A jet plane on a large treadmill

[GeezerSteve]

why are you focusing on the wheels?

Because someone changed the original hypothetical by adding an impossible set of assumptions, bringing the limits of the wheel bearings into play. His new set of assumptions vitiates the essence of the original hypothetical, i.e., a test of whether the solver can distinguish propulsion via thrust vs. driven wheel. IMO, he should have started a new thread.

[Harry]

Proof that the U.S. school systems are failing the country.

I know, right ?

I'm sure in China most 2nd graders could solve this question easily.

[jono]

Because he changed the original hypothetical by adding an impossible set of assumptions, bringing the limits of the wheel bearings into play. His new set of assumptions vitiates the essence of the original hypothetical, which was a pretty clever test of whether the solver can distinguish propulsion via thrust vs. driven wheel. IMO, he should have started a new thread.

I didn't change anything. And I pretty politely pointed you to grskier's post when you first suggested that I had. He probably could have started a new thread but in the tradition of this thread it all seems oddly appropriate.

Interesting that you ascribed the change to an attempt to win an argument, but I guess that makes sense from your perspective. In fields where this kind of discussion is the norm it's not about winning, it's about getting the right understanding of reality. (Or imagined reality, in this case.) No offense to you personally, but we need less lawyers.

[wyeaster]

is this the physass room? i'm not smart and don't know shit about aviation but i would have thought no air flow over the wings no lift.

[GeezerSteve]

I didn't change anything. And I pretty politely pointed you to grskier's post when you first suggested that I had.

Okay mom. I changed "he" to "someone." My point is that the original hypothesis presents a valid test re whether someone can intuitively distinguish propulsion by thrust vs. wheel driving. Whomever decided to abandon that assumption killed the elegance of the original hypothesis and invited a pissing match.

No offense to you personally, but we need less lawyers.

Fewer? Of course you intend that as an insult. Duh. Maybe we need fewer anal retentive know-it-all engineers or would-be engineers who junk up thought experiments by adding assumptions that kill the point of the original.

[jono]

I don't intend that as an insult. If you're good at what you do enjoy. My observation is that the perspective that says every discussion is an argument to be won is more common than I'd like. That's just my opinion.

Your take on the original question's elegance is interesting as well. It's as simple as you describe if you ignore several slightly messy things, sure. But in the physics realm the question also requires determining what can legitimately be ignored and what can't. Your description would skip that step. Again, not an insult, just an observation on the differing perspectives.

[MagnificentUnicorn]

Yes, if treadmill speed=-plane speed, which was the original question. On page 31 and some 11 years on grskier brought a new question: what if treadmill speed = -wheel speed? That's different because if the wheels can spin fast enough to keep plane speed at zero that's what happens. Until they explode.

Somehow both questions cause difficulty.

Yeti did say equivalent to 60 mph wheel spin, indicating wheel speed. You say you're not being argumentative and in your circles you just look for reality. That's horseshit, you're being argumentative. You're either the smartest dumb guy in the room or you know you're wrong and you're just trying to argue your way out of an impossible problem. Or you're a troll.

[MagnificentUnicorn]

Your take on the original question's elegance is interesting as well. It's as simple as you describe if you ignore several slightly messy things, sure. But in the physics realm the question also requires determining what can legitimately be ignored and what can't. Your description would skip that step. Again, not an insult, just an observation on the differing perspectives.

The whole thing, the original question and the new one are messy, just thought experiments and not possible unless the Chinese decide to build something like this to prove you wrong.

[mcski]

Yeti did say equivalent to 60 mph wheel spin, indicating wheel speed. You say you're not being argumentative and in your circles you just look for reality. That's horseshit, you're being argumentative. You're either the smartest dumb guy in the room or you know you're wrong and you're just trying to argue your way out of an impossible problem. Or you're a troll.

He'd find a way to fuck up the Aristocrats joke too.

[jono]

The whole thing, the original question and the new one are messy, just thought experiments...

Agreed.

