Will The Plane Fly?

[Nasher]

Can't open the straightdope link

Does the plane fly or not?

[Nos4r2]

Here it is:-

Dear Cecil:

Cecil, always enjoy your column, however you've got this [airplane and conveyor belt business] absolutely wrong. . . --strafe, via the Straight Dope Message Board

It's all about the interpretation of the question. Unfortunately, Cecil commingled two different interpretations in his column. --zut, via the SDMB

My confidence in Cecil has taken a gigantic hit. . . Cecil has fallen into the common trap of believing that the velocity of the treadmill in this case is what is important. It's not. What is important is the acceleration of the treadmill. I swear, on pain of retaking physics before I graduate as an ME, that if I accelerate the treadmill at a rate of 2 x (force from engines)/(mass of tires) that the plane goes absolutely nowhere. treis, via the SDMB

Cecil replies:

I knew this was going to happen. Everyone else, forgive me. This week's column is for the geeks.

Here's the original question: "A 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?" (The Straight Dope: 060203.)

The implicit assumption is that if the conveyor belt's speed backward exactly counteracts the airplane's "speed" (whatever that means) forward, the plane remains stationary relative to the earth and, more importantly, to the air. (We assume the winds are calm.) With no wind moving past its wings, the plane generates no lift and can't take off.

But the assumption is false. While the conveyor does exert some modest backward force on the plane, that force is easily overcome by the thrust of the engines pulling the plane ahead. The plane moves forward at roughly its usual speed relative to the ground and air, generates lift, and takes off. Many people have a hard time grasping this (although it can be easily demonstrated in the lab), but eventually they do, smack their foreheads, and move on. We'll call this Basic Realization #1.

Message-board discussions of this question tend to feature a lot of posters who haven't yet arrived at BR #1 talking right past those who have, insisting more and more loudly that the plane won't take off. Then there's a whole other breed of disputants who, whether or not they've cracked the riddle as originally posed, prefer to reframe it by proposing progressively more esoteric assumptions, refinements, analogies, etc. Often they arrive at a separate question entirely: Is there a way to set up the conveyor so that it overcomes the thrust of the engines and the plane remains stationary and doesn't take off?

The answer is yes. Understanding why is Basic Realization #2.

The conveyor doesn't exert much backward force on the plane, but it does exert some. Everyone intuitively understands this. To return to the analogy in my original column, if you're standing on a treadmill wearing rollerblades while holding a rope attached to the wall in front of you, and the treadmill is switched on, your feet will initially be tugged backwards. Partly this is due to friction in the rollerblade wheel bearings, but partly--this is key--it's because the treadmill is accelerating the rollerblade wheels and in the process imparting some angular (rotary) but some linear (backward) momentum to them. You experience the latter as backward force. Eventually the treadmill reaches a constant speed and the rollerblade wheels cease to accelerate. At this point you can easily haul in the rope and pull yourself forward.

But what if the treadmill continues to accelerate? Different story. In principle it's possible to accelerate the treadmill at a rate that will exactly counteract any forward force you care to apply. (This is a departure from the original question, which said the conveyor belt compensated for the plane's speed,, not its force.) The only mathematics needed to demonstrate this is the well-known physics axiom F = ma--that is, force equals mass times acceleration. Given that the conveyor exerts some backward force F on the plane, we simply crank up the acceleration as much as necessary to equal any forward force F generated by its engines. Result: The plane stands still and doesn't take off. Welcome to BR #2.

You may say it's impossible to build a constantly accelerating treadmill, that eventually we run into the limitation imposed by the speed of light, etc. True but irrelevant--BR #2 has an intrinsic elegance that transcends such practical concerns. Why didn't I bring it up in the first place then? You've got to be kidding. It took an entire column to get BR #1 across, and a second one to convey (I hope) BR #2. One fricking thing at a time.

--CECIL ADAMS

[jyasaki]

Originally Posted by Cookee

Can you explain how the conveyor has an effect on the thrust of the engines? The engines do not propel the wheels, they push against the air, therefore the plane will go forwards in relation to the air and the surrounding ground, and at double the speed in relation to the conveyor.

The conveyor velocity does not equal the engines velocity as they are not connected!

Exactly right.

The question itself is a red herring, as, in the setup given, you could not have the engines running at take-off power and have the plane remain stationary on the treadmill (at least not for long.)

The plane would start by moving in the same direction as the treadmill (no power output.) As the engines spooled up, the thrust against the air would cause the plane to overcome friction of the rolling gear, and would slow it's backwards movement. At equilibrium, the plane would match the speed of the treadmill, and would appear to remain stationary. A fraction of a second later, it would be moving forward. It would continue to accelerate, ultimately reaching takeoff velocity, with it's rolling gear turning at twice that speed.

