To achieve the same thing in that treadmill scenario you would have to use an additional drive mechanism to create a rearward force which is deliberately applied to the plane.

Anonymous said...

"The propellers or jets create thrust that pushes against the surrounding air and causes the plane to move forward. A plane wouldn't move at all in a vacuum chamber."

Then how does a rocket fly in outer space, which is a vacuum? The engines cause the plane to go forward not because they push on the air around them, but by momentum conservation. If fuel is shot out backwards by the engines, you have momentum created behind the plane (say in the -x direction). Since there are no external forces acting on the plane/fuel system, this newly created momentum in the -x direction must be balanced by exactly the same momentum in the +x direction. This means the plane starts moving forward.

When you blog and berate people saying they don't understand simple physics, you should make sure you understand all the physics you talk about.

Calion said...

'"The propellers or jets create thrust that pushes against the surrounding air and causes the plane to move forward. A plane wouldn't move at all in a vacuum chamber."

Then how does a rocket fly in outer space, which is a vacuum? The engines cause the plane to go forward not because they push on the air around them, but by momentum conservation.'

A jet plane throws air behind it to move. True, "pushes against the surrounding air" was shorthand, but it amounts to the same thing. Rockets carry their own reaction mass to throw behind them. Okay, if you were somehow to provide the jet engines with oxygen to combust their fuel, that fuel would provide some small amount of reaction mass, probably moving the plane forward. A prop plane would not move at all in a vacuum chamber.

Disprover said...

Okay, let's get off the shole question for a bit.

Look at the wheels. DO you really think that the planes uses them for acceleration?
First, if that were true, as soon as the wheels left the ground, it would turn into something like a hang-glider.
Second, the wheels couldn't PRACTICALLY balance the plane. Even (on the near impossible case) you manage to do so, as soon as the plane accelerates, it's rear is gonna hit the ground, and a lot of sparks will ensue if it continues.
Therefore, the engines have to be the main propulsion system.

So, back to the question. With the facts above, we concluded that the wheels do not propel the plane, but the engines do. The wheels would just be rolling, just doing their thing, having NO effect on the plane, while the plane does its "go fly" performance. So, we "yes" group WINS.

Ben said...

"If the wheels were perfect - that is, there is no friction in the bearings (and no deformation of the wheels as they spin) - then something interesting happens. When we turn on the treadmill, the plane stays stationary on its own. The wheels simply spin along the track, and impart no force to the plane."

I'm not so sure about this. Imagine if you put the wheel on the treadmill without the plane. When you start the treadmill the wheel will roll but it will also move backwards. With the plane attached the whole thing would move, even with frictionless bearings. It would be very slow so the treadmill would have to be unreasonably powerful, but I think this could theoretically put any amount of backwards force on the plane if the treadmill could keep accelerating. The limit in this case would be the friction between the tyre and the treadmill. The plane would have to slide to take off.

Disprover said...

The ENGINES cause the forward momentum, not the wheels. The engine is not being affected by the treadmill, because the treadmill only works on things touching it. Sure, the wheels can create a lot of friction, but all that might happen are some sparks, and maybe the plane will catch fire.

Oh yeah, the "yes"ers already know they're right. Look here. --> http://www.youtube.com/watch?v=IbRcg3ji_Pc

MikeTwo said...

Definitive. I like it.

I came to the same conclusion after converting the question slightly. If I put the plane on a dyno (that measures cars), and ran the engines, would it stay on the dyno?

Nope. It would pop right out because the force is pushing on the air, not generated from the tires.

I liked the airplane on ice and car in a vacuum comparison. That's great!

Anonymous said...

As this is only a thought experiment, then if we consider the belt has infinite acceleration and finite speed (But very large speed). The friction of the planes wheel bearing is non zero, so there is a force acting to stop the wheel from turning. Therefore, given a large speed of the belt, there will be a large force acting against the turning of the wheel, and hence against the movement of the belt. 3rd law of motion means there is then a force acting backwards on the plane, counteracting the thrust.

So the question is then, can a plane take off if it has its brakes on?

Ryan said...

If its Qantas it aint going anywhere!

Anonymous said...

After writing on this subject—and the ridiculous turns that it tends to take—(http://uberregenbogen.livejournal.com/3115.html), i've come to wonder if the original question was meant to be: would a treadmill moving under a stationary aeroplane—instead of it moving down a runway—allow it to lift off? In other words: would the treadmill satisfy the requirements. The point of this scenario is that the vehicle remains stationary to the air, and is NOT asking if it would be ABLE to move. The answer, in this case is no.

I can well imagine this question being asked of students in elementary (or maybe middle) school science class—both to test their knowledge, and to encourage them think.

It may be impossible to ever find out what the original positor was trying to illustrate.

At any rate, it has become a rather interesting study in interpretation and human nature.

Anonymous said...

"So the question is then, can a plane take off if it has its brakes on?

"September 9, 2008 10:03 PM"

Yep! Here, the thrust of the plane has to overcome not the small friction of the wheel bearings but the larger friction of the rubber of the wheels against the treadmill.
It will take a greater proportion of the plane's total thrust but will eventually be overcome and the static wheels will skid along the runway as the plane accelerates to take off speed.

Michael said...

Excellent article, should hope to kill all those pesky no-flys.

There is one problem though - you say that a frictionless plane on a treadmill (without any propeller) would stay still. This is not true, as there is a force needed to cause the wheels to rotate, which will cause the plane to go backwards.

But if the plane has frictionless wheels with zero mass - then it'll stay still :)

BreakableC said...

A mistake -
"stationary to the ground" is different than "stationary to the air".

Being stationary or not stationary to the ground has no relation to taking off.

You wont take off if you are "stationary to the air".

Anonymous said...

What really happens is that the conveyor belt speed gets high enough to create sufficient headwind for the plane to take off with zero ground speed.

duff said...

You wont take off if you are "stationary to the air".
True, but the plane won't be "stationary to the air", and WILL take off!

What really happens is that the conveyor belt speed gets high enough to create sufficient headwind for the plane to take off with zero ground speed.
I really hope you're trolling...

cosmicnomad said...

Man I can't honestly believe this debate still rages on. Folks this is a "thought experiment" and relies heavily on the actual question....

