A jet plane on a large treadmill

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Originally Posted by jono

I was thinking that, too, but unfortunately if the treadmill matches the wheel speed it will be locked when you lock the brakes, not freewheeling.

Aaronwright, I was not referring to the OP scenario but to the one that grskier quoted where the treadmill matches the wheel speed. In that scenario wheel speed = treadmill speed so the plane never moves, it doesn't matter how you power it (that issue was resolved on page 2 or something). You can prove the scenario I outlined a little less rigorously/more intuitively if you consider the treadmill's feedback system to be slightly imperfect so that it lets the plane rock forward before responding. In that case the response would be a massive force which would push the plane back (because it would be more than the thrust). Then it would have to correct again, and basically the plane would move fore and aft really slowly as the wheels went faster and faster. Assuming the control is perfect you'd never see the plane move.

Bottom line, if the treadmill is going to keep pace with the wheels it has to keep the plane from rolling forward (because rolling forward means the wheels are going faster than the treadmill). That requires a massive force (equal to the thrust since the only forces acting on the plane are thrust and the wheel bearings) which spins the wheels really fast. If the wheels could handle it they could be spun up to ludicrous speed, but if we assume they're real they just explode.

You can ignore the math if that's not something you're familiar with, I put it there because Mustonen seemed like he'd get it that way better.

I think the more common hangup for this example is that while people are familiar with F = m*a, the torsional/rotational equivalent of T = I*alpha doesn't see much use so most people aren't ready to do anything but neglect the mass of the wheels. That just happens to fail when a very large torque is applied to the wheels.

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The plane needs to accelerate it's ground speed to make the rpm of the wheels faster AND the treadmill speed in relation to the wheel rpm. The treadmill matching the increasing rpm of the wheels because of forward motion can't hold the plane in place because the plane has to be moving forward for the rpm to increase. It will take off before any theoretical maximum rpm of the wheels is ever reached or if it has infinite rpm because the airframe only has to reach a ground speed of 180 mph or whatever for a specific plane. Your scenario only works if planes are propelled by their wheels.

I'm beginning to think you might be just trolling.

You're ignoring the fact that the wheels turn if the treadmill moves, even with no plane speed. Set a stationary plane down on a moving treadmill and go from there, same result. The plane on the treadmill doesn't have to move for its wheels to turn any more than the wheels have to turn for it to take off (assuming airspeed above stall). The treadmill and the thrust provide two halves of a force couple (moment, torque) which spins the hell out of the wheels.

Here's another thought experiment that's sort of tangentially related: Imagine a merry-go-round with nine large humans sitting at the edge in a perfectly balanced array. Digitaldeath and all his soldiers plus seven guys from Montana (only one sheep). So they're sitting in carefully selected locations. You come along and start pushing. How long does it take you to get the outside rail spinning at 20 mph?
Not going to happen instantly, is it? If only you had the thrust of four 747 engines and you could apply 380,000 lbf to the edge in just one spot. Know what would happen? The axle at the middle would break off because you'd be applying both a force and a torque and even if the bearings were frictionless and didn't mind the torque the axle wouldn't take that force.

Full disclosure, I'm only guessing that the 747 axle and bearings would survive until the tire explodes. Because I don't really care.

What I want to know is, how does a pontoon plane take off without wheels?

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Originally Posted by stfu&gbtw

What I want to know is, how does a pontoon plane take off without wheels?

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Same way the (2016 version) 747 does: without wheels, the treadmill doesn't turn at all, so the pontoons send off a lot of sparks as the thing skids along hoping not to start any fires until stall speed is exceeded and the pilot pulls back on the stick. I've never tested it personally, but Mr. Rutan assures me that doing so will get any plane off the ground, no matter what the FAA says. But you should wear safety goggles just in case.

if they put the airplane on the treadmill in reverse can they roll back the odometer?

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Originally Posted by jono

You're ignoring the fact that the wheels turn if the treadmill moves, even with no plane speed. Set a stationary plane down on a moving treadmill and go from there, same result. The plane on the treadmill doesn't have to move for its wheels to turn any more than the wheels have to turn for it to take off (assuming airspeed above stall).

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You're ignoring that fact that the question is about MATCHING wheel speed. This implies that the plane is moving because that's the only way a planes wheels normally roll when they're on the ground. In this question the plane starts at a stand still and then moves forward because of thrust and that's when the wheels start to roll. Talking about stationary planes on treadmills is just argumentative.

