Can The Plane Take Off?

[spm 1]

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.

[fryer98 30]

No.

[Ouch-8s 4]

Of course it can.

[JoeyJoJo 18]

No.

Of course it can.

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[Jelly-Filled Ace 1]

Harrier.

[spm 1]

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

[spm 1]

Harrier.

No this is a standard jet liner.

[Ouch-8s 4]

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

[DCJ001 0]

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.

[JoeyJoJo 18]

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

I'm internationally famous.

[checkymcfold 0]

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.

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.

[Ouch-8s 4]

too late

[Dogpatch 2]

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.

[spm 1]

I'm internationally famous.

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

[hblask 1]

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.

[coesillian 0]

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.

QFT

[fryer98 30]

This has been discussed to death several places on the internet.

Where is this place you speak of?

[spm 1]

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.

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

[hblask 1]

Where is this place you speak of?

I couldn't tell if you were asking for links or making a joke.If a joke: ha haIf a link: Straight Dope and the followup. This site also has discussions. Also, just search on "plane on conveyor" for lots more.

[Dogpatch 2]

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

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.

[hblask 1]

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

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.

[spm 1]

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.

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.

[checkymcfold 0]

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

[LongLiveYorke 38]

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...

[Dogpatch 2]

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.

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. ^