Will a treadmill runway operated at ANY speed keep me from taking off? Nope. I will require a small amount of thrust to overcome wheel bearing and tire to treadmill friction. After I've applied this thrust, you may increase the speed of the treadmill and I will remain stationary. But once I apply takeoff thrust (full throttle) I will take off....

Bonehead who said that the treadmill speed would increase to a point that would create headwind is an idiot. I would love to hear how he thinks the treadmill creates headwind.

ALL a plane needs to take off is air flowing fast enough over the wings. PERIOD. If I am unfortunate and do not have a treadmill to play with, i can wait for a hurricane, or possibly a tropical storm.... if my plane is pointed into the wind, and the windspeed exceeds takeoff airspeed, the plane will fly with the engine off. Mind you it would be a bumpy ride and we'd probably crash in the end, but the plane will fly.

Now this whole treadmill thing is just insane.... The original question never mentioned anything about a vacuum or outerspace or friction in bearings, etc. It simply said if the treadmill matches the speed of the plane, will the thing take off or not? It is a really simple answer: If the speed of the plane is less than takeoff airspeed NO. If the speed of the plane exceeds takeoff airspeed YES.

Can a treadmill runway in ANY way stop my plane from taking off if I as the pilot want to take off? Not a chance. It can not happen. There is no way.

Anyone who thinks a treadmill runway can prevent a plane from taking off is just "plane" stupid. (pun intended)

All of this about wheel bearings and friction is pointless.... I've heard peeps say that if there were an "infinite speed of the treadmill" and similar things..... My wheels won't fall off and the bearings won't fail no matter how fast that treadmill is going because the question stated: the treadmill matches the planes speed. And I promise that my plane will take off in about 45 seconds no matter how fast your treadmill is going, which is long before the bearings will fail or some other such nonsense.

It is ALL about the question.

And dear lord I hope you folks on the "no fly" side of this aren't pilots. And if you are please tell me who you fly for so i may book travel with someone more intelligent flying my plane. I'd like to know that if something goes wrong my pilot has a clue. And if all else fails I'll have to buck up and spend the extra money and fly myself.

mikeyberman said...
This comment has been removed by the author.
mikeyberman said...

Strictly speaking, cosmicnomad, a treadmill travelling near the speed of light could break the plane in many ways. Aside from basic stuff like unimaginable friction with the wheels, due to Special Relativity a treadmill travelling near that fast would have hugely increased mass, possibly resulting in lots more gravitational pull on the plane (depending on the original mass and speed of the treadmill).

But yeah - if the treadmill is going as fast as the plane, then of course it'd take off.

And unfortunately some of those on the "no fly" side ARE pilots (I've seen a few)... And anyway, when they did it on Mythbusters their pilot thought it wouldn't fly....

Mind you, he wasn't a commercial pilot...


They should put this as a question in Physics exams. It'd be too much fun.

Anonymous said...

I know I'm going to regret wading into this..

I read the post and saw no mention of one important effect. I skimmed the comments, and only one (anonymous) person mentioned it. Duff called him a troll and Cosmicnomad scoffed at him and asked:

"I would love to hear how he thinks the treadmill creates headwind."

It's very simple. There is a no-slip boundary condition between the treadmill surface and the air. The layer of air in contact with the surface moves along with it, at the same speed. The air velocity decreases with height. This is the headwind the anonymous commenter was talking about.

Contrary to the claim of the author, resistance to forward movement is not constant, and it is not simply due to friction in the wheel bearings. The air around the airplane is not stationary wrt to the ground. It is moving and creating wind resistance which varies with treadmill speed. It also creates lift.

cosmicnomad said...

But man I love getting responses such as this.... OF COURSE, there may be some minuscule bit of airflow created by the treadmill and OF COURSE there are varying amounts of friction in several components of this system.

It might be interesting to see if the treadmill could create enough headwind to register on the airspeed indicator let alone get the plane to V1 or V2 speeds. But alas my friend. This is not what the question was about.

I'm sure we could analyze this to death considering that no one has mentioned that a treadmill this large would cost more than the plane. Now we have economics in our once simple question that was intended to illustrate a simple thing like thrust is generated by the propeller and a treadmill has relatively no impact on the speed of the plane.

And while I'm at it, Duff was an idiot. His quote was:

"What really happens is that the conveyor belt speed gets high enough to create sufficient headwind for the plane to take off with zero ground speed."

I'd like to see this conveyor belt....

duff said...

And while I'm at it, Duff was an idiot. His quote was:

Why, exactly, am I an idiot? for calling the headwind poster a troll? It certainly seemed to me that the only reason he posted that ridiculous claim was to stir up the argument again... maybe I should have called him a flamebait instead? Or maybe you think those words you quoted and attributed to me were mine - sorry, you're wrong, I was cleary quoting the poster immediately above me, the one I called a troll.

I quoted what he said, then responded to it. I never said I agreed with him, and I don't - his claim is simply ludicrous.

You should make sure you know what you're reading and responding to before calling people idiots, it makes you look like one yourself.

hata-botsad said...

In fact, I can bet I CAN prevent plane from taking off by controlling the treadmill.
I will simple start it moving in the SAME direction with plane. Since wheels are idealistic, they DO NOT slide - we take it as axiom, just as we did with "frictionless" wheels.
The plane remains static. Simply, there's NO WAY it can overcome the treadmill movement without making its wheels to slide - a sort of event prohibited by rules of conundrum.

Ellegant solution for no-fly, isn't it? Please note - it DOES NOT contradict the conundrum in any of three your original interpretations. In none of them did you address the treadmill's direction issue.

Am I not a smart guy?

mikeyberman said...

I'm sorry to say it, hata-botsad, but you are not a smart guy as you have ignored the crux of the whole argument:

Regardless of what the treadmill does, regardless of what the wheels do, the plane will always be able to push itself forwards through the air.

If the plane can push itself forwards, then it will accelerate forwards, and eventually it will have accelerated enough to take off.

hata-botsad said...

mikeyberman,

The following argument - Regardless of what the treadmill does, regardless of what the wheels do - is merely senseless. What did you mean by this? There IS strong connection between plane and earth - through wheels and treadmill respectively.
In static position, the plane lies on its wheels. Dont forget about gravity.

Please, read once more my argument - the treadmil is accelerated IN THE SAME direction with plane. This changes everything absolutely.

