[Guest]

This is a very highly debated topic, even though scaled tests have been conducted. The popular Mythbusters show on discovery did it full scale, but some still dispute the way they did it. You can probably find thousands of forums that host this same question, and I wouldn't be suprised if it has even been posted here before. So here goes!

A large passenger jet sits on a tredmill the size of a normal runway that they would normally take off on. When the jet starts up, it climbs in speed slowly. The tredmill matches the jet's speed EXACTLY. For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as-well.

The grand question: Will the plane take-off?

Assume that:

The wind is at 0 MPH

The Jet is powered by turbines

Edited September 6, 2008 by RedRum

[Guest]

according to Scraff's assertions, if the plane just sat on the runway and the runway started moving in the opposite direction the plane would stand still because the wheels are "free spinning"

I never asserted any such thing.

[unreality]

I think I can help and explain it better to Ysan, AAA and Bb:

Say the treadmill is running while the plane is just sitting on it: the plane does not move! It stays in place, the wheels spinning at the speed of the treadmill, but since the wheels are free-spinning, the plane stays in one place.

Now say that the plane turns on its jets - it now moves forward, regardless of the speed of the treadmill. The wheels are now spinning at speed A+B, where A is the treadmill speed and B is the airplane's speed.

In the case where A adjusts to match B, the wheels always spin at 2B (or 2A, same thing). But A doesn't affect B. The treadmill can be whipping up a pace of 300 mph, and the plane can just put on 100 mph, but the plane does not go back, it goes forward at 100 mph - REGARDLESS OF THE TREADMILL. Assuming that the wheels can take the speed of moving 400 mph of course

Since the plane still goes forward at its usual pace, it's just the same as if there was no treadmill!!! It takes off! The only change that the treadmill causes is increasing the speed of the free-spinning wheels

[Guest]

I think I can help and explain it better to Ysan, AAA and Bb:

Say the treadmill is running while the plane is just sitting on it: the plane does not move! It stays in place, the wheels spinning at the speed of the treadmill, but since the wheels are free-spinning, the plane stays in one place.

Sigh. You're not helping; this is incorrect. As AAAsn888s replied, and incorrectly claimed that I asserted to the contrary, the plane would move along with the treadmill. And as taliesin replied, inertia comes into play and the plane will resist movement to some degree during accellaration of the treadmill. As the treadmill goes on to move a steady speed, the plane will move at the same speed right along with it.

Now say that the plane turns on its jets - it now moves forward, regardless of the speed of the treadmill. The wheels are now spinning at speed A+B, where A is the treadmill speed and B is the airplane's speed.

Let's not make this more complicated. The problem does not include a plane trying to overcome it traveling in reverse before thrust is applied.

[Guest]

Sigh. You're not helping; this is incorrect. As AAAsn888s replied, and incorrectly claimed that I asserted to the contrary, the plane would move along with the treadmill. And as taliesin replied, inertia comes into play and the plane will resist movement to some degree during accellaration of the treadmill. As the treadmill goes on to move a steady speed, the plane will move at the same speed right along with it.

To a degree this in not the case, I agree with what UR posted. In a ideal situation where there is no friction on the wheels of a plane. If the aircraft was sitting on a treadmill that was moving at 300km/h the place would stay stationary. The only thing that will move will be the frictionless wheels.

Now if the aircraft starts it engines, since they apply force into the "AIR" therefore the plane has thrust. Because the wheels DONT TRANSFUR force between the Aircraft and the Treadmill, instead jst spin up to speed, the Aircraft with begin to move forward. This increases the speed of the treadmill, which turns the wheels faster. This continues to happen until the Aircraft has enough speed to take off (Vr) or until the aircraft has driven off the end off the treadmill.

[Guest]

To a degree this in not the case, I agree with what UR posted. In a ideal situation where there is no friction on the wheels of a plane. If the aircraft was sitting on a treadmill that was moving at 300km/h the place would stay stationary. The only thing that will move will be the frictionless wheels.

