Imagine a plane is sitting on a treadmill

No, not really. The problem is in the interpretation of the question.

Imagine a rocket tethered. So long as the tether is strong enough the rocket will not lift off.

Now imagine a jet engine on a plane at 'take-off' thrust. If the brakes are on (and strong enough) the plane won't move, but obviously the air behind the plane will be going like billy-o from the jet.

The conveyor belt is the brake, even though the wheels are free-spinning. It is just a virtual brake.

The original question states: The conveyor belt is designed to match the speed of the plane exactly but moves in the opposite direction.. ie. It matches the speed of the plane exactly, no matter what the jet/s is/are doing. The plane is therefore stationary.

So, while the whole thing is hypothetical, because it is unimaginable that the conveyor belt could keep up with the forward momentum of the jet/s at take-off thrust, said imaginary conveyor belt is always maintaining the plane at the same place... and so there is no airflow to the wings... and no lift.

Geeezz...

Stick to fucking about with lasers!

Alright. Explain to me where it gets the lift to take-off.

But, as has been pointed out many times...

If you read the question as "the treadmill will go as fast as it needs to go to stop the plane from moving" then it will be accelerating at about 40g, or 800mph in 1 second. Given a couple of seconds of this, the crazy speed of the conveyor will start to drag air along with it until there is enough air flowing along to provide some lift. It may not fly off but it will "take off".

Or if you read the question so that is actually has a possible outcome, then "It matches the speed of the plane exactly but moves in the opposite direction" would be read as "The plane moves x-kmh forwards and the conveyor belt matches that speed but in the other direction, i.e. x-kmh backwards." Lets say we get up to 300kmh from the plane, the belt will be moving 300kmh backwards, "matching exactly, but in the other direction" the planes speed.
The rolling resistance of the planes wheels doing 600kmh will be utterly insignificant compared to the thrust of the engines.

The biggest question is, however, why am I continuing to feed your trolling? (No offense )

given:

and

would mean: the conveyor belt does not move.

think of it this way: a person is wearing roller blades and steps onto a treadmill (with the wheels aligned to the direction of the treadmill). The treadmill is turned on and the person only stands there (no attempt to run / skate) holding onto the railing. How hard to they need to hold on?

Don't forget that hypothetical conveyor belt would bend underneath the weight of the plane and would in essence become a runway full of speed bumps and added friction incircling the tires.

Ok... The whole bloody thing is hypothetical anyway. Before we get into the realms of acceleration loads and speeds, and then start claiming that a conveyor belt couldn't do this, we have to realise that we're in the land of fantasy anyway. When was the last time you saw a conveyor belt the width and length of a runway, and capable of running at Mach 2?

Next, what defines take-off? The plane bouncing on the conveyor belt, or full-flight? I am interpreting it as full flight. Maybe that is where I am going wrong. Maybe I am also going wrong in trying to imagine a conveyor belt the width and length of a runway, and capable of Mach 2 in the first place. It don't exist. It never will exist.

Plane's acceleration relative to ground

But, it could still be on the ground???

A "take-off" is defined as the plane being no longer in contact with the ground. So, if it is 0.01mm ABOVE ground then it is, theoretically, flying... Bloody aircraft techies

"take off" as in lift off the ground due to lift in the wings generated by airflow over the wings.

If we are in a fantasy hypothetical land then you need to accept that our fantasy hypothetical treadmill *will* be capable of doign mach 5 within 5 seconds, mach 10 within 10 seconds etc. I'm no expert, but the wind dragged past the wings by the treadmill goign at such speeds, even in hypothetical fantasy land will be enough to generate lift in them.

What is the diameter of the wheels? What are the wheels made of? What is the friction of the bearing/s? What is the weight of the skater? Etc., Etc., Etc.

Not if our hypothetical, fantasyland conveyor belt was made out of the smoothest, lowest air-friction material, Cocker. No airflow would be generated.

AHA!!!
If you had a material that had no friction at all, the wheels would simply slide across it!
You need a surface with friction in order for the treadmill to have any force interaction with the plane.

If you are saying that your material has no friction with air and yet has friction with rubber, then you are just being utterly silly.

edit: Anyways, thats it for me. Thank you and goodnight.

Now where have I heard that before?

Yesterday, at around the same time.

Just seen the question, haven't read the thread. But no is the answer

Is snow slippery and white?

Come on. I'm not trolling. I'm just saying that the whole issue is just a matter of interpretation of the original question.

Does take-off mean that the plane leaves the conveyor belt, even by a nanometer, or does it mean that it soars into the air in full flight?

In the eventuality that the plane does leave the conveyor belt, then the take-off thrust takes over, the conveyor belt has no contact with the plane, and providing said take-off thrust is enough force, the plane will fly.

However, we're in the land of hypotheticals, where if one interprets that the plane never leaves the conveyor belt, even by a nanometer, then it is always at the same position, matched by the conveyor belt... which, of course could never happen in the real world... but remember, we're in Hypothetical Land here.

No mention has ever been made of the material of our fantasy conveyor system, nor the amount of air it would move... so one may, for the purposes of the hypothetical question, assume that it moves zero air.

If contrary, one assumes that it moves a quantity of air then obviously at a certain point enough airflow is applied to the wings.

I am both in the 'Yes, it would take off' and 'No, it wouldn't take off' camps, because we don't have enough information about our hypothetical situation.

The plane is moving eastwards of a fixed point at take off speed. The belt is moving westwards of a fixed point at take off speed. The wheels are revolving at twice the speed. Why do you not see that this satisfies the parameters in the question? The plane and belt are moving at the same speed relative to a fixed observer. Where in the question does it mention the speed at which the wheels are revolving?

