The "Plane on a Treadmill" Question

[Griff]

9 pages on topic, impressive. Unless the runway is moving air, you've got nothing but a over-powered paper weight.

[orthodoc]

I changed my mind. Bruce is right; the jet engines aren't pulling air over and under the wings; in fact, the engine doesn't even have to be on the wing. The engines are pushing the plane to achieve atmospheric air flow over and under the wings. Since the treadmill plane isn't moving relative to the atmosphere, the needed air flow around the wings doesn't happen and there's no lift; just a lot of engine revving and wheel-spinning. It doesn't matter what 'ground speed' the instruments record, the plane has no velocity relative to the air around it. The thing won't fly, any more than a kite will fly if you hold its string while running on a treadmill.

That's my story, and I'm stickin' to it. :p

[9th Engineer]

and it keeps the covers from falling down into the sewers

[DanaC]

*pokes head into room.....realises is totally out of depth and retreats*

[9th Engineer]

But the engines still exert a force against the body of the aircraft, and since the runway can't exert any force in the absence of friction, their is a net acting force on the aircraft

[Griff]

but no lift

[xoxoxoBruce]

Originally Posted by 9th Engineer

and it keeps the covers from falling down into the sewers

Yes, I forgot that important part.

[xoxoxoBruce]

Originally Posted by orthodoc

snip~ Since the treadmill plane isn't moving relative to the atmosphere, the needed air flow around the wings doesn't happen and there's no lift; just a lot of engine revving and wheel-spinning.
~snip :p

Nope, the engines push the plane through the atmosphere (air), and what the ground and wheels are doing under it has absolutely no bearing on the plane moving through the air. Up she goes, into the wild blue yonder. Flying high, into the sky.

[orthodoc]

Originally Posted by xoxoxoBruce

Nope, the engines push the plane through the atmosphere (air):

That's just what the engines don't do in the case of the treadmill plane. They aren't moving it through the atmosphere. It's stationary with respect to the air around it, therefore no flow, therefore no lift.

If you run on a treadmill, does air flow past your face (assuming no fan!)?

[Q baby]

Originally Posted by Kitsune

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?

Oh, Kay....but where in the original post does it say that this hypothetical plane...has wings?

[xoxoxoBruce]

The plane isn't running on a treadmill, that's not how it moves. It moves by pushing through the air...the treadmill has no bearing on the plane.

[footfootfoot]

Originally Posted by glatt

Good point. The question doesn't clearly state that there is an atmosphere, so a plane wouldn't work anyway. No lift in a vacuum.

Nor combustion w/o supplied oxygen.

Another example of the unimportance of wheels relative to a plane's taking off.
Ski planes and water planes have no wheels, hell, if a plane were lying on its belly on a greased treadmill it would take off.

[Flint]

...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.

There are two interpretations for this. Both are possible, but neither is specified by the provided information.

#1: If the "forward speed" is defined as relative to the treadmill then the plane is stationary relative to the air.

#2: If the "forward speed" is defined as relative to the ground, then it is possible for the plane to be in motion relative to the air.

Nothing in the question rules out either of these interpretations, and no amount of blustery hoopla or physics masturbation can change that.

The question is unanswerable as stated. It's designed that way on purpose.

[Pie]

Originally Posted by LabRat

Pie, compare your diagram to mine in post 67. See the difference? This is critical. The treadmill does not move the axle, it moves the wheel around the axle. Thus, the planes forward thrust has no opposite force, and moves the plane (attached to the axle) forward until lift overcomes gravity and the plane takes off.

Okay, this is the absolute last post I'm going to make on this subject. (promise!) If the wheel experiences a force, that force must be transmitted to the axle. (The other alternative is that the wheel goes that-a-way while the rest of the plane stays put.) The free body diagram holds.

The straight dope misses this point:

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.

That "pull yourself forward easily" is impossible. To move yourself forward at all (even a micron per hour) still necessitates a net imbalance in the forces acting on the axle of the wheel; this is patently impossible, given the wording of the problem. F1 == F2 by the very statement of the scenario, so no net motion.

Newton would be scratching his head.

[Ibby]

I'm with Flint and Pie. I wholeheartedly agree that, IF THE PROBLEM WAS REALISTIC AND SAID WHEEL SPEED, NOT PLANE SPEED, it would definitely take off. But the problem doesnt say that. It's unanswerable, because plane design + physics =/= the actual problem.