So, you have a plane on a conveyor belt...

[Lukaszenko]

That's a very strange interpretation of the "myth". Why did you make the "car" always turn the wheel at constant speed, but have the "plane" just apply maximum thrust regardless? Have the "car" apply constant torque on its wheel and try again.

It seems people tend to interpret the question as having the conveyor do whatever is necessary to stop the car/ plane. Because, after all, that is the very definition of a conveyor: to stop things from moving. They'll even switch your frame of reference as needed. Einstein was wrong about the speed of light being the same, because what if there's a conveyor? Subtract the speed of the conveyor from C and you get the real truth. In fact, next time you drive by a conveyor factory, or even a gym, make sure to recalibrate your speedometer to account for the conveyors!

Whatever you do, don't put a conveyor ON another conveyor. Some say that's how the Big Bang started

[Technical Ben]

It's a language, concept and logic passing fail.

Instead of thinking of a conveyor belt as "moving a wheel/road" people think of it as "moving the entire object".

It can also be a problem with bias and opinion. Such as people thinking all diesel cars are "slow" and not even accepting proof to the contrary, as in their mind petrol=fast.

[sgt_flyer]

If people want an analogy, they should think of the plane's wheels as a bearing (for minimizing friction between the two parts, 1 being the plane and the other part the conveyor)

While cars are built to use the friction between the wheel and the ground for propulsion.

[lajoswinkler]

You are falling into the same fallacy as everything else. Pushing against moving things takes a bit more power, but it doesn't cancel anything. A car on a moving treadmill will drive off JUST AS EASILY as an airplane.

There is absolutely no difference between an airplane and a car as far as this problem goes. For both, it is a stupid problem. For either one in idle, a slowly moving conveyor will keep them in place. For either one at full throttle, no conveyor speed will keep them put. It's seriously that simple. Only people who understand nothing about basic physics of motion, which is by far most people, keep trying to see a difference.

That's why there is absolutely no such thing as people running on treadmills in gyms or hamsters in their wheels. If they try to run, they will run away from it.

[magnemoe]

You are falling into the same fallacy as everything else. Pushing against moving things takes a bit more power, but it doesn't cancel anything. A car on a moving treadmill will drive off JUST AS EASILY as an airplane.

There is absolutely no difference between an airplane and a car as far as this problem goes. For both, it is a stupid problem. For either one in idle, a slowly moving conveyor will keep them in place. For either one at full throttle, no conveyor speed will keep them put. It's seriously that simple. Only people who understand nothing about basic physics of motion, which is by far most people, keep trying to see a difference.

Not entirely correct, a plane use jets or propellers pushing against the air. If plane stand stationary the wheels will simply rotate faster.

A car would feel it like it had strong wind from behind, conveyor and car moves in 100 km/h, car only get the benefit of no air resistance so it can run in high gear and very lite throttle, if you drive forward in 100 km/h the wheels and gearbox will have to move in 200 km/h yes the engine don't have to work much harder than normally in 100 km/h but you would be on your highest gearing and pretty high rpm. Many car would not even be able to go so fast as your rmp reach maximum.

[Tigermisu]

That's a very strange interpretation of the "myth". Why did you make the "car" always turn the wheel at constant speed, but have the "plane" just apply maximum thrust regardless? Have the "car" apply constant torque on its wheel and try again.

If the car were to turn the wheel faster than that, it would go forward. The plane does not apply maximum thrust, it just applies minimum, yet it is enough to go forward regardless of the speed of the conveyor belt under it.

[Shpaget]

Not entirely correct, a plane use jets or propellers pushing against the air. If plane stand stationary the wheels will simply rotate faster.

A car would feel it like it had strong wind from behind, conveyor and car moves in 100 km/h, car only get the benefit of no air resistance so it can run in high gear and very lite throttle, if you drive forward in 100 km/h the wheels and gearbox will have to move in 200 km/h yes the engine don't have to work much harder than normally in 100 km/h but you would be on your highest gearing and pretty high rpm. Many car would not even be able to go so fast as your rmp reach maximum.