If you ask 10 physics professors to answer these questions the first thing they will all do is draw free body diagrams. As such, at least 9 out of 10 would arrive at the same conclusions to each and if one first he'll readily understand why.

When people try to answer these questions by different means they often get different answers. Some have the tools to address all aspects of the question and some don't. I noted earlier that a lot of people with a rudimentary knowledge of physics don't use torque often enough to remember that part, for example, which worked fine on the original (since wheel acceleration could be neglected) but fails on the second (where wheel acceleration matters).

I'm not trolling and I'm not the smartest person in the room, I'm just the only one left willing to discuss it. DJSapp's last post pretty much aligned with the conclusion I came to, and in fact I only figured it out by reading through his posts and letting my understanding of it evolve from there. That's typical of a discussion among students of physics and it works here despite the noise. Neufox pretty much nailed the thing immediately while drunk and buzzing on a cigar. He deserves another. For some reason I sought to explain the reasoning to Mustonen since he understood the first question and seemed to have trouble with the second. I'm not sure why that should be offensive but it's the PR, so in the interest of full disclosure I probably spend less time trying to understand why you're offended than you spend trying to understand some obscure physics riddle.

[jono]

I have a new perspective on this; if the treadmill could operate at infinite speeds with infinite acceleration, but the plane was limited by normal material / bearing capabilities the wheel bearings or wheels would fail, exploding or melting before the plane ever moved forward an inch. In a perfect treadmill system the wheels would almost instantaneously accelerate to failure speeds, rendering it .

If the wheels materials were made perfect and able to accelerate to infinite speeds it would still sit in place if friction still existed.

Remove friction and the plane takes off.

Im drunk / buzzing on a cigar.

This is the correct answer to what if the treadmill speed = -wheel speed. The only thing I've been able to add to it is that the actual force applied by the treadmill won't need to be infinite, since it never needs to exceed the thrust of the plane. Still, stating the assumption as he did is correct.

[GeezerSteve]

Your take on the original question's elegance is interesting as well. It's as simple as you describe if you ignore several slightly messy things. . . .

That can be said about virtually every thought experiment. IMO the original hypothetical is indeed very effective in testing the solver's intuitive awareness of fundamental mechanics, more specifically thrust vs. wheel-driven propulsion. Cf., the 1985 Microsoft employment interview question "why are man hole covers round?," which is an effective test of intuitive spatial awareness.

[jono]

Yeti did say equivalent to 60 mph wheel spin, indicating wheel speed.

And he also said 30 mph treadmill speed, which indicated that he was answering the OP question rather than the 2016 version, hence my response to that.

[jono]

That can be said about virtually every thought experiment. IMO the original hypothetical is indeed very effective in testing the solver's intuitive awareness of fundamental mechanics, more specifically thrust vs. wheel-driven propulsion. Cf., the 1985 Microsoft employment interview question "why are man hole covers round?," which is an effective test of intuitive spatial awareness.

Ok, so how would your perspective change if I pointed out that the source of thrust doesn't change the answer to the OP question?

If the plane applied thrust by driving its wheels and the treadmill speed = - plane speed the plane would still take off at normal plane speed which would be half its wheel speed. I'm not making that up, it's absolutely true and can be proven. A lot of people who correctly ignore the doubling of wheel speed make that leap by thinking of where the force comes from but it actually has nothing to do with the problem.

The thought experiment of the first question is a bit more about figuring out that the first question is not actually the second question. Not ironic then that the second question is simply the converse.

[MagnificentUnicorn]

And he also said 30 mph treadmill speed, which indicated that he was answering the OP question rather than the 2016 version, hence my response to that.

Actually the "new" question you are referring to has been around since at least 2008.https://blog.xkcd.com/2008/09/09/the...amn-treadmill/
It's a pretty good read and even using FBDs you can come to different conclusions based on your own assumptions, which everybody does.
If you assume that the wheels are free spinning and that the treadmill operates in the normal fashion(belt moving opposite of forward motion) and that it matches wheel rpm, the plane will take off. Theorizing that the rpm of the wheels will cause them to burn up isn't relevant because the plane will never go fast enough for that to happen before it takes off. It's not much different than a float plane or a plane on skids.

