Another way to explain it:

There are two sources of force in the system. The plane engine, and the treadmill. The plane engine pushes forward, and the treadmill pushes backward. The wheels of the plane are the interaction between the two forces, and by rotating they allow the engines to move the plane forward and the treadmill to move itself backward without canceling, by rotating at the sum of the two speeds.

Under interpretation #1, the speed of the treadmill is automatically set to equal the speed of the wheels. This is only true if the engines supply no force to the system, but the question precludes that.

hehehee...I was in meetings most of the day but I checked on this thread a few times. I must say, my head exploded a long time ago. You people be too damn smart for me! :p

This has ceased being a physics discussion and become a semantics issue, hasn't it?

The question does not reference wheel speed, but plane speed. The question is what the plane speed is measured relative to. You can get two different answers, depending on what plane speed is measure relative to. The speed of the plane can be desribed two different ways. They aren't exchangable. The plane isn't on the ground. It's on the treadmill. The treadmill either cancels it’s relative motion, or has no effect whatsoever. See above. No, I’m not saying that. (The forward motion of the aircraft relative to what?) I'm not asking you to do that.
It doesn't hold the plane back, the plane is moving at exactly the speed the treadmill is moving, in the opposite direction.
The question doesn’t include wheel speed as a variable, only plane speed and treadmill speed. No kidding.
The question doesn’t include wheel speed as a variable, only plane speed and treadmill speed.

No, the treadmill stated in the question only cares about the plane speed, never the wheel speed.

Flint, think about the rotation of the Earth being the same as a giant treadmill, can a plane taking off to the west leave the ground?

Q: Does the treadmill have it's own atmosphere?
A: Not as stated in this question.

Good point. The question doesn't clearly state that there is an atmosphere, so a plane wouldn't work anyway. No lift in a vacuum.

The Earth has an atmosphere, the treadmill doesn't, IE, the atmosphere isn't relative to the treadmill, as in 9ths "Earth treadmill" question.

Yes, but the question doesn't state this treadmill is on the Earth, does it?

Umm ... isn't this solely about the action of the plane's engines and the fact that they push air through at great speed (science pushes, but it never, ever sucks:D ), creating air flow over and under the wings, and then the whole Bernoulli effect thing happens, and you get lift? So the treadmill plane should lift off ...

Am I remembering Physics 100 correctly?

otoh, will just the movement of air through the engines provide enough airflow to create sufficient lift for the plane to take off? Normally there's the engine push-through of air plus air passing over/under the wings because the plane is moving relative to the atmosphere - on the treadmill it's not. Will there be enough air moving over the wings to create the needed lift? :confused:

Now if we could just get planes to land on little bitty treadmills, we wouldn't have to build long runways anymore!

Of course not... the air moving across the wing gives lift (a very simplistic description, at-best). The treadmill negates that.

We all have been assuming that the air does not accelerate with the treadmill, which is correct. It is also why the treadmill has no effect. The jet engines push against the AIR, nothing else, so if the air does not accelerate with the treatmill then there must be a constant force pushing back on the aircraft (basic physics). Since the treadmill is only in contact with the wheels, and the wheels cannot transmit a force back onto the aircraft (no brakes being applied), there is an unballenced force acting on the body of the plain. Therefore, the plane must accelerate.

I didn't say it did. I said that wheel speed is identical to the speed of the plane relative to the treadmill.
Again, I didn't say they were. I said that they were different, and that the latter doesn't affect the former.
It cannot cancel the relative motion, because it doesn't apply any force to the plane, just the wheel. The only force pushing the plane is the engine, the engine acts relative to the air, which is not affected by the treadmill. Therefore the plane moves forward relative to the ground.
You say that a lot, but it is irrelevant. Wheel speed is equal to the speed of the plane relative to the treadmill. They are identical.

It would if it kept the plane stationary relative to the ground, which it can't.

Jet engines don't push against the air, they push against the plane. The plane will be pushed forward until it reaches takeoff velocity, no matter what speed the wheels are turning. All they do is keep the plane from dragging on the ground. Planes take off from runways that are moving at 1000 mph, under them, every day. ;)
So a man can tip open a lid that would be to heavy to lift.

9 pages on topic, impressive. Unless the runway is moving air, you've got nothing but a over-powered paper weight.

I changed my mind. Bruce is right; the jet engines aren't pulling air over and under the wings; in fact, the engine doesn't even have to be on the wing. The engines are pushing the plane to achieve atmospheric air flow over and under the wings. Since the treadmill plane isn't moving relative to the atmosphere, the needed air flow around the wings doesn't happen and there's no lift; just a lot of engine revving and wheel-spinning. It doesn't matter what 'ground speed' the instruments record, the plane has no velocity relative to the air around it. The thing won't fly, any more than a kite will fly if you hold its string while running on a treadmill.

