Airplane and Conveyor Belt Debate

[Dark Prism]

I guess what I can't conceive here is that the plane is going forward, and when it hits the conveyor belt, it isn't supposed to go forward any more. The idea being that it really is still going forward, but on the conveyor belt now. This just doesn't seem possible to me.

 

[D H]

The plane has free-rolling wheels. The plane landing on a moving conveyor belt is no different physically than a plane landing an a normal runway while flying with a tailwind or against a headwind.

 

[Danger]

The plane has free-rolling wheels.

Exactly. It's the application (if any) of the brakes that makes the difference between this and the take-off scenario. Suddenly, they're no longer free-rolling. You're quite correct that the effect would be the same as locking them up upon first touching a runway. Most tricycle gear planes wouldn't mind too much, but it could be devestating to a tail-dragger.

 

[Dark Prism]

See, I would think that the plane would continue off the end of the conveyor, as it still has it's main forward inertia through space.

Maybe this is what your saying...

 

[Dale]

They drove a car up a ramp trailing behind a moving truck. The car's wheels changed their rotation rate nearly instantly as the car transitioned from rolling at speed with respect to the road to nearly at rest with respect to the ramp.

Hehe, just finished watching the new Knight Rider!

 

[Danger]

Hehe, just finished watching the new Knight Rider!

Loved it! A lot less hokey than the original, and I really liked the way that they integrated Hasselhoff into it. I knew that he was going to be a guest star, but I expected some crappy 'formula' type of approach. This was handled very nicely. It was great that it was a stand-alone movie (ie: no cliff-hanger), but still left me wanting more. I hope that they pick it up as a series.

 

[Cyrus]

Do you think an aircraft carrier is stationary when those airplanes land on it?

QED

How many times do we have to hear this crapy question?

Thread locked, poster banned.

 

[Danger]

Do you think an aircraft carrier is stationary when those airplanes land on it?

Do you think that Earth is stationary when an aeroplane lands on it?
The question still comes down to the matter of having or not having brakes applied.

 

[Dark Prism]

Do you think an aircraft carrier is stationary when those airplanes land on it?

The difference being that the aircraft carrier is moving the same direction the plane is landing. Not only that, but it still doesn't answer the question of stopping in a small space. When those jet fighters stop abruptly on an aircraft carrier, they use giant tow wires and stop quickly enough to jerk the pilots around.Also, I humbly apologize for wanting to know more about the world around me.

The question still comes down to the matter of having or not having brakes applied.

So what your saying is that if there are no brakes applied, it will continue off the conveyor, but if brakes are applied it will stop quickly?

 

[mgb_phys]

So what your saying is that if there are no brakes applied, it will continue off the conveyor,

Yes - imagine a plane landing on ice with skis if you prefer - it doesn;t matter what the ground is doing.

but if brakes are applied it will stop quickly?

Yes - the brakes will have to be applied a bit more gently because you don't want them to go backwards as soon as the touch.

 

[MonstersFromTheId]

This has been done

Actually the idea of "landing on a conveyor belt" has already been tested, though not by Mythbusters.

At an airshow, a small plane was landed on what was billed as "the world's shortest runway" as a stunt.

A large platform was mounted to the top of a motorhome. The motorhome matched the landing speed of the small plane, speeding up and slowing down as necessary to stay under it as it landed.

As you might expect, the wheels of the plane barely turned as they settled on the platform.

Once the plane had settled its weight on the platform the motorhome simply slowed to a stop.

Here's a link to where you can see it on YouTube:

 

[russ_watters]

I guess what I can't conceive here is that the plane is going forward, and when it hits the conveyor belt, it isn't supposed to go forward any more. The idea being that it really is still going forward, but on the conveyor belt now. This just doesn't seem possible to me.

It is still going forward wrt the ground and air. The conveyor belt has no way to stop the airplane besides making the wheels spin faster and increasing the braking force.

Btw, the first answer you got (and pretty much everything that followed followed it) is correct.

Sorry, this thread isn't any better than all the other ones on the subject that we've banned. It's a simple question that people make just complicated enough to confuse themselves. Drop the complications and listen to the simple answers. There was nothing wrong with the Mythbuster's test - you're adding irrelevant complications to it and convincing yourself they matter. They don't.

Locked.

 

[knoxjeff]

Misconception of friction

I think some people may have a misconception of friction, including me about ten minutes ago.

