Counter intuitive puzzle

It was hard to miss, I mean, 24 pages.

Also it's in my signature so obviously there's no excuse to not be aware of it.
 
StarBob said:
Yes Vegeta.... we've all been sitting around here since 2006 reading every single thread and hoping we don't disappoint you...
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StarBob said:
I still don't understand the treadmill thing. I know there's a thread somewhere on it,
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You can't say anything. You knew about the old thread and didn't bother looking it up, and instead ruined my thread :frown:

I really regret making that joke.
 
I'm aware of it because I've been around that long and have been reading every page. I'm just saying that not everyone is as lame as me.

No one wants to read your sig anyways.
 
But it's got red arrows! I mean, come on.

You don't even have a sig, so you can't just dis mine like that.
 
I'm not a hipster, but I make fun of them all the time.
 
Well I thought a key condition of this thought experiment was that the treadmills speed adjusted with that of the planes, so the plane remained in a static position relative to another, non moving object.

And yes, I'm right, back to original question, on 2006 thread:

"This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction). "


So, relative to a building on the ground, the plane would never move any distance relative to the static air around until, until take off (if this occurs).

Now, how can the airplane take off without any flow of air under it's wings? It cannot and therefore will not take off.
 
Airspeed =! Groundspeed.

There will be flow under the wings of the airplane because the wheels are not providing propulsion. Same concept as yanking a tablecloth from beneath the dishes on a table. There will be a little friction, but not enough to impact the movement of the plane.

The treadmill would have to be moving much faster than the airplane in order to accumulate enough friction to keep it from taking off.
 
Higlac said:
Airspeed =! Groundspeed.

There will be flow under the wings of the airplane because the wheels are not providing propulsion. Same concept as yanking a tablecloth from beneath the dishes on a table. There will be a little friction, but not enough to impact the movement of the plane.

The treadmill would have to be moving much faster than the airplane in order to accumulate enough friction to keep it from taking off.
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But that's exactly it, nowhere in the question is a limit on the speed of the treadmill given. So presuming it has no limit, it could match the speed of the plane and prevent it taking off.
 
Higlac said:
The treadmill would have to be moving much faster than the airplane in order to accumulate enough friction to keep it from taking off.
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That's the thing though, if we assume the treadmill can keep up to any speed, it will increase speed in effort to compensate for the ever increasing wheel speed caused by the plane's movement forward. We can't actully know if it would be possible unless we set a boundary for the acceleration of the treadmill. The plane will always be able to go faster - but at some point the wheels would be destroyed. That moment would depend on if the accerlation of the treadmill is great enough to reach the critical speed of destruction for the wheels.

Or it could be that the wheel friction is too great to begin with and the plane wouldn't really get anywhere. It kind of reminds me of the issue with approaching the speed of light and becoming more and more massive requiring more energy to accelerate.

However, if it was a frictionless surface... like maybe magnetic levitation... thne it wouldn't be an issue and the plane would take off as though there was no treadmill at all... except it would still take the energy to maintain the levitation.
 
Wait, I'm wrong. ****ing stupidly wrong. If the wheels were well lubricated enough, it would be virtually impossible for the treadmill to hold the plane back.

Relative to a fixed observer, the plane will always move forwards as all the planes forward pushing power comes from the turbines or propellers, not the wheels.

Now, the plane won't just stay in a fixed position then suddenly rise up and start flying. Just no treadmill could be fast enough to hold back the place I think.
 
Solaris said:
But that's exactly it, nowhere in the question is a limit on the speed of the treadmill given. So presuming it has no limit, it could match the speed of the plane and prevent it taking off.
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I was thinking the same thing, but an analogy I created made me realize it would work if there wasn't friction.

Say you're wearing rollerskates and you stand on a treadmill. If the treadmill turns on and you're standing straight, it will push you off due to friction with the wheels and you and the treadmill. But let's say something is behind you with their hand on your back. The treadmill can go any speed, but the person behind you only has to overcome the friction generated by the wheels to keep you on it.