That's my story, and I'm stickin' to it. :p

and it keeps the covers from falling down into the sewers

*pokes head into room.....realises is totally out of depth and retreats*

But the engines still exert a force against the body of the aircraft, and since the runway can't exert any force in the absence of friction, their is a net acting force on the aircraft

but no lift

Yes, I forgot that important part. :thumb:

Nope, the engines push the plane through the atmosphere (air), and what the ground and wheels are doing under it has absolutely no bearing on the plane moving through the air. Up she goes, into the wild blue yonder. Flying high, into the sky. :cool:

That's just what the engines don't do in the case of the treadmill plane. They aren't moving it through the atmosphere. It's stationary with respect to the air around it, therefore no flow, therefore no lift.

If you run on a treadmill, does air flow past your face (assuming no fan!)?

Oh, Kay....but where in the original post does it say that this hypothetical plane...has wings?

The plane isn't running on a treadmill, that's not how it moves. It moves by pushing through the air...the treadmill has no bearing on the plane. :headshake

Nor combustion w/o supplied oxygen.

Another example of the unimportance of wheels relative to a plane's taking off.
Ski planes and water planes have no wheels, hell, if a plane were lying on its belly on a greased treadmill it would take off.

There are two interpretations for this. Both are possible, but neither is specified by the provided information.

#1: If the "forward speed" is defined as relative to the treadmill then the plane is stationary relative to the air.

#2: If the "forward speed" is defined as relative to the ground, then it is possible for the plane to be in motion relative to the air.

Nothing in the question rules out either of these interpretations, and no amount of blustery hoopla or physics masturbation can change that.

The question is unanswerable as stated. It's designed that way on purpose.

Okay, this is the absolute last post I'm going to make on this subject. (promise!) If the wheel experiences a force, that force must be transmitted to the axle. (The other alternative is that the wheel goes that-a-way while the rest of the plane stays put.) The free body diagram holds.

The straight dope misses this point:
That "pull yourself forward easily" is impossible. To move yourself forward at all (even a micron per hour) still necessitates a net imbalance in the forces acting on the axle of the wheel; this is patently impossible, given the wording of the problem. F1 == F2 by the very statement of the scenario, so no net motion.

Newton would be scratching his head.

I'm with Flint and Pie. I wholeheartedly agree that, IF THE PROBLEM WAS REALISTIC AND SAID WHEEL SPEED, NOT PLANE SPEED, it would definitely take off. But the problem doesnt say that. It's unanswerable, because plane design + physics =/= the actual problem.

The answer to the original question is no.

I took aerodynamics in high school and even though I squeeked by with a D due to a terrific Huey camofluage model I made I did learn something and that is a plane needs lift to fly.

Since ditching my flying career I have forgoten the little I did learn so
I went and made sure so I found proof.



Straight and Level Flight
In order for an airplane to fly straight and level, the following relationships must be true:
Thrust = Drag
Lift = Weight
If, for any reason, the amount of drag becomes larger than the amount of thrust, the plane will slow down. If the thrust is increased so that it is greater than the drag, the plane will speed up.

Similarly, if the amount of lift drops below the weight of the airplane, the plane will descend. By increasing the lift, the pilot can make the airplane climb.
http://travel.howstuffworks.com/airplane1.htm

First - what is the purpose of wheels (landing gear)? So that velocity of a plane is totally irrelevant to ground. Wheels will spin as slow or as fast as necessary so that velocity of the runway and velocity of plane stay totally independent.

Second - plane's velocity is determined by a force applied between plane and air. As engine force increases, then airplane acceleration (and therefore velocity) is according to the well known F=ma equation. Engine force determines airspeed - a relationship between plane and air.

Meanwhile, what do wheels do? See point first. They spin as fast as necessary so that plane's velocity is irrelevant to (independent of) earth.

Since air and runway remain at same location, then plane's velocity to air is same as plane's velocity relative to runway. Therefore wheels spin at plane's airspeed which is same as runway speed.

In this problem, we have added something unique. Runway is replaced by a treadmill. As plane moves forward 1 MPH (relative to air as in point second) then treadmill moves 1 MPH in reverse. Again, wheel's job is to keep airplane and runway completely separate (point first). Therefore wheels must now spin at 2 MPH to keep treadmill and plane independent of each other.

If wheels applied the "F=ma" between plane and runway (as in a car or bicycle), then wheels and ground would not be independent. But wheels do not move this plane. Motion is created completely by a relationship between air and plane - its jet engine. No matter how fast ground moves, plane's velocity (and acceleration) is only based upon F=ma between plane and air. No matter how fast ground moves, wheels will spin as necessary to keep treadmill and plane completely independent of each other.