As I set out to demonstrate a stationary plane due to frictional forces the wheel bearings place on the plane I found a problem in my logic. I had imagined a different universe in which friction INCREASES with velocity, which, I found out, didn't happen to be true in my current universe.

If the friction increased proportionally in the wheel bearings with the increase of the rotation of the wheels, then it seems reasonable that we could arbitrarily set the backwards force due to friction on the plane to exactly equal the forward thrust simply by increasing the conveyor speed.

As I understand it, friction only depends on the Coefficient used and the Force between two objects. And, both the Coefficient and the Force (gravity and mass of the plane) remain constant in the case of the plane-on-a-conveyor experiment. So, what force am I missing that is canceling out the forward thrust?

But what if we changed the experiment to allow ridiculously high friction wheels? Assuming a fully loaded Cessna 182 weighing in at 1160 kg and a thrust of 1,000 N the normal forward force (with coeff of friction 0.001 for the wheel bearings) would be 1,000N - 1160kg * 9.8m/(s*s) * 0.001 or about 990N. But if the wheels had a coefficient of friction of, say, 0.088 (the coefficient of sliding friction of copper on copper) then the total forward force would be about 0N which means the conveyor would create enough force via friction to keep the plane stationary. But I don't know of any wheels that use copper slabs in place of bearings.
Do I have an error in my calculations of this last example (besides blatantly ignoring significant digits)? I've been out of physics for quite a while now. Maybe I should be using rolling friction for the wheel bearings, and it doesn't have anything to with the weight of the plane?

 

[TVP45]

I Googled Cesna and found a picture of the instrument panel. The "speedometer" is unmistakably an air speed indicator.

 

[mgb_phys]

The ATR 42/72 (a french twin turboprop commuter) is almost unique in having powered wheels so it can be manouvered easily in small airports without the props running. So it might also be the only aircraft with a speedometer!

edit. Of course this has nothing to do with conveyor belts

 

[ray b]

have you seen the chopper on a turntable version?

 

[knoxjeff]

have you seen the chopper on a turntable version?

lol, That made me laugh. A whole new ball of wax has just opened up before my eyes.

 

[geoff wrights]

airplane thrust

Hi everbody, I,m new on here but had to join looks really interesting, however the real reason for searching out a forum like this is to try and have a question answered that was put to me and is really niggling me.
Please take a look at the question I have pasted . Can you help with the correct answe and reason why?
geoff
--------------------------------------------------------------------------------
An aircraft is standing on a runway that can move. The aircraft can move in one direction, while the conveyor belt moves in the opposite direction. This conveyor has a control system that tracks the aircrafts wheel speed and tunes the speed of the conveyor to exactly the same as the wheels, but in opposite direction. There is no wind,
The pilot begins to add thrust to the engines.

Will the plane take off

 

[fedaykin]

Damn it, this was even tested on Mythbusters.
Aside from some increased friction in the wheels, there will be no effect. It will take off normally (assuming you don't have a massive backward starting velocity that would screw the plane up.)
I don't think an airplane that provided its thrust through wheels would be very effective.

 

[berkeman]

Hi everbody, I,m new on here but had to join looks really interesting, however the real reason for searching out a forum like this is to try and have a question answered that was put to me and is really niggling me.
Please take a look at the question I have pasted . Can you help with the correct answe and reason why?
geoff
--------------------------------------------------------------------------------
An aircraft is standing on a runway that can move. The aircraft can move in one direction, while the conveyor belt moves in the opposite direction. This conveyor has a control system that tracks the aircrafts wheel speed and tunes the speed of the conveyor to exactly the same as the wheels, but in opposite direction. There is no wind,
The pilot begins to add thrust to the engines.

Will the plane take off

This has been discussed at length. A search on the PF for "conveyor" finds the threads pretty quickly.

https://www.physicsforums.com/showthread.php?t=212151&highlight=conveyor

Thread locked.

 

[Jwink3101]

Treadmill and an airplane

NOTE: Never mind the question! I anwered it myself.
Anyway, if you want to read it:
*********************************************************************

I search quickly, but if this has been posted, please direct me and delete this threads...Anyway:

There was a mention in the XKCD this week about the airplane/treadmill connundrum. I am including the wording I found below:
"plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

So, everyone who claims to be a physicist says it will take off. If it was just a free standing belt that could spin, I would agree, but I think the way it is asked the airplane will not take off.