Then if that person applies more force than the friction - you will move forward regardless of the speed of the treadmill.

But again, the issue is that the treadmill will increase speed as you move forward providing more friction and thus more resistance to the point where it would destroy the wheels before it could be overcome.
 
Solaris said:
"This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction). "
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It says it right there.

A treadmill would only have an effect on the speed of a stationary plane. The wheels are free to move and the treadmill has little effect beyond friction on the axle of the wheels.

Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

The force exerted by the treadmill is so little that it has no noticeable effect on any object with freely rotating wheels. A plane's propulsion is not from the wheels on the ground, but by the movement of air caused by the turbines. This movement of mass (air) propels the plane forward with a force equal to the force applied by the turbines upon the wind.

Mass(air) x acceleration(air) = Mass(plane) x acceleration(plane)

A treadmill interacts in no way with the method of propulsion. The force applied by the treadmill upon the plane is not equal to the force that the plane exerts.
 
Wheel speed = Treadmill speed + (Airplane speed w.r.t fixed observer)

Plane moves forward effortlessly (friction is negligible for a plane powered by a prop or jet.) The wheel completely negates the presence of the treadmill.

/ARGUMENT

Lets move on to other puzzles.
 
Incredible, even after Starbob gives me shit for pointing out the old thread, he continues the argument as if the other thread doesn't even exist.

Anyone who reads through the old thread would not still think the plane won't take off.
 
Vegeta897 said:
Incredible, even after Starbob gives me shit for pointing out the old thread, he continues the argument as if the other thread doesn't even exist.

Anyone who reads through the old thread would not still think the plane won't take off.
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I'm saying that it's impossible from so many different angles that the test could never be performed.

Whether or not it takes off depends on how much and in what areas you're willing to suspend reality.
 
The plane and the treadmill thing again?

Come on people, it's simple to wrap your head around.
 
StarBob said:
I'm saying that it's impossible from so many different angles that the test could never be performed.

Whether or not it takes off depends on how much and in what areas you're willing to suspend reality.
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UNDER NO GOD DAMN CIRCUMSTANCE WILL THE PLANE NOT BE ABLE TO TAKE OFF.

It is literally impossible for the treadmill to keep the airplane stationary while the aircraft has its engines going more than the negligible amount required to overcome the friction on the tires from the treadmill (which is probably less than 0.1% of the engine's possible output). If the engines are turning more than that tiniest bit, then it WILL MOVE, no matter what.
 
Krynn72 said:
It is literally impossible for the treadmill to keep the airplane stationary while the aircraft has its engines going more than the negligible amount required to overcome the friction on the tires from the treadmill (which is probably less than 0.1% of the engine's possible output). If the engines are turning more than that tiniest bit, then it WILL MOVE, no matter what.
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Well it's impossible for a treadmill of this nature to exist to begin with :D

But really, if we're going to suspend reality there, but maintain that this is a normal plane, then we have to take in to account that fact that as speed the velocity of the tires increases, the friction also increases. If we continue to suspend reality with this treadmill and assume it can go any speed at all - then as the plane moves forward (increasing the rotation of the wheels) the speed of the treadmill will continue to increase in effort to stay ahead of the wheel speed. We know it can't because the thrust will continue to be more than the friction of the wheels to the surface, and the wheel structure to the wheel.

Yet, as the treadmill speed increases exponentially to counter the ever increasing wheel speed, friction will increase and, while it wouldn't really effect the overall ability for the plane to move forward (if it actually takes 0.1% it might go to 0.5%), the stress on wheels spinning at the increased rate would result in a catastrophic failure due to increased pressure, heat, or cintrifugal force.

edit: Of course if you're willing to accept the idea of a mile long runway moving at hundreds of mph on a conveyer belt... then I guess you could say that wheels are of any strength and ultimately the plane would take off before the action of rolling at whatever speed the treadmill can accellerate to before the plane reaches lift velocity.
 
The treadmill isn't matching wheel speed, it's matching speed of the plane. It says that right in the problem.

