Physics question
 

There's a nice long thread on NASIOC right now over this simple physics question:

"Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.
Can the plane take off?"

I know the answer, but won't post it right away. Let's see if there are as many idiots here as there are over there! ;)

(Here's the NASIOC thread if you can stand the bickering... I had to leave, I couldn't take anymore. http://forums.nasioc.com/forums/show...0&page=1&pp=50)

How big are the rollers?. Maybe they can gererate enough lift out the sides onto the wings.

Hahaha..I could only read as far as your first reply.....But yeah, It should be able to take off...I imagine the wheels would be spinning really fast when they left the ground.

If the plane had a speedometer, and on a normal runway it needed 150MPH to take off, Wht would the speedo show if it took off from the treadmill?

No, I'm an aerospace engineer. I should know.

You fail. Why?

Scott there may be a flaw in your theory. It says the conveyor is designed to match the wheel speed at any given time. If that is the case how can the plane accelerate to gain lift if the conveyor is always matching speed?

My mind!!!!!!!!!!!!!!!!

I wonder how long before they start arguing about where to bury the survivors if it crashes on its non-takeoff. :lol:

If your wheels are moving at the same speed as the treadmill, apply a no slip condition then the plane isn't moving regardless of how you are applying thrust. If the plane doesn't move, you don't take off.

So, how would it relate to a boat going up stream? Same general idea.

Yeah, if the plane isn't moving, then there is no airflow over the wings. If there is no airflow over the wings, it sure ain't going to take off.

The boat also does not get airborne if the stream is going the same speed as the boat.

Assuming a frictionless model it shouldn't matter if there is a conveyor belt at all, or if it is moving with the direction of travel or against it. The wheels are just rollers. The plane will accelerate and take off because it doesn't apply thrust to the ground/conveyor/whatever, it's exhausted into the air.

That's a problem of relative velocity, this is a force balance. In order for the plane to move forward, you would have to spin the wheels faster than the treadmill or have them "slip." The problem says you cannot have either.

We don't live in a frictionless world by any means.

And the conveyor is constantly matching the wheel speed which will not allow the plane to move forward.

Amen to that.


http://images.amazon.com/images/P/B0...CLZZZZZZZ_.jpg

The question is posed as a hypothetical, hence my assumption. If you somehow constructed a giant superfast conveyor belt and sat a real 757 on it, obviously the results would be somewhat different.

Well??? What say you?

If there was no friction your wheels wouldn't spin. So obviously your assumption is invalid for this problem.

It doesn't matter what the wheels are doing. They could be perfectly stationary relative to the conveyor, while the plane zooms forward to lift speed, due to engine thrust.

How would you move forward on the belt? The wheels are going the same speed as the belt. There is no way for you to accelerate unless you are sliding or the belt is not going the same speed as the wheels.

So the plane won't take off because the plane is essentially doing a brakestand? :huh: The firction of the wheels on the roller balances the thrust from the engines, preventing the plane from moving in the exact same manner as if the brakes were locked?

Conveyor belts move. ;) If you assume zero rotation of the wheels, the whole belt could still be moving forward with the aircraft. My point is that the conveyor has no effect on anything. The plane is applying thrust independant of it, and the aircraft will start to accelerate relative to the earth, regardless of what the relative motion is between aircraft and conveyor.

(Changing my answer here after talking with Scott)

But the wheels don't provide thrust, the engine on the back does. The wheels are free-spinning (essentially), so the plane should still move forward at its normal speed, regardless of what the belt is doing.

They will be spinning twice as fast as normal, though, at takeoff.

Here's my answer:

1) The plane needs airspeed to generate lift and take off.
2) The plane's engines generate thrust by pushing against the air.
3) The plane's wheels (because the brakes are off) cannot enact a significant force upon the plane against the thrust vector of the engine.

Therefore, the plane will take off. The treadmill has nothing to do with the solution.

I dare you guys to prove me wrong without getting into rediculous agruments like "well if the conveyor is going 1 million mph the friction of the wheel bearings is so high it can't take off". The frictions/inertia of the wheels is insignificant with regards to the magnitude of the engine thrust.

So far, it looks like Austin is the only person in this thread that has a clue. Cal Poly Physics department FTW.

And JC... man, I'm surprised you missed it! :P

You guys are thinking in terms of physics, start thinking in terms of constraints. If the wheel never moves faster than the conveyer belt, how are you creating acceleration? I wish I was there to explain this to you.