Now we address other possible (and unstated) references.

Since treadmill will always move backwards (relative to air) at the same speed that plane moves forward (relative to air), then wheels will spin at twice the airspeed.

Treadmill is set to match forward airspeed. Relative to what? If treadmill's speed is relative to air and plane's speed is relative to air, then wheels spin at twice airspeed. But if treadmill's speed is relative to plane, then treadmill never moves relative to air. Now we have wheels only moving at one times airspeed.

One fact we do know. Airplane's speed is always relative to air because those engines create a relationship only between air and the plane. Treadmill's speed (in this problem) could be relative to air or relative to plane. But again, point first - those wheels always make ground independent of the plane. Wheels will always spin as slow or fast as necessary so that plane and earth velocities do not affect each other.

planes on a treadmill,,,
 

The initial premise is flawed, implying that moving the surface the plane rests on can keep the plane from moving forward or have some kind of influence over the lift achieved by the lifting surface of the plane.
As we have seen ad nauseum, the resting surface has no effect on the forward motion of the plane. Rather, the moving treadmill will make the wheels turn faster while the plane will move forward as it would normally at any given engine setting. If the forward motion of the plane where to be inhibitted (sp?) or restrained somehow so as to prevent adequate airflow over the lifting surfaces then the plane will not fly. If the plane is stationary, yet somehow adequate airflow is achieved over the lifting surfaces then the plane will fly.
Both sides of the discussion so far seem to me to have made these points but without noting the flaw in the initial premise.

If you could use this logic to launch a plane, then tell me why the navy hasn't exploited it yet?

I posted this after the hall of fame post. Maybe I should now delete that one...or maybe I just can't be arsed in the end.

They usually do. Only occasionally does the Navy launch planes illogically.
Oh, wait... Bush..... um.... nevermind. :o

Short takeoffs
 

I believe that the navy's catapult system is an application of this logic: a very short takeoff that achieves adequate airflow over the wings so as to allow the plane to fly.
Now i must look for hall of fame post referenced above,,,

Yes, the person that wrote the question (not necessarily the OP) Is either brilliant, or a total idiot.

I still interpret it to scenario #2. Wherein movement means movement relative to an outside observer of the equation, i.e. someone standing on the ground off the treadmill and not in the plane.

Was that what the question asked? Hard to say. We all (or at least 99% of us) know that a plane will not take off if it does not move through the air. The jets or prop do not provide the lift, they only provide the forward momentum.

I'm voting for "brilliant idiot".

My opinon of a lot of posters' intelligence has been confirmed by some of the posts on this thread.

Perhaps some folks will find it enlightening to hear about the time I did an engine run-up before departure on an ice-covered runway at Hazelton, PA. (The ice serving as a pretty fair analog of the aformentioned conveyor.) Engine run up involves locking the brakes and applying something close to crusing power to make sure the engine is running OK...and also involves testing other things that need to work when the engine is at cruise, like making sure both sets of magnetos are firing plugs, that the auxiliary fuel pump pumps fuel, that the prop pitch control controls the prop pitch, the vaccum pump pumps vacuum...I mean air...etc.

Anyway, usually you lock the brakes and apply power, engine revs up and various needles move as appropriate...and nothing else happens. In this case, the tire s had very little friction on the runway (well, taxiway, this was) and started moving forward, much to my chagrin, as I was not quite ready to get out on the runway yet.

So that day I took off without a runup...since I couldn't actually do one.

If I'd been lined up with the runway, had advance the thrust to full power, and had used a little bit of extra runway length to allow for the small amount of friction there was, I woudl have ended up flying without ever releasing the brakes.

It's all about the air moving past the wings...and the engine thrust will most assuredly move the airplane through the air quite handily unless something prevents it...like friction in the brakes and of wheels against dry pavement.

I still want to see experiments with a real treadmill... Bruce, surely your employer has some facilities? At least they could supply a couple spare planes they don't need anymore for testing purposes! :rolleyes:

UT got it right first.

http://travel.howstuffworks.com/airplane4.htm


A Few Words About FluidAs we mentioned, a principal concept in aerodynamics is the idea that air is a fluid. Like all gases, air flows and behaves in a similar manner to water and other liquids. Even though air, water and pancake syrup may seem like very different substances, they all conform to the same set of mathematical relationships. In fact, basic aerodynamic tests are sometimes performed underwater.

