Brain teaser
 

This turned into a pretty heated debate on another forum I visit. Which didn't really make any sense to me because it has a very simple and logical solution supported by math and physics.
But lets hear what you guys have to say:

A plane is sitting on runway that can move (some sort of giant conveyer belt). 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 opposite direction).

The question is:

Will the plane take off or not? Will it be able to run up and take off?

air speed over the wings is the only thing that should matter

Absolutely, since the wheels aren't driving it. The speed the belt is moving will have no impact on the plan at all except the speed at which the wheels are turning, which again are independant of the actual speed of the plane. the plane will accelerate and presto physics will make the plane take off.

How the hell could that turn into a debate?

just cause the ground is moving doesnt mean the plane isn't. It should still be generating thrust therefore like Phil said air flow on the wings. But what do it know.

treadmill and a rc plane.:gay:

The aircraft will not have velocity. a conventional aircraft will not take flight without velocity as there is no airflow over the lifting surfaces. only a vtol aircraft will be able to generate lift at a standstill (which is really more thrust than lift).

uh... the plane will be standing still.

no airflow around wings = no lift

this is so retarded

I concur.

Yes. :)

What was the arguement for takeoff?


edit:Turns out I'm an idiot! I was right about the retarded part, though heh

Just for the heck of it.

http://www.lerc.nasa.gov/WWW/K-12/airplane/factors.html
read #2.

http://www.lerc.nasa.gov/WWW/K-12/airplane/move.html
More useless factors involved:gay:

Yeah. Read post #6 on this thread.

Ben
AE major

Ben, we all know you're smarter than me. :D

read #2 post btw

Aww! You fixed it before I could point it out!:gay:
:)


Ben
post whorin'

I guess one conceptual issue is this: How long is this conveyor belt? Is it the length of a runway? If so, how does the conveyor belt adjust speed? Does it move 1mph faster for every 1mph the plane moves? Because the wheels are freewheeling, the thrust of the engines would eventually overcome the friction in the wheelbearings and the plane would move forward. The conveyor belt would adjust by speeding up. This would cause the wheels to spin faster, but not necessarily the plane. So the only limiting factor to the plane lifting off (assuming a long enough conveyor-belt runway) is the speed at which the wheels can spin (think toasted wheel bearings and shredded Firestone tires. ;) )

the airplane will take off

airplanes are propelled by thrust and move independently of the wheels. The treadmill will impose more friction upon the wheels and bearing but it will continue to accelerate and eventually take off.

BTW this has been going around the internet for ages.

EDIT: Damn, you guys beat me to it... that's what happens when I start a post, go take a dump and then come back and finish it.

You guys aren't thinking about this correctly.
The wheels don't drive the plane. The thrust of the motor (prop or jet or whatever) moves the plane.

Simply imagine a plane on a giant treadmill runway. When you open the throttle, the plane start to move forward through the air in relation to the earth. As the treadmill moves at the same speed in the opposite direction, all it means is that the wheels will be moving twice as fast. The plane won't know the difference, it'll still go screaming down the runway (now moving twice as fast beneath it) and take off as normal.

Silly civilians.

nobody ever said the plane was running ;)

Damn, it makes sense now. Just needed another Sam to explain it:bigtu:

go run some radios or something and leave this to the REAL pilots.

Ahhhhh, now I understand... it's a secret governement plane that moves on the mere brainwaves of the pilot and doesn't have an engine... Pilots aren't that smart, that's why they need NFO's.
Of course you must assume the engines are running.

Thrust will move the plane, but if the belt moves at an equal rate in the opposite direction, the plane will not move relative to the surrounding air.

Lift comes from the air moving over the wings, no air moving = no lift = no takeoff.

That is all, we now return you to your daily activities.

please explain why the plane won't move :rofl:

Because the plane is being piloted by a woman, and, as such, the parking brake is on.

