Plane on a conveyor belt

Ravenous

Sambostar said:

Stick it on Mumsnet, it won't even make two pages.

"I had no problem pushing my baby buggy on the conveyors at the terminal building. I don't see what the big deal is. So I'm sure it would take off if that nice Benedict Cumberbatch was doing the flying..."

LastMantra

Doesn't need to be a conveyer belt, could be a rolling road type thing, roller front and back of each wheel. When the pressure shifts from the back roller and on to the front one, it speeds up. 
You could stick a few wind-turbines behind the engines to power the rollers :-D 

Sporky

Handsome_Chris said:

I am loving this thread.  It's interesting to see how entrenched (blinkered?) in their belief of what is right.

I think most of the people supporting the paradox view can also follow the other solutions, but think that they require a different (possibly less sound?) interpretation of the question.

My view at this point is that the set-up was intended to provoke debate and argument, and was deliberately worded in a way that would inspire different solutions in different people.

I don't entirely see any need to call people "blinkered" over interpreting the question in a different way.

Sporky

Dang it - double post.

PolarityMan

Well one possible solution is that the wheel's speed remains at zero, the conveyer belt doesn't rotate and the plan takes off by sliding the whole converyor apparatus along the ground. I call this the superglue solution.

Ravenous

menamestom said:

Ravenous said:

Mkjackary said:

The only way I could see that it wouldn't take off is that the friction of the wheels causes enough back force onto the aircraft to equal the thrust created by the aircraft

But as a few people have already said, the tyres on a 747 would fall to bits once the rolling speed gets high enough. This is the one practical limit everyone seems to be ignoring.

I think if you are imagining a hypothetical high speed conveyor belt, you are also imagining a hypothetical aircraft with limitless rolling speed.

I'm imagining a 747, which is what the question said.

It's really quite a simple trick question. It's not real.

Ravenous

menamestom said:

Ravenous said:

Mkjackary said:

The only way I could see that it wouldn't take off is that the friction of the wheels causes enough back force onto the aircraft to equal the thrust created by the aircraft

But as a few people have already said, the tyres on a 747 would fall to bits once the rolling speed gets high enough. This is the one practical limit everyone seems to be ignoring.

I think if you are imagining a hypothetical high speed conveyor belt, you are also imagining a hypothetical aircraft with limitless rolling speed.

I am imagining a real 747, as that's what is in the question.

It's a simple trick question. Quite simple really

mart

Apparently it's a good time to re-visit this.
https://youtu.be/xUjcHW7SHaI

poopot

holnrew said:

Haven’t read the whole thread...

but yes the plane can take off... the plane will still move forward as the engines provide the thrust not the wheels...

Hot air out the back provides forward thrust... totally irrelevant to what’s going on with the conveyor belt...

thumpingrug

Well that was pretty obvious at page 1, I really dont understand why we had 18 pages of argument over it.

drofluf

If we all chipped in we could buy a 747 and a conveyor belt a settle this once and for all. 

stickyfiddle

Oh god it came back...

stickyfiddle

FWIW it's an excellent video from Savage and sums up my feelings from way back on page 2  

dazzajl

I've seen good forums get taken down by this one. There were relationships that never healed from the argument. 

mart

stickyfiddle said:

Oh god it came back...

I couldn't resist. I didn't feel like it had properly taken off first time around.

Handsome_Chris

mart said:

stickyfiddle said:

Oh god it came back...

I couldn't resist. I didn't feel like it had properly taken off first time around.

I get it!

viz

His video of that plane taking off didn't fulfill the conditions of this physics thought experiment though, because the reverse speed of the conveyor belt didn't match the speed of the wheels, evidenced by the fact the plane moved forwards relative to the stationary cones before taking off. Relative to the conveyor belt, the wheels were actually spinning at 50, in order to achieve 25mph takeoff speed relative to the stationary cones.

