Thursday, December 14, 2006

Now My Brain Hurts.

From David Pogue's Technology blog in the NYT:
...I found it presented at 8452:

“Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

“I say no, because the plane will not move relative the the ground and air, and thus, very little air will flow over the wings. However, other people are convinced that since the wheels of a plane are free spinning, and not powered by the engines, and the engines provide thrust against the air, that somehow that makes a difference and air will flow over the wing.”

The guy behind me at the airport told his buddy that, in fact, the plane WOULD take off, and his buddy seemed to agree. Do we have any physicists in the audience?

The emerging consensus (at least as far down as I read) seems to be that the plane wouldn't take off, because it wouldn't have enough airspeed to generate lift. But that argument seems to take it as a given that the conveyer belt is preventing the plane from moving forward, which to me seems silly. As the quote above says, the thrust would be provided by the engines, which are pushing against the air, not the conveyer belt. I liked the comment that suggested picturing a prop plane instead of a jet, since the props pulling the plane through the air is somehow more intuitive than the jets pushing it. (This is all assuming that friction would not be a factor, and I don't think this puzzle is really about friction.)

Anyone else have any thoughts on this? Can anyone explain how the conveyer belt would prevent a plane from moving forward fast enough to generate lift?


shoephone said...

Eli - this is an I.Q. test, isn't it?

English - yes
Spacial Relationships - yes
Basic Geometry and Algebra - yes.
Music theory - yes.

Physics and anything having to do with airplanes - NO. Just NO.

Rob said...

The thrust is not against the air. That's a mistake. Rockets work in a vacuum, and they can't thrust against the air. If you had an internal air tank, a jet would work in outer space, although the wings wouldn't -- no air, no lift.

So, if you turn on the jet engine, it will push the airplane forward.

Let's say we had a 20 mile conveyor belt (I don't think it needs 20 miles, but I'd hate to drop the airplane). If you start the belt moving at the takeoff speed of the jet, and then you fire up the jet and try to take off, what you will find is that, at some point, the jet remains stationary on the belt. At this point, no air would be flowing over the wings. It's stationary, and it can't take off, assuming it doesn't try to reach a higher speed.

On the other hand, if the belt starts out stationary and only moves in response to the rotation of the plane wheels, the plane will be thrusting ahead and will have no trouble taking off, assuming the wheels don't break. The belt would speed up to try to match the speed of the wheels, and the wheels would accelerate because the plane would be moving. At some point, either the conveyor belt or the wheels fail and I suspect you find out why they don't fly airplanes off conveyor belts.

Rob said...

BTW: I am a rocket scientist. Amateur, but still...

Eli said...

I wasn't 100% sure about exactly what the jet engine was pushing against, or if it was pure action/reaction, but I still can't get why the conveyer belt would prevent the from moving forward.

If the plane was floating on magnets or some kind of air cushion above the conveyer belt, it would have trouble taking off, right? So what's different about resting on free-spinning wheels?

(Again, I'm assuming friction is neglible)

Anders said...

An explanation I like: If the plane were floating above the ground, it would have no trouble taking off: the thrust force from the expelled mass of the burning fuel would propel it forward. As noted, rocket propulsion works even in empty space.

Now imagine a gremlin on the landing gear spinning the wheels while this happens. (Yes, I am thinking Twilight Zone.) The plane still takes off as before, only now the wheels spin as it does so. Big whoop: the wheels are just these free spinning attachments.

Now if the plane is in contact with a treadmill, the treadmill just functions as the gremlin: it causes the wheels to spin more while the plane rockets forward.

See also:

op99 said...

Is this an IQ test? If you were really smart, you wouldn't put the fuckin' plane on a conveyor belt in the first place.

Eli said...

Anders is my hero.

Is this an IQ test?

I think it's meant to highlight some form of fallacious reasoning - I'm just not sure which side of the debate the fallacy's on.

ripley said...

Rob's answer is correct. The jets work on Newton's 3rd principle but planes (or, more precisely their wings) work on Bernoulli's principle.

The jets won't create the conditions for Bernoulli's principle to take effect.

And Bernoulli is pissed.

Eli said...

If the jets move the plane forward, won't that create the lift? Bernoulli doesn't care if there's a conveyer belt under the air, right?

So it boils down to the question, Why won't the jets move the plane forward? Just saying that it won't take off because it's not moving forward doesn't really answer the question.

ripley said...

Basically, the conveyor absorbs the kinetic energy (thrust) the jets are creating. Kind of like spinning your tires on ice - your speedo can read 50mph (thrust), but the car's not actually moving forward because the kinetic energy isn't transferred from the source (car wheels or jets) to the entire body of the car or plane.

