Is it just me or are people fucking thick?

[Roobarb]

Nope, no it doesn't, that's what's catching a few people out (including the original poster who included the word stationary). The actual question linked to mentions no such condition.

Have a think about it, and you will notice that there's no way for the treadmill (magical or not) to keep the plane stationary, therefore it doesn't, therefore the plane moves, therefore it takes off.

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

Ok, can we get this over with now. Does the original question mean :
a) The treadmill moves so blindingly quickly it imposes an equal force backwards on the undercarriage to that generated forwards on the wings by the plane's engines.
b) The treadmill moves backwards with velocity -n, when, if stationary the plane would otherwise have moved forwards with velocity n.

Case a) is a pointless thought experiment, unrealisable in practice, and anyway there would a rotational force as the forwards and backwards forces are not aligned at the centre of gravity of the plane and at some point the fucking thing would crash into the sodding treadmill.

Case b) the plane will take off, for the many reasons already given many times.

Now, can someone kill Jedburgh please?

[Bog]

Now, can someone kill Jedburgh please?

On it.

[aureole]

I think I could understand what people were saying, if only they were a bit angrier and used more cuss worlds.

Shit off, cunt.

BTW I went, "Oh, yeah. Duh." approximately 24 hours ago.

FOR THE LAST FUCKING TIME, I DON'T UNDERSTAND WHAT YOU'RE SAYING.

SPEAK-O INGLESE-O?

[piku]

What'd happen if the plane tried to land on this mystic runway, rather than taking off?

I'm bored by the taking off thing now. Let's tackle it getting back to Earth

And no, they're not cotton buds up my nose. They're pencils.

A-wubble.

[Jedburgh]

FOR THE LAST FUCKING TIME, I DON'T UNDERSTAND WHAT YOU'RE SAYING.

SPEAK-O INGLESE-O?

WATNEY'S RED BARREL-O.

[diablo]

Now, can someone kill Jedburgh please?

Can we also agree on the two camps to resolve this.

Camp A ('and yet she does move') - people who have the physics knowledge to work it through.

Camp B ('no dice') - people who have done some physics somewhere in the distant past, probably in school, but are using the mental image of themselves on a treadmill flapping their arms and doing lots of left hand moving over right hand type movements to prove their 'theory'

Camp C - Splitters!

(okay there are three camps, I'll come in again...)

[Mark]

Wow! This one's still going! Here's how I resolved this so I could sleep last night (could be nonsense, but worked for me):

You think?

blah ... blah ... helicopter ... blah ... blah ... airplane ... blah ... blah ... nonsense about wheels

I hate to think I am going to be keeping you up tonight, but do you know what the difference between a plane and a helicopter is? Seriously, can you locate the wings on an airplane and the wings on a helicopter. If you can then presumably you'll be able to appreciate the difference between how the wings provide lift on each type of aircraft.

Geez.

Geez, indeed. The helicopter was just an example to illustrate the wheel speeds on a moving treadmill with a stationary and moving vehicle. It had nothing to do with the plane's ability to take-off whatsoever. Replace the helicopter with a harrier jump-jet if you need wings - the example still stands.


The problem is that the magic treadmill is not only magic, but absolutely impossible. It can't match the speed of the wheels.

Speed of wheels = speed of treadmill + speed of plane.

But speed of treadmill = speed of wheels.

So, speed of wheels = speed of wheels + speed of plane.

This works fine when speed of plane = zero.

It doesn't work though when, for example, an already airborne plane flying at 100 mph tries to land on the magic treadmill (I've just seen Piku has mentioned this). At this point the speed of the treadmill immediately becomes 100mph. One of two things has to happen now.

The first is that the plane has to stop immediately, so that wheel speed = treadmill speed, in which case a huge amount of energy has just popped out of existence (several tons of plane has just stopped moving forward at 100mph).

Or the wheels need to spin at 200mph to counter the 100mph forward motion and the 100 mph treadmill motion in the other direction. But if the wheels are going 200, so is the treadmill, so the wheels need to go 300. But if the wheels are going 300...

Both are impossible. I'm not sure it's worth debating an impossible treadmill.

[kalmar]

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

b) The treadmill moves backwards with velocity -n, when, if stationary the plane would otherwise have moved forwards with velocity n.

Careful of the wording. The treadmill moves with velocity -n, where n is the forward speed of the plane.

