The "Plane on a Treadmill" Question
 

The riddle/question is on every other forum. I figure I should bring the torture here, as well.

A plane is standing on a runway that can move, like a giant treadmill. When the plane's engines throttle up, it begins to move forward, but the treadmill is made to match the forward speed of the plane, only in the opposite direction. So, as the plane moves forward, it moves backwards beneath the aircraft.

As the engines throttle up, does the plane take off?

I've never heard this before. But no, a plane takes off because its wings generate lift, which it can only do when moving forward.

Why would the plane not move forward?

no, unless the engine thrust > wt. of plane... but that's a lot of thrust for your average puddle jumper.

edit: the Harrier could 'jump' off a moving runway ;)

The engines of the plane push against the air, so the runway doesn't matter. The wheels will rotate as much as they have to as the plane pushes against the air. The runway is not relevant once the plane's engines start.

No.
 

Yes, damnit! :)

No. No lift, as UT said. Planes do not take off from a stationary position. What would you expect it to do, suddently leap in the air? At what speed? From zero to what, in how many seconds? Same question: if you drop a paper airplane on the ground, will it suddenly leap in to the air and fly for no apparent reason? Same answer: No. The end.

The plane will move forward but not enough to gain enough lift. The wheels on the ground fight the force of gravity, until the plane has enough forward momentum for the wings to produce lift. Now the wheels are not fighting the force of gravity as hard so the engines have to fight it harder. That's my story and I'm stickin to it, until someone posts something that makes it look bad.

The friction of the wheels in this question and, even in the real world, is pretty much of no consequence. The engines, being as powerful as they are, should easily be able to overcome it.

Hearing people explain this question and their answer has made me drop this into my "interview pool", alongside the "explain why manhole covers are round" question. I love it. :)

Of course there is lift. The plane will move forward against the air, and twice as fast against the runway. It will take off just like it normally would. A plane's wheels are not powered. They spin freely as the engines push against the air. The air is stationary, only the runway is moving.

No! The engines (normally) move the plane forward to make air go across the wings and produce lift. No going forward, no lift, no take off.

If it were a car and depended on the friction between the tires and the ground to move forward, that would be another thing. But in this case, the backward thrust of the engine is what's moving the plane forward. I don't think the treadmill would have much of an effect on the outcome, if any.

Think of it this way. A plane already in the air flies just over the treadmill. Does the movement of the treadmill affect the movement of the plane?

It's not already in the air, and it will never get there from a staionary position. The engines DO NOT "push" the plane into the air.

Sure they do. What, you think the wheels do it?

No. The movement of air over the wings does it. No movement = no lift = it will not take off.

The engines push the plane through the air until lift is achieved. When a plane taxis on a runway, it uses its engines pushing against the air to make it move. The wheels just follow the plane along.

No, read the question:
The plane cannot move against the air, at all.

Forget the wheels. The plane needs to move against the air to generate lift, to take off. It can't move against the air, so it can't take off.

OK, OK I'm convinced.

Which makes me a worse job candidate, except that I have the ideal answer to all such interview questions:

Oh, I've already heard that one.

That is, unless you want to use a constructed answer. The answer to why manholes are round? Because men are round. Duh.

"What would you do for a Klondike bar?"
I'm sorry, but I can't discuss salary during a first interview.

Sure, all it would need is a wind blowing at the front of the plane, that is strong enough to create lift.

Spexxvet "gets it"
 

The plane pushes against the air, right?

Picture a different scene. You are in a canoe in a raging river, but you have a pole, and you are using it to push your way up the river. The water is going past the canoe at a very high speed, but since you aren't pushing against the water, this doesn't matter. You push against the ground with a pole.

Here, the plane isn't pushing against the runway, it's pushing against the air. The runway doesn't matter.

It would not take off.

not the speed that the tries rotate. The plane will not move forward, cannot take off.

No, picture the scene we're talking about: a plane hopping right into the air, straight off the ground. (Commercial jetliners are not designed to do this!) And then say to yourself "oh, gee, what an incredible dumbass I was for even entertaining the fact that this might be possible" . . .

And the "pushing" doesn't matter, either. Only the forward motion does. There is no forward motion according to the question.

You're messing with me now, aren't you? You know it takes off, but you are playing devil's advocate just to keep the argument going.

The question doesn't say that.;)

http://cellar.org/2006/ITTAKESOFF.gif

:D

ok... the pilot 'spins' up the runway to about 150 mph, quickly turns around 180 deg. and 'rides' the runway with enough speed for lift!

That's awesome, UT!

Yes it does:

It matches the forward speed, cancelling all forward motion. UT's animation repeatedly says "as the plane moves forward" but that is not the scope of what we are discussing. We are discussing a stationary plane.

Fuck the wheels, fuck the treadmill, fuck the thrust. Lift is produced by air moving across the wings. Moving.

I found it after googling for the problem... turns out it was fought over by folks on a physics board, so I feel a little less foolish...

Flint. The wheels don't matter as far as forward motion is concerned. As the graphic that UT says, the wheels will just spin twice as fast. It doesn't matter how fast the treadmill is going backward, because the plane's pushing against the air, not the ground.

:corn:

(Not being sarcastic...I find this debate fascinating)

Fuck how fast the wheels are spinning. No forward motion = no lift.

The only item of discussion here is how you read the question. Stationary planes (commercial jetliners) do not jump into the air. Ever.

