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These plane-on-a-treadmill arguments always boil down to how you envision the treadmill interacting with the plane. View A has infinite friction, speed, durability, etc - so the treadmill can always impart enough force on the plane to counteract the force of the engines, acceleration = 0; airflow = 0, so unless the plane has vectored thrust (e.g. a Harrier) it's not going anywhere. View B has the wheels freely spinning (or inadequate friction to matter), so the treadmill has no bearing on the plane's velocity relative to the air.

https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/

"there’s also a #4 crowd loudly arguing that even if the plane was able to move, it couldn’t have been what hit the Pentagon." fuckin hilarious.

The there is a bunch of us who stand at the back and say shit like; who builds treadmills for planes? do planes have to exercise or they get tired and fall out the sky? why does someone called Harriet get special treatment in this paradox? Does a freely spinning wheel still adhere to the generalised rules of good or polite society? Does it ever really matter what an airspeed is? if the answer is yes can we have cake while you explain please? why do i have to sit next to *this guy* on the plane?

I'll have to keep that for next time, thank you. Although I'd add that this is also what happens when you move from logicspace to realspace.

Nice link and explains it very well. As usual with these the question is usually phrased in an inadequate / misleading way.

I feel like [this xkcd](https://xkcd.com/169/) also applies

>The problem is basically asking “what happens if you take a plane that can’t move and move it?” It might intrigue literary critics, but it’s a poor physics question.

So basically, we just have to build a giant treadmill and try it.

This was done on Mythbusters. The plane took off.

True, but option A isn't possible in real life. You could maybe fake it by chaining the tail to a very solid wall - that isolates it to whether the craft requires air speed for lift.

No it wasn't. The expirement that they did didn't adhere to the rules of the hypothetical situation since its impossible to make something in the real world that would

Forgive me, but doesn’t that kind of make the whole argument kind of stupid? I can kind of understand arguments about the physics of Superman, like is he flying because he can defy gravity or is he jumping really high, because the whole thing is not practical. But this is an airplane we’re talking about. Applying unrealistic limitations is just stupid.

The whole argument already is stupid. The point is is that the conveyer is magical in order to make a point about how planes use their engines and not their wheels for thrust, but it's a poorly constructed idea because it creates the problem of the wheels infinitely accelerating

>;The point is is that the conveyer is magical in order to make a point about how planes use their engines and not their wheels for thrust, This is why pointing to pontoon planes is a much better real world example. They dont use wheels at all 💖

The question is stupid no matter what. If your hypothetical has any consistency to it, then the plane *will* take off. Either there’s no friction, and both the conveyor belt and the wheels of the plane spin freely and infinitely, or there is friction, and the conveyor cannot spin fast enough to halt the plane.

Which is why this entire pile of bullcrap is a useless, meaningless shit to just start an argument for argument's sake.

I mean, it's a thought experiment. Many of them are stupid.

The person I responded to said to build a giant treadmill and try it. Mythbusters did that. What some people are interpeting, which is that the treadmill always matches the wheel speed, can not be built in reality. This is because there is always lag, and other forces involved, i.e. the plane will move forward before the treadmill can counter it. And when the treadmill catches up to the wheel speed, the plane will still move forward, so the treadmill will need to speed up again. This continues until the treadmill reaches an infinite speed. In reality, you have various limits, and forces, that prevent the exact interpretation of the treadmill always and exactly matching the wheel speed.

MythBusters aren't really a great source for scientific evidence lmfao... It's a show made to entertain, not to educate, and they tend to not acknowledge shortcomings in their experiments. I haven't watched the one you're talking about, but the fact that they so confidently stated walking in the rain is drier than running (objectively incorrect conclusion) without any type of validation or thought behind it other than "we did one trial" doesn't really speak to their scientific abilities lmao. Sure they're fun to watch when you're hungover or twelve, but they're no Bill Nye. I'd be careful what you believe from a show that's conducted objectively faulty experiments in the past...

>MythBusters aren't really a great source for scientific evidence lmfao... This is a straw man, as I didn't say that. All I said was Mythbusters built a giant treadmill, put a plane on it, and tested it. Here is Adam Savage talking about that test - https://www.youtube.com/watch?v=xUjcHW7SHaI

I'm... not sure you know what a straw man is. Anyways all *I'm* saying is that I wouldn't use the results of an experiment as a source when the people who did the experiment have also done experiments carelessly and thoughtlessly enough that they came to objectively incorrect conclusions. I believe you, that they did the plane experiment. And I believe you that they go those results. The results even sound correct (upon first glance, I haven't looked too far into it so it's possible I'm wrong). All I'm saying is that you should probably cite people's experiments who *don't* routinely make egregious mistakes due to their carelessness about scientific experiments lmao. It's like my saying 2 + 2 = 4 because my cousin who failed math knows that; it's correct, but there are *definitely* more reasonable people I could cite Anyway sorry to cause a kerfuffle, I think I just have a grudge against how prevalently the "it's drier to walk than run in the rain; Mythbusters said" thing gets cited when it's *so* ridiculously incorrect. Off topic, my bad edit: whoops, forgot it was Forbidden to do anything but praise the Mythbusters 🙄 i wish y'all'd use your thinking brains once in a while

> Anyways all I'm saying is that I wouldn't use the results of an experiment as a source when the people who did the experiment have also done experiments carelessly and thoughtlessly enough that they came to objectively incorrect conclusions. Yes, I know what a straw man is, and what an ad homonym is.

my brother in christ *what* are you talking about pointing out that someone who has historically been *wildly incorrect* about things *might not be the best person* to use as *your only reference* when you're trying to make a point about *something factual* is not ad hominem holy shittt it's not ad hominem to point out that wikipedia is community edited and thus might not be correct. jesus christ i need a lie down

That you think Bill Nye is a scientist, is just baffling. LOL.

the Bill Nye comparison was because his show is *intended* to educate. Like, that's the goal of the show. The goal is to have kids learn things in fun ways. MythBusters? Their goal is to make a show that's fun to watch. Neither of those are bad things. But one of them holds *a lot less weight* when the discussion is about *fucking learning things* (hint: it's the show that's intended to educate, not just to entertain). If the discussion was about blowing stuff up in really cool ways, then *obviously MythBusters would win*. But it isn't. The discussion was about someone citing a show with the intention of science, when the show is *not about science at all*. I'm very sorry that my off-the-cuff remark about the only ubiquitous TV show that's even *remotely* scientific offended you so much. jfc what in the world...

This whole question was resolved in 1910 with the first powered seaplane flight.

If the plane's wings can't move through the air and there is no wind blowing, it can't generate lift Isn't it that simple?

Correct (unless it has > 1:1 thrust-to-weight). The problem is the question is ambiguous as to whether that's what we're talking about.

Wheels have nothing to do with the speed of the plane. The only thing the wheels do is keep the plane balanced on the ground. Unlike a car, where the wheels provide both the thrust and the stopping power. With a plane, the wheels don't do much of anything. Thrust is provided by the jet engines, while stopping power is from flaps. Imagine an alternate scenario, with a person in roller blades wearing a harness that has a rope hooked up to a winch. Put this person on a treadmill that matches the speed of the rollerblade wheels in the opposite direction. Now turn on the winch, which pulls the rope. After 10 feet of rope has been pulled, *you have moved 10 feet.* Nothing the rollerblades are doing will have any effect on that. The rope is literally 10 feet shorter, and it is attached to you. There is no other possibility than that you have moved 10 feet. Just like how the rope pulls you regardless of your rollerblades, the jet engines push the plane regardless of its wheels.

