Imagine a plane is sitting on a treadmill

And the most important one you forgot:

4) Oh bollox, I have thought about it and you are right, it does take off

This can also be porn

The whole point of confusion IMO comes from mixing kinematic and kinetic points of views here. Look at the problem from a kinematic point of view as velocities were mentioned in the problem. You have a solid object(wheel) whose velocity of its center is to the left and velocity of its bottom is to the right. Can this move? Of course you get a rotation but how about movement?

Forget any force here just think about the movements created by forces.

If the velocity of the plane is meant to be relative to the conveyor(following figure), then no movement occurs.

If the velocity of the plane is meant to be measured with respect to the ground(not the conveyor as shown in following), then this means that the center must have a velocity of 2V relative to the ground(V relative to the conveyor) and in this case plane movement will happen

no more important

5) its a bit of fun.

6) I now have a list of people i can ask to fix anything that moves...

The confusion comes from two things:
1) the speed of the conveyor matches the speed of the wheels which it can only do at zero which is not implied in the question (although, some variations contain this as a premise).
2) one is allowed to increase acceleration by increasing thrust to increase the force needed to overcome added friction which is not implied in the question.

There are three possible answers: the plane takes off albeit with some initial difficulty, the tires burn up and the plane is doomed or overcoming the added friction does not allow for take off within the parameters of the question.

It cracks me up to watch people talk about the bearings not being about to spin the wheels so fast, or the wheels will explode at X speed because they weren't designed for that, or that friction is even part of the equation.

Look people. The conundrum is this. Most people will initially think that the plane will not take off, because the conveyer belt is moving back at the same speed that the plane is moving forward so the plane, relative to the ground, is not moving and cannot gain lift.

The simple truth is that the plane will move forward, because the coveyer belt is not exerting any force on it, only on the wheels that are free to spin.

The answer to this riddle is that the plane will take off. No more arguing with complex physics. Its trival.

no it cannot. the plane is stationary, if it can take off it will be vertically up like a rocket. its the air speed that counts not the ground speed, ...that was the answer i was given by my colleague who was a pilot.

No 666, you miss the point. The engines are blowing the plane forward and the wheels form, as far as significant, a friction free point of contact between the plane and the ground. The fact that the ground is moving either forwards or backwards is entirely irrelevant to the motion of the plane. The ground moves, the wheels spin, the plane does not move. The engines will push it forwards, it will take off.

I'm glad that's settled. DW, you can close the thread now.

oh, is there a definite answer now? i stopped reading last night and i sure as hell ain't about to catch up on the 7 pages I missed. very interesting, howerver.

I think we should put it to a poll (I should have done that to begin with - let's see if it the mods can add it).

For the 50th time, the plane is not stationary. It is moving. The conveyer belt is moving just as fast in the other direction, but this does not cancel out the planes speed it just makes the wheels go twice as fast.

No it won't.

OK try this. Imagine a car on a treadmill. Start engine and spin the wheels up to 100mph. Will the car move? No. The wheels will spin but that's it. Now put the car in neutral. Wheels are spinning & it's still not going anywhere.

Now give the car a push. Backwards or forwards. What happens? Is is more difficult to move than it would be if it wasn't on the treadmill? Remember the tread merely matches the speed of the wheels, it's not providing drive. Neither are the wheels.

Now instead of a push put a jet engine on the car and start it up. Remember the jet engine acts according to Newton's third law. It throws gases out of the back and moves forward, taking anything that it's attached to with it.

Does that help at all?

From what I discussed with eurovol, if the question was worded like this...


...then it wouldn't take off. However it didn't say that, so it will take off. It's easy, look at post 2. I don't think a poll is necessary, like 10 people have already changed their mind once they realised how a plane works, there's only 1 or 2 left who still don't get it.

Where is the, "DW is probably pissin' himself laughin'" option?

Would this be a good place to point out that the wheels aren't going to turn at all since the the initial problem said the plane remains stationary on the treadmill? Airplane wheels aren't connected to motors; they roll because the force of the engine pushes the plane forward beyond their rolling resistance. If the plane's on a treadmill and being held stationary (assuming the treadmill is securely anchored against some 3 million Newtons of force), the wheels never get a chance to turn.