So the fastest the treadmill would ever spin is the speed it takes for the plane to lift off. And that would mean the wheels are spinning only twice as fast as they normally would be on a stationary runway.

There is absolutely nothing impossible or unrealistic about this scenario, and no special plane or wheels would be needed. Wheels are designed to negate friction, they can spin quite fast with no problem.
 
Friction doesn't increase with velocity bro.

And you wouldn't need any suspended reality treadmill or plane to get it to work. A commercial airliner takes off at 175 miles per hour. A large, runway sized treadmill that goes that fast is certainly a feasible task.
 
Vegeta897 said:
There is absolutely nothing impossible or unrealistic about this scenario
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I hope you find your mile long treadmill that can travel at any speed soon... otherwise you'll look like a fool.

And where have you been where friction doesn't increase with velocity? What are all these aerodynamic engineers doing then? What kind of world it would be if there was no air friction as velocity increased. Or no increase in friction as two surfaces rubbed together at increased speeds...

Not to mention all those people in race cars who rely on friction to warm their tires giving them more friction with the roadway for better handling...

they're all a buncha crazies

Also, if it was going the speed of the plane and not the speed at the wheel (which ironically is part of the plane so none of this makes sense), then yeah of course it would take off since it would be starting at 0 and as it increased in speed it would be only a matter of getting to normal takeoff speed. It would take exactly the same distance as if it were taking off normally... but that's a completly relative speed. It would be like... air speed on the ground. Ground speed (like you see on your car's speedometer) is determined by how fast the wheels are turning... and would do everything I just outlined.
 
Nobody was talking about air friction. And you were talking as if velocity has a direct influence on friction, which it does not. Friction causes two rubbing surfaces to warm up, yes, which does cause more friction, but its entirely dependent on the types of surfaces, and not only that but the difference is insignificant in the context of this situation. Beyond the initial thrust to give the plane momentum, friction is irrelevant in this situation.

Also, like I said, the treadmill doesn't need to go at "any speed." It would have to go 200 miles an hour at most. Absolutely possible, no matter how impractical.
 
Krynn72 said:
Friction doesn't increase with velocity bro.
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Your statement should have been less broad then.


Also, it is insignificant if the treadmill's velocity is based on the perceived speed of the plane and not on the actual speed of the turning wheels.
 
My statement was perfectly valid. Your statement was too vague and should have implied that you were talking about the indirect effect of friction on the tire's surface properties.

The speed of the plane is determined by the world-space movement (perceived is not the correct word) of the aircraft, not the relative speed of the wheel.
 
Krynn72 said:
My statement was perfectly valid. Your statement was too vague and should have implied that you were talking about the indirect effect of friction on the tire's surface properties.

The speed of the plane is determined by the world-space movement (perceived is not the correct word) of the aircraft, not the relative speed of the wheel.
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Saying "Friction does not increase with velocity" is not true. There are various cases in which friction correlates directly to velocity.

Perceived may not be the correct word, but I think the point was clear enough... but I guess we are all about proper syntax after making a broad statement that is in no way true. :D

Needless to say, the speed would have to be calculated with a radar/laser/gps style device because a plane would be using air speed, which is relative to all air moving around it, and ground speed, which would apparently be ignored by the magical treadmill.
 
Just drop the argument. Physics is right, the plane will take off, whether or not the wheels produce friction or not.
 
Oh course friction increases with speed.

Anyway, I'm finding it very hard to suppose what speed the treadmill is actually going at. Someone said it was going at the speed of the plane, but what speed is this? Relative to a fixed observer off the treadmill? If this is the case and the plane isn't going anywhere, then the treadmill, by definition isn't moving but obviously this cannot be the case as the plane is going at full throttle and so would otherwise be moving.

So therefore, just through simple word reasoning, the plane must be moving and therefore have airflow.

Therefore, if the whole experiment is going to be other than so simply obvious, then we must define the speed of the treadmill as:

that which is necessary to keep the plane in one place (ergo, it cannot take off, but I think this impossible)

Or

The rotational speed of the wheels, (in this case I'm not sure).
 