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Originally Posted by Big Steve

Hung up? WTF? This thread is about a thought experiment based on the assumptions in the OP. Duh. Anyone can win an argument if he can change the assumptions.

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Yeah.... we're arguing about a different circumstance. In the original, yes, the plane moves forward, treadmill moves backward, wheels spin at 2x. This one's different. Some say better, but I'm not sure how, since it's doesn't actually make sense.

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Originally Posted by jono

This post from grskier changed the question and with it the answer...sort of.

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Or.... entirely.

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Originally Posted by 2stix

Simple answer. Lock the brakes, wheels don't turn, treadmill moves in direction of plane and plane takes off. 0 wheel speed. Profit?

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Treadmill doesn't spin if wheels don't spin.

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Originally Posted by jono

in that scenario wheel speed = treadmill speed so the plane never moves, it doesn't matter how you power it (that issue was resolved on page 2 or something).

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How in the holy fuck? You're making things up. Wheel speed = treadmill speed does not mean the plane never moves, just that for the plane to move the wheels must slide. It doesn't matter how fast the wheels and treadmill are moving, for every foot the plane moves forward, the wheels have to slide on the treadmill a foot. The power involved to move the plane a foot does not change whether the wheels are spinning at infinity or at zero.

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You can prove the scenario I outlined a little less rigorously/more intuitively if you consider the treadmill's feedback system to be slightly imperfect so that it lets the plane rock forward before responding. In that case the response would be a massive force which would push the plane back (because it would be more than the thrust). Then it would have to correct again, and basically the plane would move fore and aft really slowly as the wheels went faster and faster. Assuming the control is perfect you'd never see the plane move.

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This is both changing the terms of the question substantially and irretrievably, and promoting a false premise. Even if this were so, why do you imagine the grip of the wheels to the treadmill is perfect?

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Originally Posted by jono

treadmill and the thrust provide two halves of a force couple (moment, torque) which spins the hell out of the wheels.

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No. This is where you're confused. The wheels and the treadmill are a circular system in a way that is fundamentally illogical. This is why everybody kind of breaks when trying to think through it (and do things like change the system by imagining slight imperfections or changing the terms by imagining that the treadmill is trying to stop the plane).

Wheelspeed = -treadmill speed. They cancel each other out. That is all, and it really is that simple. When the wheels start to spin because something else is pushing the thing they're attached to forwards, they spin backwards at exactly the same speed, meaning that in order for the thing being pushed to move, the wheels have to slide. Now, you can imagine that the wheels go instantly to infinity, because that makes some kind of intuitive sense. But, it's a circular system, and these things generally follow the path of least resistance. I can't think of any reason why the wheels spinning to infinity makes more sense than the wheels being held static, and it would use a lot less energy; meaning that the wheel just locking out (through some unnamed magical force, but we left reality behind a while ago) is likely the correct answer..

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Originally Posted by stfu&gbtw

What I want to know is, how does a pontoon plane take off without wheels?

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Exactly!

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Originally Posted by AaronWright

You're ignoring that fact that the question is about MATCHING wheel speed. This implies that the plane is moving because that's the only way a planes wheels normally roll when they're on the ground. In this question the plane starts at a stand still and then moves forward because of thrust and that's when the wheels start to roll. Talking about stationary planes on treadmills is just argumentative.

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You see that word "normally?" That's where you leave the context of the discussion. There's nothing normal about the plane on the treadmill, and if the treadmill moves the wheels can absolutely turn without the plane moving. In theory they could spin at any speed since the treadmill and the plane can move independently, right? That's the premise of thrust being disconnected from the wheels. But in this case there's also another condition, namely that the wheel speed = - treadmill speed. Which means that the plane isn't moving (except by sliding). Just incidentally, you're the only one not getting that part, not that that matters, I'm just pointing it out because you might find a better explanation of it in someone else's posts if mine aren't making sense to you.

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Originally Posted by Mustonen

How in the holy fuck? You're making things up. Wheel speed = treadmill speed does not mean the plane never moves, just that for the plane to move the wheels must slide. It doesn't matter how fast the wheels and treadmill are moving, for every foot the plane moves forward, the wheels have to slide on the treadmill a foot. The power involved to move the plane a foot does not change whether the wheels are spinning at infinity or at zero.

This is both changing the terms of the question substantially and irretrievably, and promoting a false premise. Even if this were so, why do you imagine the grip of the wheels to the treadmill is perfect?