Of course if you make other assumptions you can conclude that the plane would remain stationary but most of these are physically impossible because a planes wheels only roll forward as the plane moves forward. So if you imagine a scenario like that the wheels will never spin. It's like when a pilot does a run up before take off, you can engage the brakes and increase thrust and the plane won't move. Release the brakes and the plane moves. The question asked is about a conveyor belt matching wheel speed. There can be no wheel speed if the plane isn't moving.

[old goat]

A treadmill in a gym works because when you run your forward propulsion is created by your feet pushing against the ground. On a treamill this backward push is balanced by the backward motion of the tread, so you don't move (unless you do like me and set your mother's treadmill at the speed you ran in college and almost get thrown through the living room window). With a prop or jet propelled plan the treadmill has virtually no effect--no matter how fast the treadmill goes the plane will still move forward--slowed minimally by the rolling resistance of the wheels. So the original thought(less) experiment is impossible. But for the sake of argument let's put wings on a wheel powered land speed record car--the record is 400mph. If the treadmill moves backward at 400 mph the car/plane won't move, there will be no movement over the wings, and the vehicle won't take off, which is a good thing becase if it did and the wheels left the treadmill it would crash.
Anyone who doesn't understand this should look up Bernoulli's principle and "airfoil".
Anyone who thinks that jets work by pushing against the air should look up Newton's third law of motion. (After all--rockets work in space where there is no air, and the only difference between a jet and a rocket is that the rocket has to carry it's own oxygen while the jet uses the oxygen in the air).
BTW--a steeply climbing jet uses a combination of lift from its wings and thrust from its engines to climb.

Now here's a question for you aeronautical engineers--if lift is proportional to the square of velocity, how can a plane fly level at different speeds. Is it solely through the action of the elevators or are there other factors?

[MagnificentUnicorn]

Ok, so how would your perspective change if I pointed out that the source of thrust doesn't change the answer to the OP question?

If the plane applied thrust by driving its wheels and the treadmill speed = - plane speed the plane would still take off at normal plane speed which would be half its wheel speed. I'm not making that up, it's absolutely true and can be proven. A lot of people who correctly ignore the doubling of wheel speed make that leap by thinking of where the force comes from but it actually has nothing to do with the problem.

The thought experiment of the first question is a bit more about figuring out that the first question is not actually the second question. Not ironic then that the second question is simply the converse.

Yes it's absolutely true that a plane can take off with thrust provided by a source other than a jet or prop, look at aircraft carrier catapults, but if that's the only source of propulsion the plane won't "fly" for very long. This just goes back to you being argumentative.

[GeezerSteve]

Ok, so how would your perspective change if I pointed out that the source of thrust doesn't change the answer to the OP question? [discussion premised on material change to original assumption omitted]

I used the the term "thrust" in the context of the original hypothetical assumed a jet airplane, i.e., thrust provided by a jet engine.

[jono]

Actually the "new" question you are referring to has been around since at least 2008.https://blog.xkcd.com/2008/09/09/the...amn-treadmill/
It's a pretty good read and even using FBDs you can come to different conclusions based on your own assumptions, which everybody does.
If you assume that the wheels are free spinning and that the treadmill operates in the normal fashion(belt moving opposite of forward motion) and that it matches wheel rpm, the plane will take off. Theorizing that the rpm of the wheels will cause them to burn up isn't relevant because the plane will never go fast enough for that to happen before it takes off. It's not much different than a float plane or a plane on skids.

Of course if you make other assumptions you can conclude that the plane would remain stationary but most of these are physically impossible because a planes wheels only roll forward as the plane moves forward. So if you imagine a scenario like that the wheels will never spin. It's like when a pilot does a run up before take off, you can engage the brakes and increase thrust and the plane won't move. Release the brakes and the plane moves. The question asked is about a conveyor belt matching wheel speed. There can be no wheel speed if the plane isn't moving.