The question could have been better reworded as 'does the plane move relative to ground'. Of course when it moves with an increasing speed, it will eventually take off.

The speed that the wheels are revolving is irrelevant.

Thinking about it more and more, DW would have done better asking the immortal question, "How long is a piece of string?"

God people this was already discussed. There are TWO ways of interpreting the question.

The first is that the conveyor moves with the same *air-speed* as the plane, in this case the plane takes off as normal but with the wheels spinning twice as fast.

The second is that the conveyor goes at whatever speed necessary to keep the plane at zero air-speed. In this case the conveyor needs to accelerate at near warp speed and whether the plane actually takes off or not depends on all sorts of other conditions.

I think we need to finish this now.

If the plane is still relative to the ground, it will not take off. It requires air movement against it to take off, which it will not get.

If the plane is still relative to the ground, it will not take off. It requires air movement against it to take off, which it will not get.

A conveyor spinning at 80000 mph would generate quite a lot of wind...

So will this thread.

It's not really a good assumption, that the belt will generate a head wind flowing over the wings at the necessary speed to generate enough lift for take-off

I don't know where you guys get that the wheels are rotating at 2x normal speed either.

The aircraft is rolling over the belt at x kmh. Since aircraft wheels are non-driven, the wheels are rotating on the belt (matching the speed of the belt) in the opposite direction, also at x kmh. The aircraft is therefore not moving in space, only relative to the belt. Its true airspeed is 0kmh, which is not enough to generate enough lift for take-off.

EDIT: Assumption I have made is that there are no hurricane-force headwinds.

Sin, if you are trying to turn this into the world's longest thread, you've got a long, long, long way to go. Check out this thread (on another forum) which is currently 268 pages: http://www.singaporeexpats.com/forum/ftopic1180-4005.html

@adi, please read the thread...

@chicago 268pages is nothing

I vote we petition DW to close this tread. Its had it glory, be a shame to let it drag on. Close it and we can all toast to DW and the tread this evening.

If the conveyor belt can increase the speed without limit, then NO.
( since then there would be no air to lift the plane, even if the flaps are moved down ).
If not, at some point it will take off, since there would be air flow.

For lifting the plane, there has to be uplift over the wings, as we all know.

I am sure the plane has reached its destination so far and has returned back.

@Tom


Fundamentally false arguments.

Ref: 1st case. In which direction are the wheels rotating and how are they rotating 'twice as fast'? Twice as fast as what, when they are in contact with the belt which is moving at the same speed as the aircraft but in the opposite direction?

Ref: Both cases. What do you think is the difference between the belt moving at the same air-speed as the plane and the the plane having zero air speed?

Adi, you gotta read the tread, you are 48 hours behind here.

You're assuming that the limitation is from the belt and not from the jet engine. The max thrust of the jet engine is also limited.

@dolfan

I have been reading it. I just didn'T contribute until now.

The belt needs to move with (an extremely high) constant acceleration to keep the plane still, so if there is not enough wind for take off, just wait a bit longer...

Or alternatively, actually read the thread where this has been explained about 600 times.

Imagine a similar scenario:

Kid is sitting on a skateboard. Skateboard is on one of those belts you see at the gym, for gym-joggers.
I give him thrust forwards by giving him a shove in the back..same effect as a jet-engine.
However, the belt he is on matches the effect of the thrust he receives but in the opposite direction.
What happens? He moves relative to the belt but he does not move relative the the air around him. His TRUE airspeed is 0.

God the fog outside today is about as dense as some of these posts. Okay- planes don't need friction with the ground to move forward (like a car does, as the cars source of movement is power to the wheels) a plane could have wheels and take off from slippery ice, or skis and take off from water. In both scenarios (perhaps the first is better) there isn't any friction with the ground- but miraculously the plane moves forward anyway! Why you may ask? Because the engines on the wings (or wherever) aren't powering the wheels, they displace air like humongous fans, therefore pushing the plane. Nowhere in the initial riddle does it mention the conveyor belt matching the speed of the wheels, just the plane. So what if the conveyor spins 200 mph? It's no different than a plane with wheels on slippery ice- the wheels are irrelevant because they NEVER push the plane to begin with.

No, it does not.

yep I knew that. thanks. Eitherway...assuming "perfect" belt, engine, it will never fly.

Twice as fast as during a normal take-off. Plane goes forward at 200mph (relative to the AIR/EARTH), ground is moving backwards at 200mph, hence wheels are spinning at 400mph.


Ermm, the answer is in your question. The first case the plane has air-speed, the second it doesn't

Kitty,

What speed do you imagine the wheels are rotating at?

You'd have done well to have read the thread, as opposed to charging in with the wrong answer and making yourself look pretty stupid in the process. It was determined 48 hours ago that the plane will take off. Anyone still voting 'no' either hasn't read the thread or has a known problem with accepting facts.

Yes it does. The belt needs to exert a constant force on the plane to exactly match the forward thrust from the engines. This force causes the plane wheels and the belt to spin up. As the force is constant (to match the engine thrust), the acceleration of the wheels and belt is also constant (according to Mr Newton). Why do you disagree?

sG,

The first case the plane has air-speed, the second it doesn't
You're confusing phrasing with content.

ground is moving backwards at 200mph, hence wheels are spinning at 400mph.
So the wheels are moving at 2x the speed of the ground that they are in contact with?

Yes, what does this tell you is happening?