A jet plane on a large treadmill

[Svengali]

The mile behind club?

[jono]

The mile behind club?

Well done sir

[stfu&gbtw]

Good plan, but hopefully the pilot won't be in the bathroom with you so I'm not sure how you're gonna see the look on his face.

I always wondered why those guys look at me so funny... I even courtesy flush sometimes...

No idea what I'd do without you guys.

[iceman]

I'm just trying to keep it real. Little bit of fact-checking and shit.

[jono]

Also conceded that the treadmill could theoretically oppose the thrust from the jet engines (up to the weakest interface). Just because it could, I'm not sure it would. Not as the question is worded. In a calculus world, maybe, but as described, there isn't a way for the system to ever begin to move.

I think once you waste enough time pondering the impossible to get this deep into it there is an intuitive sense that such a system would be unstable if it moves. IOW, we expect the speed to diverge from anything stable to infinity. That's not based on a simple view of the problem statement, but I think it's accurate--I don't think the system is stable in the sense of being self-restoring/correcting, and that's intuitive without proof.

A perfect control system can be imagined to correct an unstable system, of course, but imperfect control systems can also be built to stabilize them. Unstable aircraft are a great example where a controller has to predict the result of current conditions rather than only waiting for feedback and reacting. Jong Lafitte noted last page that this works with a little cooperation from the pilot. It also works if the controller is programmed to sense current conditions (and immediate future results of them) based on present and very recent conditions (to discern what the pilot is doing in case he's less cooperative--maybe STFU skipped the courtesy flush or something).

I don't remember how it was done, but many years ago I was required to write a program that would allow a motor to balance an inverted pendulum. Think of a Segway but a little simpler as I recall. Happily, all I remember about it now was that the laws of motion for an inverted pendulum can be described using differential calculus and terms from the equations were used to drive the controller. It worked, even though nothing it was built from was perfect.

So I don't know how short it could be or how low on power (if plane thrust is the minimum with a perfect controller, you'd need more in reality) but I think you could actually build a very short (hopefully scaled down) version of this that would work without needing infinite power or a highly cooperative pilot (although that would help, too). Some industrious professor of engineering is probably planning to torture his students with it already.

Strong points about how people solved the first one; lot of ways to get there and as Steve pointed out, it's a thought experiment, so maybe that's the point. I'd prefer to think in the PR it's a canvas for ever better jokes about the resulting cognitive dissonance, but I'm happy to contribute to the canvas if I can't find paint.

[stfu&gbtw]

I'm just trying to keep it real. Little bit of fact-checking and shit.

I always thought it was weird they called it a "jump" seat, but figured that's why there isn't a hole in it.

[mcsquared]

I think once you waste enough time pondering the impossible to get this deep into it there is an intuitive sense that such a system would be unstable if it moves. IOW, we expect the speed to diverge from anything stable to infinity. That's not based on a simple view of the problem statement, but I think it's accurate--I don't think the system is stable in the sense of being self-restoring/correcting, and that's intuitive without proof.

A perfect control system can be imagined to correct an unstable system, of course, but imperfect control systems can also be built to stabilize them. Unstable aircraft are a great example where a controller has to predict the result of current conditions rather than only waiting for feedback and reacting. Jong Lafitte noted last page that this works with a little cooperation from the pilot. It also works if the controller is programmed to sense current conditions (and immediate future results of them) based on present and very recent conditions (to discern what the pilot is doing in case he's less cooperative--maybe STFU skipped the courtesy flush or something).

I don't remember how it was done, but many years ago I was required to write a program that would allow a motor to balance an inverted pendulum. Think of a Segway but a little simpler as I recall. Happily, all I remember about it now was that the laws of motion for an inverted pendulum can be described using differential calculus and terms from the equations were used to drive the controller. It worked, even though nothing it was built from was perfect.

So I don't know how short it could be or how low on power (if plane thrust is the minimum with a perfect controller, you'd need more in reality) but I think you could actually build a very short (hopefully scaled down) version of this that would work without needing infinite power or a highly cooperative pilot (although that would help, too). Some industrious professor of engineering is probably planning to torture his students with it already.

Strong points about how people solved the first one; lot of ways to get there and as Steve pointed out, it's a thought experiment, so maybe that's the point. I'd prefer to think in the PR it's a canvas for ever better jokes about the resulting cognitive dissonance, but I'm happy to contribute to the canvas if I can't find paint.

Holy fuck. What are you even saying? Differential Calculus? The plane will take off. The wheels will be spinning twice as fast as the plane is actually moving forward until it takes off.

[jono]

We were discussing a different question.

[MagnificentUnicorn]

Actually I think the original question was about matching wheel speed but some moron screwed it up. At the very least, both questions have been rattling around since 2005.http://www.straightdope.com/columns/...plane-take-off Either way the questions pose a similar problem.