When you say 'the jets move the plane forward', normally they do - but in relation to the ground and the stationary atmosphere. If the ground (in this case, the conveyor) is moving at the same speed the jets are trying to transfer to the plane, there's technically no forward motion. To put it another way, there's forward motion in relation to the surface of the conveyor belt, but not in relation to the earth's surface or the atmosphere.

No (relative) forward motion thru the atmosphere means there's no air moving across the wings, so Bernoulli doesn't kick in.

Theoretically, if a strong enough headwind came up during the experiment (800mph or whatever) the plane could take off momentarily, even from the conveyor belt. I'm not sure if it would actually start flying, though. Hmm...

My head hurts...

Anonymous said...

Hi Eli, it's Bill, your handy neighborhood Physicist.

Force = mass times acceleration. Doesn't matter if it's a jet, wing, or rocket. If you apply a force to accelerate a mass one way, you get a force back on you in the opposite direction. For a jet to provide thrust, it accelerates air, a rocket accelerates the combustion products, a wing accelerates air downward to produce lift.

The idea that the plane won't move forward is incorrect. Unless the friction between the wheels and the belt prove as much of a force on the plane as the engines do, the plane will accelerate forward, which means that air will be accelerated by the wing, which means that lift will be generated, which means that the plane will be able to take off.

The prop idea is interesting because in fact you can generate lift on a stationary wing by blowing over it (that's why from the Wright Brothers to modern day we use wind tunnels). I've seen stunt pilots actually do this...point into the wing, hold the brakes, max the throttle and take off vertically (Bob Hoover in a Piper Cub.)

In further useless information, Ferarri has a wind tunnel with a rolling conveyor belt to be able to test the aerodynamics of their cars at speed with the wheels rolling at the correct rate. Maybe we can borrow it to prove a point.

Anders said...

> Kind of like spinning your tires on ice

The reason it is not like that is that a plane is not driven through its wheels the way a car is. The wheels on a plane are free-spinning, not connected to any drive mechanism.

It is true a winged car on a treadmill would not generate any lift. But if you applied a force from your arm, you could easily push a matchbox car forward over a treadmill (even without the wheels slipping). A rocket strapped on top of a matchbox car would go forward in the same way. Think of the plane as like that.

Eli said...

Thanks, Anders and Bill! That's really what I think the fallacy is.

I think there's also a subliminal red herring in the description of the belt as spinning at the same speed as the wheels, which calls to mind a "passive" treadmill which is actually driven by the wheels or feet that are on it. But that's not what this conveyer belt is. It's going at the same speed as the wheels, but *not* because they're transferring any force to it.

ripley said...

I confess I hadn't thought about the passive nature of the wheels and the concept of friction (or none) against the conveyor. I guess you won't find me piloting a 747 on a conveyor belt anytime soon.

On the plus side, we Did knock down the Sun Sphere.

Anders Weinstein said...

> I think there's also a subliminal red herring in the description of the belt as spinning at the same speed as the wheels,

Indeed, the meaning of this stipulation is unclear. Suppose the plane is moving forward with respect to the surface of the Earth at 100 MPH. (You can even imagine that after being accelerated to this speed as if by a slingshot, its engines are turned off and it just continues to move at a nearly constant velocity -- though air drag would ultimately slow it to a stop) Does the condition mean the treadmill spins the opposite way at 100 MPH? OK, no problem then: the plane still moves forward with respect to the earth, but if there is no skidding, the wheels rotate twice as fast as they would if traveling over fixed ground. That is, a speedometer attached to the wheels would read 200 MPH, not 100 MPH.

Or is it supposed to mean the controller tries to speed up the treadmill at this point to 200 MPH? But then the wheel rotation would increase so they spin at the equivalent of 300 MPH. And so on for any increase in treadmill speed you try -- you can't catch up. So it would normally be impossible for the treadmill to match the "speedometer speed", i.e. the wheel speed wrt to the treadmill surface.

The only way a conveyer belt could hold the plane stationary wrt the Earth would be if the frictional force on the plane from the treadmill could be made strong enough to completely offset the thrust of the engines, so that the airplane remains stuck in place wrt the ground, in spite of the thrust of its engines. That is quite unrealistic, though I think it is not impossible in principle. But then it is not achieved simply by controlling the treadmill to "match the speed of the wheels" but rather by revving the treadmill to the speed, whatever it is, where (incredibly) the frictional force needed to spin the wheels at that rate is enough to hold the plane in place.