As the question was proposed, by the time you thought about an answer, the plane would be long gone.

The key here is that a planes thrust comes from pushing air, not turning something against the ground.

jky

[Cookee]

Originally Posted by yoyo

Cookee; Your either having a laugh or going bananas!!

But I'm right it takes off!

[yoyo]

Originally Posted by yoyo

No airflow across the wings...No take off. This and that end of chat.....

The above statement is still correct........or is it not

[J S]

Originally Posted by yoyo

The above statement is still correct........or is it not

It is not correct. The plane still has airflow over its wings.

James

[jwalker]

Originally Posted by jyasaki

The key here is that a planes thrust comes from pushing air, not turning something against the ground.

Forget the plane because all that is being considered is can a body mounted on wheels be accelerated up to a given speed* when the surface it's on can be accelerated to the equal in the opposite direction. (*Because it's a plane that speed is take off speed)

If a jet car was powering on the salt flats and the flats moved rearward to match the forward motion of the car, would the car move forward relative to the earth?

[J S]

Would a good way to look this to consider two things that all people on here know about. Speed over ground and speed through the water. If you take for example a tide running at 14kts that could be the treadmill and for the boat to stay still it has to power up to 14kts water speed and this would be the same as the airflow over the wings.

Thought that might be a good comparison.


James

[Nos4r2]

Originally Posted by Cookee

But I'm right it takes off!

Yes, you're right it does take off (with the wheels moving at slightly more than double normal takeoff speed).

For Yoyo's situation (no airflow across the wings and no takeoff) to come about,the treadmill has to accelerate at a rate that far exceeds the acceleration of the plane.

Originally Posted by doctored to be clearer

The conveyor doesn't exert much backward force on the plane, but it does exert some. Everyone intuitively understands this.If the plane is on a treadmill and the treadmill is switched on, the plane will initially be tugged backwards. Partly this is due to friction in the plane wheel bearings, but partly--this is key--it's because the treadmill is accelerating the plane wheels and in the process imparting some angular (rotary) but some linear (backward) momentum to them. The plane experiences the latter as backward force.

For that backwards force to keep the plane stationary, it has to be equal to the thrust coming from the plane's engine.

Look at it this way.If we ignore the rotary forces and friction on the wheels the backwards force exerted on the landing gear has to equal the forward force or thrust from the engines.

So, using Force=mass*acceleration let's chuck some numbers at it.
The backwards (F=ma)of landing gear has to equal (F=ma) of the plane

So for argument's sake lets assume the wheels have a mass of 1 newton and the plane has a mass of 10 newtons. The force exerted on the plane by it's engine thrust is 100 newtons-therefore the same 100 newtons has to be exerted on the plane backwards by the wheels.
From F=ma we get a=F/m therefore
a(plane) =100/10 metres per second per second
100 newtons(exerted on wheels)=1xacceleration or 100metres per second per second.
a(treadmill)=100/1 metres per second per second

Therefore based on the numbers,the treadmill speed has to increase by 100metres per second every second to equal the forces exerted by the plane-whereas the plane is only capable of 10 metres per second per second of acceleration.

Clear now?

[Cookee]

Originally Posted by Nos4r2

Yes, you're right it does take off (with the wheels moving at slightly more than double normal takeoff speed).

Actually I think they will be going at some sort of infinite speed, but I reckon the power of the jet is capable of overcoming the friction in the wheel bearings etc.

Here's how the 'mericans discussed it http://www.offshoreonly.com/forums/s...ight=treadmill - this has been around for a while now! (some years)

[yoyo]

Originally Posted by J S

It is not correct. The plane still has airflow over its wings.

James

read the statement again!! I dont imply that there is airflow. The statement is correct.

[jwalker]

Originally Posted by Nos4r2

Therefore based on the numbers,the treadmill speed has to increase by 100metres per second every second to equal the forces exerted by the plane-whereas the plane is only capable of 10 metres per second per second of acceleration.

The question stated that the imaginary conveyor can match the plane.

You can't ignore the friction, rolling resistance etc. otherwise the contact with the ground could be considered not to exist and then you'd just be accelerating a body in free air.

Whether the forces would be ginormous has no bearing on in.

[visualpecepts]

If the plane is stationary, then according to the questions rules, the conveyor belt must also be stationary.
So you can not have the conveyor moving at a speed which keeps the plane in a static position or the rule is broken. That means the plane must move forward so that the conveyor belt can move at the same speed as the plane.

edit: thought about it a bit more and infact it would be impossible for the conveyor to be moving at the same speed as the plane without the plane stopping which means the conveyor would also have to stop. Therefore the questions premise that the conveyor would accelerate at the same speed as the aircraft would be impossible to achieve under the rules of the question. It's a dumb question.