Another important concept is the fact that lift can exist only in the presence of a moving fluid. This is also true for drag. It doesn't matter if the object is stationary and the fluid is moving, or if the fluid is still and the object is moving through it. What really matters is the relative difference in speeds between the object and the fluid

The question was written from the point of view of an observer, right? That observer is the one doing the measuring of the forward speed. It's forward speed relative to the observer.

That observer could be:
1. standing on the ground,
2. floating in the air,
3. standing on the treadmill, or
4. sitting in the plane

1&2: If the "forward speed" observer were in situation 1 or 2, the question would be written as it is, and the forward speed of the plane would be measured relative the the observer, which is the same as the ground. This would be your interpretation #2. It's how I and most here read the question.

3: If the observer is standing on the treadmill (3), he/she would have the perspective of the treadmill. If the treadmill starts moving, the observer won't feel motion because they are attached to the treadmill, They will feel a tailwind. Since the observer is writing the question, the question would be about planes taxiing in tailwinds, not about moving runways. The question doesn't mention winds anywhere, so the question is not from the point of view of the treadmill, and the plane's forward speed is not measured from that reference. Your interpretation #1 above is not a credible interpretation of the question as written, because nowhere does the question mention wind. Wind is not a part of the question, and the question does not mention wind. While this post may contain wind, there is none in the question.

4:Finally, if the observer is in the plane, he/she will see both the ground move and the runway move even faster. I don't think anyone believes this is written from the point of view of the plane, so I won't go into it further.

The question does not define "forward speed" in a way that makes the question answerable.

Maybe not for you, but it's clearly written from the point of view of an observer standing on the ground, otherwise it would talk about wind.

Occam's Razor
 

What has Occam's Razor got to do with this situation?

There is no wind in the question, so it's written by an observer on the ground.

Uh guys, there's no point in debating it. That plane is long gone.:rolleyes:

Not making unwarranted assumptions or adding extra information.

The question does not define "forward speed" in a way that makes the question answerable, and you can't make it so, without going outside of what is stated. (See: most of this thread.) Step #1, often overlooked, is to read the question and establish what is being discussed. In this case, you can't - the question does not contain the information. Any attempt to re-write the question means you are not answering the original question.

Flint,
 

I owe you an apology. You did note the flaw in the original premise and i missed it. Please excuse me.

I used to be friends with this guy, Scott. He was always right, no matter what, and if it looked like he was wrong he'd press the issue until he was right, in some sense. Any sense.

One day we're driving through Atlantic City and we realize we need to turn right to get to where we wanted to go.

Scott: Turn here!
UT: No, it's one-way.
Scott: No, that's two-way.
UT: I saw the sign.
Scott: That couldn't be.
UT: And there was no turning lane.
Scott: Maybe it was taken up by a double-parked car.
UT: Dude, I'm sure of it. I'm driving. I'm paying more attention to all the signs and the road.
Scott: But maybe I'm paying more attention because I don't have to drive!
UT: OK, here's the next crossing street, I'll turn right here, and then I'll turn right again and we can take a look at the street.
Scott: Done!
UT: OK... yep, there's the sign.
Scott: Oh. Hrm. Hmmm. But look - that doesn't look one-way there. You see, don't you, how I could have made that mistake? There's a solid line down the middle of the street. And the whole thing is not very clearly marked. They use terrible signs here. In fact, I think it used to be a two-way street and they just made it one-way. It looks like that car is parked in reverse. You see, don't you? Anyone would have thought that was two-way.

The question states the plane moves forward and the ground(treadmill)moves backwards. When you throttle up the plane will take off. The only assumption is the plane is capable of flying in the first place. :eyebrow:

I'm gonna guess this former friend was/is single:D

Relative to what? Not stated.

The former friend who was so certain of everything, became uncertain that he was male. He had a sex-change operation and yes, remains single, although she dropped the personality trait of certainty somewhere along the way.

Many of us find humility at some point in our lives. Some of us find it harder than others.

Relative to the same observer who sees the treadmill moving. If the observer sees the treadmill moving, he isn't on it.

I'll try to remember this.

Now I'm sorry I made a joke about that friend. :blush:

This isn't a first person account of an actual event, it's a hypothetical. It could just as likely be written from an omniscient perspective, as the events described are not actual events. The question doesn't make this distinction, so you can't. If you re-write the question, you're no longer answering the question.

You mentioned Occam's razor before. Is it simpler to have one point of view of both the plane and treadmill, or is it simpler to have a point of view that is jumping all over the place?

Consider that the one point of view keeps the question clear, and the multiple points of view or omniscient point of view muddies the meaning of the question.

How does Occam's Razor apply here?

If it's not stated, then it's relative to where it was and nothing else.:cool:

It is simpler to have one point-of-view. But the question doesn't state which one. It's unanswerable.