Make an experiment, or imagine one. You hold a free-spinning wheel in your hand. Move it up and down the wall. Now, can you move it "up" the wall, having the wheel spinning "down", without slide effect?

Can plane move forward with its wheels moving backward, without slide - its THAT simple.

hata-botsad said...

Well, I revised my theory and have to admit now, its wrong.
The plane will take off, refardless of treadmill's direction.
Still I dont give up hope of finding another way to prevent such event.

mikeyberman said...

Of course a plane can move forward with its wheels moving backward...

Eventually the plane will catch up to the treadmill's speed, so then it will be stationary in the frame of reference of the treadmill.

Any inertial frame of reference will hold the same laws of physics, so we can think about this from the treadmill's frame of reference (i.e. we are attached to the treadmill moving along with it):

At first the plane and the wind will move backwards. Then the plane will accelerate forwards, until it is stationary (and the wind will continue moving backwards). Then the plane will accelerate more, and it will move forwards, until it has sufficient velocity relative to the wind to take off.

cosmicnomad said...

sorry Duff. was looking only at the guy who quoted you.

now for the new thing. a treadmill moving in the SAME direction as the plane will only contribute to increasing the airspeed of the plane, thereby making it easier to take off. This is exactly why aircraft carriers head into the wind to conduct operations...

And this whole business of the wheels having anything at all to do with the plane's velocity is nonsense. The wheels actually only interact with the treadmill. Think about it like this... A seaplane will take off upstream on a river no matter how fast the river is flowing.... (don't get into rapids, rocks, and other idiotic variations....). If the river is flowing at 60mph, I will need to apply power to counteract that, and once i do, i will begin to move forward relative to the shore. Once I'm moving forward to generate sufficient airspeed to fly, the plane will take off. Now I will give it too ya that the drag induced by the pontoons will be prohibitive in a 60mph river, but the original question mentioned a treadmill and there aren't any 60mph rivers that i am aware of.

A treadmill can not prevent a plane from taking off.

mikeyberman said...

hata-botsad, i congratulate you. Very rarely do people change sides in this argument, and very rarely do people admit they have been wrong.

I applaud you :)

cosmicnomad said...

mikey you are on now?

mikeyberman said...

i am always on. i am a god.

cosmicnomad said...

got an IM prog? I am on as signsystems on yahoo

mikeyberman said...

too lazy :P

i feel like some delicious Family Guy

cosmicnomad said...

ah just figured we could chat. no biggee if you don't want too

mikeyberman said...

feel free to add me, mikeyberman AT gmail.com on MSN, but I won't be on for half an hour or so.

cosmicnomad said...

is that the same as Windows Live Messenger? things change so much..... *sigh*

mikeyberman said...

haha yes yes it is... crazy confusing technology...

Dane said...

I agree with the results.

But there is one important detail:

"The propellers or jets create thrust that pushes against the surrounding air and causes the plane to move forward."

Jet planes generate a forward force by pushing air backwards out of the engine, which then creates (by Newton) an equal and opposite forward force on the plane. It does NOT push backwards on the air behind it. For more information, look up the rocket principle.

darklooshkin said...

this article is awesome. with the insight granted to me by 34, the (mostly nude) goddess of the internet, i hereby infer that the people arguing about this are a) on drugs and/or b) insane. given the lack of spelling mistakes (aka youtube comments syndrome), i deduct that it is more likely the people doing this fall into category b.

mikeyberman said...

darklooshkin, I find it ironic that you make a spelling mistake in the very sentence in which you criticise people for being unable to spell. You mean to say "deduce", not "deduct".

And before you say I spelt "criticise" incorrectly, the 's' is the British/Australian spelling, whereas it's spelt with a 'z' in America.


But yes - people who argue the plane won't fly are generally insane. And so are some of those who say it will (e.g. the one's who claim it will entirely from the headwind created by the treadmill...)

Greg said...

"Imagine a plane without wheels. The fuselage would sit on the runway, and as you fired up the engines, it would skid spectacularly along the runway, possibly spewing sparks in its wake and doing quite a number on the body of the aircraft. No matter how fast it was going, the frictional force against the airplane would be constant; friction does not depend on speed"

The friction would actually be less as the plane gained speed wouldn't it? The faster the plane goes the more force is pulling it up (even while lift < weight). So the faster the plane goes, the less the normal force is and the less the friction is

mikeyberman said...

Nice thinking Greg :)

However the original quote was still wrong - friction is normally proportional to speed, and sometimes proportional to speed squared.

So I'd imagine friction may first increase at low speeds, then as the plane approaches takeoff speed it might decrease as you said...

Anonymous said...

cosmicnomad, while the "plane will fly" is quite obvious, your swimming pool anology is not so good, unless you are wearing skates.

You need to be able to swim (with arms only, while your feet remain on the treadmill) with enough force to overcome the friction between your feet and the rubber treadmill - I doubt you can manage that.

Your example is exactly the same as skates, treadmill, handrails, but substituting water for handrails. You still need to be wearing skates.

Anonymous said...

I first heard about AoaT from the mentioned MythBusters episode. Initially, I was a "no-fly" on the basis that if the plane is going forward at speed X and the treadmill is cycling backwards at speed X, then the plane cannot go forward to achieve lift.
I was, of course, thinking about airplane wheels like car wheels, and when they did the small scale test and mentioned that the wheels rotate independently, it all made sense and then I realized that there would be no speed a treadmill could go at that would prevent the plane from going forward. However, the wheels would be spinning at the planes liftoff speed plus whatever the treadmill was doing.

Anonymous said...

For the "Yes" people the wheels are a red herring. A plane without wheels would also take off....that about demonstrates the silliness of this question.

Anonymous said...

In many ways this is a question about the difference between static friction and kinetic friction.

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deathbytoaster said...

The air flowing under the wings causes lift due to the shape of the wings. If the plane is on a treadmill not moving through the air, the airspeed is theoretically zero under the wings.Meaning there is NO LIFT. Whoever asked this question doesn't even have a clue what aerodynamics are.

mikeyberman said...

deathbytoaster, what you said about lift is true, however you must keep the following in mind:

the plane is able to move relative the the wind, as its thrust comes from pushing against the wind. Regardless of what is underneath it, the plane pushes backwards on the wind, resulting in it moving forwards. Once it's moving forwards fast enough, it's able to take off due to the relative motion between the air and the wings.

duff said...
This comment has been removed by the author.
duff said...