[DJL]

Originally Posted by visualpecepts

It's a dumb question.

That’s the conclusion I come too.

If you take the real world scenario and place a model plane on a treadmill it would easily take off (until you get to the point where the treadmills going soooo fast the wheel/bearing friction is greater than the engine can overcome, or the wheels fall off).

[Nos4r2]

Originally Posted by jwalker

The question stated that the imaginary conveyor can match the plane.

You can't ignore the friction, rolling resistance etc. otherwise the contact with the ground could be considered not to exist and then you'd just be accelerating a body in free air.

Whether the forces would be ginormous has no bearing on in.

You're missing the point.

What I'm saying (and I know I'm right-it's schoolboy physics) is that for the plane to stay stationary then the conveyer has to be accelerating a magnitude faster than the plane would be-therefore the conveyer can't be matching the plane's speed...and that's not the question.

QED- plane will take off.
The wheels won't be moving at some sort of infinite speed either.

--plane@150mph-over-the-ground------>
<--conveyer@150mph-over-the-ground---

give a difference of 300 mph (or 300mph closing speed if you want to imagine there being an object or a line drawn on the conveyer).The speeds are matching...

<edit-where's AndyB007 when you need him?> (and yes, I know mass is in KG not Newtons but the result is still the same at 1G)

[Bigmuz7]

Well it seems fairly simple to me

Despite the rolling resitence on the tread mill which the engines will overcome (or whatever) for the plane to stand still, no matter how fast the tread mill moves, the planes engines will overcome this whilst standing still ok ?.. The belt speed could go on for ever, but the plane will never take off, until it moves forward relative to the airspace which surrounds it, since the air space is static compared to the belt speed, once the plane moves forward, to an extent, the belt speed is irrelevant, as its friction is minimal compared to the forward air speed needed to lift off.. the plane will need to exceed the load on the belt for sure, and derive enough forward speed to lift off so..static air is what it is pushing against.. with its thrust, (less the drag from the belt which is minimal).. so yes ..it will take off once its gained enough speed from the static air around it .. be damned those physicists

[truble]

ok lets put this in 2 boating,,if a boat is in a river and water is running at x speed,,the boats motor has to be kept at x revs to keep it stationary,,,if the speed of water in creases so does the boat revs to keep stationary,,,question,,,will the boat sit on the plane at a stationary speed,,,to equal the water passing under it if the water was at a theoretical speed to the hull plane speed,,,u have all the forces ,,thrust equaling the friction created by the water,,but no wind,,

[Nos4r2]

Originally Posted by truble

ok lets put this in 2 boating,,if a boat is in a river and water is running at x speed,,the boats motor has to be kept at x revs to keep it stationary,,,if the speed of water in creases so does the boat revs to keep stationary,,,question,,,will the boat sit on the plane at a stationary speed,,,to equal the water passing under it if the water was at a theoretical speed to the hull plane speed,,,u have all the forces ,,thrust equaling the friction created by the water,,but no wind,,

That analogy is wrong as the propeller is pushing against the water rather than the air.

Try it with a jet engined boat (bluebird for example) and the analogy works.

[Hightower]

Originally Posted by Andy Moore

This will get em arguing at work.

Imagine a plane is sitting on a massive hypothetical conveyor belt, as wide and as long as a runway. The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction.

To the letter of the question this statement could only have two answers. Think about it.

It doesn't state that the belt is revolving at the same speed as the aircraft is traveling (surface speed), the question reads "the conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction" it actually implies the whole belt assembly is moving not the surface speed of the thing That means if take off speed is 200mph then the whole belt assembly would move in the opposite direction to the plane during acceleration to 200mph (or 400mph in relation to the plane) the effective result being that the plane would crash off the end of the conveyor belt well before take off speed was acheived assuming that the plane needed all of the runway to take off in the first place. Of course if the plane could take off in less than half the distance of the runway length, then the plane would acheive take off speed and would fly away.

So yes it's a crap question, one that's not specific enough for a definitive result.

By the way, for what it's worth!

If the question was different and stated the surface speed of the belt matched the speed of the plane then I would say that speed is a measure of distance over time, yes? Miles per Hour!

So the plane would have to be moving for the conveyor to move, yes? Agreed!

So if the plane was moving at 200mph (which is speed over ground) then it would take off, the conveyor surface speed would be moving at 200mph in the opposite direction and the wheels of the plane would be revolving at twice the normal take off speed.

But that's a load of rubbish as the question doesn't state the surface speed of the belt as being the same take off speed.

[jwalker]

A good bevvy tonight was it, Andy?