Airplane and Conveyor Belt Debate

[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 https://www.physicsforums.com/showthread.php?t=101259" thread.

 

[Chris Rox]

A Plane is sitting on a treadmill that is set to

Move at exactly the opposite speed and direction to that of the plane


will the plane be able to take off?


People have been arguing with me for days no saying that it wont.

this is my theory and i would like a few of you on here to let me know if i am right or wrong.


The treadmill is set to move in the opposite direction to the plane but at the same speed

so if the body of the plane is traveling at 20 mph to the left then the belt of the treadmill is traveling at 20 mph to the right

people have been constantly arguing with me that this means the plane will be standing still then.

This is my theory.

the plane is powered by jets which use the exhaust gases to provide the thrust.

the wheels on the plane arent powered and do not provide any drive or forward motion

as the plane apllies the thrust will it be able to move forward and eventually take off?

i am the only one out of about 40 people that says yes, they are all saying no it will sit still because the treadmill is going in the opposite direction to the plane at an equal speed.


the wheels of the plane and the treadmill are in no way related to the jets of the plane


so if the plane is traveling at 200 mph to the left then in theory the treadmill will be traveling at 200 mph to the right

so

will the plane be sitting still?? Or will the wheels be turning at 400 mph in the direction of the treadmill and the plane will be traveling at 200 mph and be able to take off??



PLEASE HELP, IT FEELS LIKE ME AGAINST THE WORLD IN THIS ARGUMENT!

 

[ZapperZ]

Er... what is with this question that seems to be popping up every couple of weeks? Is some website running a contest or something?

Please read these two threads that have appeared already. Continue your discussion in the last thread.

https://www.physicsforums.com/showthread.php?t=103024
https://www.physicsforums.com/showthread.php?t=101259

Zz.

 

[Chris Rox]

thanks to everyone who agreed the plane would take off


i knew the plane would take off,

people were too busy worryong about lift and air pressure, the plane has to move first to achieve both of these

the point being argued here is wil the plane move in the first place to be able to achieve these factors??

the answer

yes

so will the plane be able to take off??


yes

 

[w_benjamin]

actually, it won't fly.

 

[Danger]

How do you figure that? This thing has been put to bed.

 

[w_benjamin]

The amount of energy the conveyor exerts on the plane is directly proportional to the amount of energy the plane exerts on the conveyor effectivly cancelling each other out.

 

[russ_watters]

The amount of energy the conveyor exerts on the plane is directly proportional to the amount of energy the plane exerts on the conveyor effectivly cancelling each other out.

While that's true, that amount of energy (force, really) is relatively small because the wheels of the plane spin freely. Because of that, the conveyor cannot, in reality, exert a strong enough force to stop the plane (though it can spin the wheels so fast they burn up).

Again, you have to be careful with the wording of the problem. The consensus here is that the wording of the problem says the plane moves forward with respect to the ground and the conveyor moves backwards with respect to the ground, making the wheels spin at twice the plane's forward speed.

Let me reiterate that all of the difficulty with this problem is all in the wording and the problem's adherence to reality. Had it been better stated (both here and in whatever forum it was first posted in), it would be very, very simple. Ie, modified to match reality, the question would simply be:

Can a conveyor belt prevent a plane from taking off?

The answer from a theoretical standpoint (assuming negligible friction in the wheels) is a simple no. From a more practical standpoint, it's probably still no, but there is always the chance that the wheels could burn up before the plane reached takeoff speed.

 

[w_benjamin]

This is where we might agree to disagree. To me, wheel speed is defined as how much distance a wheel COULD travel at a given rpm. This is how race teams and testing facilities for cars define it. When they're testing a vehicle on a dyno, the vehicle speed is considered 0 while the wheel speed is whatever the have going at that particular time. It is also how they plot data for tire grip when a tire is spun up. At the start the vehicle speed is less than the wheel speed. The car eventually builds vehicle speed until the car moves forward at the same rate as the wheel.

 

[w_benjamin]

Remember, if you put a car on a set of rollers, and run it for 150,000 miles, the car didn't go anywhere, but does the drivetrain stil have 150,000 miles on it?

 

[w_benjamin]

The original wording of the question is thus:

"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? "

 

[Danger]

In the case of a car on a chassis dyno, look at it this way. If you have that sucker spooled up as fast as it can go, sitting still, and push it from behind with another vehicle, it's going to move forward. Think of the propellor or jet engine as that other vehicle.

 

[w_benjamin]

An imperfect scenario as the second car is not turning the wheels of the first. In the question, it states the conveyor will not turn any faster than the wheels of the plane will. Therefore, the conveyor does not contribute to the turning of the wheels. If the conveyor does not turn the wheels of the plane, what does? (I'm going somewhere with this, trust me.)

 

[Wishbone]

im new to this debate, however, from the question at hand, can we assume that the plane is stationary? Are we dealing with a treadmill situation where the force you push on the ground, there is a separate force of the belt pushing you backwards? If this is true, then the plane obviously won't take off...

 

[Danger]

An imperfect scenario as the second car is not turning the wheels of the first.

And the engine of an aeroplane has no connection to the wheels.

 

[w_benjamin]

Ah, Newton's Cradle! The force acting upon an object does not need to be connected to the object. The thrust of the plane begins to try to move forward. This includes the wheel. Since the wheel is in contact on the ground it can either a)skid or b) roll, depending on which is easier. The thrust is indeed acting to turn the wheel.

 

[Danger]

Okay... let's try it this way then. Suppose you have one foot on solid ground, and the other in a roller skate on an opposing treadmill. If you push forward with your anchor leg, what will happen?