[Jong Lafitte]

Now I think its a trick question. The conveyor CAN'T be "exactly" the same speed as the plane, ever, due to the nature of the plane. An imaginary perfect treadmill might be able to speed up so fast and to such a speed as to prevent the plane from moving forward as thrust increases, but that speed would need to be FAR greater than the speed that is set to only, as the question sets forth, EXACTLY the speed of the plane, so, its not matching the speed of the plane in that instance, its spinning fast enough to generate enough friction to keep the plane stationary.

example: The plane is at a thrust that would generate 30mph ground speed on the gear and the treadmill is moving at 30mph in the opposite direction so the plane is stationary.

so hold that thought and imagine that you paint on your rollerblade jorts and you get to the gym with a wheelchair on a skateboard on your rollerblades and you get on the treadmill somehow. Set the speed to low and notice how easy it is to move forward towards the front of the treadmill just by pulling on the hand rails. It is not that much harder to do this at full speed either.

This is because friction does not increase in direct proportion with speed. It increases very little with speed (notice how even with wind resistance, you car speeds up as it rolls downhill in N) so its pretty easy to pull yourself forward even at high speed.

So back to the plane that's on the conveyor going 30. It is going to take very little thrust to keep it at 30. Now, lets say the pilot gives it some more thrust. One of two things happens right, the plane moves forward or it does not.

Lets say the conveyor moves up to match the new speed immediately. This cannot stop the plane from moving forward, even if its just a little. Its too easy for the plane to move forward at such a low treadmill speed. But, if it moves forward, then the belt isn't really matching the speed of the plane at that point is it, as the plane has moved forward, thus clocking more distance than [the sum of the rotations of the length of the] belt itself over the same amount of time.

So what about the magical treadmill that can spin fast enough to generate enough friction to keep the plane stationary regardless of thrust? Well, then it has to spin so fast that its no longer "matching the speed of the plane" to achieve that result. In that case, its a question of whether a conveyor at any speed could do that and that's not the question.

So, the plane will always move forward against the belt unless the belt can spin faster than the speed of the plane, which the question does not allow for. However, the belt can never truly EXACTLY the speed of the plane (without pilot cooperation), the plane will always have the jump because there is not enough friction to allow the belt to match the speed exactly, so the plane will take off unless the pilot is trying to keep the plane stationary on the treadmill.

[MagnificentUnicorn]

Now I think its a trick question. The conveyor CAN'T "exactly" the same speed as the plane, ever, due to the nature of the plane. An imaginary perfect treadmill might be able to speed up so fast and to such a speed as to prevent the plane from moving forward as thrust increases, but that speed would need to be FAR greater than the speed that is set to only, as the question sets forth, EXACTLY the speed of the plane, so, its not matching the speed of the plane in that instance, its spinning fast enough to generate enough friction to keep the plane stationary.

example: The plane is at a thrust that would generate 30mph ground speed on the gear and the treadmill is moving at 30mph in the opposite direction so the plane is stationary.

so hold that thought and imagine that you paint on your rollerblade jorts and you get to the gym with a wheelchair on a skateboard on your rollerblades and you get on the treadmill somehow. Set the speed to low and notice how easy it is to move forward towards the front of the treadmill just by pulling on the hand rails. It is not that much harder to do this at full speed either.

This is because friction does not increase in direct proportion with speed. It increases very little with speed (notice how even with wind resistance, you car speeds up as it rolls downhill in N) so its pretty easy to pull yourself forward even at high speed.

So back to the plane that's on the conveyor going 30. It is going to take very little thrust to keep it at 30. Now, lets say the pilot gives it some more thrust. One of two things happens right, the plane moves forward or it does not.

Lets say the conveyor moves up to match the new speed immediately. This cannot stop the plane from moving forward, even if its just a little. Its too easy for the plane to move forward at such a low treadmill speed. But, if it moves forward, then the belt isn't really matching the speed of the plane at that point is it, as the plane has moved forward, thus clocking more distance than [the sum of the rotations of the length of the] belt itself over the same amount of time.

So what about the magical treadmill that can spin fast enough to generate enough friction to keep the plane stationary regardless of thrust? Well, then it has to spin so fast that its no longer "matching the speed of the plane" to achieve that result. In that case, its a question of whether a conveyor at any speed could do that and that's not the question.

So, the plane will always move forward against the belt unless the belt can spin faster than the speed of the plane, which the question does not allow for. However, the belt can never truly EXACTLY the speed of the plane, the plane will always have the jump because there is not enough friction to allow the belt to match the speed exactly, so the plane will take off unless the pilot is trying to keep the plane stationary on the treadmill.

Never go full retard.

[Jong Lafitte]

Never go full retard.

Interestingly, that link you posted earlier I didn't see before I wrote all that out but that poster has a pretty good explanation. In the OP question, as that link points out, there is a paradox because it says it is set to match the planes speed exactly.

[GeezerSteve]

IMO the only reasonable interpretation of the original hypothetical is that the treadmill will match the speed of the airplane's wheels. Yes, it could have been written more artfully.

[jono]

Interestingly, that link you posted earlier I didn't see before I wrote all that out but that poster has a pretty good explanation. In the OP question, as that link points out, there is a paradox because it says it is set to match the planes speed exactly.