The air flowing under the wings causes lift due to the shape of the wings.
Actually, it's OVER the wings that causes lift due to Bernoulli's principle... :)

If the plane is on a treadmill not moving through the air, the airspeed is theoretically zero under the wings.
That's a pretty big IF right there. Are you sure the plane won't be moving through the air?

Fact is, it will be. The wheels are free-spinning and the engines are "pushing against" the air, not the treadmill, and so the treadmill actually has almost no effect whatsoever on the plane's ability to move.

signsystems said...

test

Kenneth said...

It's a scary thing, seeing so many idiots roam free on the internet....

Yes, the aircraft will take off!

The velocity of the treadmill and wheels are irrelevant. The wheels are only there to keep the undercarriage from wearing down when on ground, and has nothing to do with propelling the aircraft forward.

My beautiful little Rans S-6ES (the bigger brother of the aircraft used by Mythbusters), with it's beautiful little engine, will start skidding with brakes on, on asphalt, with the engine running at about 2.000 rpm. At takeoff however, the engine runs at 3.300 rpm, and no realistic amount of friction caused by tires or bearings will keep it from getting airborne.
It simply can't be done...

Even in theory, the treadmill would always lag behind, because the wheels would be accelerating with the rate of the treadmill + the groundspeed of the aircraft In relation to the ground, not the treadmill).
The propeller and engine wouldn't care how fast the treadmill was going, because as far as they know, they are propelling the aircraft through the air.

The only way to keep the aircraft stationary on the treadmill is to tie it down, but then neither the wheels nor the treadmill would move, because the aircraft would be unable to initiate any movement of the wheels in the first place.

James said...

"It says that the conveyor belt must match the speed of the plane.

What speed? If the plane stays stationary, there is no speed.

To have speed, the plane must already be moving and thus it cannot stay stationary."

Exactly, the entire statement is in semantics.

If I asked the original question, but replaced plane with car and asked if the car would move forward... the answer would be yes, the car moves forward. The belt and car will be moving X MPH, but the speedometer (rotational speed of the wheels) will be 2X.

I guess a way of rewording the question would be... if the conveyor exactly matches the rotational speed of the wheels, will the plane move? The answer would be no.

Awesome OP, pretty much the original question is really crappily worded and the answer boils down to semantics.

James said...

Sorry, to clarify.. I think you've admirably proven that it would be nigh on impossible for the conveyor belt to match the rotational speed of the free spinning wheels of a plane.

James said...

One last thing, there is an additional frictional force in play in addition to the bearings which DOES increase with velocity.

The friction between the rubber tires and the road, called "rolling slip". This would, indeed, make it possible to have a conveyor run fast enough (albeit really flipping fast) to stop the plane!

Kenneth said...

No, the only thing that can keep the aircraft from going is a rope.

Anonymous said...

"This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction)."

Right there. Sure, that would actually be an impossible mechanism, however, if such a machine could be built the plane would not move. There is no one at the control of the treadmill, in the original question it says that it is tuned perfectly.

duff said...

Unbelievable. Does this never end?

Anonymous: The plane still moves. Think about it:

The plane moves forward at speed x relative to the ground. The control system measures speed x, and drives the belt backward at speed x relative to the ground.

The speeds are matched, and the plane is still moving at speed x relative to the ground because the SPEED doesn't matter to the plane! The free-spinning wheels, which have nothing to do with the plane's propulsion, take away almost all of the friction between the belt and the plane and thus reduce the FORCE that the belt exerts on the plane to almost 0. The force exerted on the plane's engines GREATLY exceeds 0, and Newton's laws of motion take over. The plane has a net force, and so the plane moves. Period, end of story.

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Cameron said...

I disagree with you. The airplane would not take off.

Kenneth said...

Well Cameron... Unless you are able to produce a compelling arguement for your statement, i'll consider your statement to be a product of lack of intelligence...

Anonymous said...

I'm pretty sure that anyone that argues that the plane doesn't move is just trying to egg folks on. It just *has* to all be a big joke, because no one can be that ignorant after reading all the evidence.

Although there is the argument of...

Scott Jones said...

The military already answered this question in 1967 with the Custer Channel Wing Hybrid Jet. This is the full video.

http://www.youtube.com/watch?v=-Sn5JL9t_C4&feature=related

And this is an explanation by the inventor.

http://www.youtube.com/watch?v=7FhFlxbV-AU&feature=related

Please spread the word, no need to argue whats already been solved.

Anonymous said...

it's an abstract thought experiment. the assumption is that the conveyor belt matches the plane's speed ALL. THE. TIME. get it? no humans involved. just abstract function "plane goes with y speed, conveyor goes with x=y speed". in this case, the plane will not move against the air, which results with no air flow around the wings, resulting in the plane remaining stationary till the world ends. the mythbusters argument lets it take off only in flawed, real life conditions. i repeat again, this is a thought experiment, things like human error, material imperfections and data transfer lag do not apply here.

duff said...

Hey anonymous... what is the mechanism by which the thrust from the engines is counteracted by the treadmill?

If the plane is not moving, how does it have a speed to be measured and matched?

The planes moves as normal, it's wheels spin at twice the speed, and it takes of pretty much normally.

Kenneth said...

Hey Anonymous,

How many factors do you want to leave out here? If you leave in physics and aerodynamics, and don't tie the aircraft to a stationary object, it will depart when the engine is started and the throttle firewalled, regardless of what the conveyorbelt is doing...

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Dubaya said...

I saw the MythBusters episode having never heard of the debate before and must confess I thought it wouldn't fly. Like you state though, the main reason for this was how I interpreted the question. The MythBusters used a graphic to help explain the thought experiment which probably did more harm than good because it made it seem as if they expected the plane to take off from a stationary state. I understand your friction arguement and agree that if the plane wants to it would overcome friction and move.

A better experiment would be to attach a propeller or jet to a model car with no gears to show that no matter how fast you make the treadmill go you can make the car move forward without the distraction of flight, plus four wheels are a lot more stable then the wheels on that sad model plane the MythBusters used.

Rex Kramer said...