If I understand you, the above part of the problem set means "no forward motion" to you. I don't think it does. It would for a car. It doesn't for a plane.

It doesn't mean that to me. I would say there is most certainly forward motion in the way I described it. The wheels are free spinning despite the treadmill.

No, this part does: There aren't two different reasons for the wheels to spin. They only ever spun because the plane was trying to move forward, and the treadmill matches the forward speed, cancelling it. If the plane thrusts harder, the treadmill continues to cancel it's motion. There is no tip-over point, here. The treadmill prevents the plane from moving. The plane cannot take off from a stationary position.

Get a motorized treadmill and a bicycle. Hold the bicycle in place and turn the treadmill up as high as it will go. Are you having to fight very much to keep the bike stationary? No -- the friction between the bike frame and wheels is very low. Now, push the bike forward. Is it taking much effort? Not at all.

It doesn't matter how "hard" it is. In this scenario, you can't do that.

The plane will move forward, no matter how fast the treadmill is going. The treadmill can't cancel the forward motion of the plane, because the plane's speed is not determined by the wheels. If you hold a hotwheel car in your hand, and put it on a treadmill, you can move it forward no matter how fast the treadmill is going. Likewise, the jet engine will move the plane forward no matter what the treadmill and wheels are doing.

Now, if it were in a wind tunnel, and air was blown to cancel the jet engines, that would be a different story.

You're right: if you ignore the question you can get whatever answer you want.

Nothing in the question says the plane is stationary. Just that the treadmill moves. But the treadmill can not stop the plane! The assumption that the plane is made stationary by the treadmill is something that you are bringing in, and is the trick part of this trick question.

The thrust of the engines pushes the plane and axles the wheels are spinning on forward (as stated in the problem). Once the plane begins to move, then the treadmill turns on. The treadmill accounts for and this forward motion, speeds up, and causes the wheels to spin around the axle. The friction holding the still plane in one place is gravity, a downward force. Once the treadmill is going, the thrusters create a vector of force in the forward direction enough to overcome the downward force of gravity. The plane continues to move forward faster and faster and the treadmill/wheels continue to spin also, but again, only around the axle. Eventually the plane will gain enough forward speed to create lift under it's wings as it would on a stationary runway.

My initial response was no take off, until I tried to explain why, then I had to change it to damn, I think it will take off.

It doesn't say "wheel motion" - it says forward speed. No forward speed. Forward speed cancelled. No motion. No lift.

I'm confused. If the treadmill does not negate the forward motion of the plane caused by the jet engines, the entire question seems moot and pointless in its quest to be clever. If it DOES, as it seems the question meant to intend, then I agree with Flint.

But I'm not a scientist and I don't even play one on TV.

Sorry I'm late to this discussion, but I'm with Flint. The problem, as stated, does not allow for the plane to develop any velocity relative to the air. Only this relative velocity (wing vs. air) can give you lift. (All aeronautics engineers: No Lift Without Drag!)

Doesn't matter what happens "in real life," this statement
makes it moot.

Hey, that's what I said, Pie...and now I feel really intelligent because you ARE a scientist-type. :)

In fact, a plane that's stationary with respect to the runway can take off -- if there is a strong enough headwind. Don't believe me? Try holding on to a kite on a windy day.

No, it won't: Again: not "wheel motion" but forward speed. The specific scanario we are discussing involves a stationary plane.

Yes it can, because the question says it can, and does. That is what we are discussing:

Flint, the wheels are in contact with the runway. The wheels are spinning around the planes axle. The forward thrust of the plane moves the axle forward, while the wheels keep spinning around the now moving axle.

After thinking for a bit, it seems pretty clear to me that the plane will not move forward, and hence will not take off. I have written a cogent, well-argued, absolutely devastating post to explain to all you fucking idiots who think the plane will take off, that it will not.

As is my habit, I then reread the post and went about editing it to make it more organized, introduce additional supporting points, and just generally kick rhetorical ass. (Anybody who thinks my posts are incoherent should see my first drafts.)

In the process of doing so, I became convinced that the plane would indeed take off.

It's all about the wheels. What forces are at play here? We've got the engine pushing forward. We have the treadmill furiously spinning backward. Since this is physics word problem land, we don't have to worry about friction, and we're ignoring considerations of the plane changing speeds. It's true that the engines are pushing against the air, not the ground--but they're also pushing against the plane. The treadmill is also exerting a considerable force of identical magnitude in the opposite direction. However, this force has no purchase on the body of the plane. Because the wheels are spinning freely, none of the reverse force from the treadmill is applied to the plane.

I think we can all agree that we'd like to see it tried, preferably with a 747 or a Concorde.

Picture a bike on one of those moving things in the airport. If you stand off of the moving tread, and hold on to the bike while walking forward at the same speed the tread is moving backward, the bike will move forward. The wheels will now be spinning twice as fast, but the bike will be moving as fast in the opposite dirsction as the tread. In the plane example, the forward thrust of the engines = you holding onto the bike. The plane will move forward, ever faster.

Right steve!! because they are spinning around an axle.

The treadmill will have some backwards force, but not enough to prevent the plane from moving forward.

The treadmill is moving 140 mph backwards while the plane is moving 140 forwards. In order to prevent the plane from moving, the treadmill has to accelerate to the point where it produces more drag on the wheels and axles than the jet engines do. Not 140 MPH, more like 14000.

The stated scanario is that all forward motion is cancelled. As to "how" the treadmill does this, that's a different question.