I have riddle type of question

[mewmew]

So on another forum we are in a huge argument and so I come to you guys for help with the following:

Suppose you have an airplane on a runway that is a huge conveyor belt. The conveyor belt moves with the opposite velocity of the plane at all times, what happens when it tries to take off?

Now, I think we have two cases at hand, one where the runway moves with the opposite speed of the plane itself, and one in which the runway moves with the opposite speed tangental to the outside of the tire.

Can anyone shed any light onto how this would actually work, assuming just newtonian mechanics and what not.

I think it will take off in both cases. but am looking for a solid argument for each. Thanks

[simon009988]

i not sure what u mean but i think the plane wouldn't take off because a plane only files because there is a difference in air pressure on the wings and if only the runway is moving and not the air molecules the plane would stay still (if only the tires were moving exactly in opposite to the runway)

[mathman]

The ability of a plane to take off depends on its speed relative to the air, so what is happening on the ground is relevant only as it affects air speed. An example of this principle is taking off from an aircraft carrier. The carrier is pointed against the wind and the plane takes off against the wind. Similarly at airports the preferred direction for takoff is against the wind. An analogous logic is used for landing, also against the wind, to get minimum ground speed for given airspeed.

[mewmew]

I understand that, I know how a plane flys(well, the basics atleast) and know that this problem comes down to if the plane can move or not. I, as well as others I have talked to, say that the conveyor belt will only make the wheels spin faster but have little effect on the plane. The wheels aren't locked like on a car, so the plane can generate forward movement relative to the earth independent of how fast the wheels move. Say the plane is going 100 m/s relative to the earth, the coveyerbelt is going -100 m/s relative to the earth, so the wheels, or a point on the wheel, should spin at 200 m/s, if this was a car it would be easier, but because its a plane the situation is harder to imagine.

[berkeman]

Who cares what the wheels are doing. If the plane is not moving relative to the earth and the associated air, the wings cannot generate lift. This seems like a pretty straightforward puzzle. Why are you guys debating it somewhere? Care to make a little wager... :-)

[mewmew]

It is not as easy as you make it sound, just because the belt moves backwards and the plane is moving forward(with equal and opposite speed) doesn't mean the plane is going to feel the backwards motion, because it has wheels independent of its engine that can spin however fast they want. It isn't really a straight forward question.

[berkeman]

Wanna bet? You got a PayPal account? :-)

[mewmew]

No where in the question does it say the plane is stationary in respect to the earth.

Here is what I am thinking:

The moving belt should only cause a small change in the planes speed, but it will cause the wheel of the plane to spin. If you have a treadmill and something on wheels you can try it, as it is easier to imagine or even actually do. If you turn on the treadmill you can put something on it that has wheels like a tonka truck and then with little force move it in the opposite direction the treadmill is moving, can you not? If this is the case than certainly the plane could do it because its engine is just like your hand and then it could of course take off.

I am more interested in what the forces all are that cause this to happen and what is going on with those forces, as I don't really understand all of that part of the question.

[Danger]

How bloody many threads do we have on this thing, anyhow?
The plane will take off unless the belt is moving so fast that the wheel bearings seize up.

[berkeman]

No where in the question does it say the plane is stationary in respect to the earth.

Well, I guess it was where you said this:

Suppose you have an airplane on a runway that is a huge conveyor belt. The conveyor belt moves with the opposite velocity of the plane at all times, what happens when it tries to take off?

"Opposite velocity at all time" is the part where I guess you threw me. You need to define your reference frame better (the earth?), and define what the velocity of the treadmill is with respect to it, and what the velocity of the plane is with respect to the reference frame.

[RandallB]

So on another forum we are in a huge argument I hope you’re talking about some other forum web site, not double threading on this one.

Now, I think we have ...
one in which the runway moves with the opposite speed tangental to the outside of the tire.
No this would be the same a stationary runway, the tangential speed of the tire in contact with the runway is always ZERO. The top of the tire would be moving forward at double the speed of the axle. Tires don’t leave skid marks on takeoff.

This is a logic problem that requires assumptions: assuming zero wind and the airplane speed unlike a car is measured against the wind and (because no wind) the stationary markers on the sides of the treadmill runway.
And since the runway only moves as a complement to the movement of the airplane it’s only important the runway move backwards at takeoff speed. As defined in the problem it only gets there if the plane also does so moving forward & therefor takes-off.
Note also that the bottom of the tire is still moving at Zero with relation to the treadmill which is moving backwards. The axle moves with the plane so the top of the tire is moving at 4 times takeoff speed.

Pretty simple, what’s to argue about?
I assume since you can afford one expensive runway you can afford wheels that don’t seize up when over spun.

[mewmew]

How bloody many threads do we have on this thing, anyhow?
The plane will take off unless the belt is moving so fast that the wheel bearings seize up.I searched and found nothing, searching for conveyor, airplane, and plane. Also, if you read through I made it clear that I pretty much know what the answer is, as I posted an example and what not. I am interested in the forces involved that make it so.

I hope you’re talking about some other forum web site, not double threading on this one. Yes, I am.

the tangential speed of the tire in contact with the runway is always ZERO. Why does the tangental speed have to be 0 for a tire rolling on a regular runway?

My main question, as stated above in an earlier post, was what where the forces acting on the system. I have pretty much figured that out so it doesn't much matter, its nice though to see some people who know what they're talking about explain things sometimes though. If this question is a sore topic or anyone has a link to the other thread please tell me and Ill close this one.

[Integral]

See this (http://physicsforums.com/showthread.php?t=101259) thread.