This old chestnut

[prepman]

Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.

Can the aeroplane take off?

It's an old one but a goodie, once you know the correct answer it's a bit boring, but there are loads of variations on this question which have different answers...

Only if it's 'taking off' a celebrity or politician. (impersonation...groan...)

 

[Nomad]

Insufficient data given in the question so assumptions have to be made :
If the planes engines are off, NO
If engines are running and plane tries to take off as normal, YES (but the wheels will be turning twice as fast as normal on the conveyor belt)

More fun questions for OP to post in the future ( I failed when I tried question 7) https://sharpbrains.com/blog/2008/11/17/top-15-brain-teasers-and-games-for-mental-exercise/

 

[Munkul]

No - the plane moves forwards in the air - the bottom of the wheels (in contact with the conveyor) rotate rearwards. The conveyor has to move forwards (as that is opposite to rearward) at the same speed as the wheels - so they would stay stationary.

The top of the wheel rotate in a forward direction when the plane is going forward.

Actually upon some further thought, the way you put it, does it actually hold up?

The plane moves forward at 1 m/s.
The bottom of the wheels turn rearwards at 1 m/s.
The conveyor (in the conditions stated) has to turn at the same speed as the wheel surface speed but opposite, so it moves forward at 1 m/s.
The wheels can no longer turn rearward and in effect stay still.
Therefore the conveyor also cannot move forward as it has to match the speed of the wheels.
So how does the conveyor move? Which it has to, if the plane is moving forward.

Do we then, in effect, have 1 = 0?

 

[prepman]

No because wheel speed doesn't produce lift, air movement over the wings does.

NEXT!

Edit: actually do we presume that only the conveyor is moving? There is no mention that the plane is under power only that it's say on the conveyor.

The clue is in the name aircraft.

 

[Screwdriver]

The crux of this otherwise simple "problem" is the impossibility of "the conveyor belt moves opposite to the wheels".

If the conveyor belt is set up so that it "moves opposite" to the wheels and the wheel begins to move even slightly, you have a positive feedback loop with undefined parameters. The wheel moves forwards so the conveyor drives it backwards which increases the forward speed of the wheels. Ad infinitum

In an instant, the entire system speeds up to infinite velocity and collapses into a black hole (where it belongs).

 

[prepman]

The crux of this otherwise simple "problem" is the impossibility of "the conveyor belt moves opposite to the wheels".

If the conveyor belt is set up so that it "moves opposite" to the wheels and the wheel begins to move even slightly, you have a positive feedback loop with undefined parameters. The wheel moves forwards so the conveyor drives it backwards which increases the forward speed of the wheels. Ad infinitum

In an instant, the entire system speeds up to infinite velocity and collapses into a black hole (where it belongs).

The question is ambigous, It implies that there is no forward motion due to the wheels matching the conveyor. Therefore no airflow to lift the plane. A different interpretation is a different answer. As you say it's a non-question.

 

[daleyd]

Actually upon some further thought, the way you put it, does it actually hold up?

The plane moves forward at 1 m/s.
The bottom of the wheels turn rearwards at 1 m/s.
The conveyor (in the conditions stated) has to turn at the same speed as the wheel surface speed but opposite, so it moves forward at 1 m/s.
The wheels can no longer turn rearward and in effect stay still.
Therefore the conveyor also cannot move forward as it has to match the speed of the wheels.
So how does the conveyor move? Which it has to, if the plane is moving forward.

Do we then, in effect, have 1 = 0?

But if the conveyor didn’t move (and aircraft was travelling forwards with respect to the ground - not the conveyor belt) then the wheels would be rotating. What you have to assume (as well as make a lot of other assumptions ) is that the conveyor somehow anticipates the movement of the wheels and at very same instant turns at the exact same speed in the opposite direction. In reality you could probably get a system close, as soon as it senses movement of the wheel rearward it would accelerate forward but in a real world system there would have to be some error in order for it to work.

 

[KemppiFrog]

Drinking my mid-day cuppa.... The wheels won't move if the belt doesn't drive them, so what ever speed the belt goes, the wheels match. So the belt is not matching the wheels, it is driving them.
So, it is irrelevant to the speed of the aircraft through the air.
Along with wot he said above ^^

 

[Munkul]

in a real world system there would have to be some error in order for it to work.

