This may be old and have been covered before but I haven't seen it......

A plane is standing on a runway that is made of a large conveyor belt. The plane fires up its engines, but as it moves forward, the conveyor belt senses the speed of the plane's wheels and moves at exactly the same speed in the opposite direction. Can the plane take off?

I'm after good solid logic and math rather than just a yes or no on this one.

No.

Of course it can.

[/thread]

Harrier.

Hey Joey. I posted your thread about 'Embarrassing Touchings' on a site that I use in the UK. They loved it.

No this is a standard jet liner.

yeah that would probably be best before anyone says something silly, which is what always happens with this question.

Other than a Harrier jet, no. The principles involved are not the speed of the wheels on the surface below but the speed of the wings with relation to the surrounding air.

I'm internationally famous.

unless the conveyor belt moves the air, too, i think the plane's good to go.

edit for a more full explanation:

barring the rotational-inertial/frictional force in the wheels that will actually move the plane backwards when the conveyor belt goes (which would always be less than the full force of the conveyor belt, anyhow, unless the wheels were locked still), the engines that are "pushing off the air," at least functionally, don't experience a counteractive force to the engine in any appreciable way. hence, the plane still goes forward.

too late

No, it won't take off. Lift is caused by air moving over the wings. If the plane isn't making forward momentum and there is no air blowing, it won't take off. No math needed.

Is that a statement or a question?..... well you are now, if only at least to a small community.

This has been discussed to death several places on the internet. There are two types of replies -- those who accept the problem at face value, in which case the plane takes off, and those who assume all sorts of ridiculous friction variables that would only exist under extreme conditions, and in that case, no, it wouldn't take off, it would be torn to pieces.

QFT

Where is this place you speak of?

In this case we are only talking about the theoretical aspect, not the actual.

I couldn't tell if you were asking for links or making a joke.

If a joke: ha ha

If a link: Straight Dope and the followup. This site also has discussions. Also, just search on "plane on conveyor" for lots more.

Theoretically or actually... the plane is not moving. It won't take off.

Go the gym, get on a treadmill. When you run you will feel no wind on your face. No wind, no lift.

Now, attach a chain to the front landing gear and put the plane in a wind tunnel. It's not making forward momentum, but the wind being forced over the wings would cause lift and the plane would take off.

If you assume that the wheels of the plane continue to serve their function to eliminate friction, the plane will take off as usual. Planes move forward by pushing against the air, not the ground (like in a car does). It doesn't matter whether the ground is moving or standing still.

But wait, you say, the problem says the speed of the conveyor offsets the speed of the plane. There's the trick -- this can never occur in a plane with functioning wheels. If you assume massive amounts of wheel friction (basically reducing the problem to a fuselage lying on the runway), then no, it can't take off.

The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. But of course cars and planes don't work the same way. A car's wheels are its means of propulsion--they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane's wheels aren't motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, 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, as you correctly conclude, make the plane's wheels spin madly.

A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.

As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

you guys could save a lot of breath and say "checky was right." jesus.

The lift comes from air moving past the wings, so all we need is relative velocity between the wings and the air. So, if the plane was tied down but it was in a wind tunnel where wind was blown past its wings, it would start to rise.

I'm not sure I fully understand your scenario completely. There are two issues involved, from what I gather. The motion of a plane comes from its engines, which blast air backwards and move the plane forward through action/reaction. So, unlike a car, it doesn't move forward based on its wheels. It only has wheels to reduce friction between the plane and the ground. With a car, the friction between the wheels and the ground is necessary because it makes the car go forward. With a plane, ideally there would be no friction between the plane and the ground, and it would just sort of hover and slide above the ground, completely controlled by its engines.

So, back to the problem. The belt is set to move at the exact opposite speed of the wheels. So, the wheels can never advance relative to the ground without "slipping." In this case, the wheels may as well simply be fixed, unable to spin. But, given enough strength from the engines, the plane will start to advance forward. The maximum force of friction that can be provided between the wheels and the ground is mgMu, where m is the mass of the plane, Mu is the coefficient of friction between the belt and the rubber of the wheels, and g is the acceleration due to gravity. If the engines can provide a greater force than the force of friction, so the plane will start to drag along eventually as the engines go harder and harder. Eventually, the plan may drag along and pick enough speed to take off (if the engines are strong enough). Or, the engines may not be strong enough, the plane will slowly move forward, dragging its wheels, burning a lot of rubber, but never get enough velocity to take off.

So, the answer is that it depends on how strong the engines are. I think this is correct...

A wheel's function is to reduce friction? I thought it was to roll.
There is still friction on the tire, otherwise it wouldn't roll, it would just slide.
The plane is still not pushing against the air, it's not doing anything but sitting still, the wheels are rolling uselessly under the frame.

Edit: I'm wrong here. ^

Can a float plane take off on a river?

Of course.

How is that different from a plane on a treadmill?

Not at all.

Yes, that and whether you assume the wheels continue to function. If the treadmill were to accelerate to speeds such that it caused enough friction in the wheels to exert a meaningful amount of force on the place, the plane would be slowed. I suspect that ordinary plane wheels turning that fast would quickly melt down; then you'd have a plane riding on legs; which would quickly melt down to the fuselage, and I doubt any plane has enough power to take off then.....