You are absolutely correct, and in any real world scenario the plane would take off - but that isn’t what we are talking about. Even in your roller blade scenario the wheels would have to turn faster than the treadmill in order for the person to move forward, or there would have to be slippage. Absent those two mechanisms, the roller blades could not move forward. Since in our (impossible) thought experiment, those things are not occurring - the plane won’t take off. Firing up the engine will cause the treadmill to turn faster.

What happens with the rope scenario? The rope has gotten shorter. "The premise is not valid" is far more valid than "the treadmill matched the wheel speed so even though the rope is 10 feet shorter you still didn't move!"

Very, very bad injuries, I'm assuming. The person on rollerblades would have been yanked off their feet. Otherwise, the force would find the path of least resistance: Probably the human body. The concept of this question as stated is impossible in the real world. You cannot build a setup to this specificity. But when you try, and fail, you do get what you are describing. First rule of machines is you can never build a perfect 1:1 machine in terms of energy usage. You always expend more energy, friction gets involved, etc. It makes thought experiments like this a clusterfuck.

But not you have to take into account the power of the winch. If the treadmill is always able to increase its speed to infinity, the winch cannot pull, unless it is also infinitely powerful, in which case you get an unstoppable force pulling an immovable object

The winch is not on the treadmill, it's in front of it. As the rope gets shorter, the person wearing rollerblades gets pulled forward. Nothing the treadmill does can affect that in any way. Note that the winch does not have to "overpower" the treadmill. All it has to do is pull the weight of the person. Imagine that the winch is on a tow truck designed to pull the weight of cars. And in much the same way -- or rather in exactly the same way -- the thrust of the airplane engines pushes the plane forward. Nothing the treadmill does can affect that in any way.

The rope may not be able to get shorter if the winch cannot impart a greater force than the treadmill can. If there is friction and rolling resistance in this hypothetical, then the treadmill is imparting a force.

The treadmill is imparting negligible force. Imagine standing on a normal, real life treadmill while wearing rollerblades. Kick it up to max speed. You could probably hold yourself in position with a single pinky finger. Even assuming an infinitely fast treadmill imparts a huge amount of force because it's infinitely fast, the contest is between a winch strong enough to move cars versus rollerblade wheels. The wheels literally have zero chance in that contest. From another angle, the winch in this hypothetical gets magic powers like the treadmill gets. It works regardless of any forces opposing it.

>Even assuming an infinitely fast treadmill imparts a huge amount of force because it's infinitely fast, It doesn't impart a "huge amount of force", the force is literally infinite. >The wheels literally have zero chance in that contest. If your winch can overpower an infinite force, which I doubt. >the winch in this hypothetical gets magic powers like the treadmill gets. It works regardless of any forces opposing it. Now all you have to do is compare two infinities to figure out which one is larger, good luck.

I understand that practically a winch is much better and pulling something with wheels than a treadmill is at pushing something with wheels, so it’s hard to visualize, but a treadmill spinning at 14 quadrillion feet per second will overcome a 10 horsepower winch, if there is friction in the wheels. Would probably snap the rope tbh.

No no, you *did* move. The *roller blades though didn’t*, because they *cannot* move. For all intents and purposes the roller blades here act as a completely immovable object attached to your feet.

Except the engine thrust is completely isolated from the treadmill. In this situation it is better to treat the thrust and the treadmill as two isolated systems that never interact.

The treadmill prevents the plane from moving forward, so no air is drawn over the wings, so no lift

Wrong. The treadmill prevents nothing. In order to arrest movement the treadmill would have to act directly on the engines. It doesn't.

There is still a force imparted by the treadmill which opposes the thrust of the engines that is produced by the treadmill. As the plane starts moving forward due to the decoupled thrust from the engines, the treadmill speeds up enough to impart enough rolling resistance to overcome the thrust, and the plane goes nowhere. This assumes the treadmill can spin really, really, really fast.

That means the mechanism that is counteracting the jet propulsion is friction on the wheels. Those wheels would quickly melt.

Yes, but the plane's wings WILL move through the air. The conveyer belt does nothing to affect the plane's forward motion because the plane generates thrust by interacting with the air, not the ground.

I think what you're missing is that, if the plane moves relative to the air while still being on the ground the wheels will spin faster than the conveyor. The experiment indirectly defines the plane as being stationary as that's required for the wheel speed to match the conveyor speed.

IMO the question boils down to "what happens when an unstoppable force meets an immovable object." It sets up a contradiction that has no answer. The "unstoppable force" is what you call View B. The "immovable object" is what you call View A. But rather than choosing between them, I think the question is usually worded is a way that requires you to accept *both*, setting up the contradiction. It is funny to me that you always end up with half the people saying "you don't understand; the force is *unstoppable*. It can't be stopped!" and the other half saying "no *you* don't understand; the object is immovable. It can't be moved!" with neither side being able to see the contradiction.

When an "unstoppable force" meets an "immovable object" the force continues on in another direction.

Agree

The wording of the argument, as I have always seen it, only allows for option A. The premise always (as far as I have seen) includes a statement that claims the belt is capable of matching the wheel speed. Therefore, if it is capable, it will have to destroy the landing gear almost immediately in order for the plane to remain stationary. There is no allowance for option B, since the premise depicts what the conveyor belt is capable of as a statement of fact.

Here is a different way to look at it. Imagine you are in kid's red wagon on a treadmill. At the end of the treadmill is a wall that you can push against. The wheels on the wagon spin freely, we will get to friction in a bit. So, now you start pushing on the wall. The wagon slowly moves forward. The treadmill, in trying to match the wheel speed, starts going. But because you are still pushing, the treadmill has to go faster and faster. So, even if the treadmill is going 100 mph, you can still push against the wall to make it move forward. The questions are, can the treadmill go to infinite speed if there is no friction involved, or how much friction is there in the wheels and at what speed would your pushing not be able to overcome that friction? If there is no friction, then even at infinite treadmill speed, you can still push against the wall to move forward. Which means the plane would always take off. Of course, in real life, there is friction. There is friction on the wheels, but also friction on the treadmill's mechanism. This means the treadmill will have a maximum speed it can go. As for plane wheels, we know jets have no problem taking off at close to 200 mph. I am sure they can go faster and still take off, but I can't find numbers for this. Which means a treadmill would have to go faster than 200mph, at a minimum. And I suspect much faster than that. And don't get confused here. This is talking about the plane's wheel friction resistance, and not the speed of the plane. The plane's speed is relative to the speed of the air, which we assume is not moving. Which means the plane can always push against that air.

View A may seem practical but it is not. It's wrong. View B is the only actual correct view. No matter how much friction the treadmill puts on the wheels, and how infinitely fast those wheels spin, it's not going to stop the plane because the plane is not powered by the wheels. The best analogy I saw the other day when this came up on Reddit was the wheels and treadmil are akin to a plane on ice. The plane would still take off on ice since it's propelled forward by the jets.

