do the treadmill/wheels have to accelerate infinitely? as the plane WILL move forward and take off, the wheels must always go faster than the treadmill, so it must speed up to compensate.

therefore the aircraft will stay stationery, with the thrust used up to keep it stationery.

No, if my thinking is right the thrust from the engines ignores the treadmill altogether, the plane will roll forward however fast the treadmill is going and (presuming it’s a short treadmill and a plane that needs a lot of airspeed) fall off the front of it. Still won’t take off but not for the reasons you say.

…I think.

However, the scenario in question dictates that the belt will match the speed of the wheels, therefore speeding up, and the thrust increases, therefore the aircraft will stay stationery, with the thrust used up to keep it stationery. No flight.

That’s one of the scenarios. The one that can’t work. It can’t even start. It could in a normal car, or with legs in the running example, where forward motion is generated by force through the wheels/trainers onto the treadmill.

But with the plane, where the wheels move ONLY because the plane starts to move, it just can’t hold, unless the plane, the wheels and the treadmill are all stationary. Or the plane is on a treadmill which is on the back of a truck, and the truck is accelerating to match the plane in order to stay underneath it.

See my earlier post about sitting on your bike on a treadmill – takes very little force to hold yourself in place as you only need to overcome friction therefore very little of the planes thrust is used to overcome friction, most is used to push it forward.

And friction is a fixed force and doesn’t increase with speed, despite what scu98rkr suggested about running the treadmill faster to creat more friction…

There we go. The alternate scenario, where the treadmill matches the speed of the tyres, can only continue to hold true if the treadmill itself (the whole thing, including the mechanism) moves forward to match the speed of the plane as its prop or jet accelerates it through the air to… TAKE-OFF!

Boom.

I can’t help looking back in. I see we’ve reached the ‘arguing over the semantics of the question phase’.

miketually – Member
Yet again, I can’t help looking back in. I see we’ve once again reached the ‘arguing over the semantics of the question phase’. Again.

FTFY!

😀

actually, we’ve gone beyond that. Either that or we haven’t.

Answers thus:

a) Yes
b) Yes, or no depending.

The semantics are irrelevant, it’s yes regardless! Jesus wept.

The plane will not take off on the spot, that’s stupid, it would still require a 10,000ft conveyor belt, just as it would a runway.

As aP said, the wheels just stop the bottom of the plane getting scratched! The engines are pushing the air backward to accelerate, by what mechanism does the conveyor belt stop this happening? All it’s doing is opposing the motion of the wheels.

Another example for you then… Ice. Car on solid ice, zero friction (for arguments sake). Foot to the floor. Wheels spin, car doesn’t move.

Aircraft on same, frictionless surface… engines spool up, plane moves forward. Ta da!

The semantics are irrelevant

the semantics* are very relevant, I didn’t see the original question/thread, I thought the scenario was short conveyor belt, stationary plane in which case the plane obviously would not take off (not from the conveyor belt anyway)
If the scenario is runway length conveyor belt then yes of course it will take off.

*fairly bloody important hypothetical details so possibly not semantics

The question is “Will a plane take off from a conveyor belt?”.

Some people interpret this as ‘can it gain speed on the spot then magically lift off’, which is of course a no. However, there are no stipulations about the size of the conveyor belt.

As has happened here, people say “there are 2 questions, one where you mention the conveyor belt moving in the opposite direction to the plane, at the same speed”, but that is totally irrelevant. To turn it around… there is no circumstances under which a conveyor belt can stop a plane taking off.

Anyway, we’ve gone full circle, in my very first post I said that it could be done, but would require a runway-length conveyor belt.

To turn it around… there is no circumstances under which a conveyor belt can stop a plane taking off

That statement is wrong in so many ways I wouldn’t even know where to start with it 😀

Why, pose me a situation whereby a conveyor belt would stop a plane taking off?

And I don’t mean ‘by having one the size of the plane and putting it in the sea’, because then it’s a lack of land, nothing to do with the conveyor belt!

luggage conveyor truck putting a hole in the fuselage?

Big pile of conveyor belts half way down the runway?

I remember the original discussion.I only read the first few posts of the first page and my brain went hurty.

But then I’m a girl, so the only relevant issue is “what colour is the aircraft?”.

Big pile of conveyor belts half way down the runway?

😆

luggage conveyor truck putting a hole in the fuselage?

That’s the truck, and planes can still fly with holes in them.

whilst not quite stationary, this is worth a watch

[video]http://www.youtube.com/watch?v=rxg0ESxbLww[/video]

[video]http://www.youtube.com/watch?v=TTuDeKxjPck[/video]

In order for the plane not to move forwards the treadmill will need to generate a force on the plane equal to and opposite to that produced by the thrust of the engines. This would mean that right from the start of take off thrust being applied (and I think TOGA thrust can be spooled upto in 2-3 seconds) the friction of the wheels rotation to transmit this force would need to be huge. This might be possible in a model plane with low take off speed and small wheels and iffy bearings but for a full sized commercial plane it isn’t going to happen .

Why, pose me a situation whereby a conveyor belt would stop a plane taking off?

Well you’ve already ruled out my factitious answer based on lobbing it in the engine intake, however..

Because I was bored I did some fag packet calculations based on a Cessna Mustang twin engined light business jet.

2 engines 6.49Kn thrust = 6490*2 = 12980N
Max Takeoff weight = 3930KG = 38553N

Calulation of frictional coefs
Fr = Cr. Fv
Cr = Fr/Fv
= 12980/38533 = 0.33

Rolling resistance in sand is about 0.33
So if you’re conveyor belt was covered in deep sand it would’t even move in the first place, but well assuming that the belt has the same properties as tarmac.