"A plane is sitting on runway that can move" Nothing in the problem says there is actually any movement by the plane or the runway. It's all just sitting there looking pretty.

It clearly states, WILL IT BE ABLE TO RUN UP AND TAKE OFF?

The answer if obvious if you would think about it.

Planes arent cars, they arent driven by wheels, they are driven by thrust created by engines fixed to the body of the plane, so therefor all it is doing is pushing it through the air while the wheels roll on the ground.

The only was the ground moving the opposite direction could possibly make the plane go any slower, is the SMALL extra amount of frictions on the bearings the wheels spin on caused by the extra speed, which will minimal.

Damn guys, this isn't that hard.
Forget about airplanes, let's go with something simpler!
Pretend this experiment is happening in your spare room.

Strap a rocket on your back and stand on a treadmill (pretend it's the fastest treadmill ever and can achieve the same speed as your rocket) wearing rollerblades. Lite off the rocket and the treadmill at the same time.... still think you're going to stay on the treadmill?
Really, just imagine yourself there on the treadmill hunched over with that rocket blasting away and the treadmill going at mach 4 and you NOT MOVING??? Come on guys, it isn't that hard.

For those of you saying "nobody said it was blah blah blah..." aren't sticking with the spririt of the thought process. It's designed to get you to realize that the wheels don't drive the vehicle and are independent of the motion of the ground.

How about this one: "If a plane crashes on the border of two states, which side do they bury the survivors"... HAHAHA, survivors don't get buried.
Then you say, well everybody dies sometime so naturally they'd get buried wherever the family thought was good and blah blah blah and ruin the joke.

DAMNIT, NOW YOU'VE GOT ME SECOND GUESSING MYSELF!!!!!!!!!!

Shit, could I be wrong about this? I've got a whole room full of pilots here talking about it and we're split 50/50.

I keep my treadmill in the bedroom so that I have a place to hang stuff.:gay:

Samnavy; you are perfectly right if it is a physics question.:bigtu:

But a "brain Teaser" is normally a logic question, which is why people look for other answers than first come to mind. My English teacher would have flunked me if I didn't first analyze the question. Oh, wait, she did.:eek:

this is why i let others figure things out, then take what the say, try to understand it, and pass it off like I've known all along.

seriously, this isn't difficult at all, but everytime i see it it turns into a huge debate.

My dad's a pilot, I'll ask him.

Let me ask you guys who are having trouble with this a question. Take a 747 and assume that at 200mph it will take off. Now change the normal wheels to rollers skate wheels, will it still take off at 200mph?

Take a random car with 20" wheels running the engine at 5000rpm, take the same car attach 13" wheels running the engine at 5000rpm. Which setup will be traveling faster?

Strap a rocket engine to the car and tell me how the wheels will effect the speed at which the car can travel under the power of the jet engine.

Prolly the car with 20" wheels, since you can't really find 13" tires in 185/400 profile. :gay:

Seriously though, this question cannot be answered without specific data concerning the materials involved.

This combination of the airplane and treadmill is a simple servo feedback mechanism. Same sort of thing that keeps the disc in your DVD player spinning at a constant linear velocity despite increasing track circumference, or adjusts the speed of a capstainless tape machine as the wrap around the reels grows and shrinks.

We have the airplane engine producing thrust against the atmosphere, which we'll assume is still. This will tend to cause the airplane to accelerate forward. Then, we have the treadmill, which senses the absolute movement of the airplane and starts reeling backwards.

Since the airplane is coupled to the runway only by its wheels, which are non-driven, then the only mechanism by which force can be transmitted from the treadmill to the airplane is through the wheels. And since the wheels are freely mounted to the airplane through bearings, only the friction in the bearings can account for force being transmitted from the surface of the treadmill to the airframe.

If the treadmill is able to move fast enough to produce sufficient drag within the wheel bearings such that the force transmitted from the treadmill surface to the airframe is sufficient to equal the thrust of the engine, then the airplane will remain stationary. And a millisecond later the wheel bearings will sublimate, assuming the tires haven't long since exploded.