Not true, it still imparts a force that acts opposite the thrust of the engines (assuming friction and rolling resistance exist) It’s really small but a treadmill that can spin infinitely fast can apply an infinitely strong force, which is enough to overcome the thrust of the engines and the plane goes nowhere

But no such treadmill can exist, unless you say friction isn't a factor. And if friction isn't a factor, then the wheels of the aircraft are obviously can also spin infinity+aircraft speed fast, therefore the problem is unsolvable as a theoretical-mathematical one, because to "solve it" you have to apply different rules to the treadmill than to the plane, which of course defeats the entire purpose of the scenario.

The assumption in the original question is that the treadmill can always match the wheel speed. If it can always match the wheel speed, any external force pushing the plane forward would cause the treadmill to speed up enough to apply an equal, opposite force. Obviously no such treadmill can exist, but this isn’t a real life hypothetical, it’s a silly physics postulate in which very specific assumptions are made. If you assume a real model for everything except the infinitely powerful treadmill and infinitely strong structures, it is true that the plane goes no where. Obviously again this is not something that could or would ever happen in real life, but that’s not what the question is asking

But even in the hypothetical, no such treadmill can exist, because if the wheels have friction with the treadmill without being able to slip, then their speed will always equal the treadmill speed. If you turn on the treadmill without the aircraft turning on its engines, the wheels will start to spin and the aircraft will remain stationary because the wheels have no friction with their mountings. Wheel speed(W) = aircraft speed(A) + treadmill speed(T). And yet treadmill speed is supposed to counter aircraft speed. Treadmill speed = - aircraft speed. It's supposed to do so by perfectly matching wheel speed. Treadmill speed = wheel speed. You end up with the following equations W = T + A, or we isolate for T= W - A T = - A T = W Now insert, and get T = T + T. This equation is only solvable for T (and therefore W and - A) being 0, but the scenario also requires at least T and W to not be zero. It is therefore impossible to solve, hypothetically or not.

We’re arguing two different things here. The answer becomes different with differing assumptions. The whole point of making my argument in the first place is that there exists a set of assumptions in which the original postulate still makes sense (generally plane on treadmill) but the plane stays stationary. You are absolutely correct in your analysis, if you make the assumptions you are choosing to make, and the assumptions that you are making are much more aligned with the real world than mine. But I was just making my assumptions for fun

It always boils down to the question itself, usually the question is phrased so that the conveyer matches the speed of the plane, sometimes it also refers to the (angular) speed of the wheels. The answer also depends on if you view this as an ideal physical system or realistically. Ideal system - plane speed: The plane takes of. Realistic - plane speed: The plane probably takes of as long as its engines can overcome the added roll resistance and the conveyer is stable enough to not damage the plane. Ideal system - angular wheel speed: The conveyer and the wheels speed up infinitely but the plane still takes of. Realistic - angular wheel speed: The conveyer and the wheels will speed up towards infinity but now it depends on how fast they do that and at what point the wheels or the conveyer break. But my guess would be that the wheels disintegrate way before the plane can reach take-off speed. In no possible scenario stays the plane in the same position.

But even if there is infinite friction between the wheels and the treadmill the plane would still move and therefore take off since a plane doesn't move by turning it's wheels it moves by acting on the air itself, so since the wheels don't actually drive the plane with infinite friction the plane would remain stationary if the plane was turnt off and the treadmill moved theoretically of course

The misunderstanding is understandable. The situation is a bit counter-intuitive from our everyday experience of how cars work. I had a hard time understanding it until I saw the [Mythbusters](https://www.youtube.com/watch?v=YORCk1BN7QY) episode where they tackled this one.

I, and probably many other people, thought the plane would sit on a conveyor belt that matched the plane's speed like the running bands in gyms. But in the video the plane is moving while it's on the ground, thus eliminating the whole purpose of the conveyor belt, which was supposed to keep the plane in one place.

Yeah, because the treadmill would have to spin up to infinity ... it's impossible. In the real world, the plane can take off.

Correct, because the wheels are irrelevant to the plane's motion. The plane generates thrust through its turbines or propellers, which interact with the air, not the ground. The conveyer belt can spin as fast as it bloody likes, the plane doesn't care because it's wheels spin freely.

Because the movement of the conveyor belt, and the wheels is irrelevant to a plane’s ability to take off. What you imagined is impossible. The actual hypothetical has a clear answer. The plane can in fact take off.

God I hate that Mythbusters segment. The question usually says "the treadmill exactly matches the speed of the plane's wheels." What Mythbusters built was a treadmill that goes pretty fast. That's not the same thing. It would be as if I asked "what happens if you drive a car 60 mph on a treadmill that goes 60 mph in the other direction." And you tested it by building a treadmill that only went 20 mph. The car would move forward, but you haven't answered the question.

Are we keeping this realistic, or using spherical cows? Let's assume, no friction and no other forces other than the simple ones. So the wheels have no friction, which means there is no force pushing back on the plane. So, the plane starts to move forward. The treadmill tries to match the wheel speed, but can't counter it since it can't push the plane back. The treadmill goes faster and faster to try to counter it, until it reaches infinite speed and still isn't pushing the plane back. The question, as you interpet it, makes no sense, as the treadmill can't match the wheel speed without friction. So, what happens with friction? Well, if the planes wheels have friction, then so does the treadmill itself. Which means the treadmill will have a maximum speed. Regarding the planes wheels friction, we know that commercial jets take off at close to 200mph. So friction up to that speed is no problem. So, we could make a wheel that has a very large friction factor, and then we could make it so the plane could not overcome this and could not take off. But, we could do the same thing without a treadmill, by just removing the wheels which increases friction by a great amount. Which leaves us to our last scenario, realistic best cases. A treadmill has multiple points of friction from the rollers, the belt, the gears, and several more. The plane only has wheel connection, wheel to air, and wheel to belt frictions. And we know wheels can easily over come 200 mph friction resistances. So you would need a very high speed treadmill. So, could you make a treadmill that is fast enough so that the planes wheel frictions can't be over come? I would say that would be a diificult project, as it is easier to reduce the wheels frictions, than all the different treadmill friction points.

>Are we keeping this realistic, or using spherical cows? >Let's assume, no friction and no other forces other than the simple ones. So the wheels have no friction, which means there is no force pushing back on the plane. >So, the plane starts to move forward. The treadmill tries to match the wheel speed, but can't counter it since it can't push the plane back. The treadmill goes faster and faster to try to counter it, until it reaches infinite speed and still isn't pushing the plane back. >The question, as you interpet it, makes no sense, as the treadmill can't match the wheel speed without friction. Basically, I'm fine with any answer to get to this point. If you make the assumptions you'd normally make for a question like this, you end up with nonsense. Then you can either stop there -- my preference -- or you can start breaking assumptions. Depending on which assumptions you break, you'll get different answers. The problem is when people -- like Mythbusters -- don't acknowledge any contradiction at all.

So the fact that the 'conveyor' that they bodged together does not "exactly matches the speed of the plane's wheels." negates the results? It sounds like you're nit-picking and angry about the details because what you thought would happen was not what happened.