When I run on a treadmill, I remain stationary compared to the ground. So if you were to ponder putting a plane on a treadmill, isn't it inherent to the question that the plane will remain stationary to the ground? The intent of the question is to test a person's knowledge of lift, not the detailed physics of putting a wheeled object on a treadmill. So the answer is "No, a plane cannot take off on a treadmill." To answer it any other way is to be an ass.

Rex Kramer said...

Or, you change the premise and talk about a mile-long treadmill and now you're into the difference between applying force to the wheels vs. to the object itself. But if you want that answer, why not just replace the treadmill with an iced over runway? A car would sit and spin, and so would my legs, but a plane would still take off. A good question, indeed, but not if you use the premise of a treadmill.

duff said...

"So if you were to ponder putting a plane on a treadmill, isn't it inherent to the question that the plane will remain stationary to the ground?"

No. If the plane being stationary to the ground were the important part, they would have picked a mechanism that would actually keep it stationary, such as large fixed blocks in front of all of the wheels - or maybe even removing the wheels completely, and replacing them with long poles in holes in the ground.

"The intent of the question is to test a person's knowledge of lift, not the detailed physics of putting a wheeled object on a treadmill."

Wrong. The intent of the question is to test a person's knowledge of force and motion. When you or I are walking, we exert a force on the ground to accelerate. The treadmill counters this force, and prevents our acceleration. Planes do not push on the ground to accelerate, and so a treadmill would not be able to cancel their force, and would not prevent their acceleration.

This question isn't about a "wheeled object" on a treadmill, because a car is a wheeled object that would be held stationary by a treadmill. It's about an object that doesn't use the ground to accelerate on a treadmill, and it checks whether or not you can realize that difference.

Anonymous said...

Of course, if the plane was a weird model that, while it's on the ground, moves like a car, and changed to propeller/jet once in the air, you would be able to stop it. This would also work with a car.

Am I correct in this?
Assuming I am, all my confusion in this matter has been resolved, so thank you.ctor

Anonymous said...

...how did that 'ctor' get there?

Anonymous said...

wings on a car = no go
wheels on a plane = yes go

Anonymous said...

I don't understand your standing-on-a-treadmill-with-rollerblades example. I can easily understand that it would take very little force to move yourself forwards but, from what I understand when you do it your wheels start spinning faster whereas the speed of the treadmill remains the same. Doing this experiment on a sort of "treadmill" that would actually slip under your feet with the exact same speed as you roll your wheels would mean that moving forwards would be impossible, or would it?

Is it incorrect to say, that the speed of any certain dot on the outer ring of the plane's wheels is actually higher than the speed of which the treadmill is moving backwards when the plane starts moving forwards?

duff said...

If you insist on using the speed of the wheel, then it is impossible for the treadmill to match the speed of the wheel unless the plane (or roller blade) is not moving - and if the plane isn't moving, then the plane won't fly. No trouble there.

Problem is, when someone pulls you on the roller blade, or when the plane turns on its engines, then you WILL move, and it will be impossible for the treadmill to match the wheel speed. The plane will fly, and there is no way for the treadmill to stop it.

Two speeds moving in opposite directions won't cancel out unless there is a connection between the objects - and in the case of a plane and a treadmill, the free-spinning wheels essentially remove the connection.

Ten98 said...

This is fucking funny, people are STILL debating this in the very comments thread of the website that was supposed to settle the argument.

As long as the wheels are well oiled, the plane takes off. Get over it.

Coalesce said...

I hate you for crushing my illusions, and deeply thank you for alleviating my ignorance.

There is one less 'no-fly' in the world.

jh said...

The plane will fly. However, it does not have to move forward.
I’m saying that even with the plane remaining stationary IT CAN TAKE OFF.

I know it is the airflow on the wings that create lift in an airplane, and that the propeller’s airflow against the wings is not enough to generate the sufficient lift, so let me explain myself.

Let's imagine that at the signal the pilot accelerates, so the propeller exerts a good amount of thrust on the plane. The treadmill operator will react and start the treadmill going at a speed to counteract the plane’s movement. This will create a rolling resistance on the plane’s wheels. However, this resistance depends on the tyre, the surface it is rolling against, the bearings and the normal force on the wheels (as we have zero lift for the moment, that means the plane’s weight), but it is little dependant on speed. That means that in order to counteract even a small amount of propeller thrust, the treadmill will have to go extremely fast.

Now let’s assume we have a long (let’s say >20 times the plane’s length) and wide enough (at least twice the plane’s span) treadmill, and capable of achieve ridiculously high speeds.

Of course, there is no such a treadmill, and in the real world, the plane will move forward and take off, but this is a thought experiment and I say there is a treadmill like the one I described before.

The movement of the treadmill at an extremely high speed will cause a BACKWARDS LAMINAR FLOW of air near its surface, due to the air’s viscosity. See http://en.wikipedia.org/wiki/Viscosity. The maximum air speed will be at the treadmill’s surface, and will decrease with height. This air speed, (acting in the first seconds significantly only in the lower regions of the plane), together with the rolling resistance in the wheels, with counteract the propeller’s thrust. If we increase the treadmill’s speed, there is theoretically the capacity to generate enough airflow to counteract the propeller’s thrust. It is like having a big fan in front of the plane. Eventually, the air speed at the wings, produced by the movement of the surface of the treadmill will create enough lift and the plane will take off, without moving in relation with the ground.

james said...

i know this was a while ago but i wanna point something out to mikeyberman.
you misread darklooshkin's comment about spelling errors. he wasn't criticizing, he was saying that you guys must not be on drugs because of your LACK of spelling errors, which means you must be insane.

Anonymous said...

Yes, the plane will take off if you suspend disbelief that anyone would have or operate a "treadmill" (or any other surface) long enough to accommodate the ground roll necessary for the plane to reach the necessary ground speed at which its wings reach the necessary airspeed to fly.

To look at it another way, how long a treadmill would you need to LAND a plane safely and then stop? Answer: About as long as any other runway surface with similar friction.

Anonymous said...

