Physics-Engineering riddle. A plane sitting on a runway

[Bad_Doggie]

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction. The engines are running at take-off thrust, the brakes are off, etc. Everything is normal save for the fact the plane is on a treadmill.

Can the plane take off?

 

[Sean]

No. Lift is generated by the difference in pressure of air moving above and below the wings. No movement through the air, no lift.

 

[scrymettet]

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction. The engines are running at take-off thrust, the brakes are off, etc. Everything is normal save for the fact the plane is on a treadmill.

Can the plane take off?

nope.

 

[Peregrinator]

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction. The engines are running at take-off thrust, the brakes are off, etc. Everything is normal save for the fact the plane is on a treadmill.

Can the plane take off?

I don't think it can. I think what gives planes lift is the movement of the air across their wings--specifically the Bernouli effect of the air accelerating over the arched top of the wing. If the plane were on a treadmill, it would be still, relative to the air.

I'm not entirely certain that that applies equally to jets, though.

 

[bronzeage]

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction. The engines are running at take-off thrust, the brakes are off, etc. Everything is normal save for the fact the plane is on a treadmill.

Can the plane take off?

If turn the plane around to face the other direction, can it take off in half the distance?

 

[Sean]

I'm not entirely certain that that applies equally to jets, though.

Jets only provide thrust, not lift. Unless it's a VTOL like the Harrier.

 

[Peregrinator]

Jets only provide thrust, not lift. Unless it's a VTOL like the Harrier.

Yeah, that's what I thought.

 

[Sean]

If turn the plane around to face the other direction, can it take off in half the distance?

Half? Maybe. Shorter, certainly. That's why aircraft carriers use catapults.

 

[KRCummings]

This is an old riddle and is really rather easy.

The plane does take off because even though the belt matches the 'speed' of the plane, the thrust of the engines still move it forward.

Look it up.

 

[phrodeau]

I may be wrong, but I believe that the engines, if they are turbine jets, could not achieve "take-off thrust" unless the plane has reached sufficient motion relative to the air.

 

[Sean]

This is an old riddle and is really rather easy.

The plane does take off because even though the belt matches the 'speed' of the plane, the thrust of the engines still move it forward.

Look it up.

If the plane is stationary wrt the air, no lift.

 

[Peregrinator]

This is an old riddle and is really rather easy.

The plane does take off because even though the belt matches the 'speed' of the plane, the thrust of the engines still move it forward.

Look it up.

Ohhh, right. The engines still move it relative to the air. The ground isn't relevant, is it?

 

[KRCummings]

The treadmill is compensating for speed, not force.

Seriously, folks.

 

[Peregrinator]

If the plane is stationary wrt the air, no lift.

True, but why would it be? It's not driven by friction with the ground like a car is.

 

[KRCummings]

If the plane is stationary wrt the air, no lift.

The plane isn't stationary. It's a trick.

 

[Peregrinator]

The treadmill is compensating for speed, not force.

Seriously, folks.

Speed relative to the ground. Lift comes from velocity of the air over the wing.

 

[Sean]

The treadmill is compensating for speed, not force.

Seriously, folks.

But there is no force in an upward direction without a forward velocity.

 

[Bad_Doggie]

This is an old riddle and is really rather easy.

Look it up.

Old but still good. Gets people thinking.

Looking it up you will get arguments for both sides

 

[Peregrinator]

But there is no force in an upward direction without a forward velocity.

There would still be forward velocity. The ground directly under the plane isn't material.

 

[Sean]

There would still be forward velocity. The ground directly under the plane isn't material.

Shit, you and KRC are right, I think.
ETA: The wheels would actually be moving twice as fast. Nice question.

 

[KRCummings]

But there is no force in an upward direction without a forward velocity.

Here's the original question: "A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?" (The Straight Dope: 060203.)

The implicit assumption is that if the conveyor belt's speed backward exactly counteracts the airplane's "speed" (whatever that means) forward, the plane remains stationary relative to the earth and, more importantly, to the air. (We assume the winds are calm.) With no wind moving past its wings, the plane generates no lift and can't take off.

But the assumption is false. While the conveyor does exert some modest backward force on the plane, that force is easily overcome by the thrust of the engines pulling the plane ahead. The plane moves forward at roughly its usual speed relative to the ground and air, generates lift, and takes off. Many people have a hard time grasping this (although it can be easily demonstrated in the lab), but eventually they do, smack their foreheads, and move on. We'll call this Basic Realization #1.

Message-board discussions of this question tend to feature a lot of posters who haven't yet arrived at BR #1 talking right past those who have, insisting more and more loudly that the plane won't take off. Then there's a whole other breed of disputants who, whether or not they've cracked the riddle as originally posed, prefer to reframe it by proposing progressively more esoteric assumptions, refinements, analogies, etc. Often they arrive at a separate question entirely: Is there a way to set up the conveyor so that it overcomes the thrust of the engines and the plane remains stationary and doesn't take off?

The answer is yes. Understanding why is Basic Realization #2.

The conveyor doesn't exert much backward force on the plane, but it does exert some. Everyone intuitively understands this. To return to the analogy in my original column, if you're standing on a treadmill wearing rollerblades while holding a rope attached to the wall in front of you, and the treadmill is switched on, your feet will initially be tugged backwards. Partly this is due to friction in the rollerblade wheel bearings, but partly--this is key--it's because the treadmill is accelerating the rollerblade wheels and in the process imparting some angular (rotary) but some linear (backward) momentum to them. You experience the latter as backward force. Eventually the treadmill reaches a constant speed and the rollerblade wheels cease to accelerate. At this point you can easily haul in the rope and pull yourself forward.

But what if the treadmill continues to accelerate? Different story. In principle it's possible to accelerate the treadmill at a rate that will exactly counteract any forward force you care to apply. (This is a departure from the original question, which said the conveyor belt compensated for the plane's speed,, not its force.) The only mathematics needed to demonstrate this is the well-known physics axiom F = ma--that is, force equals mass times acceleration. Given that the conveyor exerts some backward force F on the plane, we simply crank up the acceleration as much as necessary to equal any forward force F generated by its engines. Result: The plane stands still and doesn't take off. Welcome to BR #2.

You may say it's impossible to build a constantly accelerating treadmill, that eventually we run into the limitation imposed by the speed of light, etc. True but irrelevant--BR #2 has an intrinsic elegance that transcends such practical concerns. Why didn't I bring it up in the first place then? You've got to be kidding. It took an entire column to get BR #1 across, and a second one to convey (I hope) BR #2. One fricking thing at a time.

 

[phrodeau]

So while it's holding place on this treadmill, I'm going to attach a chain from the hangar to the tail fin.

Will the plane leave the ground?

 

[KRCummings]

So while it's holding place on this treadmill, I'm going to attach a chain from the hangar to the tail fin.

Will the plane leave the ground?

For about 3 seconds until the tail falls off and everyone dies a horrible death.

 

[Cap’n AMatrixca]

This reads like a bad segment of the Boortz show...

How much air movement does the conveyer belt kick up?



Friction...

 

[KRCummings]

This reads like a bad segment of the Boortz show...

How much air movement does the conveyer belt kick up?



Friction...

Shut the fuck up, idiot.
You come in after the fact and try to act smart. You don't fool me or anyone else.

Fuckin' moron.