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

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1 minute ago, LordFerret said:

If truly a conveyor varied its speed to a point to hold a real airplane steady in one place,

Which basically can't happen, because no matter how fast the treadmill is going the wheels will just spin faster while the plane accelerates in the other direction.

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Just now, LordFerret said:

Again, you're missing it. If the plane is held stationary, wheels spinning, engine roaring, without air passing over the wings there will be no lift - no flight.

You're missing it.  The plane is not being held stationary by the treadmill.

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5 minutes ago, LordFerret said:

The MythBusters video is misleading. If truly a conveyor varied its speed to a point to hold a real airplane steady in one place, which is the concept/question asked in the OP, it would not fly. For a plane to fly, the engines must pull it forward... the forward motion causes air to pass over the wings, which generates lift.

Sure. But eventually drag between the treadmill and the air increases the air speed with respect to the plane, thus generating lift. The plane might crash eventually, but it takes off.

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Just now, Geonovast said:

You're missing it.  The plane is not being held stationary by the treadmill.

Are the engines running? If so, then it could take of like a normal airplane (although the wheels are going to explode anyways, but hey, it is a hypothetical plane, right?)

If the engines aren't running it won't do anything at all.

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2 minutes ago, Bill Phil said:

Sure. But eventually drag between the treadmill and the air increases the air speed with respect to the plane, thus generating lift. The plane might crash eventually, but it takes off.

First reasonable reply I've seen on this yet.

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1 minute ago, LordFerret said:

First reasonable reply I've seen on this yet.

Not really.  The only increase in drag is going to be in the wheel bearings.  The wheels will be spinning twice as fast as in a normal takeoff, but that's it.  The only way you're going to stop the plane is by melting the bearings to the point a seizing, and the treadmill would have to be going WAY faster than the plane to do that.

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There is one thing not clear here:

Are the engines running fast enough so the plane could move faster than the threadmill or not? Are the engines running at all? This is a trick question, there is an important thing missing here.

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5 minutes ago, Geonovast said:

Not really.  The only increase in drag is going to be in the wheel bearings.  The wheels will be spinning twice as fast as in a normal takeoff, but that's it.  The only way you're going to stop the plane is by melting the bearings to the point a seizing, and the treadmill would have to be going WAY faster than the plane to do that.

If the plane isn't moving (if) as a result of the treadmill, eventually the treadmill will speed up the air above it due to friction. Nothing to do with wheel bearings. Friction increases airspeed. Friction is not itself increasing.

This whole problem is too ambigious to solve. Each side "knows" the answer but, in truth, the two sides are solving different physics problems, based on individual interpretations.

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3 minutes ago, Bill Phil said:

If the plane isn't moving (if) as a result of the treadmill, eventually the treadmill will speed up the air above it due to friction. Nothing to do with wheel bearings. Friction increases airspeed. Friction is not itself increasing.

This whole problem is too ambigious to solve. Each side "knows" the answer but, in truth, the two sides are solving different physics problems, based on individual interpretations.

The biggest problem (And likely the source of the differing viewpoints) is the comparison of liner movement to rotational movement.

So maybe the question would be "Could the plane take off before the wheels explode?

Might be more fun to put a helicopter on a merry-go-round spinning at the same speed as the rotor, but opposite direction.  I would hope we could all agree that that wouldn't take off, but would be a ton of fun to watch.

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2 minutes ago, Geonovast said:

I would hope we could all agree that that wouldn't take off

Well, of course it wouldn't.  The pilot would pass out from the spinning.

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5 hours ago, DatBoi said:

Imagine the KSC runway was replaced by a giant treadmill that would run backwards at the exact speed of the wheels on your airplane. Can you take off?

"the exact speed of the wheels on your airplane"

If your plane accelerated, the treadmill would too, thus keeping its velocity zero or close to zero. If the treadmill speed was constant, then the plane could take off, but the OP doesn't say its constant.

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So, in effect, since there's no force holding the plane from accelerating, the treadmill and wheels are constantly accelerating to the point that physics no longer matters, and the plane takes off because it no longer needs to obey the law of gravity.

In short, the problem asserts a condition that cannot occur, and the reality of a plane on a treadmill results in flight.