 

[w_benjamin]

If the treadmill works as stated in the question, it won't move.

 

[w_benjamin]

And you're not pushing against a solid object in the question. You're pushing against a fluid(believe it or not), so the scenario again an imperfect one.

 

[Danger]

Man... I'm running out of examples here. Let's try it again.
Based upon the fact that we're already considering the wheels to be indestructible with perfect bearings:
Eliminate the wheels completely and treat both the plane and the treadmill as frictionless surfaces. Now fire up the jets.

 

[w_benjamin]

"Based upon the fact that we're already considering the wheels to be indestructible with perfect bearings:"

Why would I do that? The wheels aren't going to be going fast enough to need that.

On a frictionless surface, then yes the plane would take off. The question does not give you that parameter, however, so you shouldn't use it in your argument.

 

[w_benjamin]

You also don't need to eliminate the wheels if you have a frictionless surface as the wheels aren't going to turn, hence the conveyor won't either.

 

[Danger]

The original post actually states that the conveyor matches the plane's speed, not the rotational speed of the wheels. If the plane is not moving forward, therefore, the belt will not move backward. Now, just for the heck of it, substitute a Harrier hovering over the belt in place of the frictionless body. Again, same result.

 

[russ_watters]

If the treadmill works as stated in the question, it won't move.

No, the way the question reads, the treadmill doesn't move until the plane starts moving with respect to the ground. Once the plane starts moving forward with respect to the ground, the conveyor belt starts moving backwards with respect to the ground. But since the plane is moving with respect to the ground, it is also moving with respect to the air - so it takes off.

If the question meant what you are saying, not only would the plane not move, but the treadmill wouldn't move either. Nothing at all would be happening.

As yourself this: if the plane isn't moving with respect to the ground, how does the treadmill know what speed to move at?

 

[ukmicky]

Won’t fly. No increased air flow over the wings means no lift.

The engine is producing thrust in order to push the plane forward through the air, which increases the forward momentum of the plane which increases the speed of the airflow over the wing which then produces lift.

However the plane is attached to the ground through the wheels and the ground is moving in an opposite direction and counteracting the forwards velocity of plane so that it always remains at 0

which means no increased airflow over the wings. so no lift.

But if the engine was given full power a prop could theoretically produce enough movement of the air over the wings to produce some lift but it wouldn’t be enough as the flow would be moving inefficiently with a corkscrew motion.

A quick question if I may though. If the plane had jet engines on the wings and the engines were placed on full power would the air movement and vortexes created from the engines sucking in air and pushing it out again create enough circular motion over the wings to create lift?

 

[russ_watters]

However the plane is attached to the ground through the wheels and the ground is producing an equal and opposite force to the engines, keeping the plane forward velocity at 0.

That isn't what the problem says. The problem mentions the speed of the treadmill, not the force. Not the same thing.

 

[FredGarvin]

However the plane is attached to the ground through the wheels and the ground is moving in an opposite direction and counteracting the forwards velocity of plane so that it always remains at 0
which means no increased airflow over the wings. so no lift.

No. No and no. The plane is not "attached" to the ground in any fashion other than the force of friction.

If the plane had jet engines on the wings and the engines were placed on full power would the air movement and vortexes created from the engines sucking in air and pushing it out again create enough circular motion over the wings to create lift?

What vorticies are going to be created by the engines? We work very hard with airframers to make sure that flow is as undisturbed as possible on both the inlet and exhaust. The wings and fuselage are the most probable sources of vorticies and those are usually restricted to the wing tips and roots.

 

[Danger]

There are far too many groundhogs on this thread.
Will everyone please stop and consider that those of us who fly the bloody things have a pretty good idea of how they work.

 

[w_benjamin]

y'know for a physics forum, this place doesn't use the laws of physics very much to solve 'em. And the ORIGINAL original question that started this whole thing goes thus:

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?

 

[w_benjamin]

back to my original statement for the original question..., not the garbled one that sm0ke produced: no, it won't fly.

 

[pervect]

No, the way the question reads, the treadmill doesn't move until the plane starts moving with respect to the ground. Once the plane starts moving forward with respect to the ground, the conveyor belt starts moving backwards with respect to the ground. But since the plane is moving with respect to the ground, it is also moving with respect to the air - so it takes off.
If the question meant what you are saying, not only would the plane not move, but the treadmill wouldn't move either. Nothing at all would be happening.
As yourself this: if the plane isn't moving with respect to the ground, how does the treadmill know what speed to move at?

This is the most literal interpreation of the original question. However, such a system would not keep a car from moving, much less a plane, as I remarked earlier. For instance, if the car moved west relative to the Earth at 30 mph, the conveyer would move east relative to the Earth at 30 mph, making the speed of the car relative to the conveyer 60 mph.

It seems likely that the intent of the conveyer was to keep the car from moving, but without more clarification of the question by its originator, we can't be positive of this.


Of course both versions of the question have been answered already.

 

[w_benjamin]

With russ's version, that's abosultely right. The version I was given was as stated above, and that is a VERY different question.

 

[hypermorphism]

The conveyor and wheels are mostly irrelevant. The air is not attached to the ground, and the airspeed is the only indicator that matters. The airplane is certainly not attached to the ground. The question is similar to asking whether a plane will take off on ice, or whether a groundspeed of 0 means a plane is falling out of the sky.
This question made AVweb as analogous to the "fatal" downwind turn.

 

[Danger]

That's a great link, Hyper! Thanks.