That's because cars are not designed to drive with a 200 km/h tailwind. If, however, you modify the transmission for it to be capable of spinning the wheels at 200 km/h with idle throttle, you would have no problem driving on a 200 km/h treadmill, even with a regular engine providing only the power required to overcome the losses in the transmission and the rolling friction, which is negligible compared to aerodynamic forces a typical car usually encounters when driving at 200 km/h on a regular road.

[K^2]

If the car were to turn the wheel faster than that, it would go forward. The plane does not apply maximum thrust, it just applies minimum, yet it is enough to go forward regardless of the speed of the conveyor belt under it.

Not true. An airplane in idle travels at a brisk walking pace on the ground, due to friction in wheels. Which, incidentally, about the same for a car in first gear. Both can stay put on a conveyor belt of just about any sane speed by adjusting the throttle.

[WestAir]

Not true. An airplane in idle travels at a brisk walking pace on the ground, due to friction in wheels. Which, incidentally, about the same for a car in first gear. Both can stay put on a conveyor belt of just about any sane speed by adjusting the throttle.

And that friction is ridiculously low too. Once you give it breakaway thrust you can idle at about 20 knots for probably your whole (straight) taxi without touching the levers at all. (In my experience, anyways. Never had the opportunity to try and idle taxi a 747 at MTOW, but I digress.)

As an aside to the OP, I agree with the others that this question is nonsensical. Reality is not a cartoon, and as K^2 has said conveyors are not magic. (Though if you manage to invent one, please tell me how before you go public. I'd love to get an award for inventing observable magic.)

[FungusForge]

Yes the plane would take off. Since unlike cars and trains, an aircraft gets it propulsion from moving air through its engine (whether it be propeller or jet turbine). As such, as long as the wheel brakes are off the plane should take off with no issue. Since the wheels have such low friction without the brakes on, this question isn't too different from asking if a hovercraft could move with a conveyor belt beneath it.

[K^2]

And that friction is ridiculously low too. Once you give it breakaway thrust you can idle at about 20 knots for probably your whole (straight) taxi without touching the levers at all. (In my experience, anyways. Never had the opportunity to try and idle taxi a 747 at MTOW, but I digress.)

Yeah, I don't know how it scales either. But the equilibrium on idle for a 172 is much slower than 20 knots. Though, it will carry on at that speed for quite some time before slowing down significantly, sure. That's kind of how it tends to work when you have a heavy object with very low friction and very low idle thrust.

[GeneralVeers]

I do not think that comparing the landing to a take-off is a fruitful endeavour. The loads are rather different.

Not on the wheels. When taking off, friction in the bearings exerts a force that tries to slow the plane. When landing, friction in the bearings exerts a force that tries to slow the plane. This friction is the only way the conveyor belt can even exert a force on the plane at all.

[Randazzo]

I forgive those of you who think I'm an idiot because you didn't read the thread.

However, you've nobody to blame but yourselves for bringing this back to life.

[mrfox]

And that friction is ridiculously low too. Once you give it breakaway thrust you can idle at about 20 knots for probably your whole (straight) taxi without touching the levers at all. (In my experience, anyways. Never had the opportunity to try and idle taxi a 747 at MTOW, but I digress.)

In larger jets, the taxi speed can run away quite rapidly (40kts plus) at idle thrust. Many rear engine jets will deploy one of the engines in reverse to save on brake wear while keeping taxi speeds in check.

[WestAir]

I operate rear engine jets, (MD 80s) and the first thing that would happen besides me having my monthly bid awarded schedule pulled without pay is a long phone call with the chief pilot about why I threw a plane into reverse instead of using the brakes that are there.

After that I'll probably end up working in South Africa flying Caravans.

Edit: According to google, a lot of Citations and even MD-80's use idle reverse as speed control. I've never heard about this practice before. Thanks for teaching me something new!

Edited October 5, 2015 by WestAir

[K^2]

This friction is the only way the conveyor belt can even exert a force on the plane at all.