Edited by razark

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2 minutes ago, razark said:

So, in effect, since there's no force holding the plane from accelerating, the treadmill and wheels are constantly accelerating to the point that physics no longer matters, and the plane takes off because it no longer needs to obey the law of gravity.﻿

In short, the problem asserts a condition that cannot occur, and the reality of a plane on a treadmill results in flight.

I just realized that I phrased my last post wrong. What I mean to say was:

Quote

If your plane accelerated, the treadmill would match the new, faster speed of the wheels, thus keeping the velocity of the plane relative to the ground zero or close to zero. If the treadmill speed was constant, then the plane could take off, but the OP doesn't say its constant.

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My understanding of the OP was that the speed of the treadmill was not constant.

If that were so, wouldn’t the plane be unable to take off? There would be no air passing over the wings to create lift as the acceleration/final speed of the plane would match the treadmills. When running on a treadmill, you wouldn’t feel air rushing over you. Wouldn’t that be because relative to an outside observer/ground/air you are actually stationary?

Edited by Atlas2342

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An identical thread has been merged into this topic.

Edited by Dman979

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What I mean to say was:

And then, the engines would accelerate the plane.  Which would accelerate the wheels, and the treadmill would then accelerate, and then the plane would be held stationary, so it would then accelerate due to thrust, which would accelerate the wheels, which would accelerate the treadmill to hold the plane stationary, the thrust from the engines would then accelerate the plane, which would... loop ad infinitum, to the point at which the wheels and treadmill are now moving at infinite speed (and still accelerating), physics has long since failed, and the plane is now airborne and not airborne at the very same time, because we can just ignore physics and common sense.

Again, the problem asserts a situation that cannot ever occur, and the plane is only prevented from flying by the absurd ever-accelerating treadmill.

No one has yet demonstrated what force counteracts thrust to keep the plane stationary, beyond the magic wheel/treadmill equality.

Edited by razark

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1 minute ago, razark said:

And then, the engines would accelerate the plane.  Which would accelerate the wheels, and the treadmill would then accelerate, and then the plane would be held stationary, so it would then accelerate due to thrust, which would accelerate the wheels, which would accelerate the treadmill to hold the plane stationary, the thrust from the engines would then accelerate the plane, which would... loop ad infinitum, to the point at which the wheels and treadmill are now moving at infinite speed (and still accelerating)...

and so the wheels would explode and then the plane would explode and everyone would die, so the real question is "Can the plane take off intact?", and the answer is No.

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I have to walk away. I'm getting a headache.

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Ok, I think there is some confusion happening here.  The wheels of are not driving the aircraft forward, it's the propeller.  If you really want to mess with the aircraft try it with the parking brakes on, on the back of a flat bed truck driving down the highway the opposite direction the aircraft is pointing.

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and so the wheels would explode and then the plane would explode and everyone would die, so the real question is "Can the plane take off intact?", and the answer is No.

Well, we've got a plane on a treadmill acted upon by magic forces, and a treadmill that can accelerate past the speed of light, powered by more energy than the universe could ever produce...

I'd say it's fair to assume a magic plane, as well.

Short version: No, the plane can't take off, because no such system can exist as described.

Edited by razark

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1 hour ago, Atlas2342 said:

If that were so, wouldn’t the plane be unable to take off? There would be no air passing over the wings to create lift as the acceleration/final speed of the plane would match the treadmills. When running on a treadmill, you wouldn’t feel air rushing over you. Wouldn’t that be because relative to an outside observer/ground/air you are actually stationary?

It all depends on whether you're viewing the question as a linguistic challenge or an engineering one.

Short answer is:  The airplane will take off just fine.  Because the conveyor belt won't affect it.  The conveyor belt moving (or accelerating) won't affect the airplane in any appreciable way.  When the conveyor belt accelerates, all it does is accelerate the spin rate of the plane's wheels; it won't make any difference to how the plane itself moves.

By way of illustration, let's take the simpler case of an airplane that doesn't have any engines.  It's basically just a big heavy chunk of metal on roller skates.  Let's consider what happens:

1. Imagine that the plane is sitting stationary on the conveyor belt.  And the conveyor belt is stationary, too.  Nothing moving.  Simple enough, right?
2. Now, let's assume that the plane doesn't have its brakes set-- there's nothing stopping it from rolling forward or backward other than the (very small) amount of rolling friction of its wheels.
3. Okay. Now turn on the conveyor belt's motor so that the conveyor belt accelerates backwards (relative to the plane).  What happens?
4. Answer:  The plane just sits there, nearly stationary!