Yeah that was my conclusion also. Some form of feedback delay or loss. In a pure system with instantaneous feedback and no losses it is impossible.

With the conveyor going the other way and accelerating to infinity, any fixed loss or delay will just slow down the rate of acceleration but it will still get there.

 

[daleyd]

Yeah that was my conclusion also. Some form of feedback delay. In a pure system with instantaneous feedback and no losses it is impossible.

A positional sensor would get you close (but probably no cigar depending how you interpreted the question!) - if you were to look at the position of the wheel and keep it at say 12 o clock with respect to the belt - at a perfectly steady conveyor speed you could keep the position exact, but any acceleration/deceleration of the belt or wheel would mean an error for a short period until it caught up. The problem this gives is that the conveyor speed is now no longer matching the wheel speed (which is now 0). So I think my theory sounds OK until you dig deeper....my head hurts...

I think the only way you can have the belt speed match the rotational wheel speed is with 0 forward movement of the plane wrt ground, everything at rest.

 

[slim_boy_fat]

It's all a bit "If a tree falls in a forest and there's no one there...."

 

[daleyd]

If you introduce some delay and the belt is lagging the wheel speed then in my mind it’s possible the wheel speed will stabilise somewhere around half the air speed of the aircraft? Eg aircraft moves forward at 100 mph, wheel speed gets to 50 mph and belt speed 50 the opposite way?

 

[George A2Y]

Assuming the aircraft performs its normal routine it would take off, the wheels however would never rotate as the conveyor would maintain the ground speed of the aircraft, therfore maintaining their original rotational speed of the wheels.

 

[Pete.]

Munkul were all going to club together and get you some lithium in oil so you stop posting these mind-bending conundrums

 

[Munkul]

@Tangledfeet care to weigh in?

 

[Nick67GT]

Just the sort of question I wouldn’t want to be asked at an interview.

The ensuing debate would probably descend into a brawl……

 

[Pete.]

Just the sort of question I wouldn’t want to be asked at an interview.

The ensuing debate would probably descend into a brawl……

Or in the pub

 

[bricol]

Actually upon some further thought, the way you put it, does it actually hold up?

The plane moves forward at 1 m/s.
The bottom of the wheels turn rearwards at 1 m/s.
The conveyor (in the conditions stated) has to turn at the same speed as the wheel surface speed but opposite, so it moves forward at 1 m/s.
The wheels can no longer turn rearward and in effect stay still.
Therefore the conveyor also cannot move forward as it has to match the speed of the wheels.
So how does the conveyor move? Which it has to, if the plane is moving forward.

Do we then, in effect, have 1 = 0?

You're forgetting the axle the wheel is running on is being shoved along by a number of jet engines - so the conveyor has to move to keep the wheel still.

 

[bricol]

Imagine holding a bike on a treadmill, as long as you hold it still, the surface speed of the wheel must be exactly the same as the belt speed (Assuming it's not skidding or anything). If you push the bike forward a little, while the bike is moving, the wheel is turning slightly faster than the belt. If the belt speed matches the wheel speed, bike cannot move forward. It doesn't matter how fast (Or even which direction) the belt is moving, if the wheel's speed matches it, the bike is stationary.

Reasoning it like that, the question essentially becomes "What happens if you push something that can't move?", which is easy, it doesn't move.

Try it.

Hold the bike still - the wheel spin. Now shove the bike fast enough to make the wheels stop rotating relative to the belt . . . and you will have shoved it off the end of the belt and your other half is shouting at you about all the noise, oil on the floor, mud from the spinning wheels up the curtains . . .

 

[KemppiFrog]

Since this needs a bit of drift.. There was a story doing the rounds about a photo shoot in the early days of the E-Type. It was in the studio and they needed the engine sounds etc. So they jacked up one rear wheel and wound it up then dropped the clutch..... LSDs weren't too common back then and the car made a hole in the studio wall. I sort of doubt it But it sounded good at the time.. at the expense of snappers..