>So the fact that the 'conveyor' that they bodged together does not "exactly matches the speed of the plane's wheels." negates the results? Yes, of course it does. The fact that the treadmill "exactly matches the speed of the plane's wheels" is integral to the question. If you remove that requirement, it's a completely different question.

What if the speeds matched +/- 80%? What if the speeds matched +/- 99.99%? The important fact that you are willingly overlooking is that it does not matter if the speed matches or if one is faster than the other. The conveyor speed is irrelevant to the situation and the plane will take off. Don't bother answering my questions. You just want to be angry that you're not right and you're just going to move the goalposts again.

>The important fact that you are willingly overlooking is that it does not matter if the speed matches or if one is faster than the other. The conveyor speed is irrelevant to the situation and the plane will take off. I'm not overlooking this. I agree with it. Given the problem statement, the plane must take off. What *you* (and Mythbusters) are overlooking is the second half of the problem statement. The treadmill exactly matches the speed of the wheels. For this to be true, the plane cannot be moving. Therefore it cannot take off. That's a contradiction, so the true answer to the question is that the scenario is impossible. You want to resolve the contradiction by simply ignoring half the question, but that's not how this works. > What if the speeds matched +/- 80%? What if the speeds matched +/- 99.99%? I don't know. I'm not super interested in doing the math to find out the threshold where the plane would be able to get enough speed. But it's irrelevant, because that's not what the question says. >Don't bother answering my questions. You just want to be angry that you're not right and you're just going to move the goalposts again. Cool it.

Because that's what happens in the real world. In the real world, the treadmill can't speed up to inifinity. In the real world, the plane will always take off. It's a poor physics question, because the problem is at once saying the plane can't move, yet this is not physically possible. -> https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/

>Because that's what happens in the real world. In the real world, the treadmill can't speed up to inifinity. Correct. Which is why the answer to the question is "that's not possible." Not "the plane takes off because I ignored half the question."

Ok, … I guess I subscribe to the xlcd view that the discussion is pointless either way because the problem is poorly phrased.

I don't think it's poorly phrased. I think it's very intentionally phrased to be contradictory. I actually think the phrasing is really clear.

Could they figure it out mathematically by calculating the difference in forward motion between the 20mph belt and nothing? Or at least come close.

"figuring it out mathematically" is what people have been arguing about for years with this question. Mythbusters purported to definitively answer the question by actually testing it in real life, but they simply didn't.

They did, they tested the actual possible scenario, not the impossible one that only exists in the imagination…

The original scenario is impossible so they tested a *different* scenario which is possible. That didn't mean they answered the original question.

That makes sense. From what I saw described here it definitely didn't sound like MB tested it correctly, but it's not really possible to.

Mythbusters didn't have a magical conveyor belt, though. Obviously in a real world situation, the plane is going to take off. But the premise demands a magical belt that can instantaneously match the speed of the wheels. This means the only outcome is the belt instantaneously spinning to a sufficient speed to destroy the landing gear before the plane takes off.

Why do you have a magical conveyor belt, but realistic wheels? Here is a different way to look at it. Imagine you are in kid's red wagon on a treadmill. At the end of the treadmill is a wall that you can push against. The wheels on the wagon spin freely, we will get to friction in a bit. So, now you start pushing on the wall. The wagon slowly moves forward. The treadmill, in trying to match the wheel speed, starts going. But because you are still pushing, the treadmill has to go faster and faster. So, even if the treadmill is going 100 mph, you can still push against the wall to make it move forward. The questions are, can the treadmill go to infinite speed if there is no friction involved, or how much friction is there in the wheels and at what speed would your pushing not be able to overcome that friction? If there is no friction, then even at infinite treadmill speed, you can still push against the wall to move forward. The wheels, even at infinite speed, have no friction. Which means the plane would always take off. Of course, in real life, there is friction. There is friction on the wheels, but also friction on the treadmill's mechanism. This means the treadmill will have a maximum speed it can go. As for plane wheels, we know jets have no problem taking off at close to 200 mph. I am sure they can go faster and still take off, but I can't find numbers for this. Which means a treadmill would have to go faster than 200mph, at a minimum. And I suspect much faster than that. And don't get confused here. This is talking about the plane's wheel friction resistance, and not the speed of the plane. The plane's speed is relative to the speed of the air, which we assume is not moving. Which means the plane can always push against that air.

The conveyor belt is magical because the premise dictates it. The belt is capable of exactly matching the wheel speed to keep the plane stationary regardless of speed. Xkcd explains it nicely here: https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/ You are part of the #2 crowd, who can't let go of reality, and I'm part of the #3 crowd who is strictly adhering to the rules of the thought experiment.

> You are part of the #2 crowd, who can't let go of reality, Did you miss where I talked about a no friction treadmill and wheels? I covered both #2 and #3. Once again, if the treadmill is magic, why can't the wheels also be magic? As someone strictly adhering to the rules of the question, no where does it say either are magical, or either are realistic. Which means if we make one magic and the other realistic, then the realistic one will fail first, of course. Magic wheels, realistic treadmill, then the treadmill fails, and vice versa. Another way to put this, without friction, what is stopping the plane from moving? And from your link, where he does say the wheels would break the wheels, but immediately after says "The problem is basically asking “what happens if you take a plane that can’t move and move it?” It might intrigue literary critics, but it’s a poor physics question." And I agree, with that interpretation, it is an impossible question. Like asking what happens when a truly unstoppable force meets a truly unmovable force.

You phrase this so pointlessly negatively. "Can't let go of reality"? If it's not applicable to reality then it's a stupid fucking question anyway and not worth discussing.

These takeoff on conveyer belt hypotheticals are dumb because the answer is either A. The plane will takeoff because it moves through air thrust and the wheels will simply spin faster if they need to move forward on a treadmill. Or B. It’s a mythical treadmill that perfectly adjusts to impart enough force backward on the plane to prevent forward thrust from moving it. Which would take impossible amounts of friction and technology that doesn’t exist. Tldr; These scenarios are vague and pointless, one answer is uses real physics and technology (plane takes off) or one answer uses borderline magic (plane doesn’t take off)

For me this is my sticking point as well. The given parameters are basically impossible to perfectly duplicate so this can really only be a thought experiment. An interesting one but not one that seems to stay civil in social media. It would probably be an interesting conversation to see between tipsy scientists even if 99% of it would fly over my head.

Doesn't require magic, just requires both wheels and treadmill to remain still.

It would require the airplane to not be providing thrust. The tire speed = plane speed + treadmill speed. If the plane is providing thrust the tire will move faster than the treadmill unless the treadmill is moving forward with the plane.

Right. Per the question, the treadmill will match the wheel speed. It doesn't suggest that it'll try to match it and fail to. It says it'll match it. So, the entire system must remain at rest. If the engines start providing thrust, the wheels will turn faster than the treadmill, and the stated premise is no longer applicable.

Right so the answer is kind of convoluted. If the tires and treadmill match then no the plane won’t take off because the engine can’t be running. But if it is then the plane can take off, but the tires won’t match the treadmill.

Bingo, and the primary debate is whether the question allows the tires to not match the treadmill or if they fundamentally must match. In the former scenario, the plane can move, and ultimately take off, in the latter scenario, the engines must remain off.