The correct answer is that the original question is meaningless because none of the speeds are attached to reference frames.
This is the reason there is so much debate because people pick a 'natural reference frame' for their speeds depending on how they want to view the problem. Speed is a relative concept, there is no such thing as the 'speed of a plane'.
My first thought was to use the experiment to teach students about lift, so the plane speed was relative to the treadmill and the treadmill was relative to the Earth. This keeps the plane stationary relative to the air and it wont take off (actually it breaks any realistic planes wheels but it's a thought experiment). The wheels must impart some friction on the motion of the plane for this to work since otherwise the treadmill could not slow down the plane.
If there is no friction in the wheels then we could turn the treadmill on and the plane would just sit in place. The treadmill might just as well not be there. The plane will take off once it reaches take off speed relative to the earth.

Anonymous said...

"If the wheels were perfect - that is, there is no friction in the bearings (and no deformation of the wheels as they spin) - then something interesting happens. When we turn on the treadmill, the plane stays stationary on its own. The wheels simply spin along the track, and impart no force to the plane."

This is not actually true. What you probably meant to include is that the wheels are weightless. Otherwise, the wheels will apply a force to the plane because they have an unbalanced force on them.

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b said...

@what you call "fact" C: well you say "The most powerful conveyor belt in the world couldn't do it. David Copperfield couldn't do it. It can't be done."

and I object: Chuck Norris could do it.

Anonymous said...

Sorry, this all might be correct, but the plane wouldn't take off.
Ok, it depends on the question, but if the treadmill runs exactly as fast as the wheels are turning, than we have a bigger Problem. The engine of the airplane starts moving the plane, this caused rotating wheels and the treadmill starts running. This accelerate the wheel, that let the belt run faster ...
In a very short time it reaches the speed of light, gain mass and all collapse into a black hole - the plane did not take off.

Nathan said...

In treating the thought experiment as if it need deal with the design of actual planes, you do damage to the proper interpretation of said thought experiment's purpose. Hypothetically, of course, we can list all the possible interpretations and deal with them in uncontroversial ways (I take you to have done this partially and innadequately). Our job, as interpreters, is not simply to list all the meanings that COULD be relevant, we must also try to make sense of which one of these the thought experiment actually is--for this task, understanding the purpose of those who employ it is crucial.

The reason that actual plane designs and actual treadmills are unimportant is that planes and treadmills are only mentioned to pump intuitions about certain FUNCTIONAL roles that each of these are to play. Thus, because the question is one of liftoff while remaining stationary relative to the environing atmosphere(a question, that is, about the way that wings create lift) we must treat of the plane/treadmill such that remaining stationary is the result. This need not require one's not trying to take off (as you suggest), as a plane that only achieves lift on the basis of a kinetic chain through its wheels is not inconceivable (of course, it would not be able to fly after take-off, but this is not PRIMARILY a thought experiment about planes and treadmills) and, in the case of this thought experiment, perhaps necessary for maintaining the intelligibility of the intuition we're trying to pump.

Under a reasonable interpretation of 'plane' and 'treadmill', the plane would not take off. Simple as that.

duff said...

"In treating the thought experiment as if it need deal with the design of actual planes, you do damage to the proper interpretation of said thought experiment's purpose"

Who are you do declare what is the proper interpretation of the riddle?

It is a much more reasonable interpretation that the author of the riddle intended to play upon the reader's natural inclination to misapply the effects of a treadmill on the motion of a runner or a wheel-driven vehicle to the motion of the airplane - thus leading to the incorrect assumption that the plane is to remain motionless. Once the reader can abandon their preconception, they can quickly arrive at the correct conclusion, that the plane will not remain motionless.

"Under a reasonable interpretation of 'plane' and 'treadmill', the plane would not take off. Simple as that."

What a ridiculous assertion. A treadmill prevents the motion of a car or runner by moving the ground backwards so that the car or runner doesn't move forwards. Moving the ground backwards under a plane does nothing to prevent the plane from moving forward. No reasonable interpretation of "treadmill" would ever prevent a reasonable interpretation of "plane" from taking off.

Nathan said...

"Moving the ground backwards under a plane does nothing to prevent the plane from moving forward."
Of course not, with an actual plane. That's my whole point--the only way to read intelligibility into this thought experiment is to take up the mantle of interpretive authority.
We ask: what is the point of this thought experiment? How can we read the meanings of the terms used such that the thought experiment doesn't fall apart due to merely accidental facts?

Now, as who I am is clearly unimportant to whether or not I'm right about our hermeneutic orientation to this problem, I'm going to ignore your worry about worry about what kind of authority I am. I am a philosopher, but that doesn't give me any special bearing here. The move we must make, to make sense of this thought experiment, is simply to work from the idea of a plane that uses a motor to turn its wheels and create the speed necessary for lift(or the idea of a treadmill that connects to a portion of the plane that won't minimize the resistance the treadmill is to create such that the treadmill is capable of matching, negatively, whatever forces are created which move the plane forward). This kind of plane would not lift off on a treadmill that could keep up with its tire speed and this is not unintelligible.

The thought experiment works on these grounds, and that's all the authority I need--to put it another way, my claim is simply adherence to the principle of charity.

duff said...

"The move we must make, to make sense of this thought experiment, is simply to work from the idea of a plane that uses a motor to turn its wheels and create the speed necessary for lift"

So, in other words, to arrive at the answer we want - that the plane won't fly - we must first assume that the plane is, in fact, a car (or, bolt the plane to the ground).

Planes don't use their motors to turn their wheels to create their speed. End of story.

"to put it another way, my claim is simply adherence to the principle of charity."

So... you're begging us to accept your interpretation. What are you, a socialist? ;)

People put too much credence in these "thought experiments", in my opinion. Sure, a treadmill could be manipulated to prevent the motion of the plane - if you ignore all of reality accept the mass of the wheels. Why is this an acceptable answer?

Again, it's so much simpler, and requires so much less suspension of reality, to accept that the author intended to take advantage of the reader's misapplication of the effects of a treadmill on a car or runner onto the plane to lead them to the wrong answer, and to force them to abandon their preconceptions (a difficult task for most people) to arrive at the correct answer - that the plane will fly.

Nathan said...

Here is an explanation of the principle of charity, I assume that my explication of the thought experiment will be rather clear if you take the time to understand this basic presupposition of all rational debate:
http://www.csus.edu/indiv/m/mayesgr/phl4/Tutorial/phl4charity.htm
http://en.wikipedia.org/wiki/Principle_of_charity

duff said...

"Here is an explanation of the principle of charity"

My comment about begging was a joke - hence the winking smiley. I do actually understand the principle of charity, I just disagree that the thought experiment interpretation is the more logical.