I agree though, it's definitely not A, that was inventively dreamed up by someone who initially jumped to the wrong answer and then tried to science their way out of it

[Mir Nyet]

See, I turn my back for an hour, and all of a sudden everyone gets angry

Having thought about this some more, my money would be on the plane tipping forwards onto its nose if the threadmill could match the rotational speed of the wheels, something akin to the plane getting the rug pulled out from under it If the rotation speed was matched, then the wheels would resist moving, but the plane would not...

[Roobarb]

I'm pretty sure it means B.

Well, like you said, if it meant A you may as will stick a big brick in front of the wheels.

At which point, with all 4 engines of a 747-400 at full thrust, the landgear will have a 1M Newton force pushing horizontally back at it. I'm inclined to think it probably wasn't designed to withstand that kind of stress

edit:correction

[Mir Nyet]

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

b) The treadmill moves backwards with velocity -n, when, if stationary the plane would otherwise have moved forwards with velocity n.

Careful of the wording. The treadmill moves with velocity -n, where n is the forward speed of the plane.

I agree though, it's definitely not A, that was inventively dreamed up by someone who initially jumped to the wrong answer and then tried to science their way out of it

Oi... I feel a slapping coming on

[kalmar]

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

b) The treadmill moves backwards with velocity -n, when, if stationary the plane would otherwise have moved forwards with velocity n.

Careful of the wording. The treadmill moves with velocity -n, where n is the forward speed of the plane.

I agree though, it's definitely not A, that was inventively dreamed up by someone who initially jumped to the wrong answer and then tried to science their way out of it

Oi... I feel a slapping coming on

Actually, you don't get the credit, it was phattslagg's concept

[PumaG]

The plane... sitting on this mystic conveyor... needs to move forwards in order to take off. To do this it has to roll forwards using its wheels (indirectly powered by the engines). Like the original evil post says, this mystic conveyor matches the speed of the wheels exactly.

So the pilot turns on the engines, takes off the brakes on the wheels and... the mystic conveyor starts up and immediately matches the wheel speed exactly down to the macro nano pico metre per quantibillisecond.

Bearings, friction and things like that aren't mentioned, so we can't reason about them. They're beyond the scope of this thought experiement - up there with what the pilot had for lunch and the number of terrorists on board and immigrants in the baggage hold.

Therefore plane no worky...

In the real world, the plane might well fly because of bearing resistance and whatnot. Unfortunately in the real world it would be impossible to make a conveyor this large that worked so obviously this isn't about the real world.

if you suspend a plane in the air with string, tied to an overhead bar (no wheels, no ground) it still thrusts forward right ?

[fred_zen]

Bar?

[tufty]

blah ... blah ... helicopter ... blah ... blah ... airplane ... blah ... blah ... nonsense about wheels

I hate to think I am going to be keeping you up tonight, but do you know what the difference between a plane and a helicopter is? Seriously, can you locate the wings on an airplane and the wings on a helicopter. If you can then presumably you'll be able to appreciate the difference between how the wings provide lift on each type of aircraft.

Geez.

I don't think you got slapped enough for this one, so here's another slapping for you. It's meant in a fairly nice way, though.

There is no significant difference between a powered fixed-wing aircraft and a helicopter in terms of the way they generate lift. They may look different, but both of them use a motor in order to move their wings relative to the air. If you replace "air" with "supporting medium", you can include hydrofoils, too.

The only significant difference between a helicopter and an fixed-wing aircraft or hydrofoil is that a helicopter moves the wings relative to its own body, thus decoupling "wing movement relative to the medium" from "aircraft movement relative to the medium". In practice, this means that a helicopter can fly in any direction without having to face that way, at the cost of not being able to use its own weight as a "motor" to drive its wings forwards and glide to a landing[1]

So, in fact, the basics of the question would be exactly the same if you replaced the aircraft with a helicopter, as would the answer. Of course, it's blindingly fucking obvious that a helicopter, which takes off largely vertically, would not be affected by sitting on a rolling road; it's less obvious that the same is true of an aircraft which is why we're still here on page 1004.

Oh, and for those that still believe the aircraft wouldn't take off, I've been asked to point out that my earlier comments about pixies were merely jokes, and that you shouldn't allow them to confuse you.

Simon

[1] Actually, this is not entirely true, many helicopters can operate in "autogyro" mode at least to a certain extent in the case of engine failure.