If we were talking about fictional frictionless wheels I'd agree also. The OP, the Mythbusters experiment, etc., describe ordinary real-world airplanes. Unreality's statement "Say the treadmill is running while the plane is just sitting on it: the plane does not move!" is incorrect and isn't going to help anyone understand why a plane on a treadmill as described in the OP will take off just fine.

[Guest]

If we were talking about fictional frictionless wheels I'd agree also. The OP, the Mythbusters experiment, etc., describe ordinary real-world airplanes. Unreality's statement "Say the treadmill is running while the plane is just sitting on it: the plane does not move!" is incorrect and isn't going to help anyone understand why a plane on a treadmill as described in the OP will take off just fine.

Think about it this way. Get a treadmill, and a pair of roller blades. Put the roller blades on and jump on the treadmill. You will not move ( if you do very slowly) now if you grab the bad and pull yourself forward, this simulates thrust and you move forward..

I dont see how to explain it easier than this

[Guest]

Think about it this way. Get a treadmill, and a pair of roller blades. Put the roller blades on and jump on the treadmill. You will not move ( if you do very slowly) now if you grab the bad and pull yourself forward, this simulates thrust and you move forward..

I dont see how to explain it easier than this

Stand on a long treadmill and start it up. Will you move in the direction of the treadmill at the same speed instantaneously? No. Will you "not move!" as unreality claimed? No. It won't take long for you to be moving pretty close to the speed of the treadmill. I also can't explain it any easier than this.

[Guest]

Stand on a long treadmill and start it up. Will you move in the direction of the treadmill at the same speed instantaneously? No. Will you "not move!" as unreality claimed? No. It won't take long for you to be moving pretty close to the speed of the treadmill. I also can't explain it any easier than this.

How do can you explain this?

[Guest]

Alright folks, nine pages in and there are still plenty of folks differing on opinion of whether or not the plane will take off. Not exactly helping to argue about what happens to a plane with frictionless or non-frictionless wheels that is resting on a treadmill traveling towards the plane's tail.

Back on topic...

[Guest]

How do can you explain this?

Will add this for clarification (sorry Martini):

I meant stand on the treadmill with rollerblades on.

[Guest]

I am so glad to see you all are having fun with my post. I suppose I should clarify somthing.

The tredmill only matches the airplane's "ground speed." There isn't a way that a tredmill could match an airplane's air speed. The wind tunnel example given in a few posts would prevent the plane from taking off provided it matches the plane's air speed.

Edited September 7, 2008 by RedRum

[Prof. Templeton]

Wow. This thread really "took off".

[Prime]

I think the OP misstated the problem. The way I heard it, the treadmill matches the speed of the plane's wheel rotation exactly -- not the planes speed.

That way the puzzle practically states that the airplaine remains stationary.

The Myth Busters' experiment completely failed to create those conditions. As you pull the runway from under the plane, its wheels compensate an rotate faster. It would be very difficult to create conditions stated in the puzzle. We'd have to use a chain for the treadmill and sprackets for the wheels. And the speed of the treadmill should be tremendous. The friction in the axels of the wheels would have to equalize the thrust of the jets.

Fortunately, we need not bother to make the experiment, since the puzzle impicitly states that the plane remains stationary.

[Guest]

I think the OP misstated the problem. The way I heard it, the treadmill matches the speed of the plane's wheel rotation exactly -- not the planes speed.

It doesn't matter. When a plane on a normal runway takes off, the wheels moves in relation to the plane's speed. When the plane takes off on a runway as explained in the OP, the plane takes off in its normal manner and spin twice as fast as they normally would.

That way the puzzle practically states that the airplaine remains stationary.

No, the riddle doesn't practically state any such thing. The plane takes off.