As stated in the problem, it appears the wheels continue to work and the question is not about the frictional destruction of a plane. In that case, the plane takes off just as if the ground were stationary, as the friction of the wheels is negligible compared to the forward force of th plane's engines.

I see your reasoning and you are beginning to persuade me. The truth of it is this, at some point the thrust from the engine is going to overcome the speed of the treadmill and the plane will move forward.
Another way to put it would be to take away the landing gear and treadmill and just think of the plane.
If the plane was suspended in air and all of a sudden dropped, would it be able to remain in the air if the pilot engaged the engines? Of course it could because the thrust would start forward momentum, therefore wind and lift.

Now you seem to be stating a completely different problem: if a plane with the engines turned off sits in a certain place on a moving conveyor, will it take off? Because if the engines are on, the propeller/jets are pushing against the air.

You're absolutley right. I jumped at the question without thinking it through and I apologize for the dick tone of that first sentence.

This is why this problem keeps cropping up -- because our "obvious" first instinct is so wrong. I think most people go through the same process -- I know I did. In that way it's a great problem. There are some people who refuse to come around, which is great fun, but you thought it through and realized the real answer faster than most!

Well, if I had been a good little boy and stayed in school, I'd be in the Air Force right now. I love planes and flying, so I thought I was gonna be the smart guy on this one at first.
I was stupid as a kid, but I'd like to think I have the ability to know when I'm wrong and adjust my thoughts.

The plane will not take off. It is being operated by Jet Blue, and will idle on the runway for 9 hours, not allowing anyone off. You may receive a refund.

Zing.

A better plane question is one I had to answer to my instructor when i got my ticket.

If a plane is flying straight into a 100 mph wind and it's relative speed is 100 mph then it's ground speed is exactly zero. Now if this plane turns 180 degrees as fast as it can, say 6 seconds, will it stall?

The answer is no.

However, if David Blaine was the pilot that it would not only take off, but it would also turn into an elephant. I hear he's magic.

great question. you guys didn't explain the answer very clearly (i'm an idiot), but eventually i got to it.

checky was right.

The plane was on a giant ice cube.

I admit it, I only came in to see what Loogie posted.

but I don't get it.

Same here, but I get it cause I actually read the whole thing.

To find the right answer, I seriously skimmed through the thread till I found a post by LongLiveYorke

And yes, he's right

http://dsc.discovery.com/fansites/mythbust...ythbusters.html
Maybe they can help

I thought the answer was obvious, but after lookinh at the answers, I'm confused by the question.

The way I orginally interpeted the question was that if the aircraft tries to move forward at 10 mph, then the belt moves backward at 10 mph and nulls out the forward momentum. Therefore the aircraft doesnt move relative to a stationary observer on the ground.

What happens if the belt moves backward at 10 mph with the aircraft engines turned off? I would guess the plane would move backwards. If not, then theres something about the setup of this imaginary problem that isnt being mentioned or I'm misinterpeting the question.

You would see the same thing with an airbaot on a moving river. If the river is moving at 20 mhp backwards and you throttle forward at 10 mph, you move backwards at 10 mph. You would have to throttle more than 20 mph to move forward.

So, wait.... the plane committed suicide?

Now I'm really lost.

Yes, you are missing something. A boat on a river pushes against the water. (Same with a person walking or a car driving on a treadmill). A plane does not push against the runway, it pushes against the air.

Yes, an airplane would move backward if the engines were turned off, but only because of the friction in the bearings of the wheels, which is negligible when the engines are turned on. (That's the whole point of having wheels on an airplane -- to eliminate friction with the ground so that the engines pushing against the air makes the plane move forward).

I didn't read every single post... but I am confused....

Why is this thread 2 pages long, and how is there even a discussion?

In fact, how did someone even ask this question?

Is this not the most obvious thing ever?

Funny how you didn't answer the question.

The obvious answer is no, because 99% of people would think about it like a car or person on a treadmill.

The correct answer is yes, but you have to realize that a plane has nothing to do with touching the ground. As hblask said... if the wheels serve their purpose, then what the ground is doing isn't even an issue.

How do you figure? I read more of the replies, and I still don't see how the plane can take off if you are assuming it's a super treadmill.

Yes the jets push against the air, which causes the plane to move forward, but with the treadmill underneath, the wheels can't travel over the ground to produce the lift from the air onto the wings. The plane would remain stationary as long as the you don't question the capacity of the wheels and treadmill.

Are you saying at some point the jets will be too strong and the plane will roll off the treadmill regardless?

I mean seriously, you all need to stop trying to sound smart with your replies and just spell it the fuck out if you really want people to come around to what you're saying.

The assumption is that there is zero friction within the bearings of the wheel.

With that said, it doesn't matter if the treadmill is moving forward, backward, or not at all. There is no link between the plane and the treadmill, because there is zero friction within the bearings. The plane moves forward as fast as the engines can push it, and the wheels spin in accordance to the treadmill, and neither affects the other.

Add a negligable amount of friction in the bearings, and the engines have to work a bit harder to overcome it, but as stated, as long as the wheels are doing what they are supposed to (remove/reduce friction between plane & ground) the plane is going to take off.