Higlac said:
Just drop the argument. Physics is right, the plane will take off, whether or not the wheels produce friction or not.
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It will take off if the speed of the treadmill is that of equivalent air speed of the plane. If it is the speed at the wheel, it will not take off because it will perpetually increase with the speed of the treadmill and BLOW THE **** UP... which will make the plane crash and everyone will die.
 
Will someone who thinks it will or will not take off tell me how the speed of the treadmill is determined.

All speed should be judged relative to a fixed observer in an Air Traffic Control tower for the sake of simplicity. This renders terms like 'wheel speed' and 'air speed' one and the same.
 
As long as there is some form of air current going along the ailerons and wings of the aircraft, it will lift off.

Nothing else matters.
 
Acepilotf14 said:
As long as there is some form of air current going along the ailerons and wings of the aircraft, it will lift off.

Nothing else matters.
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So if it's stationary and I blow on it, it will take off? Come on, wise up. I think I kinda know what you're trying to say. But we all need to be very clear here.

I want to know, what speed the treadmill moves at, relative to what.
 
Solaris said:
So if it's stationary and I blow on it, it will take off? Come on, wise up. I think I kinda know what you're trying to say. But we all need to be very clear here.

I want to know, what speed the treadmill moves at, relative to what.
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Obviously, if the treadmill moves at the relative wheelspeed, then everything goes kaput. But that's not the point of the argument, nor is it what the accepted treadmill movement is like.

As for lift while stationary, take a thin strip of paper, hold an end between your thumb and forefinger. Blow over your fingers, the paper will lift. Same concept. Blah blah, paper isn't plane, but the physics are exactly the same.
 
The point of my argument is that the treadmill has no effect on the plane's speed. The lack of friction between the plane and treadmill makes any countering motion useless.
 
And where have you been where friction doesn't increase with velocity? What are all these aerodynamic engineers doing then? What kind of world it would be if there was no air friction as velocity increased. Or no increase in friction as two surfaces rubbed together at increased speeds...

Not to mention all those people in race cars who rely on friction to warm their tires giving them more friction with the roadway for better handling...


they're all a buncha crazies
Click to expand...
The reason cars have friction on their tires is because of the actual grip of the tire, the surface grip (the road), the weight of the car, the car's aerodynamics, tire heat, and the heat of the air in the tire.

Increased heat in the air of a tire increases tire pressure and affects the contact patch (surface area of the tire in contact with the road) of the tire. However, you need to setup the air pressure in the tire appropriately, because air pressure in the tire can also lower the contact patch (if the tire bulges).

At increased speeds (velocity), you have increased down-force from the aerodynamics - in a Formula 1 race-car this can be equivalent to greater than 1000's of lbs of weight pushing down, but it varies with the amount of aerodynamic downforce of the vehicle and velocity. More speed, more downforce. This downforce is generated from air friction of the aerodynamics.

This increased down.force., combined with increased tire heat creates more friction. (hot tires grip better, but increase tire wear, i.e. create more friction)


There is also the factor of the weight of the wheel: think about when a plane lands. The initial friction is the tire grip versus the weight of the wheels and tires. Thus we have tire smoke and tire screech when a plane lands. Otherwise, the wheel is almost instantly increased to the speed of the plane. If the grip of the tire on the road was higher (perhaps by means of a wider tire), and the weight of the wheels and tires was lower, the wheels would spin up to match the speed of the plane even faster.

Another factor, although a fairly insignificant one, is the friction of the wheel bearings.


However, if you discount all of the other variables I've just mentioned, and consider only the velocity of A WHEEL, friction does not increase with wheel velocity in any significant way since the friction of a perfectly round wheel is extremely low. Gravity easily overcomes this, otherwise, shit wouldn't roll.
 
Higlac said:
Obviously, if the treadmill moves at the relative wheelspeed, then everything goes kaput. But that's not the point of the argument, nor is it what the accepted treadmill movement is like.

As for lift while stationary, take a thin strip of paper, hold an end between your thumb and forefinger. Blow over your fingers, the paper will lift. Same concept. Blah blah, paper isn't plane, but the physics are exactly the same.
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Yes, but you need a significant amount of airspeed and I really don't see what that has to do with this example.