Rolling resistance of stationary tire on tarmac is approximately

C = 0.005 +1/p(0.01+0.0095(v/100)^2)

p = pressure in Bar (~ 6 bar for this aircraft) v = speed in kmh)
so at 0kmh C =0.005+1/6(0.01) = 0.006
at 100kmh = 0.00825
at 1000Kmh = 0.16
at 1500Kmh = 0.36
So with a ground velocity of 15000kmh we have a rolling resistance that requires a force to overcome which is greater than the combined thrust of the engines.
So if the belt is moving backwards at 1500kmH the plane will not be making any forward progress.
Of course at the tires will have exploded by that point, somewhat increasing the friction. 🙂

So if the belt is moving backwards at 1500kmH the plane will not be making any forward progress.
Of course at the tires will have exploded by that point, somewhat increasing the friction.

not sure about that, metal rims of the wheels probably have less drag on the ground than rubber would

not sure about that, metal rims of the wheels probably have less drag on the ground than rubber would

I’d go with that.

You also can’t ignore the fact that you’re talking about the tyres exploding, but overlooking the ability of this (incredibly theoretical!) conveyor belt to move at 1500kmh.

I must admit I was thinking commercial aircraft rather than light. But ok. I’ll give you a slow clap, for the maths 🙂

Why, pose me a situation whereby a conveyor belt would stop a plane taking off?

If you could get the belt moving at the right speed then the boundary layer could result in the air flow on the underside of the wing being the same as on the top resulting in no lift being generated (I’m not doing the calculations to check this by the way).

Bruce! We did those maths! The viscosity of the air would have to be ~3 orders of magnitude higher than it is (at sea level) for the boundary layer to grow to the wing!

surely the rolling resistance is only relative to how good the bearings are? if you have super-duper 100% efficient bearings, the rolling resistance is irrelivent? Or am I missing something

You did the calculations in 2 1/2 minutes. I’m impressed!

OK, so a conveyor belt in a big pressurised dome. The no people were right all along!

surely the rolling resistance is only relative to how good the bearings are? if you have super-duper 100% efficient bearings, the rolling resistance is irrelivent? Or am I missing something

That would be largely true if you were dealing with something like a train where the wheels are to all intents non deformable. But with a pneumatic tyre it deforms, and this deformation requires force/energy that is not all returned in a useful manner. Generally speaking the lower the pressure in the tyre, the more it deforms, and the faster it rolls the quicker it deforms, so as speed increases so does the force required to deform the tyre.

That would be largely true if you were dealing with something like a train where the wheels are too all intents non deformable. But with a pneumatic tyre it deforms, and this deformation requires force/energy that is not returned in a useful manner. Generally speaking the lower the pressure in the tyre, the more it deforms, and the faster it rolls the quicker it deforms, so as speed increases so does the force required to deform the tyre.

But don’t forget the hysteresis! For a high pressure tyre, the tyre deforms, but as it rotates it returns to its original undeformed state, the elastic pushing against the ground in a useful way. Some losses of course, but hysteresis is one of my favourite words…

but..

as speed increases, the force required to deform the tyre increases, would it ever get to a point where the inflexibility of the tyre stops it deforming? ie would (at 1000mph) the tyre start to kinda ‘float’ into a perfectly spherical shape? Centrifugal forces would push the rubber out into a spherical shape, and in addition, as the tyre is circular, there might not be enough accelleration to deform it. Above a certian speed, these forces would be strong enough to hold even a completely flat tyre in a complete circle?

This really is getting absurd now! Back to perfect spheres in a vacuum…

So the tyre would eventually grow enough to take the structure of the tyre or plane out…

I read this as you can’t answer the question without further information.

So the tyre would eventually grow enough to take the structure of the tyre or plane out…

I don’t think so, as the structure of the tyre would stop it from expanding too much. Obviously at infinate speed the centrifugal force would out-do even those forces and it’d expand more, but at that point it’d loose contact with the wheel and just roll off down the runway?

I don’t think so, as the structure of the tyre would stop it from expanding too much. Obviously at infinate speed the centrifugal force would out-do even those forces and it’d expand more, but at that point it’d loose contact with the wheel and just roll off down the runway conveyor?

FTFY 😉

What a larrf. We have two possible GCSE level questions intended to demonstrate the idea that airspeed isn’t groundspeed, and most of you are arguing with someone answering the other question, and some of you are answering both at once. Backwards.

Can a plane take off at a standstill by running on a treadmill?
(No, because airspeed isn’t groundspeed.)

Can a plane with a runway sized treadmill take off even if the treadmill runs against it?
(Yes, because airspeed isn’t groundspeed.)

Thread over.

except its not, as described in the thread, if a treadmill’s running fast enough, it creates air pressure which reduces lift on the wings, and drag on the tyres which would slow the aircraft down

Not at GCSE level it doesn’t.

And in the real world if it’s the treadmill that acclerates to match but oppose the plane’s groundspeed, then it won’t get nearly fast enough to do either.

And in the real world if it’s the treadmill that acclerates to match but oppose the plane’s groundspeed, then it won’t get nearly fast enough to do either.

What gave you the idea we’re talking about the real world?

So if the conveyer is running at such a speed that the rolling resistance of the wheels equals the thrust of the engines then the plane won’t take off. Tick

But how would it ever reach this steady state? The only way to achieve this is if the rolling resistance of the tyres matches exactly the thrust of the engines as they are accelerated from a standstill.

So all you need is an aircraft engine that can accelerate faster than the conveyor and your plane will still take off, preventing the conveyor from reaching its speed of victory.

or you could just have the conveyer belt running full pelt the whole time, and the ‘start’ of the conveyer is against a wall to stop the plane falling off the back?

twoundred!