Assume bearings that are frictionless bearings but not frictionless wheels. So, once the plane starts moving forward, the treadmill will accelerate backwards creating a force on the wheels. So, the way I see it, the treadmill and wheel speed will increase unbounded, but in a perfect system, this will stop the plane from moving. The belt would have to be constantly accelerating or else the plane will take off.

A lot of people argued that it is like a plane taking off on water where it just moved forward, but this is not the same situation. The belt is ACTIVELY moving backwards.

Does my analysis make sense?

 

[Jwink3101]

Nevermind. I thought about it more and realized that while the wheels and the treadmill speed will increase, the thing that is interesting is the force on the air and the plane will move forward.

My flaw was that if you have a stationary plane and turn on the treadmill, the wheels will turn but the plane will not in the ideal situation.

So, nevermind...

 

[Cyrus]

Oh dear god not this stupid question again.....

The answer, of course, is that the airplane does take off. Search the forums if you want to know why. This thread is locked.

We need a big bold disclaimer saying DONT POST THIS QUESTION ON THIS FORUM ANYMORE!

 

[atyy]

My tentative answer:

Consider a plane on a rigid surface with only static friction (Fr) that increases with applied force up to a maximum (Frmax).

In the case of a plane without wheels, the plane cannot accelerate unless the jet force (Fj) is greater than Frmax. In this case, the plane will take off, since the puzzle doesn't even make sense unless Fj>Frmax.

But a plane with rigid wheels can accelerate if Fj is less than Frmax, which is reasonable if we assume the wheels always roll without slipping.

Assume Fj is applied through the center of mass of the wheel of mass M, radius R and moment of inertia about its axis I.

Let Ap be the translational acceleration of the wheel relative to the ground.
Let alpha be the rotational acceleration of the wheel about its axis.
Let Ab be the translational acceleration of the belt relative to the ground.

1: Fj-Fr = M*Ap (used 'F=ma')

2: Fr*R=I*alpha (used 'torque=I*alpha')

The plane is moving forwards, the belt is moving backwards, so the translational acceleration of the plane relative to the belt is (Ap+Ab), so for rolling without slipping:

3: (Ap+Ab)=alpha*R

Solving for the friction gives:

Fr=I*(Fj+Ab*M*R^2)/(I+M*R^2)

Thus if Ab=0, then Fr<Fj, and the plane can accelerate.
But for sufficiently great but finite Ab, then Fr=Fj, and the plane cannot accelerate by rolling. It also cannot accelerate by sliding since Fj<Frmax.

 

[cristo]

Search the forums if you want to know why. This thread is locked.

Cyrus says it all!

 

[Pavel]

Airplane on the treadmill

A friend of mine told me about this mush discussed thought experiment (http://en.wikipedia.org/wiki/Airplane_treadmill_problem ). We immediately got into a debate, but we shortly reached an agreement. I wanted to run it by somebody who understands physics and tell me if we got it right.

Our consensus is that if we make an idealized and unrealistic assumption that the treadmill will instanteneously match the speed (or more appropriately force) of the airplane, the latter will NOT take off. The key word here is "instanteneously": the time between the increased jet force and the treadmill counterforce (mediated by the friction of the wheels) is absolute ZERO! However, since this is physically impossible, the plane will always take off.

Does this sound right? The only thing that bugs me is that there's an assumption in our agreement that the counterforce produced by the accelerating treadmill will increase without bound (I presume non-linearly). If this assumption is wrong, meaning there's a limit, then the force from the thrust (unlimited for the sake of the argument) will eventually overcome the counterforce from the wheels and the plane will take off even in the platonically idealized situation. What do you think? Thanks.

Pavel

 

[Phrak]

I can't follow your argument, but the Wikipedia article got it right.

You would be better understood stating the conditions, and leaving the argument out of it.

 

[atyy]

Wikipedia links to The Straight Dope, who provides two different answers, but without equations. I had a guess for the equations that roughly corresponds to each of the different answers: https://www.physicsforums.com/showthread.php?p=1864130

 

[Pavel]

I can't follow your argument, but the Wikipedia article got it right.

You would be better understood stating the conditions, and leaving the argument out of it.

