Let's say you had a giant treadmill with an airplane on it

[Rekks Inbound]

Nah, you can't just quit!


"Oh yeah, now the plane is pressurized. And look......Buster's head imploded!"

:laugh:

And Much Laughter Ensued!

Peace.

Rekks

 

[PCL_128]

No, there wouldn't. The hypothetical is that the treadmill is able to retain the aircraft from moving forward. The treadmill is able to compensate for wheel friction and thrust. Therefore, the aircraft does not move forward through the air surrounding the wings.

RTFQ......again.

Again, what you describe (and what the original question asserted) is completely impossible by the rules of physics. The treadmill doesn't have the capability to compensate for the thrust of the engine because it doesn't act in opposition to thrust.

What about wheel bearing and tire friction? The treadmill would have to turn at an exponetial amount, but it would work. This would cause the aircraft to not fly.

The only thing the thrust of the engine has to overcome is the friction of the bearings in the wheels. That would be overcome with barely any thrust from the engine. After that, the treadmill is no longer producing any force on the aircraft to stop it from accelerating.

 

[CopilotDoug]

As much as I hate to admit it...PCL128 is right. The hypothetical is not possible. Russian, Your "Thinking outside the box" as you say is not a desirable attribute and in no way should be rewarded for "Creativity" Please give us your address and we will have a "team" dispatched to your house in order that you may be "corrected" accordingly. As soon as power is applied to the engines, the airplane will roll forward off of the treadmill. END OF STORY

 

[The_Russian]

Answer this:

If the aircraft was at idle and the treadmill started moving, would the aircraft roll backwards?

 

[PCL_128]

Answer this:

If the aircraft was at idle and the treadmill started moving, would the aircraft roll backwards?

That's not relevant to the situation. In the scenario, the engine is running and producing takeoff power. Again, once the engine overcomes the drag produced by the wheel bearings (just barely over idle power), then the airplane will begin moving forward, no matter how fast the treadmill moves.

 

[WhiteKnight]

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.
--CECIL ADAMS

 

[Flyer1015]

OMG this thread is still going! I thought we had all reached an amiable solution about 10 pages ago in this thread?

 

[The_Russian]

That's not relevant to the situation. In the scenario, the engine is running and producing takeoff power. Again, once the engine overcomes the drag produced by the wheel bearings (just barely over idle power), then the airplane will begin moving forward, no matter how fast the treadmill moves.

No, because the treadmill would keep the aircraft in the starting position. If you read the question, the treadmill's ability is unlimited. If you are going to eliminate the hypothetical and say the treadmill's speed is limited, then one could easily say that the max tire speed would be exceeded. This would result in failure of the tires bringing the aircraft to a stop. If the treadmill was still rolling, the aircraft would be moved backwards.

 

[Flyer1015]

It doesn't matter how fast the treadmill is moving. The aircraft thrust comes from the engines, and it will roll. Just go back 10 pages in this thread and see the "correct" answer posted. PCL_128 is right, btw.

 

[The_Russian]

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.
--CECIL ADAMS

Correct. BR#2 would lead us to answer this question by the original poster.

I thought I would dust off this old gem to kill the PIC thread.

Let's say you had a giant treadmill with an airplane on it.

As you add power and begin to move for the takoff roll, the treadmill speeds up and keeps the plane in the same relative position. As the plane goes faster, the treadmill speeds up, always maintaining the aircraft's relative position.

Would you ever be able to take off?

GO!!

The aircraft would not take off due to the variable speed of the treadmill.

Good post WhiteKnight. BR#1 and BR#2 are both correct answers for their appropriate questions.