The Myth Busters' experiment completely failed to create those conditions. As you pull the runway from under the plane, its wheels compensate an rotate faster. It would be very difficult to create conditions stated in the puzzle. We'd have to use a chain for the treadmill and sprackets for the wheels. And the speed of the treadmill should be tremendous.

The treadmill would move the same speed as the plane in the opposite direction.

[Guest]

I think the OP misstated the problem. The way I heard it, the treadmill matches the speed of the plane's wheel rotation exactly -- not the planes speed.

I take it back; it does matter. If that's the way you heard the riddle you heard it wrong as that would lead to a paradox.

If the plane moves forward at 20 MPH, then its wheels will do likewise, and the treadmill will go 20 MPH backward. But if the treadmill is going 20 MPH backward, then the wheels are really turning 40 MPH forward. But if the wheels are going 40 MPH forward . . .

The riddle was stated correctly by the OP. Paradox or not in your scenario, what gets a plane moving are its props or jet turbines, which push the air backward and impel the plane forward. What the conveyor belt, wheels, etc, are up to is mostly irrelevant. Let me repeat: Once the engines are fired up, the plane moves forward at pretty much the usual speed relative to the ground, and more importantly the air, regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is make the plane's wheels spin madly.

[Prime]

Over the years, this puzzle comes in and out of fashion. I don't know who originally came up with it and what they meant. However, "treadmill matches the speed of the plane exactly" is ambiguous and does not seem to present a puzzle.

If it means that the belt and the plane match their speed with respect to each other -- that is meaningless. Such is always the case, regardless whether the treadmill moves at all, and with what speed.

If the belt matches planes speed with respect to the ground, but in the opposite direction -- there is no "puzzle" in it. The plane just has to overcome a bit of additional friction of faster rotating and/or skidding wheels. If its engines (of any kind) have enough power (and we expect, they do), then what's there to solve?

On the other hand, if the belt matches the rotation of the wheels (no skidding is implied) -- that sends people on a cerebral jorney, considering all the irrelevant stuff, like type of engines, air speed/ground speed, etc.. While overlooking the fact that the puzzle practically states that the plane remains stationary. Though, difficult, if not impossible, it would be to create those conditions in practice.

The version of that puzzle that I heard quite a while ago, was very careful to state that the belt was designed to match the rotation of the wheels.

[Guest]

Over the years, this puzzle comes in and out of fashion. I don't know who originally came up with it and what they meant. However, "treadmill matches the speed of the plane exactly" is ambiguous and does not seem to present a puzzle.

It presents a hell of a puzzle. It's precisely why there's such division on whether or not the plane would take off.

If it means that the belt and the plane match their speed with respect to each other -- that is meaningless.

Of course it's not meaningless; it's straightforward. If the plane is moving 20MPH in one direction, the treadmill is moving 20MPH in the opposite direction and the wheels of the plane would be moving twice as fast as they would if it had taken off on a regular runway.

Such is always the case, regardless whether the treadmill moves at all, and with what speed.

No, if the treadmill does not move at all the plane is moving away from points on the treadmill belt at a slower rate than it would be if the belt was moving.

If the belt matches planes speed with respect to the ground, but in the opposite direction -- there is no "puzzle" in it. The plane just has to overcome a bit of additional friction of faster rotating and/or skidding wheels. If its engines (of any kind) have enough power (and we expect, they do), then what's there to solve?

What's to solve? Plenty of people on dozens of message boards believe the plane can't take off. This is like understanding the Monty Hall riddle, explaining it and asking "what's to solve"?

On the other hand, if the belt matches the rotation of the wheels (no skidding is implied) -- that sends people on a cerebral jorney, considering all the irrelevant stuff, like type of engines, air speed/ground speed, etc.. While overlooking the fact that the puzzle practically states that the plane remains stationary. Though, difficult, if not impossible, it would be to create those conditions in practice.

The riddle does not practically state that the plane remains stationary. The plane takes off!