And the phrasing of the question is very important. The treadmill moves at the exact same speed of the air plane, I'm curious how this would work. As the speed of the treadmill does have an effect on the speed on the plane, not all that significant, I accept, but it makes a difference.

Due to that, I'm not sure such a treadmill would be mathematically possible, perhaps someone smart could have a crack at it.

But of course, forgetting that the plane would take off. However, if the question supposes a mathematical impossibility, then it's not a fair question to ask.
 
This is the most retarded discussion ever, as it always is. The whole point of the question is assuming that the treadmill matches the plane's speed exactly, which means THE PLANE IS NOT MOVING RELATIVE TO THE AIR OR GROUND OR ANYTHING BUT THE TREADMILL. Which means it cannot take off. The question has nothing to do with a "10 mile long treadmill", that's no different than a real airstrip if you're assuming the plane can move faster forward than the treadmill can match in reverse speed. The point is to confuse people who don't understand that a plane has to be moving through air in order to gain lift. Talk about overanalysis.

That's honestly why this is such a dumb question/thought experiment- nobody actually agrees on the initial conditions. If the plane moves relative to the ground, it takes off. If it doesn't move relative to the ground, it can't take off. The answer depends on whether you have a magic treadmill that is capable of 100% matching in reverse the speed of the airplane on it (can't take off) or if you have a human controlling the treadmill attempting to match the reverse speed of the plane (not possible therefore plane ends up moving forward and takes off).
 
The Monty Hall problem is quite difficult and clever, but still easy to understand once you got it. I think I will tell it some some of my math nerd friends, see if they fall for it.
 
Ennui said:
This is the most retarded discussion ever, as it always is. The whole point of the question is assuming that the treadmill matches the plane's speed exactly, which means THE PLANE IS NOT MOVING RELATIVE TO THE AIR OR GROUND OR ANYTHING BUT THE TREADMILL. Which means it cannot take off. The question has nothing to do with a "10 mile long treadmill", that's no different than a real airstrip if you're assuming the plane can move faster forward than the treadmill can match in reverse speed. The point is to confuse people who don't understand that a plane has to be moving through air in order to gain lift. Talk about overanalysis.

That's honestly why this is such a dumb question/thought experiment- nobody actually agrees on the initial conditions. If the plane moves relative to the ground, it takes off. If it doesn't move relative to the ground, it can't take off. The answer depends on whether you have a magic treadmill that is capable of 100% matching in reverse the speed of the airplane on it (can't take off) or if you have a human controlling the treadmill attempting to match the reverse speed of the plane (not possible therefore plane ends up moving forward and takes off).
Click to expand...

Haha no ennui, you're incorrect and seriously misunderstanding this. I'm loving how much fun this thought experiment is.


Suppose this for a second. Say the plane is accelerating on the treadmill, the treadmill is very long, and is turned off.

Once the plane reaches 100mph (relative to an air traffic control tower ATC) the treadmill is turned on, and reaches 100mph within a second relative to ATC.

The plane continues to accelerate and the treadmill tries to keep up with it. But the friction the treadmill is imposing on the plane is wholly insufficient to stop it accelerating and taking off.
 
OK THE PLANE MOVES RELATIVE TO THE TREADMILL. THE TREADMILL CANNOT KEEP UP WITH THE FORCE THAT THE PLANE IS PUTTING OUT TO ACCELERATE TO TAKEOFF SPEED.

The treadmill will not exert enough force upon the plane's wheels to counteract the acceleration caused by the plane's turbines.

There is not enough friction between the treadmill and the plane to cause any sort of force against the plane. Newton's first and second laws tell us this. If the treadmill just slips past the wheels, then there is no acceleration upon the plane, therefore the air being moved past the turbines is still exerting an equal and opposite force upon the plane causing it to accelerate and eventually take off.

Speed relative to the treadmill is not important to the physics of flight, what is important is the speed of the air past the wings.
 
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