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Do you have any background with calculus? If so, consider the infinitesimal time step, dt. The problem can be defined in those terms and you still get the same answer; I wasn't planning to do that, but the basic element of that approach is what I suggested and it absolutely does not redefine anything, it's just another approach.

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No. This is where you're confused. The wheels and the treadmill are a circular system in a way that is fundamentally illogical. This is why everybody kind of breaks when trying to think through it (and do things like change the system by imagining slight imperfections or changing the terms by imagining that the treadmill is trying to stop the plane).

Wheelspeed = -treadmill speed. They cancel each other out. That is all, and it really is that simple. When the wheels start to spin because something else is pushing the thing they're attached to forwards, they spin backwards at exactly the same speed, meaning that in order for the thing being pushed to move, the wheels have to slide. Now, you can imagine that the wheels go instantly to infinity, because that makes some kind of intuitive sense. But, it's a circular system, and these things generally follow the path of least resistance. I can't think of any reason why the wheels spinning to infinity makes more sense than the wheels being held static, and it would use a lot less energy; meaning that the wheel just locking out (through some unnamed magical force, but we left reality behind a while ago) is likely the correct answer..

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I'm assuming that the only magic in the system is the treadmill. You are looking for a way to lock the wheels, and I'm just assuming that they accelerate according to the applied torque. There's no mechanism to lock the wheels and since the tires' coefficient of friction is higher than the max the jets can overcome they don't slip until they fail.

What if there's an RF airplane on a treadmill inside a pontoon plane that's floating in a pool of orange jello on mars? How high do I have to be for the jello to take off?

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Originally Posted by stfu&gbtw

What if there's an RF airplane on a treadmill inside a pontoon plane that's floating in a pool of orange jello on mars? How high do I have to be for the jello to take off?

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Just slightly higher than you've ever been. And then a little higher than that. Continue until liftoff.

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Originally Posted by stfu&gbtw

What if there's an RF airplane on a treadmill inside a pontoon plane that's floating in a pool of orange jello on mars? How high do I have to be for the jello to take off?

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It depends if one of the pontoons is stuck in David hasselhoffs a-hole.

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Originally Posted by jono

Do you have any background with calculus? If so, consider the infinitesimal time step, dt. The problem can be defined in those terms and you still get the same answer; I wasn't planning to do that, but the basic element of that approach is what I suggested and it absolutely does not redefine anything, it's just another approach.




I'm assuming that the only magic in the system is the treadmill. You are looking for a way to lock the wheels, and I'm just assuming that they accelerate according to the applied torque. There's no mechanism to lock the wheels and since the tires' coefficient of friction is higher than the max the jets can overcome they don't slip until they fail.

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Yes, calculus occurred to me. I'm sure you understand that calculus is imperfect and can only be used to approximate solutions to problems.

We're still talking around each other. There are two points that you're missing:

(1) You're caught up in the force of the jet engines being applied to the inertia of the spinning wheels. There is no mechanism for that to happen. This makes sense with a motorcycle or a car, but not when torque is not being applied through the wheels. Again, imagine a free spinning, perfectly balanced giant lead wheel mounted on a sled. Push the sled when the wheel is not spinning. Push the sled when the wheel is spinning and accelerating under a monstrous application of force. The force required to move the sled is the same under either circumstance.

(2) This ignores the logical problem of how the wheels and treadmill can ever spin at all. Again, the treadmill isn't designed to stop the plane. (!) It's designed to perfectly match the speed of the wheels. When the wheels spin forward, the treadmill spins backward. The wheels can't spin forward unless the plane moves forward. The plane can't move forward unless the wheels slide. If the wheels slide, there's no reason for them to spin. Ergo, the system locks.

Ok, it sounds like you just haven't drawn the free body diagram of the wheels. Is that something you're familiar with? Because the mechanism by which torque is applied to a wheel that is free to spin on a bearing becomes quite clear when you see the FBD. A free-spinning wheel (any of them, an undriven wheel on your car or bike, for example) is acted upon by two horizontal forces, friction at the ground and forward thrust from the vehicle trying to move which acts horizontally at the wheel bearing. The distance between them is the radius of the wheel and together this forms a force couple (equal and opposite forces separated by a distance) which applies a torque, force x distance.

The difference in inertia of two different wheels on a bicycle, for example, can absolutely be felt in terms of how quickly the bike will accelerate.

So the torque I'm referring to is the thrust transferred through the frame and landing gear to the wheel bearing as a horizontal force, multiplied by the radius of the tire. And I trust that the perfect control system will apply an equal and opposite reaction force at the belt because that's the only amount of force that would keep the belt speed matched to the wheels.