The version of that puzzle that I heard quite a while ago, was very careful to state that the belt was designed to match the rotation of the wheels.

And that's more of a riddle? The plane takes off either way for reasons that I already stated. What gets a plane moving are its props or jet turbines, which push the air backward and impel the plane forward. What the conveyor belt, wheels, etc, are up to is mostly irrelevant.

And I also explained why the treadmill belt exactly matching the speed of the wheels is paradoxical.

[Guest]

Over the years, this puzzle comes in and out of fashion. I don't know who originally came up with it and what they meant. However, "treadmill matches the speed of the plane exactly" is ambiguous and does not seem to present a puzzle.

If it means that the belt and the plane match their speed with respect to each other -- that is meaningless. Such is always the case, regardless whether the treadmill moves at all, and with what speed.

If the belt matches planes speed with respect to the ground, but in the opposite direction -- there is no "puzzle" in it. The plane just has to overcome a bit of additional friction of faster rotating and/or skidding wheels. If its engines (of any kind) have enough power (and we expect, they do), then what's there to solve?

On the other hand, if the belt matches the rotation of the wheels (no skidding is implied) -- that sends people on a cerebral jorney, considering all the irrelevant stuff, like type of engines, air speed/ground speed, etc.. While overlooking the fact that the puzzle practically states that the plane remains stationary. Though, difficult, if not impossible, it would be to create those conditions in practice.

The version of that puzzle that I heard quite a while ago, was very careful to state that the belt was designed to match the rotation of the wheels.

There is way ( short of cutting engines off teh plane) to keep the plane stationary on a treadmill..

[Prime]

And that's more of a riddle? The plane takes off either way for reasons that I already stated. What gets a plane moving are its props or jet turbines, which push the air backward and impel the plane forward. What the conveyor belt, wheels, etc, are up to is mostly irrelevant.

And I also explained why the treadmill belt exactly matching the speed of the wheels is paradoxical.

I'll disagree that the type of the engine is relevant in any case. If it's internal combustion engine that rotates wheels, then the problem comes when the plane takes off an loses its friction. Otherwise that engine would work as well as a jet.

I don't see any paradox, nor the explanation. (But I didn't go through the entire topic.)

However, we may have a concensus here. If the belt matches speed of the plane (whatever that means) -- then the plane takes off, and I still don't see what's the riddle there. Is it, whether the plane's engines can overcome a little bit of additional friction?

If the belt matches the rotation of the wheels -- the plane does not take off. Although, in practice, you'd have to make the belt a chain, the wheels sprockets, and rotate the belt fast enough so that the friction in the axels matches the jets' thrust. (Or when the system starts reaching relativistic effects -- approaching speed of light.)

Either way the riddle seems simple.

The real puzzle is, why this riddle raises so much passion and heated argument? Not necessarily on this forum, I mean, in general. It is all over the internet. All people around the world divided into two camps. And the war is about to break out with airplanes taking off moving conveyors and dropping logical bombs on the enemy.

[Guest]

The real puzzle is, why this riddle raises so much passion and heated argument? Not necessarily on this forum, I mean, in general. It is all over the internet. All people around the world divided into two camps. And the war is about to break out with airplanes taking off moving conveyors and dropping logical bombs on the enemy.

I think this is because not a alot of people know a lot about aircraft. So they try and relate it to the closest thing they know, and that would be a car. In realitiy a car is completely wrong and it is this asumption which makes people believe one side over the other

[Guest]

I think this is because not a alot of people know a lot about aircraft. So they try and relate it to the closest thing they know, and that would be a car. In realitiy a car is completely wrong and it is this asumption which makes people believe one side over the other

It becomes interesing if the car has wings and a turbine engine too. ......

So, we have several people arguing against a yes/no answer - if there are one of the doubters out there look up the youtube video for treadmill aeroplane myhtbusters, I am told it's there somewhere.