To fulfill the thought experiment the truck driver needed to accelerate such the plane didn't move. Because the question says "the conveyor belt is designed to exactly match the speed of the wheels". So he needed to drive at 50mph backwards. But then the plane would have gone to 75. So the driver would have needed to accelerate to 75. But then the plane would have gone to 100. So the driver would have needed to accelerate to 100. But then the plane would have gone to 125. So the driver would have needed to accelerate to 125. But then the plane would have gone to 150. So the driver would have needed to accelerate to 150. But then the plane would have gone to 175. So the driver would have needed to accelerate to 175. But then the plane would have gone to 200. So the driver would have needed to accelerate to 200. But then the plane would have gone to 225. So the driver would have needed to accelerate to 225. But then the plane would have gone to 250. So the driver would have needed to accelerate to 250. But then the plane would have gone to 275. So the driver would have needed to accelerate to 275. But then the plane would have gone to 300. So the driver would have needed to accelerate to 300. But then the plane would have gone to 325. So the driver would have needed to accelerate to 325. But then the plane would have gone to 400. So the driver would have needed to accelerate to 400. But then the plane would have gone to 425. So the driver would have needed to accelerate to 425. etc

Stratavarious

No

mart

viz said:

... So he needed to drive at 50mph backwards. But then the plane would have gone to 75. So the driver would have needed to accelerate to 75. But then the plane would have gone to 100. ... etc

That's pretty much where I got to when this first came up - the conveyor belt would need to be constantly accelerating. But then after this latest video I realized it's simpler than that:

viz said:

His video of that plane taking off didn't fulfill the conditions of this physics thought experiment though, because ...

... those conditions are simply impossible.

If the belt exactly matches the speed of the wheels, then the plane doesn't move, but the plane's engines ensure that it will move, so the belt's task is impossible. If the plane's thrust makes it go at 25mph, then whatever speed the belt goes at is 25mph too low to keep the plane still.

Putting that another way, the belt is trying to stop the plane from moving by pulling its wheels the other way. But that can never work, since the wheels on a plane are essentially just free wheels, not connected to anything by gears or chains, free to spin however they want.

The question is ingenious because it's based on a contradiction, but that contradiction/impossibility is hard to see. Hard because we don't like impossibilities - our brains are wired to look for other interpretations instead - and hard because the physics is complicated enough to distract us quite effectively. And it looks like even the mythbusters folks are still too distracted to see that.

viz

mart said:

viz said:

... So he needed to drive at 50mph backwards. But then the plane would have gone to 75. So the driver would have needed to accelerate to 75. But then the plane would have gone to 100. ... etc

That's pretty much where I got to when this first came up - the conveyor belt would need to be constantly accelerating. But then after this latest video I realized it's simpler than that:

viz said:

His video of that plane taking off didn't fulfill the conditions of this physics thought experiment though, because ...

... those conditions are simply impossible.

If the belt exactly matches the speed of the wheels, then the plane doesn't move, but the plane's engines ensure that it will move, so the belt's task is impossible. If the plane's thrust makes it go at 25mph, then whatever speed the belt goes at is 25mph too low to keep the plane still.

Putting that another way, the belt is trying to stop the plane from moving by pulling its wheels the other way. But that can never work, since the wheels on a plane are essentially just free wheels, not connected to anything by gears or chains, free to spin however they want.

The question is ingenious because it's based on a contradiction, but that contradiction/impossibility is hard to see. Hard because we don't like impossibilities - our brains are wired to look for other interpretations instead - and hard because the physics is complicated enough to distract us quite effectively. And it looks like even the mythbusters folks are still too distracted to see that.

Yep it’s a thought experiment that lives in the realm of physics, and like other infinity-based experiments it can’t be achieved in the reality of our world. The conveyor belt can never match the planes wheels to keep the plane stationary, even if the plane is pushed with the force of a little finger (assuming no friction). The wheels and the belt would *theoretically* immediately, instantaneously, spin up to infinity and then you’re in the realm of a null answer. 

In reality what happens is that the plane’s wheels exceed the speed of the belt, therefore the plane moves forward, therefore the plane takes off. As per the video. 

But that’s not what the problem asked for.

But I’m happy to live with that.












So long as the question is rephrased as “Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to try (unsuccessfully of course!) exactly to match the speed of the wheels, moving in the opposite direction. Can the plane take off?”