Why is that?  It's because the wheels have a very tiny moment of inertia relative to the overall mass of the plane, and also have a very small amount of rolling friction.  So when you start pulling the conveyor belt backwards, there's very little "friction coupling" with the airplane-- it's like that magic trick where you yank the tablecloth out from under a bunch of dishes and they all stay in place.  The plane would just sit there, nearly motionless, no matter how fast the conveyor belt goes.  All that happens is that every time the conveyor belt accelerates a bit faster, it causes the plane's wheels to spin that much faster.  But the plane itself basically just sits there.

Now... the plane won't sit completely still.  The rolling friction of the wheels is very very small, but it's not quite zero, so yes, the fact that the conveyor belt is accelerating the wheels and the wheels are fixed to their axles and the axles are attached to the plane will, indeed, cause the plane to start accelerating backwards.  But it will do so very, very slowly, with a very low acceleration, e.g. less than a hundredth of a gee.  So, pretty darn close to stationary.

...Okay, now take the same exact situation, but the plane has engines.  In this case, the engines are using the (stationary) air for thrust, not the conveyor belt, so the speed of the conveyor belt doesn't matter.  As long as the engines have enough oomph to overcome the tiny, less-than-hundredth-of-a-gee backwards acceleration due to rolling friction of the wheels, they'll easily accelerate the plane and it will take off just fine.

Of course, all of the above discussion has been assuming that you're using plausible real-world physics and engineering.  If you want to posit something silly like "the conveyor belt can move at half lightspeed!" or whatever, then the problem becomes a lot more hand-wavy.  One problem right at the core of this "problem" is that it's using misleading linguistics.  You can't have an infinitely powerful motor on a conveyor belt.  Or rather, as soon as you say you have one, then all the math goes kablooie and you basically can say anything you want.  Saying "I have a conveyor belt that accelerates as necessary to keep the plane stationary" is nonsensical.  It's not a thing.  It's like saying "I have a car that runs fast enough to make <arbitrary thing unrelated to car's speed> happen."

The only way for this problem to be an actually well-defined problem and not just linguistic trolling, would be to specify the numbers involved.  Specifically, 1. what acceleration can the plane manage from its engines?  2. what speed can the wheels spin before they burst?  3.  what's the rolling friction of the wheels?  4.  what's the takeoff airspeed of the plane?  and 5. what's the max acceleration that the conveyor belt can do?

That last question is the kicker.  Unless you specify what acceleration the conveyor belt can manage, you're playing word games, not engineering games.

The plane will accelerate, and the conveyor belt can't stop that no matter how fast it goes.  All the conveyor belt can do is make the plane's wheels spin faster.  The wheels have a certain maximum speed they can tolerate before they explode.  So, it's basically a "race".  One of two things will happen, based on how powerful the conveyor belt's acceleration is relative to the plane's.

• Either the plane will reach takeoff speed and lift off before the wheels explode...
• or it won't, and the wheels explode, and then bad things happen.

Knowing which one happens would require knowing the numbers mentioned above.

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I mean once the wheels give out, rip everyone in that plane, and the plane itself, so you cant really consider it a takeoff in any normal sense. Now lets all settle down before I have to mute this thread.

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I mean once the wheels give out, rip everyone in that plane, and the plane itself, so you cant really consider it a takeoff in any normal sense.

You're assuming the wheels will fail before the treadmill.

Edited by razark

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I think I used all my likes on this thread...

I have trouble believing a conveyor belt can accelerate fast enough for friction from the aircraft's wheel bearings to counteract the thrust. If that was the case, the bearings would quickly seize. At which point, the conveyor belt would hurl the aircraft backwards. The sudden acceleration would probably cause the plane to pitch forward, giving the wings a positive AoA with respect to the direction of travel. The aircraft would then take off backwards . It would probably then crash back down as the engine slows the backwards velocity, assuming it didn't suffer a prop strike when pitching forward.

Normal physics: yeah, the conveyor does nothing to the thrust accelerating the plane, which will take off normally.

Special case: floatplanes fighting against the current will have difficulty taking off, as water offers much more resistance than wheels, until the floats start hydroplaning.

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