Putting it my way - I am flying a plane that lowers on approach to a giant treadmill, (I forget to slow sown enough to land), as my wheels make contact the tread mill matches the speed, my thrust continues so i pull back on my joy stick and go up again - I have removed the standing start - can the doubters explain why my aircraft should have stoped when the weels match speed (which is never gonna happen)

Or assume you are holding a plane on a treadmill then push it forward - as would the engines - any reason it wld stay there when you push it forward just because the wheels are free to spin?

How about you are in a seaplane, the current runs fast but smooth, and the surface of the water has no friction (I kmow i'm removing the friction, it equals the treadmill/wheel speed) - will the plane take off? The movement of water with no friction is similar to the free spinning wheels - the thrust moves the plane through the air causing lift

Trust it's becoming unarguable soon

[Guest]

I'll disagree that the type of the engine is relevant in any case.

I don't know what you're talking about; I never stated the type of engine is relevant.

If it's internal combustion engine that rotates wheels, then the problem comes when the plane takes off an loses its friction. Otherwise that engine would work as well as a jet.

Planes don't work that way, but if they did, then no, the plane would not take off as Bonanova explained in his response in the original topic.

I don't see any paradox, nor the explanation. (But I didn't go through the entire topic.)

I explained it in a reply to you.

However, we may have a concensus here. If the belt matches speed of the plane (whatever that means) -- then the plane takes off, and I still don't see what's the riddle there. Is it, whether the plane's engines can overcome a little bit of additional friction?

If the belt matches the rotation of the wheels -- the plane does not take off.

Where do you see a consensus? You're the only one I recall agreeing to this. It doesn't matter if the belt matches the speed of the wheels. I explained why in direct response to you twice, and instead of refuting my argument, you merely repeat yourself.

Although, in practice, you'd have to make the belt a chain, the wheels sprockets, and rotate the belt fast enough so that the friction in the axels matches the jets' thrust. (Or when the system starts reaching relativistic effects -- approaching speed of light.)

Either way the riddle seems simple.

Approaching the speed of light? What are you talking about? The wheels sprockets? What does friction in axles matching a the jets' thrust mean? In your scenario, you want the belt speed to match the wheels' speed. Why is all this necessary?

[Guest]

To add another thought - if a plane has a normal take off on a static runway, are the wheels driving it along? You need to know that the answer is no - they provide less friction for the plane to move - it could just as easily run on a cushion of air, which if it did, it would be the same as frictionless wheels on a treadmill

lets assume the treadmill surface is covered in oil - and there is no friction (zero friction), the jet will move the plane's wheels practically can't grip and won't freely spin - Will it move forward and take off

Pls lets forget about cars, skates and other UUFOs Unidentified UnfFyable Objects ... Further it maters not which propulsion system is used - jet or prop (push or pull)...

and I thought this was dead!

[Guest]

Just a kind of guess but i think it could take off.

[Prime]

Approaching the speed of light? What are you talking about? The wheels sprockets? What does friction in axles matching a the jets' thrust mean? In your scenario, you want the belt speed to match the wheels' speed. Why is all this necessary?

I must note one more thing that I omitted in previous posts.

In the model, where the conveyor matches the wheels rotation, and the plane does not take off -- it is not just friction that counteracts the force of the jets. As the plane edges forward, the belt has to move faster to match the wheels' rotation. The wheels rotate faster. There is an acceleration in RPMs. Acceleration requires force. As speed becomes comparable to the speed of light the acceleration becomes more and more costly in terms of energy required. People build humangous reactors requiring massive amounts of energy to accelerate just a small atomic particle to speeds nearing the speed of light. Against acceleration of airplaine's wheels to some considerable speed, jet engine has not a prayer. And at some point the friction in the axels would become enough to set the airplaine on fire.

Pulling conveyor belt from under the plane is not the most effective way to stop it. But theoretically, or, at least, logically, it can be done.