The "Plane on a Treadmill" Question

[skysidhe]

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

[tw]

A plane is standing on a runway that can move, like a giant treadmill. When the plane's engines throttle up, it begins to move forward, but the treadmill is made to match the forward speed of the plane, only in the opposite direction. So, as the plane moves forward, [treadmill] moves backwards beneath the aircraft.

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.

[hideouse]

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.

[Aliantha]

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.

[xoxoxoBruce]

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

[hideouse]

Originally Posted by Aliantha

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.

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,,,

[enipla]

Originally Posted by Flint

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

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.

[Kitsune]

Originally Posted by enipla

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

I'm voting for "brilliant idiot".

[MaggieL]

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.

[SteveDallas]

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!

[skysidhe]

Originally Posted by Undertoad

I've never heard this before. But no, a plane takes off because its wings generate lift, which it can only do when moving forward.

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

[glatt]

Originally Posted by Flint

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 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.

[Flint]

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

[glatt]

Originally Posted by Flint

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.

[Flint]

.