No plane can take off until a sufficient airflow is established across the wing. No air across the wing (and this "riddle" establishes that fact), no lift, no take-off.

Or should I wait for the 499th response to snipe a top spot with this information?

woof.

Where does it say the plane remains stationary?

OK. The treadmill matches the speed of the wheels. So if the wheels don't move, the treadmill won't. Imagine a plane at full throttle. How much force is needed to stop it from moving. Answer: a lot. So it is going to move, isn't it? There's no rope holding it back. The brakes are off. What is going to stop it moving?

Umm... here in the first post:

The treadmill matches speed of the wheels whatever that might be. The plane remains stationary. No airflow over the wings. No take-off.

woof.

That would work if it was a car, where the wheels drive by friction against the treadmill. But drive is provided by the engines & the wheels are free to rotate at whatever speed they like.

That's floored logic Mr BD, if the plane is going forwards with an air-speed of 50mph, and the conveyor is going backwards with a speed of 50mph, does that satisfy the statements made in the original post?

Nope, the wheels just rotate at double speed - the plane still moves as the actual force that is making the plane move is that exerted by the engines, surely? Therefore the treadmill has little effect at all, except to spin the wheels, which as a result must now turn twice as fast for the aircraft to take off. It still takes off though.

Correct Jimbo.

Did nobody link these in here yet? From the Straight Dope:

"A plane is standing on a runway. . ." No, it's not. Here's why.

An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?

If a plane flew low and I was able to reach up and spin the wheels backwards, how much would the plane slow down? Answer: hardly at all. It wouldn't even notice.

I say yes. All that matters is the speed of the plane relative to the air. If the plane goes fast enough, it will take off.

The treadmill doesn't factor into this equation at all.

Wheel, until you have airflow across the wing, there's no source of lift. No matter how fast you can get those wheels turning the conveyor belt is going to match that speed and the airplane remains stationary resulting in no airflow across the wing. The conveyor belt is the size of a runway but the plane never gets to the end of the runway. Even if you had a thrust:weight ratio above 1.0, the plane ain't going to take off.

DW must be pissing himself laughing over this thread.

No airflow over wing = No lift = No take-off.

woof.

And he says exactly the same as I said ages ago.

You really ought to go back and read the thread first BD. What force is stopping the plane accelerating forwards to get air-speed?

Why does a plane move? Is it the wheels pushing forward, like a car? Nope, it moves according to Newton's third law. So assuming the friction and rolling resistance are low, it will move forward. How much resistance would a treadmill going backwards exert? Answer: exactly double the resistance which a stationary runway provides. Which isn't really a lot - air resistance is what counts.

Edit: actually there might be a power in there somewhere, but it's still insignificant compared to the air resistance.

haha.. BadDoggie is so wrong.. how can we get so far and have people still not realise that the plane does have speed/airflow over the wing. I guess some people just haven't read the thread.

Absolutely what Wheel and sGB27 are saying. The plane takes off - the extra resistance from the treadmill is as nothing compared to the thrust provided by the engines.

BD your theory, surely, only works where the wheels are driven, which, obviously, in this case they're not, n'est pas?

Gen: Cecil is not infallible (though he's a hell of a lot better than Savant), and he confirms in BR#2 that the plane will not take off if the conveyor can continue to match the speed of the wheels (constant matching acceleration, not a steady speed). This is the riddle as DW wrote it: The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction. Constant acceleration. The plane doesn't move, only its wheels do.

woof.

Actually not, it would be pretty much the same, friction doesn't change with speed. Try slipping the clutch on your car and revving the engine, the force transmitted is pretty constant no matter if the engine is revving 1000 or 6000 rpm. Edit: or hold the brake pedal down with a constant force at high speed, you will notice that the car brakes a pretty much constant amount even though the discs are turning slower and slower as you slow down.

The bit you're getting wrong is this: the wheels are moving relative to the treadmill.

What does the plane move relative to?