On the other hand, if the airplane's wheel bearings are not perfectly frictionless, then neither is whatever mechanism drives the treadmill/runway. It is unlikely that a structure massive enough to move a runway could be designed to have a lower internal friction then a wheel bearing, in which case the treadmill would be unable to move fast enough to exert sufficient force upon the airframe.

Actually, you know what? I just re-read the original question, and realized that I mis-read it the first time. It's actually very simple. Let me quote the original poster:You catch that? The conveyor isn't trying to keep the plane stationary, it's merely moving the surface backwards at a rate equal to the absolute velocity of the airplane. It's not accelerating wildly trying to keep the plane from moving, it's just moving backwards at a 1:1 rate. So the wheels of the airplane are going to be turning twice as fast as they would be during a normal takeoff, but the airplane will still launch with no problem whatsoever. Just like taking off with a 100 MPH tailwind.

Don't ask a pilot, ask an engineer. :cool:

If the conveyor belt is keeping the plane stationary, relative to the surrounding ground, then it has no airspeed...therefore no air molecules flowing over the wings to let them do their whole lift-generating thing...

It doesn't matter if it's powered by engines driving the wheels, jet engines or a nuclear reactor, if it has no airspeed across the wings, it's not taking off.

Put another way, if the jet had equally powerful jet engines attached in the opposite direction of it's usual ones, and they were both set to full power, would the plane just hover stationary above the ground?

Of course not!!

If the airplane had two engines, one rear and one forward, then you'd be correct. But that's just the thing- the airplane is rigidly coupled to its own engine, but it is not rigidly coupled to the ground. The airplane *will* move forward, despite the fact that the ground is moving backwards beneath it, because the engine is acting upon the *air*, which is stationary. It's not like we threw an anchor out of the airplane, we're just adding a bit more drag.

As the ground begins to roll backwards, it will simply cause the wheels to spin faster as the engine acts upon the air to propel the airplane forward. By the time the aircraft reaches Vr, the runway will be scrolling backwards at -Vr, and the wheels will be spinning at a rate equivilant to 2Vr, but the airplane will still be moving forward relative to the atmosphere. Ergo: airflow over the wings.

In order to keep the plane from moving forward, you'd have to move the whole atmosphere, not just the ground.

Let me put this in more everyday terms. Say you're in a swimming pool. You are swimming forward, and yet you are somehow managing to drag one toe on the bottom of the pool. (you're a really good trick swimmer.) At the same time, the bottom of the pool begins to move backwards at a rate equal to your forward progess through the water. Will this cause you to stop? Of course not. Your arms are exerting far more force upon the water than the floor of the pool is exerting upon your toe, and since the *water* is not moving backwards, you will continue to swim forward.

Im goin with this one BROTHERS!

The HULKSTER says, "No airflow = no flying yo!"

Why do they use big ol' fans on the dyno??? Because there is no airflow!

But does a jet really need airflow? Hummm...uhhh I give up, just tell me!!!

Kill me now.

U Got a problem with the Hulkster BROTHER!? LOL

I'm j/p BROTHER!

Changing my answer. God-damn geniuses!!!

As sam and Joe pointed out (others too) The fact that the plane has wheels allows the belt to be an insignificant factor in this equation.

So, the thrusters push the plane foward relative to the ground/air. The wheels spin backwards on the belt but that's irrevelant. The only thing that changes is that the wheels are spinning backwards (at an increased rate) as the plane accelerates down the runway. I'm going with pilot/engineer on this one.

Plane takes off


Quote FTW.

No, you're not wrong. Let them think about it a little. They're stuck in "car mode" instead of airplane mode.
You have to remember an airplane moves relative to the parcel of air that it's in, not the ground.

Yes, Philip, but if the airplane is stationary, it's got no airflow...you have to move relative to the ground to get airflow, dude.