Fair enough, but in the special cases of the questions asked here there is specific information in each that defines which of those assumptions to use. That's the source of confusion once you get right down to it.

[jono]

I used the the term "thrust" in the context of the original hypothetical assumed a jet airplane, i.e., thrust provided by a jet engine.

And I'm pointing out that the difference between that and using "thrust" from the wheels is that when drawing a FBD you would go about it differently. If you were solving it as a simple thought experiment using fourth grade math you wouldn't care where the force came from and you'd get the same answer. What I'm saying is that your interpretation indicates a physics-style solution rather than the simplest thought experiment.

[jono]

Yes it's absolutely true that a plane can take off with thrust provided by a source other than a jet or prop, look at aircraft carrier catapults, but if that's the only source of propulsion the plane won't "fly" for very long. This just goes back to you being argumentative.

Refer to the OP. I'm just answering the question, it's only about takeoff, not flight afterwards. I'm going to go ahead and stop arguing with you about whether I'm argumentative or not though. I think we may use language a little differently because you seem offended and I haven't been trying to insult you. I'm going to have to ask you to show me what you found offensive if I'm going to have a chance to avoid it in the future.

[Jong Lafitte]

A gyrocopter could take off, or not. Also, a helicopter with wheels could take off, or not. The rotor moves the blades relative to the air to generate lift. If you assume that the treadmill set-up can keep the wings of the plane stationary relative to the air, then would not the plane will be deprived of its method of moving its wings relative to the air, thus not taking off? All the theories I've seen that have the plane taking off seem to have the plane overcoming the treadmill and moving forward at some point? Am I missing something? Without the plane moving forward relative to the air, the can't be lift without alternative means, such as redirecting the thrust downward like a Harrier.

[jono]

A treadmill in a gym works because when you run your forward propulsion is created by your feet pushing against the ground. On a treamill this backward push is balanced by the backward motion of the tread, so you don't move (unless you do like me and set your mother's treadmill at the speed you ran in college and almost get thrown through the living room window). With a prop or jet propelled plan the treadmill has virtually no effect--no matter how fast the treadmill goes the plane will still move forward--slowed minimally by the rolling resistance of the wheels. So the original thought(less) experiment is impossible. But for the sake of argument let's put wings on a wheel powered land speed record car--the record is 400mph. If the treadmill moves backward at 400 mph the car/plane won't move, there will be no movement over the wings, and the vehicle won't take off, which is a good thing becase if it did and the wheels left the treadmill it would crash.
Anyone who doesn't understand this should look up Bernoulli's principle and "airfoil".
Anyone who thinks that jets work by pushing against the air should look up Newton's third law of motion. (After all--rockets work in space where there is no air, and the only difference between a jet and a rocket is that the rocket has to carry it's own oxygen while the jet uses the oxygen in the air).
BTW--a steeply climbing jet uses a combination of lift from its wings and thrust from its engines to climb.

Now here's a question for you aeronautical engineers--if lift is proportional to the square of velocity, how can a plane fly level at different speeds. Is it solely through the action of the elevators or are there other factors?

Check out high bypass turbofans.

Planes change their angle of attack at different speeds and airfoil lift coefficients vary with angle of attack. So, the elevators are the control for that.

[mcski]

Xkcd banned this question. Makes sense considering Jono

[east or bust]

Of course if you make other assumptions you can conclude that the plane would remain stationary but most of these are physically impossible because a planes wheels only roll forward as the plane moves forward. So if you imagine a scenario like that the wheels will never spin. It's like when a pilot does a run up before take off, you can engage the brakes and increase thrust and the plane won't move. Release the brakes and the plane moves. The question asked is about a conveyor belt matching wheel speed. There can be no wheel speed if the plane isn't moving.

And this is why calculus would be useful for solving the problem. Because the treadmill changes it's speed instantaneously to any incremental change in wheel speed. When the engines apply thrust the plane will start to accelerate and in turn the wheels will spin. The treadmill matches the acceleration from 0 velocity.