I have to take back a piece of the conclusion, though: the 2016 plane probably never moves. It weighs 910,000 lbs and has 380,000 lbs of thrust and that thrust is very unlikely to be able to budge even the semi-molten stubs of the gear. The friction coefficient would have to stay below 0.4something and I think that's a little unlikely.

why are you focusing on the wheels? planes dont fly with their wheels....no air flow over the wings, no flight!

Because to get to speed for the wings the wheels have to move. In grskier's version they spin really fast because the treadmill matches their speed, which makes them the recipient of all the applied force for as long as they can take it.

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Originally Posted by Mustonen

Yes, calculus occurred to me. I'm sure you understand that calculus is imperfect and can only be used to approximate solutions to problems.

We're still talking around each other. There are two points that you're missing:

(1) You're caught up in the force of the jet engines being applied to the inertia of the spinning wheels. There is no mechanism for that to happen. This makes sense with a motorcycle or a car, but not when torque is not being applied through the wheels. Again, imagine a free spinning, perfectly balanced giant lead wheel mounted on a sled. Push the sled when the wheel is not spinning. Push the sled when the wheel is spinning and accelerating under a monstrous application of force. The force required to move the sled is the same under either circumstance.

(2) This ignores the logical problem of how the wheels and treadmill can ever spin at all. Again, the treadmill isn't designed to stop the plane. (!) It's designed to perfectly match the speed of the wheels. When the wheels spin forward, the treadmill spins backward. The wheels can't spin forward unless the plane moves forward. The plane can't move forward unless the wheels slide. If the wheels slide, there's no reason for them to spin. Ergo, the system locks.

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Your first point just needs a FBD, as I described above (that sled example needs something though, I can't make out what you're describing there; every way I interpret that the torque on the wheel changes the required push force, but I think you'll get that with proper FBD's).

But your second point would be much better addressed if you take another look at calculus. While it's often imperfect for describing the real world (though no moreso than algebra, technically) the technique works perfectly for describing perfect systems like the treadmill imagined here. There's no logical reason to lock the wheels, there's nothing to physically cause that and the magic control system can't reach past the belt. So the question is what can it do and the answer is apply speed to belt. With changing speed we have acceleration and with acceleration we have force, in knowable quantities as shown a page or so back. You keep saying the control isn't designed to stop the plane and that's correct, but since matching the wheels' speed can only be achieved at forces that match the thrust that fact comes along for the ride.

somebody should post the question to reddit and send it to boeing.

Isn't this a little like asking if a plane could take off with an unlimited runway and a hard tailwind? The basic question being how much speed and heat can the rolling gear withstand and for how long....and how stable is the system with rolling gear spinning at a land speed of like 200 or 300 mph?

Pretty similar. If belt matches wheels the land speed (and tail wind speed) probably hit something like 500-600 mph before the tires fail but whatever speed that is they get there real quick.

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Originally Posted by stfu&gbtw

What if there's an RF airplane on a treadmill inside a pontoon plane that's floating in a pool of orange jello on mars? How high do I have to be for the jello to take off?

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See, it's not a question of high vs. not high. It's a question of substances...

According to my sources, to really make this happen you need just the right combination of jenkem, krokodil and salvia.

Please get on this right away and report back soon, many are curiously awaiting your results.

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Originally Posted by jono

Pretty similar. If belt matches wheels the land speed (and tail wind speed) probably hit something like 500-600 mph before the tires fail but whatever speed that is they get there real quick.

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How about this? You have a cessna on the treadmill with a takeoff speed of 80mph, but a steady 50mph headwind....that craft would only need a forward speed of about 30mph to lift off, at 30mph the treadmill would be moving oppositely creating the equivalent of 60mph of wheel spin. That'll take off for sure.

JESUS H. CHRIST! ARE YOU PEOPLE RETARDED?

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Originally Posted by ill-advised strategy

How about this? You have a cessna on the treadmill with a takeoff speed of 80mph, but a steady 50mph headwind....that craft would only need a forward speed of about 30mph to lift off, at 30mph the treadmill would be moving oppositely creating the equivalent of 60mph of wheel spin. That'll take off for sure.

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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.

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Originally Posted by ill-advised strategy

JESUS H. CHRIST! ARE YOU PEOPLE RETARDED?

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At least half. Not sure where I fit in, though, but the 747 takes off.