I honestly hate this "thought experiment", because it falls into the camp of "assume a perfectly spherical lizard in a frictionless universe". Sure, if we assume a magical conveyer belt that can instantaneously match the speed of the plane's wheels up to and including infinity in a universe where friction does not exist, it will prevent the plane from taking off, but who the fuck cares? Physics is the study of reality, not the study of parallel universes where those same physics don't even apply the same. And in actual reality, a plane on a conveyer belt will take off.

It won’t prevent the plane from taking off, but as soon as thrust is applied from the engines, the treadmill and wheels will both accelerate to infinity and the plane will still move, breaking the terms of the problem. So the only solution given the magical scenario of the problem is for the plane to remain stationary with zero thrust from the engines. It’s a really stupid hypothetical.

To be fair the premise of the question is broken. As soon as the plane moves forward the wheels turn faster than the treadmill. In that instant the treadmill will turn faster which spins the wheels faster but the wheels will always be speed of treadmill + forward speed of plane. Therefore in that instant the treadmill would have to spin up to infinite speed creating an infinite amount of energy and likely destroying the universe. Therefore the plane would not take off.

Not to mention that if the treadmill spins up to infinite speed, it would impart that speed to the surrounding air through viscous forces resulting in a relative motion between the air and wings of plane, generating (infinite) lift, causing the plane to take off

"take off" might be worded a bit optimistic. With an infinitly strong storm I would call it "blow away"

It’s simple. The wheels and ground surface have absolutely nothing to do with the ability to take off. The thrust comes from the propeller/engines. That’s the only thing that matters.

That's fine, the engine generates thrust which must move the plane forward whatever the wheels are doing. But then what speed will the wheels be turning at just before the plane takes off? Let's say that the plane needs an airspeed of 50mph to take off. If the plane is moving forward at 50mph, then the wheels must be turning 50mph faster than the treadmill. But the treadmill instantly matches the speed of the wheels, so the speeds must be equal. How do we resolve that contradiction? If you tried to do the experiment in the real world, something must fail. Either the wheels can spin faster than the treadmill can actually match, or the treadmill is capable of moving fast enough to destroy the wheels and then it's meaningless to say that the treadmill still matches their speed.

The wheels literally don’t matter at all. The plane could take off without wheels. They are just to reduce drag on the runway. Sea planes don’t have wheels. Planes with skis instead of wheels.

When the belt is matching the speed of the wheels, the wheels can't move forwards from rolling, meaning the only way they could move is if it slides. So essentially the question becomes "could a plane take off if it's breaks are applied"

Or better. Will the plane topple over if the wheels construction is solid rubber without moving parts.

The plane does not need to move forward on the ground to create lift. The treadmill can only affect ground speed. The engines are creating thrust via airspeed. They are sending air through at hundreds of miles per hour which creates lift on the wings. So then the plane will lift off the treadmill and then move forward.

Assuming no wind relative to the ground on which the treadmill is built, it would have to move relative to that ground to generate the lift.

The engines are moving the air under the wings creating the lift. A quick search turned up literal video proving this.

That is not how planes work, otherwise every plane would have VTOL capability. The engines provide thrust which pushes the plane forward, this movement provides the airflow over the wings which creates lift. This is why runways exist.

It's really simple for me now that I've seen it so many times. I drew a free body diagram of a plane and the big question is the force on the wheels. Someone tried to tell me that the friction in the bearings increases with speed, but the whole point of bearings is that it doesn't matter. The conveyor belt is simply unable to exert a meaningful amount of force to the airframe. The engine pulls the plane forward as normal. Many take the idea the conveyor belt stops the plane from moving as a given, so you need to make them question why they assume this is the case. As others have said, it would absolutely be the case with a car so I think that's where it comes from.

The problem statement states, fundamentally, that the treadmill will match the wheel speed. If the plane is moving forward, the wheels are turning faster than the treadmill, so therefore the situation you're describing is no longer relevant to the question. The only way for the wheels to never turn faster than the treadmill is for both to remain completely still. That's the only ambiguity in the problem. How much is the relative speed between the wheels and the treadmill enforced as part of the problem? Are we supposed to treat the system as if it will behave normally, and the treadmill will *fail* to do what we've been told it *will* do? Or do we take the statement that the treadmill *will* match the speed of the wheels as a given, and any situation that causes the wheels to spin faster than the treadmill fail to answer the question correctly because it disregarded that premise? Yes, there are *also* people that think the wheels generate the force to move the plane, but that mistaken belief is not enough to explain all of the arguments over this question.

Thank you for also understanding the whole thing. It says it right in the premise, and people are just happy to ignore it for whatever reason. There's like a middle ground of people who understand part of the problem, who are trying to lump the people who understand the whole thing in with the people who think its going to act like a car.

People assume it because it says it in the rules of the situation "if a conveyor belt *CAN* match the speed of the wheels instantaneously..." Or something similar. It's right in the argument. That means the belt is capable of doing what it says. That means the belt is going to have to destroy the landing gear to keep the plane from moving. Because the argument told us it can.

Does the problem not state the conveyor moves backwards at the same speed the plane moves forwards? If that's the wording then the plane takes off at the same air speed it normally would, but twice the ground speed. I don't think any version of this enforces that the conveyor keeps the plane still

If the wheels physically cannot move the plane forward how does it generate lift?

The force to move forward comes from the propellers, not the wheels. The wheels only provide upwards force to support the plane on the ground, that's why they are wheels and not sleds.

The mythbusters tested this, the plane took off

This question is exactly as stupid as those math problems that boil down to order of operations mistakes. It's a vague, unclear question without enough detail to actually be answered. The only correct response is to ignore it. Everybody participating in the conversation is wrong.

This isn't true. The answer is there and it's unambiguous once you lay out all the facts, the problem is that people who think the plane would not take off simply aren't thinking about how planes work. They assume a plane is propelled by its wheels. If it were, then it's correct that the plane would need to 'drive' forward at the same speed as the treadmill was going backwards, just to stay in one spot. The reality is, the plane is propelled by its engines, and the treadmill has virtually no impact on their ability to push the plane forward. I say virtually no impact, because there is a small amount (comparatively) of friction generated by the wheels spinning on the plane's axles, which is the real force that the plane needs to overcome in order to move forwards. If you've ever held anything on a treadmill, you can replicate this very easily - you'll know that to keep an object with wheels from moving backwards on a treadmill, you only need to hold it with the lightest of touches. You certainly don't need to apply the same amount of force as it would take to push the object forwards at the same speed the treadmill is going backwards. Then if you wanted to move that object forwards on the treadmill, it would only take slightly more effort. The reason is because you're not actually pushing against the backwards motion of the treadmill, you're simply countering the friction generated by the wheels. Likewise, to push the object forward at 1mph on the treadmill, you simply need to use enough force to move it 1mph, plus the tiny amount extra required to overcome the friction. That principle scales all the way up. A plane, on a massive treadmill, is pushed by its engines, not its wheels, and so to move forward it simply needs the normal amount of thrust, plus a bit more to overcome the friction of its wheels on its axles.

This is the best explanation I have seen for this problem. Simple, easy to envision and even test for yourself.