Exactness (or lack thereof) doesn't change the outcome, only the details. If the plane's speed is matched it takes off and if the wheels' speed is matched it does not. If the treadmill is off by +/-10% or something the answers are both still the same.

[MagnificentUnicorn]

Exactness (or lack thereof) doesn't change the outcome, only the details. If the plane's speed is matched it takes off and if the wheels' speed is matched it does not. If the treadmill is off by +/-10% or something the answers are both still the same.

A 747's tires have an rpm of roughly 916 and make roughly 15 revolution per second at a takeoff speed of 180 mph. Would the wheels have a higher or lower rpm if the wheel speed or the plane speed were matched with the treadmill speed?

[Mustonen]

This is because friction does not increase in direct proportion with speed.

No, but force from inertia increases with acceleration. Jump on that treadmill when it's already spinning, and you'll be moved in the direction the treadmill is spinning, even if the hubs are friction free.

[jono]

A 747's tires have an rpm of roughly 916 and make roughly 15 revolution per second at a takeoff speed of 180 mph. Would the wheels have a higher or lower rpm if the wheel speed or the plane speed were matched with the treadmill speed?

Depends? If you take the easy way out by sticking the latter plane up on blocks and spinning the wheels backwards by whatever means possible until the treadmill launches the plane, 15 rps. If you try to beat the treadmill I'm guessing the tires explode somewhere between 500-800 mph, which is a lot faster than in the OP version (~30 rps).

[MagnificentUnicorn]

Depends? If you take the easy way out by sticking the latter plane up on blocks and spinning the wheels backwards by whatever means possible until the treadmill launches the plane, 15 rps. If you try to beat the treadmill I'm guessing the tires explode somewhere between 500-800 mph, which is a lot faster than in the OP version (~30 rps).

What the fuck are you talking about? I'm not sure. Are you assuming that the treadmill is operating in the usual fashion, surface of belt moving in opposite direction of thrust, or the belt is moving in the same direction? Are you assuming that the tires are somehow coupled with the belt surface? It's already been shown in a physical experiment that the usual idea of a treadmill has no affect on a planes ability to take off.

If the belt matches the speed of the wheels, then the speed of the wheels is not affected. Think of a pitching machine or maybe a pasta roller. What I want to know is if the belt of the treadmill matches the ground speed of the plane will the wheels spin faster or slower than the wheel speed matching treadmill. Either way the plane takes off.

[stuckathuntermtn]

I picked a bad week to quit sniffing glue.

[jono]

What I want to know is if the belt of the treadmill matches the ground speed of the plane will the wheels spin faster or slower than the wheel speed matching treadmill. Either way the plane takes off.

Oh ok, so you're bringing in a third question. My response assumed the conditions of question number two where treadmill speed = - wheel speed, and you're saying the treadmill goes the same way and speed as the plane regardless, is that right? If that's the case the wheels don't spin. (Assuming, as usual, that someone or something makes the treadmill go that speed and direction).

[johnnyg82]

Planes wheels are not driven.

Put a Back to the Future Delorean on a treadmill though, would it still travel through time?

[MagnificentUnicorn]

Oh ok, so you're bringing in a third question. My response assumed the conditions of question number two where treadmill speed = - wheel speed, and you're saying the treadmill goes the same way and speed as the plane regardless, is that right? If that's the case the wheels don't spin. (Assuming, as usual, that someone or something makes the treadmill go that speed and direction).

No, I'm not. I'm wondering if that's your assumption, read again. The two basic treadmill questions are nearly the same. In which version will the planes wheels spin faster, ground speed matching treadmill or wheel speed matching treadmill? Given a wheel rpm of 916 at takeoff of 180 mph under real world conditions.

[MagnificentUnicorn]

Planes wheels are not driven.

Put a Back to the Future Delorean on a treadmill though, would it still travel through time?

Yes, I think we've all agreed on that.

[jono]

No, I'm not. I'm wondering if that's your assumption, read again. The two basic treadmill questions are nearly the same. In which version will the planes wheels spin faster, ground speed matching treadmill or wheel speed matching treadmill? Given a wheel rpm of 916 at takeoff of 180 mph under real world conditions.

The wheels in the OP question have been shown to spin about 2x normal. In 2016 version from page 31 the wheels go the same speed as the belt but in the opposite direction, meaning if the wheels try to roll forward the belt goes just as far in the other direction. In that version the plane never moves but the wheels are free to spin up to any speed and the treadmill will match them. As such, they will go more than 2x the normal speed, assuming they don't fly apart. I'm guessing they would fly apart at 3-4x normal landing speed, but that's entirely a guess.

[Jong Lafitte]

Same RPM. Huh. I dunno if its what you're getting at but I just realized I've been thinking of the 'speed' matching feature of the treadmill as matching the 'speed' of the plane as it relates to the surface of the belt. Really, it seems that the belt in the question is only set to match the same speed (in the other direction) as the speed of the plane as it is calculated by how fast the wings are moving relative to the ground. The plane gets off even easier.