The tires will blow and here is why:

http://ap.bridgestone.co.jp/pdf/Data_Sheet_Terminology.pdf

http://www.goodyearaviation.com/img/pdf/effects.pdf

http://www.airweb.faa.gov/Regulatory_and_G...LE/TSO-C62e.pdf

The effective weight of the total tread at 400 mph would be 67,500 lbs, not to mention the heat.

Nope, the conveyor needs to match the force of the engines, not the speed or acceleration. The question doesn't mention anything about matching forces.

Or: is momentum affected by the treadmill? What is the momentum of the plane relative to?

In order to match the speed of the wheels, the belt would have to move at twice the speed of the plane, which is not what the question specifies. But that would just cause the wheels to spin faster as there is still no resistance to the forward motion of the plane.
Therefore the belt can never match the speed of the wheels.
Therefore plane will take off.
QED

0 = 0

huh? in fact the belt has just as much chance of reaching the speed of the wheels as a fixed runway does.

I'm definitely enjoying myself.

For the record, there is a correct answer. Some people are right for the right reasons, some are right but for the wrong reasons and some are just plain wrong.

I'm not going to bother stating my answer because it doesn't matter. The debate will continue regardless of the explanation given or who gives it. If you google this question, as I'm sure many of you have, you'll inevitably find people who've answered the question correctly and umpteen people who emphatically disagree with the correct answer.

If you're still not 100% sure about your answer I suggest rereading the question, purging your head of assumptions and starting from scratch.

First time I've ever seen Baddoggie so utterly wrong.

The conveyor's speed is measured relative to the earth.
The plane's speed is measured relative to the earth.
If one moves, the other moves in the opposite direction at the same speed (again, both speeds relative to the earth, NOT each other).

It is therefore logically, physically impossible for one to "cancel out" the other or for the plane to remain still while the conveyor moves. This all goes against the basic premise of the question. If that's not how you read the question, you're just plain reading it wrong.

Why impossible to cancel out then?

Maybe I'm seeing this a whole lot differently than you.

The conveyor's speed is measured relative to the earth.
No, the way the question was worded, the conveyor's speed is relative to the plane. It will always match the plane's speed.

> The plane's speed is measured relative to the earth.
The plane's ability to take off is measured by the windspeed across its wings.

> If one moves, the other moves in the opposite direction at the same speed
Right...

> (again, both speeds relative to the earth, NOT each other).
Wrong. The conveyor belt is moving relative to the plane. The entire belt is stationary and is able to cancel out the forward motion of the plane since the plane gets its roll via the wheels.

>If that's not how you read the question, you're just plain reading it wrong.
That may be the case. Or I may be reading it differently based on how I parsed the original question.

woof.

It does? So planes have huge transmissions pumping propulsive forces through the wheels so they can take off, right? And as soon as the plane takes off the transmission switches to propel via the engines? Or perhaps not...

Think about the ball bearings in a skateboard or rollerblade wheel- they are a good analogy to this hang up everyone seems to have with the airplane's wheels: the ball bearings move exactly the same speed as the wheel, only in the opposite direction. So a plane sitting on this massive "conveyor belt runway" will just sit there, wheels spinning away and not moving, much like a skateboard wheel if you just pick it up and flick the wheel. And like the airplane, the skateboard moves because you push it with your feet, as the plane moves by the turbine engines blowing air- thus pushing it. Does this analogy help anyone, or make any sense???

@BD - I think this sums it up neatly:

http://www.deviantart.com/deviation/44285447/

Dammit! I didn't want to get sucked up into this one. CURSE YOU DEE DOUBLE-YOU!


No, but think about how a plane moves. It throws shedloads of air backwards to move itself forwards (Newton's third law), whether via propeller or turbine or even JATO rockets. It sits on wheels which have considerably less rolling resistance than skids. Their rolling resistance is broken and it begins to move forward. The forward motion allows more air to go over the wings, inducing lift.

Now if there's a conveyor belt under the plane which can match the speed of those wheels exactly and constantly the plane won't move forwards relative to the earth and air above it. No air would be passing over the wings to create the lift. The plane couldn't fly.

woof.

The relevant point however, is that a plane doesn't move because of it's wheels (as a car does) a plane moves because of the thrust from the turbine engines. That's why there are planes that can take off from water, etc.