Imagine a plane is sitting on a treadmill

Actually I think the question is cleverly worded to show how ridiculously over thought a simple answer can be to come up with.

HEY! Where was *MY* 4 leafed clover? Bastard!

Good grief, we're at 55% - it's going down!

But at least try to be logical when you can. If the plane is moving forwards with speed X, and the conveyor is moving backwards with speed X, that doesn't mean the plane is stationary, merely that the wheels are spinning at 2X. If the plane was stationary, then X would be 0 and the conveyor wouldn't be moving either.

OK... back from lunch.

I think I'm beginning to see from where the difference of opinion is being generated.

I'm assuming that if the aircraft is just sitting there, with engines turned off, then the plane will move with the belt, as it moves.
The 'other side' are thinking that when the belt moves, because the wheels are free-wheeling, the aircraft will remain stationary, so any thrust from the eingines will move it forward.

Now we're into inertia and gravity arguments...

Kind of like those "how many ____ does it take to screw in a lightbulb" jokes, only in this case insert TTers and the answer is "too many".

@ Adi

Belt and plane move at the same speed, so your scenario doesn't work. It's all in the question.

Edit: equal and opposite speeds: plane 0, treadmill 0, plane +10, belt -10.

yes you are right Adi, so long as you move the belt *slowly* the plane will stick to it. Slowly, as it slow enough not to overcome the static friction in the wheel bearings. Unfortunately though, as soon as you fire up the engines, the static friction in the wheel bearings is overcome by a factor of like 200 by the thrust from the jet engines, at that point onwards, for all intents and purposes, there is no friction.

Is that true? I mean, I can accelerate the belt until it is running pretty damn fast and the aircraft could still be sitting in place relative to the belt... or not? I'm not that up on inertia and gravitational effects here. Isn'T it related to the rate of acceleration and not speed?

People have pushed Jumbo jets, so the resistance is not very high.

@adi, Yes, as I calculated way back in like post 200 or something, the belt would need to accelerate at about 40G to counteract the thrust generated from the engines.

My favourite part of the question is,


.

I'm still laughing at that bit.

So, given that there is no stated limit on the belt, the belt could accelerate at 40G and counteract the thrust of the engines?

I thought that until I re-read the wording of the question.

Not so funny now. It would not be outside the bounds of reality to build such a device, just utterly pointless and obscenely expensive.

Going for the "the treadmill counteracts the planes speed" side of the story, the accelerations required for the treadmill to achieve take it swiftly outside reality.

If you read the question correctly, its all 'fairly' realistic.

Weemun, Explain please

Exactly. We all agreed this pages ago. But that assumes you interpret the question to mean "the belt goes at whatever speed is needed to keep the plane stationary". The other interpretation is that the "the belt goes at the same speed as the air-speed of the plane", which is totally different.

I'd Like to congratulate DW on a most successful thread.

My little brain is filled with rose petals and candy floss so I have nothing else to add to the discussion...

OK, so we're all now agreed that the answer is 'there isn't enough information to decide one way or another'?

So... you mean well within NASA's budget?

No Adi, because the plane moves. If the plane is at 0 mph, how fast is the treadmill turning?
It's not a trick, the question says it moves at the same speed as the plane, therefore it must be at 0 mph too.

No, because if the belt accelerates at 40G there are two problems (and a comment):
1) There is probably not enough friction between the belt and tyres to actually spin them up this quickly
2) After a few seconds the belt we be moving fast enough to create a signicant air-flow over the wings of the stationary plane. It's only a matter of time before this is fast enough to create lift.
3) And, maybe it's just me, but the question clearly does not allow a belt accelerating at 40G (it goes the same speed as the plane!)

Methinks this thread is ripe for a hijacking.

That's correct. I came across it on another site and thought it would be fun here. I was right!

Yes, a "massive conveyor belt as wide and as long as a runway" which has been "designed to match the speed of the plane exactly" but in the opposite direction is so terribly realistic.

woof.

With a short take off plane or even RC it would be doable though.

OK. Accepting your assumptions (crucially that the belt cannot accelerate at 40G), I could buy the plane moving.

Now quick. close the thread!

EDIT: This (or similar) scenario is found on a lot of internet pages.

Take a radio controlled plane onto a conveyor they use to test cars. Fairly realistic I'd say.

See. I am totally right about this.

So the flat-earthers are clinging on by interpreting this phrase to mean:

"The conveyor belt can go a zillion miles an hour if that is what is needed to keep the plane in one spot".

Numbnuts.

It's not hard is it? Plane 0mph, treadmill 0mph. Plane +10mph, treadmill -10mph. And so on.

According to the question it is impossible for plane +0mph, treadmill -500mph.

Well I was going to go on about how you could spend billions and billions on a commercial jet sized one and use utterly obscene amounts of energy to spin it up to a max speed of say 400mph..