The problem with that is that if the plane is moving forward, the wheels are spinning faster than the treadmill, and that breaks the stated premise that the treadmill matches the wheel speed. Yes, if you think real treadmill and real plane, scaled appropriately, the plane will have no trouble taking off, because as you say the wheel speed has nothing to do with *generating* plane speed. But it will never take off without the wheels turning faster than the treadmill. And thus, it is not the situation being described. The situation as described is, at best, awaiting clarification for if the wheels literally *cannot* turn faster than the treadmill. If they can, then what you describe is what will happen. If they cannot, then the plane cannot move forward with respect to the treadmill, which means it cannot move forward with respect to the ground, and thus it cannot take off without a super strong headwind (which might be at least partially generated by the treadmill itself). If we assume no special contraption has been set up to *keep* the planes wheels from spinning faster than the treadmill, then the only way for this system to work, physically, is for the plane to remain at standstill, and thus the wheels, and the treadmill, will always remain at the same speed, 0. The moment the plane attempts to move by normal means, the wheels will move faster than the treadmill, and the premise breaks down completely.

I can see your thinking, but it's not quite right - even if the speed of the treadmill is pegged to counter the forward speed of the wheels, or the plane, or anything, it won't fundamentally impact the plane's ability to move forward. The treadmill will just speed up, eventually the treadmill and the wheels will be going twice the speed of the plane, and the plane will take off anyway, because the plane is still only overcoming the friction of its own wheels, NOT the speed of the treadmill. Here we get into nuances around tolerances, increases in friction due to heat etc...but let's not forget - this has been demonstrated to work, IRL. Even if one refuses to believe the science, just go on YouTube and watch someone do it. The only way it the plane doesn't take off is if the question has been worded to specifically to break it. And I've never seen this question asked in such a way. Disclaimer, I cannot find OP's link to the question here, so if it's actually an edited version of the question intended to double bluff, then I'll hold my hands up and admit I was wrong, simply because I'm assuming this is the normal version of this question.

>even if the speed of the treadmill is pegged to counter the forward speed of the wheels, or the plane, or anything, it won't fundamentally impact the plane's ability to move forward. If the plane moves forward, the wheels move faster than the treadmill, correct? If that situation is fundamentally not allowed, which per the question it appears not to be, the only way to solve the system is for both wheels and treadmill to remain still, and the only way for both wheels and treadmill to remain still is to not move the plane. A not moving plane cannot take off. Anything logically incorrect in any of that paragraph? *Every* time I've seen the question, it's been worded to specifically say that the treadmill matches the speed of the wheels. You have to assume that what it *means* is that the treadmill will *attempt* to match the speed of the wheels, but will fail to do so. I've never seen the question worded in such a way as to imply that interpretation, but given that we're trying to find some way to resolve a hypothetical, it's a reasonable suggestion. In real life, the treadmill would fail to match the speed of the wheels, and the plane would take off. Per the question, the plane and treadmill must stay still to allow them to remain at the same speed, and the plane will remain on the ground, and nothing will move. Any other scenario is a paradox.

Ok how does it actually move forward? The wheels will be matching the treadmill, lets say 20mph. Then as the thrust of the engines start to move the plane forward... 20.1mph. The threadmill immediately matches the speed so the plane will stay stationary. The closest thing I can think of is a dyno. You put a cars drive wheels on freewheeling rollers. Which is basically a treadmill that immediately matches the speed of the wheels. Drive the car as fast as you want it doesnt go anywhere. Without forward motion no lift. The method of motion wont matter when the thing touching the treadmill is immediately cancelled out by the motion of the treadmill.

The wheels on landing gear are free spinning. If the pilots haven't engaged the brakes, they just spin. All the thrust and forward movement happens to the body of the plane, not on the ground. The engines push against the air behind the plane, equal and opposite reaction, the plane moves forward You could have a 3,000 meter long treadmill instead of a runway and the plane would still take off normally because all the wheels do is spin. They would spin twice as fast as normal, but that's all they would do

I fully understand that the wheels are free spinning. But they do need to rotate while the plane is on the ground for it to move forward. While its on the ground the wheels need to move faster than the ground in order to move forward. If the ground is constantly moving fast enough that it cancels out any forward motion it wont move. Fuck it can you put a plane on a dyno? Free spinning rollers are basically the same thing as a treadmill that instantly matches wheel speed. If it takes off while on a dyno then you got me.

Put a matchbox car on a dyno and move it forward. Does the dyno cancel out your hand? Would the hypothetical treadmill cancel out the forward movement from your arm and keep your hand in place? No, because you're moving the body of the matchbox car and the wheels are just doing their thing Same goes for the plane. The engines push against the air behind the plane and move the body forward, and the wheels are just doing their thing

You're making assumptions beyond what's in the question. Others may make different assumptions. The question is vague. Show me where in the question does it specify how much friction is in the wheel bearings? Or between the wheels and runway? What is meant by "the speed of the airplane? It doesn't specify. You apply your own assumptions.

What question are you talking about exactly here?

The "airplane on a runway" question that has been floating around the internet for something like a decade.

Yeah. And it’s been answered repeatedly. It’s not controversial. The conveyer belt doesn’t mean anything. Only people rejecting reality don’t see that.

What’s meant by wheel speed? You don’t have to reject reality to realize that wheel speed could mean multiple things and to use only one of those meanings to answer the question is making an assumption.

The wheels DO NOT MATTER. They are not providing the thrust. This argument is beyond ridiculous.

None of those things matter. The only assumption that I ever make is that it's a normal plane that would normally take off from a normal runway. That's a fair assumption, surely? there's no trickery here. The point is, if it can take off normally, it can take off from the treadmill. You don't need any more detail than that, it's not a marginal enough call for anything else to be relevant. The issue isn't a lack of detail, it's that people fundamentally do not understand how planes are propelled forwards, and assume it would be the same as a car, which are propelled by their wheels turning. They are wrong. The people who say the plane would take off are correct. The question is clear enough to arrive at that conclusion (usually, anyway - I can only speak to every single version of this question I've ever seen, and admit I have not seen this one).

>None of those things matter. Which is, itself, an assumption you're making beyond what's in the question.

It's not an assumption, it's a statement of fact.

Lol what fact? The question doesn't even make sense in light of actual facts so to assume it is subject to reality is not obvious.

I think you're right insomuch as they are both usually deployed to get reactions and/or troll.

This is a ridiculous response. They are not alike at all.

No, in that the "order of operations" questions have an unambiguous answer, usually. But they're equally as stupid in that there's no point engaging with them.

Order of operations is not ambiguous. Airplane taking off on a treadmill is not ambiguous. They have that in common.

>Order of operations is not ambiguous. It is though. Different people define the order of operations differently. https://youtu.be/4x-BcYCiKCk (I think the airplane question is not ambiguous; I think it clearly sets up a contradictory scenario)

>Order of operations is not ambiguous. Correct. >Airplane taking off on a treadmill is not ambiguous Incorrect. >They have that in common. Incorrect. 1 of 3. You can do better.

Dude. It’s been done in small scale, and with full sized planes. What more could you possibly need?

Yeah. In the real world of course it's possible. The physics isn't complicated. That's not at a what I'm talking about.

I believe the reply to that would be that none of those real-world tests have included the caveat that the treadmill must exactly match the speed of the wheels. For the plane to take off it must be moving forward, which means the wheels are turning faster than the treadmill is moving, which is not allowed to happen based on how the problem is worded.