That is not correct. An accelerating belt can exert quite a bit of force on an airplane, because of the wheels' moment of inertia. Which is precisely what the belt has to do if it's too constantly match airplane's wheel rotation speed. It will be accelerating.

If we simply take the "myth" at its wording, and assume that speed is measured same way as for the car, so we require that belt speed always matches rotation of the landing gear, we can actually solve this constraint problem, so long as we assume real wheel with real moment of inertia. The solution, however, produces quite insane acceleration for the belt. Something like 10g for an ultralight at full throttle, and even much higher for larger planes.

But if our only requirements is that we match the "myth" briefly, this is feasible to set up for a light plane, and an accelerated belt would, in fact, keep the plane completely stationary despite engine running at full power. Very briefly. Then the relative speed between plane and conveyor belt will get above safe limits, landing gear will disintegrate, and you'll destroy the plane. Or more plausibly, you'll run out of juice in whatever it was that you used to yank the belt from under the plane. Either way, the whole thing will last a few seconds tops.

[mrfox]

After that I'll probably end up working in South Africa flying Caravans.

That doesn't sound half bad to me!

[0111narwhalz]

Look at it this way: To what does each vehicle apply its reaction? Since Newton's laws of motion require the vehicle to apply force to something, one can examine the reaction mass used. Cars use a reaction mass which is coupled to the conveyor, namely the conveyor itself. Aircraft, however, use a remass independent of the conveyor. Therefore, the aircraft can apply acceleration regardless of the conveyor.

Friction is assumed to have a small effect upon performance.

[Shpaget]

Therefore, the aircraft can apply acceleration regardless of the conveyor.

So can a car.

Power needed to achieve a certain acceleration does not depend on the speed of the conveyor, but the speed of the car.

If the car had perfect bearings on the wheels, the conveyor would not affect the car at all.

[Sean Mirrsen]

So can a car.

Power needed to achieve a certain acceleration does not depend on the speed of the conveyor, but the speed of the car.

If the car had perfect bearings on the wheels, the conveyor would not affect the car at all.

Not quite. Perfect bearings on the wheels, perfectly round and solid wheels, and perfectly smooth conveyor surface that still has proper friction with the wheels. There are ways the wheels resist being rotated other than the bearings.

And really, I said it many times before, the idea itself is not so outlandish. The exact method is, yes, for various reasons, but a seaplane in a moving water stream can easily be prevented from lifting off, without destroying its pontoons. A typical "flying boat" design can plow through water easily enough that it may as well be a speedboat if you take away its wings. But it still has a maximum speed, on water, that isn't determined by air resistance. Make the water move against it at that speed, and even with wings it will not lift off.

All I'm saying is that there is a fringe case where the principle works.

[J.Random]

So can a car.

Power needed to achieve a certain acceleration does not depend on the speed of the conveyor, but the speed of the car.

If the car had perfect bearings on the wheels, the conveyor would not affect the car at all.

Which is exactly why the car will stay at the same spot, spinning its wheels with infinite speed.

Which is also why airplane _will_ move: the air will push it with the equal force airplane applies to it.

Seriously, guys, why is this discussion still going? It should have ended on page 1.

[Shpaget]

Which is exactly why the car will stay at the same spot, spinning its wheels with infinite speed.

And the moment the car applies any power instead of just letting its wheels spin idly, it will start moving forwards.

There is a very significant difference between a car or a plane on a hard surface and a hydroplane on water. Wheels spin very easily, while water produces a lot of drag. We can approximate the wheels to have no friction for the sake of argument, but if you introduce some form of terminal velocity for hydroplane, than you are comparing two different models.

Edited October 13, 2015 by Shpaget

[J.Random]

And the moment the car applies any power instead of just letting its wheels spin idly, it will start moving forwards.

Nope. This power will go into spinning wheels even faster, which doesn't mean that the car will move.

[Shpaget]

No, it will not.

It will go into pushing against the conveyor.

[J.Random]

And yet the conveyor cannot push it back (well, forward). Essentially, it acts as a frictionless surface. The car will not move.