Physics question

[sperry]

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)

[doubleurx]

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

[MattR]

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?

[JC]

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

[MattR]

Originally Posted by JC

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

You fail. Why?

[doubleurx]

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?

[MattR]

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

[Kevin M]

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

[JC]

Originally Posted by MattR

You fail. Why?

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.

[MattR]

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

[Nick Koan]

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.

[Nick Koan]

Originally Posted by MattR

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

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

[AtomicLabMonkey]

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.

[JC]

Originally Posted by MattR

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

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.

[JC]

Originally Posted by AtomicLabMonkey

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.

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

[doubleurx]

Originally Posted by AtomicLabMonkey

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.

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

[MattR]

Originally Posted by JC

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

Amen to that.

[AtomicLabMonkey]

Originally Posted by JC

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

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.

[MattR]

Originally Posted by sperry

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!

Well??? What say you?

[JC]

Originally Posted by AtomicLabMonkey

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.

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

[AtomicLabMonkey]

Originally Posted by JC

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.

[JC]

Originally Posted by AtomicLabMonkey

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.

[Kevin M]

So the plane won't take off because the plane is essentially doing a brakestand? 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?

[AtomicLabMonkey]

Originally Posted by JC

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.

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.

[Nick Koan]

Originally Posted by JC

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.

(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.