Exactly. The question demands a non-physical condition which makes it self contradictory and ambiguous.

The wheels are irrelevant. The plane could have no wheels and it would still take off. The wheels are just to keep it conveniently on the ground. See: seaplanes.

Yes

What was the scenario described?

Whether or not an airplane could take off on a conveyor belt that was moving backwards at the same speed as the airplane. It can, by the way. A car would remain stationary, as it relies on it's wheels for propulsion. An airplane uses thrust, making the wheels passive. You could make the conveyor move however fast you wanted, the airplane wheels would simply be spinning at the speed of the conveyor, plus the takeoff speed. Mythbusters proved this years ago.

If the surrounding air is not moving past the plane, what generates lift?

A plane creates lift using Bernoulli’s principle which states that as the velocity of a fluid increase the pressure decreases. When an aircraft moves forward relative to the surrounding air the shape of the wing causes the air above the wing to move faster than the air that goes below the wing. This creates a low pressure zone above the wing and high pressure zone below the wing. The pressure differential causes the high pressure to push the wing upward toward the low pressure and that is how the aircraft achieves flight. An aircraft on a conveyor belt is stationary relative to the air around it therefore there is no wind flowing over and under the wing. Therefore, there is no pressure differential. Therefore, there is no lift and consequently no flight. Source: am an FAA certified aircraft mechanic and I had to learn basic physics of flight in school. Source 2: https://www.grc.nasa.gov/www/k-12/UEET/StudentSite/dynamicsofflight.html#:~:text=Airplane%20wings%20are%20shaped%20to,wing%20up%20into%20the%20air.

"An aircraft on a conveyor belt is stationary relative to the air around it," Begging the question. Of course a plane not moving through the air won't generate lift. But why do you think the plane wouldn't be moving when it's not the wheels driving it forward? The thrust drives it forward; the wheels will just be free spinning at twice the speed they would otherwise if the conveyor weren't moving. Alternatively, the conveyor could be moving the other direction and the wheels wouldn't spin at all. It would not make the plane move forward twice as fast because, again, the wheels aren't propelling the plane.

The question isn’t can an aircraft create enough thrust to move faster than a conveyor belt. The question is if the belt moves at a given speed in one direction and the aircraft is moving at the SAME speed in the opposite direction could the aircraft take off. The speeds cancel each other out and you have 0 airspeed making 0 lift.

The plane can move forward at 10 mph while the conveyor moves backwards at 10 mph. The wheels translate that to spin at the equivalent 20mph (instead of the usual 10mph.) In this scenario the plane is still moving forward, not stuck at 0. That holds true for every velocity until lift off airspeed is reached. The wheels simply spin twice as fast. The friction of the wheels on slowing the plane is minimal

The wheels have nothing to do with it. They are not providing the thrust. It’s quite sad how wrong you are.

Imagine you lock the wheels so they can't spin at all but put a big enough engine on the plane to overcome the friction so you go screeching down the runway like you're in Tokyo Drift. Now do the same thing on a stationary treadmill. Wheel speed is zero so keep the treadmill speed at zero. The plane slides down the treadmill and takes off fine while wheel speed is zero and treadmill speed is zero. The treadmill could be going backwards at a million miles an hour and it wouldn't matter if you're overcoming the friction. Here's another thought experiment. The wind is blowing from the west at 50 mph and an aircraft carrier sails directly into it at 50 mph. A plane on the deck has a takeoff speed of 110 mph. How fast do the wheels need to turn relative to the flight deck for the plane to take off?

Yeah... I'm well aware of how aircraft generate lift. I've been an A&P for literally 20 years. I can certifiably say you're wrong. A car generates forward movement via friction with the ground, which is why it would remain stationary on a conveyor that was moving backwards at the same speed as the wheels. An aircraft generates forward movement via creating thrust. Whether with a propeller or fan screwing itself through the air, or with a pure turbojet creating a high-velocity stream of hot gasses behind itself, an aircraft is not reliant upon friction with the ground to generate forward movement. If you have a conveyor moving backwards at the takeoff speed of an aircraft, the wheels will simply be spinning twice as fast as they would on a stationary runway. Source: Aircraft mechanic that's been fixing planes for 2 decades.

You’re totally misunderstanding the question. It’s not can an aircraft create enough thrust to move faster than a conveyor belt. It’s can an aircraft moving at a given speed in one direction on a conveyor moving at the same speed in the opposite direction take off. If they are moving at the same speed in opposite directions the wings would be stationary relative to the air surrounding them and without air moving over the wings you get no lift.

You're misunderstanding how aircraft work. The engine and wings don't give a shit what the wheels are doing. The conveyor can move at whatever speed it wants to... The plane will still fly. The wheels will simply be spinning at conveyor speed plus takeoff speed.

First off you are saying the engine and wings don’t give a shit what the wheels are doing but then you said that the wheels will just move faster so you are arguing with yourself in your own comment. Secondly and most importantly, if the conveyor is moving at 50 knots in one direction and the aircraft is moving at 50 knots in the other direction the airspeed over the wings is 0. 0 airspeed creates 0 lift. Math doesn’t give a shit what you think.

You do realize that airspeed and ground speed are 2 different things, right? You should've learned this in school. A Cessna 152 can take off at zero ground speed, if it's facing a 50 knot headwind.

Because you would have 50 knots of airspeed over the wings. Thanks for helping me prove my point.

Sigh. You've still got a fundamental misunderstanding of how aircraft work. Let's remove takeoff speed from the equation. Forget flying for the moment, and just focus on ground movement. Conveyor moves 100mph backwards. Plane generates enough thrust to move forwards at a lowly 5 mph. Wheels spin at 105mph, plane still moves forward.

The argument exists because a plane on a conveyer belt still moves forward. The tires simply spin faster since they spin freely. A treadmill that could match this and prevent the motion would be basically magic so it’s a pointless argument.

If a plane could take off on a belt moving at the same speed as the wheels

And which side were you on? It's not obvious in the pictures who you believe to be confidently incorrect.

I believe that the plane will still take off and the incorrect one is who says the plane won’t even after they were presented with proof and facts they still thought they were right

I'm assuming the discussion was about this situation: "Will a plane take off from a runway when the runway is a conveyor belt that always moves the opposite direction and at the same speed as the wheels?" Well, then that makes you confidently incorrect. Unless the plane is capable of VTOL. You see, the hypothetical situation involves an impossible situation, namely the impossible treadmill. If you are to adhere to the rules of the argument, then *by definition* the plane will not take off, simply because the treadmill is given the power to do either one of the following: 1- The treadmill can cause enough friction in the landing gear to keep the plane stationary, which, if we're assuming friction and physics still works in this scenario, ultimately leads to 2- the landing gear have an instantaneous catastrophic failure and the plane is definitely not going anywhere. You can't just ignore the rules of the argument, even if it's impossible.