When you're jogging on a treadmill, do you feel wind rushing by your face as you move through the air?

Not on any treadmill I've ever been on.

okay, now strap a rocket on your back while your runnin' on the treadmill, light that puppy off, and see if you feel any wind on your face.

Right, you won't. As long as the treadmill can keep up to maintain your lack of motion relative to the ground/Earth's surface, you'll not feel any wind in your face.

Are you guys all in on this together trying to pull my leg or something? :D

The rocket wouldn't make your legs move faster. It would simply propel your body up the threadmill. Hence wind, and if you transform yourself into a plane, liftoff.

Yes, but you'll need some air molecules moving over your wings to do anything...how are you achieving this when you're stationary?

you have to move relative to the air, not ground.

The wheels allow the ground to move "backwards" as the plane stays still. (ignoring friction since we're in make-believe mode) The speed the wheels are spinning is an insignificant factor.

soon as one shows up we'll ask him.

Yes, but how're you moving relative to air when the plane is stationary? You guys are getting caught up in the wheels still...I don't even care about them...that's why I was giving the example of the reverse jet engines mounted to it.

no, you don't. An airplane that can fly at 45kts into a 45kts headwind will stay stationary relative to the ground.

An airplane flying 45kts into a 55kts headwind will fly backwards relative to the ground.


This isn't rocket science, it's very basic physics folks.

You wouldn't be stationary, the forward thrust of the engine would overcome the friction of the wheel bearings/your legs/whatever we're talking about now and propel you forward relative to the stationary air around the conveyor belt.

because it isn't fucking stationary.

The plane is only stationary as long as the engines are off. (disregarding friction) As soon as the engines start up, the plane moves forward through the air.

If you take friction of wheel bearings into account, The engines just have to work a little harder before the plane starts moving.

<-- 1st year engineering student, but this is stuff I learned last year in high school physics.

Think this way. The giant treadmill could be going reverse direction than the example (going foward) it would still have no effect.

It does not matter what speed or direction the wheels are travelling, thus the moving runway is a non-factor.

you're wrong.

F= M*A
A = F/M

The force in this situation is jet thrust (Ft) - frictional force of the tires to the treadmill (Ff) - wind resistance (Fr).

making the equation:
A = (Ft-Ff-Fr)/M

Now. Ff = uN (mu * normal force) and airplane tires have a fairly low mu if I recall (hard compound). However, a very large mass so there is a signifigant Ff.

The normal force is equal to Mass (M) * gravity(g) (or weight)

Equation:
A = (Ft-(mMg)-Fr)/M
For now we will ignore the wind resistance because some of you seem to think the plane is sitting still (which it's not), and therefor has no wind resistance.

A = (Ft - (mMg))/M

A = Ft/M - mMg/M

A = Ft/M - mg

Notice that A (the acceleration of the aircraft) is NOT dependant on the velocity of the ground. It is only dependant on thrust, mass, the tire friction coefficient, and gravity.

If you take into account wind resistance it is dependant on velocity, however this affects the craft the same regardless of the treadmill.

If the treadmill is moving in the same direction as the plane and at the same speed than in theory it will negate the friction in the tires and allow to plane to take off in a shorter distance. Assuming all else is the same.

Wait a second...does this this airplane have normal, circular wheels?

Funny, this is what I keep thinking :)

The only thing the engine in the plane is doing relative to the treadmill is overcomming the friction of the bearing and tire once it does that the treadmill could be going mach 4 and it wouldn't matter.

Yeah, I guess I got caught up in the idea of this magical conveyor belt that would be able to move fast enough to overcome what little amount of friction there is from the plane's wheels against the conveyor belt's surface.

But the conveyor belt would have to be going thousands of miles an hour in the opposite direction...it's pretty much impossible...but I thought that was a stipulation in the original questions...magical conveyor belt.

I stand by the fact that if you have no airflow across the wings, you have no lift.