Hi Phrak,

There's a difference between an idealized experiment, in which things are considered in principle, and an actual experiment, under certain physical conditions. When Enstein imagined what would happen if he was riding a beam of light, he was not conducting an actual experiment.

My point is that if we idealize the experiment in which the treadmill can instanteneously match the force of the airplane, it will NOT take off. However, given our experimental conditions, it's physically impossible to achieve delta time of 0. I was wondering if that was the only difference between an ideal and actual experiment that determines whether the plane will take off (assuming greater than 0 friction at the wheels).

 

[Vid]

http://blag.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/

 

[Phrak]

Hi Phrak,

There's a difference between an idealized experiment, in which things are considered in principle, and an actual experiment, under certain physical conditions. When Enstein imagined what would happen if he was riding a beam of light, he was not conducting an actual experiment.

My point is that if we idealize the experiment in which the treadmill can instanteneously match the force of the airplane, it will NOT take off. However, given our experimental conditions, it's physically impossible to achieve delta time of 0. I was wondering if that was the only difference between an ideal and actual experiment that determines whether the plane will take off (assuming greater than 0 friction at the wheels).

no, no, no. I'm not getting suckered into this. There are explicitly three different problems, as given by Vids, link. Which one are you talking about?

 

[rcgldr]

Our consensus is that if we make an idealized and unrealistic assumption that the treadmill will instanteneously match the speed (or more appropriately force) of the airplane, the latter will NOT take off.

The only force is the rolling resistance of the wheels. The tires would either explode or simply start sliding, if the aircraft had enough power, and the aircraft would take off.

The wheels interact independently with the ground and only provide a relatively small amount of rolling resistance. The prop interacts independently with the air which isn't signifcantly affected by the treadmill speed except for shear effects near the surface of the treadmill.

 

[Hootenanny]

Please note: All threads involving aeroplanes, treadmills, conveyor belts and whether they will take off, have been merged into this thread. All further discussion on this topic should be confined exclusively to this thread. Any additional threads created on this topic may be deleted or merged into this thread at the complete discretion of the mentors.

It is highly likely that any questions you may have related to aeroplanes and treadmills has already been answered. Therefore, please read this thread in it's entirety before posting a related question.

 

[Danger]

Jeez, Hoot... couldn't you just make this a sticky and lock it so no other idiots can contribute?

 

[cabraham]

Hi Phrak,

There's a difference between an idealized experiment, in which things are considered in principle, and an actual experiment, under certain physical conditions. When Enstein imagined what would happen if he was riding a beam of light, he was not conducting an actual experiment.

My point is that if we idealize the experiment in which the treadmill can instanteneously match the force of the airplane, it will NOT take off. However, given our experimental conditions, it's physically impossible to achieve delta time of 0. I was wondering if that was the only difference between an ideal and actual experiment that determines whether the plane will take off (assuming greater than 0 friction at the wheels).

Sorry but even if the treadmill CAN instantaneously match the speed of the airplane, it WILL take off. This has been experimentally proven, but I don't have the link.

Let's take it one step further. Suppose the stall speed of a given plane is 80 mph (129 kph). If the conveyor is moving backwards at 90 mph steadily while the airplane is just sitting on the conveyor, the plane is moving 90 mph backwards, or -90. The airplane engine is then started. The thrust from the engine accelerates the plane *forward*. Since its speed is originally -90 mph, its speed increases to -80, -70, -60, etc. Eventually it reaches 0 mph where it is stationary wrt an observer on the ground. It continues to accelerate to +10, +20, +30, etc. until it reaches +80 mph. At this point the wheels are spinning as if the plane was going 170 mph on the ground. But, at 80 mph the plane takes off.

The key to this problem is understanding that the conveyor moving backwards exerts very little force on the plane. The wheels have a small friction so that the backwards conveyor presents a slight drag to the forward moving plane. The engine provides a thrust which is forward in direction, but the drag backwards by the conveyor is that of wheel friction, too small to prevent takeoff. The forward engine thrust is much much greater than the backwards conveyor drag. The plane takes off. It just takes a slight bit longer to reach stall speed due to the small drag incurred. Draw a free body diagram and you will see that the conveyor motion exerts a torque on the wheel in the reverse direction. This results in a little friction in the bearing and a slight backwards drag.

Now I remember, it was "mythbusters" that shot a video showing takeoff. A search should turn it up. BR.

Claude