Sigh. The aircraft is not reliant upon friction with the ground to generate forward movement. A car is, which is why it would remain stationary. An aircraft generates forward movement via thrust, and does not care about what the ground is doing. Aircraft are all absolutely capable of taking off with zero ground speed. With a strong enough headwind, an aircraft's wings will generate enough lift to leave the ground. This is why small aircraft are tied down when they're not being flown, as a sufficiently windy day will toss it across the tarmac. For example, a Cessna 152 needs about 50 knots of airspeed to take off. If it's taking off into the wind (they usually try to do this), and that wind is moving at, say, 30 knots, the plane only needs to move 20 knots relative to the ground, in order to take off. Aircraft can even fly backwards, if the headwind is stronger than their stall speed. Piper Cubs are perfectly capable of this.

Yeah, but none of that is part of the original conversation.

That's the entire crux of the original conversation.

Wind speed is not part of the original hypothetical situation, therefore not relevant.

Aircraft are not reliant upon the ground to generate forward movement. The conveyor can move at whatever speed it likes, the aircraft will still pull itself through the air. The wheels will simply spin at conveyor speed, plus aircraft speed. If the conveyor moves at 100mph backwards, and the aircraft generates enough thrust to pull itself 5 mph in the forward direction, the wheels will be spinning at 105mph, and the aircraft will still move forward.

Maybe we can’t ignore the rules of the argument, but we should just ignore the argument all together because it’s pointless. A treadmill that could achieve that is pretty much magic so the scenario doesn’t really mean anything

It's not against the laws of physics or anything for there to be a large, fast treadmill. It's a thought experiment.

It’s impossible for the treadmill to “match” the speed of the tires. The tires move freely, so they spin at airplane speed + treadmill speed. If treadmill speed is 50 mph and the planes airspeed is 0 the tires spin at 50 mph. If the treadmill is at 50 mph and plane airspeed is 50 mph, tire speed would be 100 mph. If the treadmill speed is -50 mph and the plane airspeed is 50 mph the tire speed is 0 mph. It’s a bad thought experiment because to say the airplane won’t move requires impossible rules.

Brace the rear of the plane. The plane can't roll backwards, so the wheels will spin as fast as the treadmill runs.

Yes I already covered that. I’ll rephrase. Except when the plane is stationary on the treadmill, the tires will never spin at the same speed at the treadmill. The plane will takeoff because the wings don’t care what the tires are doing.

Absolutely. The argument is certainly impossible and pointless, but the "lol, the plane will definitely take off" crowd is confidently incorrect.

Mythbusters literally did this https://youtu.be/YORCk1BN7QY The plane doesn't care about the wheels as long they're spinning. Plus the whole point of wheels is to reduce the friction between the ground and the thing on top. If the plane has a takeoff speed of 50 kts and the conveyer belt is moving backwards at 50kts the wheels would be spinning twice as fast but the plane still takes off. The wheels spin as fast as they need to for the plane to take off

Mythbusters didn't have a magic treadmill that can instantaneously match the speed of the wheels. I'm not talking about what would happen in real life. I'm talking about the original hypothetical situation. "The treadmill can exactly match the speed of the wheels." That sentence alone means two things 1- the treadmill is magical and impossible. 2- the plane isn't taking off. That's it. There's literally no more to the discussion. I don't care what mythbusters did, because they weren't working with an impossible treadmill.

"matches the speed of the wheels" What does this mean? Does it match the speed of the aircraft or the rpm of the wheels. If it's the first it can still take off. Also even if the treadmill was spinning at 1000mph the plane would eventually take off. It would just be like there was a 1000mph tailwind.

I wouldn’t say they are wrong since it’s just a bad scenario. In the real world the plane absolutely will take off because the treadmill can’t match the tire speed and have enough friction. Since the tires spin freely if the plane has the thrust to move forward the tire will simply spin faster to allow this. So the treadmill would speed up to catch up, but then the tires simply speed up even more and the plane moves forward. Making it a rule that that plane can’t move forward would mean it can’t takeoff but is also just a made up principle that holds no bearing in the real world.

Yes, but that's literally the only rule of the original argument. "The treadmill can magically match wheel speed." Bringing "real life" back into the argument negates the question entirely.

But it can’t match tire speed. The tires would spin at the normal takeoff speed + conveyer belt speed. So this isn’t even a physics problem it’s just “hey guys in this made up scenario where I change the rules of physics, things happen the way I chose them to happen” It’s just made up nonsense at that point.

Except the conveyor belt doesn't affect the plane. The wheels of a plane don't move the plane. The propeller moves the plane. Or whatever engine it has. There is no power connecting the wheels to the motor. The wheels are a part of the breaking system, but not all of it

The plane won't take off, because there is no lift. Air needs to be moving past the wings at speed for the plane to take off. Just the wheels turning isn't going to do it.

Are we talking actual physics, or "thought experiment" physics? Another poster in this topic posted a good explanation of the actual physics, and I'm going to paraphrase it here: Imagine an RC car on a treadmill. The treadmill will automatically increase its speed to match the wheel speed of the car. Give it more gas, the treadmill accelerates to match. Car remains stationary. Wheel speed equals treadmill speed. Now, instead of the motor inside the car, use your finger to hold the car in place on the moving treadmill. Now push the car up the treadmill. You're able to push it, right? In this case, wheel speed equals treadmill speed PLUS the speed at which you're pushing it. Increase the treadmill speed. Can you still push the car up the treadmill? Yes, yes you can. This is how airplanes work. An outside force acts on the body, and the wheels are just along for the ride. This is the answer if we're assuming actual physics. Anything else is not possible in the real world.

I'm not a math guy, but can someone explain to me how if the airflow is zero to start with how can the plane generate lift if the thrust (assuming there is friction) is countered by the wheels? If there is no friction then how could the plane gain lift if the air is just moving around it freely?

Pilot gets out qnd starts blwing into the wings, air from pilot blowing hits the wings, lift generated ... easy solution

This is annoying every time it’s posted, but always interesting to me how many people think of this scenario incorrectly. A lot of people just can’t grasp that the wheels are not what’s propelling the plane forward.

Yeah there’s a real lack of critical thinking. What about seaplanes or arctic planes with skis?

It is the wording of this hypothetical that is confusing everyone. The spirit of the hypothetical is that a treadmill keeps the plane stationary. Planes can only fly if air is moving over the wings to create lift. The only way a stationary plane can take off is if there is enough wing moving over the wings to create that lift. It is rare and I have seen video of it happening but that is usually after someone has really screwed up.

When we think of a moving vehicle we always think of the wheels being powered, thus their speed limited by the motor. But what if they could spin as fast as they wanted with nothing but the frictions of the bearings acting on them? It is the of the air being moved by the propeller that powers the aircraft, thus the treadmill has no effect on the aircraft's speed, allowing it to achieve lift.

Just counter it by asking how a plane can fly east? The earth rotates (at the equator) faster than any non-military aircraft can fly, so how can we still fly east if the treadmill is a thing?

You can argue this any way you want but with your argument the earth rotates with its atmosphere and not without. That means that the ground moves at mostly the same relative speed as the air. The plain does in fact not fly "east" if you look at it from a universe standpoint. It just gets carried by the earth. Like a bug running on a rolling basketball against the spinning motion.

Here is where I always see the confusion. A plane doesn't need to move forward to create lift. Lift is what keeps the plane in the air, not ground speed. The wheels are free spinning so the treadmill will keep the plane in place until it's engines create enough lift. First the plane will lift off the treadmill and then it will immediately begin moving forward through the air.