(no subject)

[tgies]

everyone who wasn't able to figure this out on their own originally has probably read the correct answer by now but let's do this anyway just for laughs

[Poll #1416503]

Comments

[heinousbitca.livejournal.com]

one word: thrust.

[catamorphism.livejournal.com]

I thought the one word was "vectors".

[robocowboy.livejournal.com]

Thrust makes a plane go forward. Lift (http://en.wikipedia.org/wiki/Lift_(force)) makes a plane go up. No airflow past the wings, no lift. It's a glorified car until it's moving at high speed relative to the air around it.

Now, run the same experiment with the addition of a wind tunnel and maybe you've got something.

[robocowboy.livejournal.com]

If the treadmill has a control system to track the plane's speed, why am I at the controls? What if I choose to run the treadmill just a little too fast and make you go backwards? Try to take off now, airplane boy!

[teffdogg.livejournal.com]

"we conspire by our joint effort to try to keep the plane stationary"

I don't think that's how it usually goes. But if that's how we're doing it, then I change my answer to "no". How can a plane take off with us both conspiring against it? Especially if you're allowed to use the brakes.

[tgies.livejournal.com]

well I mean conspiring only by the means described, i.e. "matching the speed of the conveyor to that of the plane"

[teffdogg.livejournal.com]

I don't think that word means what you think it means.

http://www.airplaneonatreadmill.com/



1) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I begin to attempt to take flight in the plane, and you attempt to match my speed to try to keep me stationary. Will the plane take off?

2) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I throttle up the airplane and you turn on the treadmill, and we conspire by our joint effort to try to keep the plane stationary relative to the ground. Will the plane take off?

3) An airplane is sitting at rest on a very powerful treadmill. You are at the controls of the treadmill, while I am at the controls of the airplane. On some signal, I attempt to take flight in the plane, but you match my speed with the treadmill and keep me stationary relative to the ground. Will the plane take off?


Here are the absolute, 100%, bet-your-life-on-it answers to these rewordings:


1) Yes.
2) No.
3) Whoever asked this question is an idiot.

[robocowboy.livejournal.com]

Since a treadmill that can hold a plane and move a belt at a few hundred miles an hour doesn't exist in reality, this "problem" is already forcing a little pretending. It turns into the kind of thing that you have to make up assumptions for. Everybody will have their own assumptions, and there are many ways to "solve" it.

So if the assumption is that the belt can always move fast enough to keep the plane from moving forward (as unrealistic as that is) then the plane will basically just sit there. Engines blasting, wheels spinning (impossibly) fast.

It's possible that the treadmill's friction could make enough wind above and below the wings to create some lift, but I kind of doubt it.

You could angle the engines downward a bit so the plane would naturally lift off of the treadmill a bit and hop over to normal ground. Or maybe friction in the belt, wheels, and wheel bearing would cause skidding forward. Either case could cause the plane to jump onto flat ground and then perform a normal takeoff, free of the treadmill.

There are plenty of things that could be tweaked, or assumptions made, that could make it work. But the way I interpret the problem (that the magic treadmill really can do what the question asks and the plane would more or less be its captive) the plane wouldn't fly.

Kind of a silly unrealistic situation, though. Nothing worth arguing over.

[tgies.livejournal.com]

it is impossible for the belt to move fast enough to keep the plane from moving forward unless electrostatic or thermal effects of friction manage to totally lock the wheels and the plane is unable to overcome the friction between the locked wheels and the treadmill.

[robocowboy.livejournal.com]

ask a hypothetical question, get a hypothetical answer

[robocowboy.livejournal.com]

Well, if this is with a real treadmill and we're not defying the (known) laws of physics to "conspire by our joint effort to try to keep the plane stationary relative to the ground" then... yes of course the damn plane will take off. Its thrust would just push it right past the treadmill no sweat. The treadmill would be sitting in a corner, crying. I was just trying to answer the question as it was asked, as impossible or improbable as the situation may be.

[robocowboy.livejournal.com]

Well, given the guy asking the question: I assumed a little stretching was in order.

[catamorphism.livejournal.com]

Isn't the answer simpler than what anyone else said? When a plane takes off normally, the graph of its position relative to time has nonzero slope. The graph of the position of a point that remains parallel to the surface of the treadmill can only have zero slope. So if you add the two vectors, you still get nonzero slope and hence takeoff.

[tgies.livejournal.com]

Shhhh people are such silly jackoffs about physics that they actually think there's a "debate" to be had here

what everyone just fails to realize is that except for the tiny, tiny, negligible amount of friction, the free wheels are just a bearing between the plane and the ground and have no influence on anything whatsoever

[catamorphism.livejournal.com]

Physics is too hard; that's why I like math.

[robocowboy.livejournal.com]

but... but... the treadmill is magic! And in physics everything is a sphere in a vacuum!

(I agree that there's no debate and find the whole thing silly)

[flamingspinach.livejournal.com]

I said "no", but that assumes the plane is successfully kept stationary relative to the ground. You only said that we "conspire to try" to keep the plane stationary wrt the ground, which sounds a little weasely to me. The wheels and the plane's contact with the ground don't mean anything - lift (i.e., that which allows the plane to take off) is generated based on the velocity of the airstream around the foil. Assuming that the air in the room is not moving wrt to the ground, then it follows that the plane can lift off only if it is moving wrt the ground.

[tgies.livejournal.com]

i didn't say you succeed i say you conspire to try

[flamingspinach.livejournal.com]

Well then if the plane moves forward it may or may not take off depending on the speed it reaches. If at some point it is moving forward with enough velocity to generate a lift force that exceeds the force of gravity, then and only then will the plane move upwards. Prety Simple Eh

ps if the plane moves backwards fast enough it may crush the treadmill if the wing is shaped right

[tsutter.livejournal.com]

i think i figured out how lift works when i was maybe 14