But you just saved me the hastle, indeed there is no mention in the original question of scale

@Wheel, I think the other way to interpret it is that the planes "speed" is measured through the wheels, so it is the wheel speed that is matched by the conveyor. This is exactly the same as saying the conveyor goes at whatever speed is needed to keep the plane stationary, and hence will cause/requrie the 40G acceleration to keep the plane stationary.

That's what the fucking question says, numbnuts. If you want to bitch about reality, start with the super-sized conveyor belt.


The acceleration doesn't matter because, as the riddle is written, the belt matches it exactly.

> 1) There is probably not enough friction between the belt and tyres to actually spin them up this quickly
There you go making bullshit assumptions without backing them up.

2) After a few seconds the belt we be moving fast enough to create a signicant air-flow over the wings of the
Where the FUCK do you come up with this? Do you have any idea about the amount of airflow needed? The air has to go across the entire wing structure -- any air a conveyor belt could possibly kick up (not very much) is centered and couldn't go out to the wings unless it was a tiny Cessna or Archer or Katana which, in that case, couldn't ever get going fast enough to get the belt to kick up sufficient wind.

> 3) And, maybe it's just me, but the question clearly does not allow a belt accelerating at 40G
Why do you keep adding some bullshit limitation? The question clearly states that the belt matches the wheel speed exactly. Furthermore, whatever the thrust of an aircraft is, the actual forward motion starts at 0 and slowly climbs. If that weren't so we wouldn't need 12,000ft runways.

woof.

@ SGb27

I know. But it doesn't make sense if you think about it. The question says the belt matches the speed of the plane, not the wheels.

Nope, but the beauty of a constant acceleration is you just have to wait a bit longer and it will get faster

Do you have any idea of the airflow that would be produced if the treadmill rushing past you at 20,000+mph?

I dunno, but I reckon it would be more than the 250-300mph needed for lift to occur. Not the kind of thing you can experiment on a full size model but I am sure there are laminar flow equations we could use to work it out if you really need us to.

ahh, so quickly the belt would be tending towards infinity mph

surely it is the plane's air speed that the conveyor belt must match for the plane to take off?

@ BD

Have you been in a plane on a short runway where they hold it on the brakes at full (or very high) throttle and then let go? Nothing slow about it.

I think it is high time we all started calling each other 'cunts'.

I already called you a Bastard. Its the best I can do online I am afraid, my wife might be watching

I shall sum up the entire 38 pages in one post.

[newPerson] it won't take off because of blah blah blah
<big argument>
[newPerson] ok i see now

Rinse and repeat.

But wouldn´t the hypothetical `wind` be too turbulent to be useful?

No, it would be laminar flow, just like real wind except there would be gradient from the converyor speed to 0 as you moved upwards. They actually use conveyor belts exactly for this purpose (well to cancel out the gradient) in wind tunnels while testing racing cars.

uh Tim , didnt u ask me me to send u a PM last nite ? Well dude I did. Wot up. BTW the plane ain't flyin.

got the pm, you said you were going to sleep... I already voted for the plane not flying. The part I get (not at all actually, more like okay, you used too many scientific words and you are not Newton and I am not Hooke and I am not going to get into something with you over this so have chosen to accept your explanation) was about the turbulence.

[realPerson] it won't take off because of blah blah blah
<big argument by grease monkies which boils brain of real person>
[realPerson] whatever
Put the thread down and step back slowly.

could we have a real airplane problem now. may i suggest following.

you're a major airplane manufacturer with a new ground breaking plane having past its prototype stage.
your order books are filling up and the break even is in sight.
unfortunatley your engineers couldnt speak an understandable varient of any human language and have forgotten to tell you that it takes longer to build the production line plane than thought.
you start to lose order and face massive delay payments. what do you do?

For those still arguing that a sufficiently fast conveyor belt will keep the plane in place:

'But the implicit assumption here is that static friction can always supply a sufficiently large force to produce a sufficiently large torque to maintain this static situation no matter what the thrust of the engines is, and that is just not true. Friction is peculiar in that it has an upper bound determined by the normal force and the coefficient of friction. That depends on the material and characteristics of both surfaces (here, rubber and concrete), so the upper bound varies depending on the situation but it does exist.

If the thrust of the engines is sufficiently large, then the torque required to spin the wheels at the appropriate angular acceleration will in turn require a friction force that is larger than the upper bound on friction. At that point, the wheels begin to slide instead of spin. The "rolling without slipping" condition is violated and all bets are off. At this point, the net force is indeed forward and the plane accelerates accordingly. I'm betting that this occurs at a pretty low thrust but I don't have the time to look up data on a real plane and calculate it right now.'

from here (scroll down to bottom)

So the plane will take off long before the belt reaches warp factor 2