The first thought experiment interpretation basically asks - if we hold a plane motionless, will it be able to generate lift? - and asks us to assume for the sake of argument that the treadmill is capable of holding the plane still. Anyone asking this must not know much, if anything at all, about the mechanics of flight, much less the physics of how a plane and a treadmill would interact. Not only is the answer trivial, but choosing this interpretation seems to contradict your Principle of Charity, in that it assumes the worst of the questioner.

The second thought experiment interpretation asks if a treadmill can be manipulated into preventing the motion of the plane, knowing that doing so will prevent the flight of the plane. This is interesting from a physics perspective, but ultimately uninteresting because it is known that preventing the motion of the plane will prevent the plane from taking off.

The riddle interpretation relies on human nature to trick the reader into the wrong answer. We naturally make assumptions about the behavior of a car/treadmill system, and mistakenly apply those assumptions to the plane/treadmill system. This is similar to such riddles as "a plane crashes on the border of Turkey and Iraq - where do they bury the survivors?".

Applying Occam's Razor leads me to the conclusion that the riddle interpretation is the simplest, most logical, and thus more probably correct interpretation.

Kenneth said...

I'm sorry Nathan, but i have a hard time understanding both your logic, and your claim to accept your arguments...

Your chain of logic are all based on the assumption that the airplane is in fact stationary, but that is only your assumption, not a fact.

You can theorize all you want, with cars or airplanes driven by wheels, but the fact is(!) that the problem is called "Airplane on a treadmill", and as such the vehicle in the problem is in fact an airplane, not a car. If they intended you to theorize about a wheel-driven vehicle, i'm sure they would have selected a car rather than an airplane.

Defining it as a "thought experiment", it sure is convenient to be able to suspend the laws of physics to be able to reach a predetermined conclusion that the aircraft will not takeoff, the universe will implode, and so on...

However, like many other contributors to this debate, i prefer to include the laws of physics, and treat this as a real problem, not one where important factors can be left out just because they do not suit my preconceived answer.

The fact is, that in this reality, the laws of physics will let the airplane take off.

Anonymous said...

This article seems to assume that the airplane needs to be kept stationary relative to ground in order not to lift-off. This is simply not true.

The airplane needs to be kept under its take-off speed, which is an order of magnitude easier task to do, since as an airplane approaches its takeoff speed, aerodynamic drag tends to arrest most of its forward acceleration.

Suppose a plane, if let to accelerate on an infinitely long runway, can reach a top speed of 160 KIAS, but it's lift-off speed is 150 KIAS. The treadmill only needs to reduce that plane's speed by 11 KIAS, not 150 KIAS.

How hard is it to move a REAL life stationary plane on a giant-ass tread mill at 11 KIAS backwards?

Certainly significantly less than 500 mph.

Anonymous said...

KIAS = Knots Indicated Air Speed.

Kenneth said...

That is some assumption...

Can you name one plane that has as little as 11 knots margin between topspeed and takeoffspeed?

Even the cute little underpowered slow-flying plane that was tested on Mythbusters (Rans S-5 Coyote) has a margin of about 50 knots...
The larger S-6 Coyote II (that i used as a reference earlier in this discussion) has a margin of about 75 knots...

Basically, you're assuming that the plane is so underpowered that any increase in friction would keep it from taking off, but in reality, no normal aircraft has that little power, because it would be dangerous...

grandstan said...

groundspeed makes no difference to an airplanes wings, airspeed does and the wheels " freespin ' the engines thrust against the air, not the ground. the plane will always take off, no matter what the treadmill does. If a planes takeoff airspeed is 50 mph it can take off with a 50 mph headwind and no groundspeed. If it has a 50 mph tailwind it will have to have a 100 mph groundspeed to take off. There is an object something like your giant treadmill that planes use all the time, its called an AIRCRAFT CARRIER.

Jared said...
This comment has been removed by the author.
Jared said...

You accuse others of looking at the question as a trick, yet your are as guilty yourself. You ignore the spirit of the problem, and go off on tangents about how if the pilot conspires not to fly he won't. Yes, in that wording the pilot would make no attempt to fly, but just get the the nexus of the problem and forget such ridiculous and overall minute word logical fallacies.

Not that it really matters, since the problem really is just the verbal equivalent of the stone of Spartoi.

Anonymous said...

"If you run the treadmill at 5mph and turn on the plane's engines just slightly, they will provide enough thrust, pushing against the air, to keep the plane still. If you then increase the treadmill speed to 500 mph, you won't need to adjust the throttle on the airplane - it will remain stationary."

Increasing the speed doesn't increase the friction force, true, but it does increase the power needed by the engines to keep up, since power = force*velocity.
The throttle controls power, not force.

Stuer(32) said...

"Increasing the speed doesn't increase the friction force, true, but it does increase the power needed by the engines to keep up, since power = force*velocity.
The throttle controls power, not force."

Actually, that is not true. The throttle controls the power and velocity of the engine, wich is attached to the propeller, wich in turn converts the power and velocity into thrust/force. This force is not applied against ground, but the air, and as such, the speed of the ground under the aircraft is, as always, irrelevant.

Anonymous said...

But... will it blend?

Jesse said...

As long as some posters are allowing treadmills that can accelerate infinitely, and invoke laminar flow of the air to create a headwind and thus let the plane take off while remaining stationary to the ground.

Then why not have this infinitely accelerating treadmill move in the same direction as the plane's desire and thus the laminar flow creates a tail wind preventing the plane from achieving take off air speed.

And since I am presuming impossible things, I prefer to do all this in Newton's Universe where there are no black holes to collapse into.

Once again, sufficiently twisted thought can force the thought experiment to turn out which ever way you want. ;-)

Anonymous said...

if you could somehow make a giant fan to make the air surrounding the plane match the speed and direction of the plane it would also not be able to take off

Stuer(32) said...

But it's not relevant to the question at hand, is it?

Steven said...

The tires would melt, followed by the wheels, bearings and landing gear... After that, it is not pretty. :)

MarcoPolo said...

I like the way the no-flys rely on an ideal treadmill (ie unconstrained acceleration and velocity) but non-ideal wheels and bearings (ie with friction, relativistic effects). If you ignore relativity and friction in the treadmill, you must also ignore them in the wheels / bearings.