There is why you don't get the right answer. The problem imposed the constraint that the wheels on the plane have to move at the same speed as the treadmill. Therefore the treadmill IS part of the solution. You have no way of translating your motion forward.

Oh! JC, if the treadmill HAS to match the wheel speed of the planes tires, then I guess it can't move forward to create lift. So, that makes sense.

What if the treadmill does the opposite? What if it matches the speed of the accelerating aircraft exactly, so the the wheel speed is zero? For that to be true, if airspeed = X, then the conveyor belt = X also, yes? This is why I think the plane will take off. Airspeed will reach X, conveyor speed will be -X and wheel speed will be 2X.

Okay now I get it. The conditions of the question cannot be met with an aircraft. If the plane lights up its engines on this theoretical conveyor, it would EITHER remain motionless, or the conveyor could not be the exact inverse of wheel speed. At least not in this universe.

Hmm, after drawing a diagram I think JC wins assuming no slip between tire and belt. The two angular velocities have to be opposite and equal, and the only condition that satisfies that equation is when they are zero, which means no airspeed.

Technically, the wheels if they moved even the slightest bit, would eventually get up to infinite speed (as does the treadmill, due to the constraint).

The problem *is* poorly posed.

Yeah that's my conclusion. It's the one-sided die.

The sound of one hand clapping makes a 13 page (and counting) thread in nabisco OT. :lol:

Okay, JC actually called my cell phone to "discuss" this with me. He raises a good point, that due to the constraints of the problem and the use of "wheel speed" instead of "ground speed" in the problem definition, the plane can't take off, simply because the problem says so.

IMO, that's a bit of a cop out... I realize the question is poorly written, but that's because I copied it verbatim from the original NASIOC thread. I think the intent of the question is obvious, "what happens if a plane trys to take off on a conveyor belt that attempt to counteract the plane's forward speed".

So, if you want to argue symatics about the wording of the question, then the plane can't take off because the words in the question prevent it. If you'd rather use the laws of physics, as I think the original author of the question intended, the plane will take off because there's no force to counteract the thrust of the engines.

That's only true if we assume a feedback loop control system. In a purely theoretical world, the wheels could never get even a tiny bit "ahead" of the belt that would require the belt to catch up.

Wow. I really enjoyed this discussion.

Basically, if you turned on the jet's engines, the world would be unmade because the laws of physics are violated.. :lol:

Sarcasm?

Please tell me that everyone who said no in that thread (and this one) was joking. Otherwise I won't know whether to laugh or cry (or start mocking bitches).

It reminds me of that thread about what a jet (thrust) powered car would put down on a dyno :lol:


Here is another problem:

A lake is 10 kilometres wide x 10 kilometres long with a dam at one end. The water depth at the wall of the dam is 100 metres.

A soda straw is 100 metres long. It is suspended vertically and filled with water.

Is the pressure at the bottom of the dam wall more than, less than or equal to the pressure at the bottom of the soda straw?

(anyone who mentions metric gets a complimentary punch to the nuts)

No, I was serious, I don;t use my brain very often anymore, so It was nice to dust the fuckin thing off

If the question wording is correct, then it sounds like it was written by a grad student with too much time on his hands that wanted to trip people up. :lol:

I disconcur with this ... this sentence:

... implies that the wheels on the plane are free to move at any speed, and the conveyor belt will automatically change speed to match.

Damn Mike, not only are you using those mythical "meter" things again, you're also spelling 'em wrong!

Also, I'm not sure how to solve that problem... at 100 meters deep, the *water pressure* is the same in both... but I'm not sure how that translates into pressure against a dam wall.

Haha, you even spelled meters the fancy-pants way. :lol:

Water pressure == wall pressure. You win.

It means the plane can never move. Draw a diagram Mike and explain to me how you are moving without sliding or having the wheels be different speeds. Both my friend and I got this pretty fast guys, he even laughed when he read it. C'mon now, always read the problem before you start doing it. And quit your bitchin' Scott.

Yeah, but there's no way to get the wheels moving to begin with. Think of it this way: if the wheels *have* to spin at the same speed as the belt, there's no way for the wheel's axles to *ever* move relative to the ground around the belt, and therefore there's no way for the plane to ever move.

'Course, there are no physics behind that solution... it's just taking the problem definition to a new level...