Glitch said...

I agree with the "conspiracy theory", in which the pilot and treadmill operator conspire to keep the plane still, with ONE exception, which I will get to in the third paragraph.

The "conspiracy theory" works, as the author postulates, because the ordinarily negligible friction in the wheel bearings created by the treadmill can be used to counter-act the force the engines exert on the air, if the engines were adjusted to use a very weak force. The force that keeps the airplane in place in this example is called rotary inertia, where the rolling friction in the wheel bearings can create an equilibrium despite the fact that the engines are pushing on the air and not the ground, simply because the airplane is in initial contact with the ground.

However, assuming the treadmill is powerful enough, and the "conspiracy theory" scenario is in effect (the plane is at a standstill with minimal engine thrust and extreme treadmill speed) then the pilot could gradually ramp up the engine and I could increase the treadmill to keep the plane in equilibrium. The pilot increases the engine thrust at the same time I increase the treadmill speed. Eventually, assuming the treadmill is powerful enough (it would need a power output much much greater than the jet engine), the plane's jet engine could be at full throttle with the treadmill spinning at an extreme speed to keep the plane at a standstill. The treadmill speed would be many orders of magnitude faster than any takeoff speed of the plane. If the tires and bearings are strong enough, the plane would sit there all day, with the bearings glowing red hot, soaking up the energy from the jet engines and transferring it into heat.

This is overlooked by the crowd that considers itself more intelligent than the crowd that merely thinks of this in terms of a plane acting like a car on the treadmill. It's obvious that a plane exerts a force on the air and not the ground, but because the plane's wheels are always touching the ground until it can get enough momentum for the wings to work, the tires, wheels and bearings all play a factor in it's ability to move forward relative to the ground.

It's with this example that I can nullify the author's first stipulation, in which he suggests there's a scenario in which he can accelerate and I can't keep him on the ground. If I have enough power as a treadmill operator, and his engines have an upper bound thrust limit, I can always keep him on the ground.

J.A.G. said...

As mentioned in the original post, it's a matter of semantics. If we manipulate our interpretation of what the thought experiment is asking, we can come up with any answer we're comfortable with.

Q: A Boeing 787 Dreamliner is sitting on a NordicTrack Commercial 1750. The 787 throttles up for takeoff and the NordicTrack attempts to match its acceleration. Does the dreamliner take off?
A: The NordicTrack is crushed under the Dreamliner's 300,000 kilos and the plane takes off without any trouble.

Q: A Pegasus Quantum 145-912 ultralight trike is sitting on an interplanetary treadmill with the mass of 4 Jupiters. The ultralight fires up its propeller for takeoff and the treadmill begins moving to counteract the ultralight's acceleration. Does the ultralight take off?
A: The ultralight suffers severe structural failure on the runway and the pilot is crushed under the weight of the collapsing high performance Rogallo wing. It does not take off.

This is why it's pointless to have an internet debate about it...

Anonymous said...

"The plane must move relative to the ground in order to take off."
Then the harrier came along.

Anonymous said...

If the plane had no wheels, then the treadmill could keep it stationary. Otherwise its body is not connected to the treadmill, similar to a hovercraft (which could also move forward). As mentioned by author, even though a car has wheels, its body is directly connected to treadmill via the drivetrain.

Anonymous said...

I'm afraid your pompous blog is basically entirely wrong. All you have done is 'alter' the question to fit your answer.The question asks in essence 'if a plane moves forward at the same rate as the conveyor moves backwards will the plane take off' Even by your own arguement the answer to this question is no. Why I hear you ask (Whilst no doubt slapping your head in annoyance at another moron as you would no doubt call me) Well let me tell you why. The question MUST mean that the plane moves forward at the same rate IN RELATION TO THE BELT!!!!! If this is not the case then the belt might as well not be there and so the question is made moot. Allowing for this BASIC assumption then even by your own reasoning the answer is no. It goes without saying that if the pilot applies ENOUGH THRUST the plane will take off, but by doing this the plane is MOVING FORWARD FASTER THAN THE BELT IS GOING BACKWARDS!!!! That statement is (to use your word) unequivocal. It takes a certain level of moron to ignore the spirit of a question then state the frickin obvious as if it is a work of genius!And as for your 'frictionless wheels' scenario, well good luck with that and can I please have a small proportion of the trillion, zillion, billion dollar fortune that you make from inventing them! The pilot applies the amount of thrust required to overcome friction then stops CAUSE THAT IS WHAT THE QUESTION SAYS HE MUST DO!!!! Of course if he applies more thrust the plane take off, it doesn't take a self satisfied blog by you to know that, but then BY DEFINITION the question posed no longer applies.

Anonymous said...

All the conveyor belt does in the proper question is cause the airplane wheels to turn faster while the plane is taking off. That's it. And anonymous phrases a silly rewording just above my comment here -- asserting that "if a plane moves forward at the same rate as the conveyor moves backwards... which is not the question. However, assuming that it was the question, if the plane is moving forward, and the conveyor is turning at the same speed moving backwards, then the plane will take off if it reaches lift velocity. The plane IS moving forward, as anon clearly states. The only way the plane won't move forward is if the pilot applies a tiny bit of thrust, just enough to overcome the friction of the wheels, as stated in the original post above. Anymore thrust than that needed to overcome wheel friction and the plane begins moving. Anon is confusing the movement of the wheels with the movement of the plane. Until liftoff, when the wheels lose touch with the conveyor, the wheels will turn at the combined speed of the motion of the plane and the motion of the conveyor. The plane will move at the speed of the plane. Confusing the motion of the wheels with the motion of the plane is, I think, what confuses many. And snotty and dumb comments from the likes of Anon are snotty and dumb.

Anonymous said...

Nice job describing this, somebody was talking about this last night and I was initially confused as I thought of a human on a treadmill running remaining stationary. Yeeah, it's kinda embarrassing that Myth Busters needed to "bust" this, but the "Airplane On A Treadmill" wording did confuse me initially.

Anonymous said...

The description of a motionless plane on a treadmill blew my mind.

Anonymous said...

What if I was having sex with a donkey in the cockpit of the plane? Wouldn't our combined weight hold the nose down and thus prevent takeoff from occurring?

Anonymous said...

I guess this comment passes for humor in some cultures

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