A brain challenge that people get pretty passionate about


NeuroTypical

Recommended Posts

Wheels actually do have some friction in them. Heat itself creates friction and if it was possible to move the conveyor fast enough as to generate enough friction that it began acting as a brake and the engine was too weak it may be possible to actually create a stationary plane. The reality though is that you could never really apply this test to a real plane on a conveyor unless you were to make engine so weak that at full thrust it could only match the friction being applied on its axle and thus create a truly stationary plane, of course one that still wouldnt take off.

Link to comment
Share on other sites

2 minutes ago, bytebear said:

No, because it's not the movement of the wheels, but the air flow, and if the plane isn't moving forward, there is no air flow.  You can actually see lift in wind tunnels, where the plain is stationary, but the wind is flowing.

The flaw in the thinking is that a moving conveyor belt will somehow retard the motion of the airplane. This idea is built into the wording of the problem, but is fallacious. This is not a physics problem per se, but rather a problem to test whether you can correctly model the system by ignoring the implicit assumptions in the language of the problem's description.

Link to comment
Share on other sites

3 hours ago, NeuroTypical said:

And JohnsonJones wins the "first to start yelling via ALLCAPS" award!  You lose!   And your answer is still wrong - the airplane will take off and fly.  There is a hidden, critical, wrong assumption that changes everything you are saying.

And Rob Osborn has the wrong answer too.

Present your evidence then.  Thus far you have no evidence except, you say so. 

On the otherhand, you have a pilot, you have mythbusters showing it, and you have the Navy Catapults. 

This is a question asked by non-pilots to try to create a scenario that doesn't exist and easily answered by those who understand it.

Of course, those who do not understand the basics will try to say the pilots (who actually FLY airplanes), or the physicists, or the engineers are wrong...at which point one needs to ask, exactly what are they basing this idea of theirs on.

You are basing it off a intermediary medium (The wheels) which have nothing to do with taking a plane off, it has everything to do with the airflow over the wings and the thrust of the airplane.  Mythbusters based theirs off of wheels, but not the thrust, but your actual question is NOT the one they actually dealt with.  A plane kept truly stationary cannot take off, as shown by the Navy EVERY DAY they send up airplanes.  If you have some radical science, perhaps you should build and aircraft carrier better than the Navy, or explain why their aircraft are taking off horizontally from their catapults instead of going forward.

But since you won't accept MY answer from it, and admittedly I'm NOT a physicist...perhaps you will those who know better than I?

plane on a conveyor belt debunked

If you disagree, please post your evidence.  Math is acceptable evidence even if I'm not the best mathematician.

PS:  I'm don't have the most hours, but I have over 2000 hours flying time.  I know pretty much what it takes for an aircraft to take off.  When I say, if we could take off a plane from our own backyards due to some mysterious treadmill, we WOULD.  It would be a LOT cheaper.  However, despite what some may claim on this treadmill/conveyor belt thus far, the biggest proof is NONE of them have actually succeeded in doing what they say is possible.  When they claim pilots and aeronautical engineers just do not know what they are talking about...they don't understand how much we would actually WANT this scenario to be true because the cost ratio would be awesome.  Unfortunately, no one has ever built such a fanciful machine yet...

Which is probably the biggest evidence right now that it doesn't actually work the way some think it is (probably because they are accounting for ground movement rather than air movement in regards to their question).  That doesn't mean that this may not be possible, and in the future we'll all have aircraft take off from our backyards, but presently...we still have to pay hanger fees and other fees because our airplanes need a runway.

Edited by JohnsonJones
Link to comment
Share on other sites

6 hours ago, JohnsonJones said:

I believe as per the laws of physics, and as a private pilot myself, the answer would be no.

Did you mean that, no, the airplane would not take off? Because that is how I understood you, and that answer is mistaken -- as the web site you reference explains.

Link to comment
Share on other sites

2 minutes ago, Vort said:

Did you mean that, no, the airplane would not take off? Because that is how I understood you, and that answer is mistaken -- as the web site you reference explains.

I mean, in answer to the question he asked.  In it the website NOTATES the problem with the question...the question itself is flawed.

Hence, Mythbusters had to ALTER the question in order for them to even make something that remotely works.

I think the website probably ALSO mentions that it is NOT groundspeed, but the thrust that makes an airplane take off.  Mythbusters, though they accounted somewhat for groundspeed (though they could not do instant matching like you would need to), they did not really account for the thrust.  It is the THRUST that makes the airplane move, due to the equal but opposite properties.

However, if you keep something STATIONARY, the airplane cannot fly.  Even if it gets airborne, it will fall.  It has to move forward through the air.  The only exception, is if it's thrust ratio is greater than the friction (in which case your going to destroy the wheels or the belt), at which point it becomes a rocket and it is that force that propels it upwards.

Imagine a kite.  A kite needs wind against it in order to go up.  If the wind is strong enough, the kite can be stationary (and the same principle applies to aircraft, if you have a strong enough headwind, you can actually take off at a groundspeed of zero miles per hour, but as I've constantly said, the differences between what mythbusters did, and the question that is typically asked is one is based upon the ground effects the other is just mentioning keeping the aircraft stationary).  However, if there is no wind, the kite either falls, or you have to generate someway to provide that wind to the kite (sometimes by running really fast). 

However, if you have no wind, and you have no movement, and simply throw the kite up...the question then is will it go up into the air with no effort?

The answer is typically no.  HOWEVER, the mistake is thinking that the movement is in relation to your legs, when the question asked in this thread is based upon ALL acceleration, rather than simply one form or the other.  In the kite example,  your legs are the primary point of movement in the assumption...however, that does not necessarily need to be true.  If you have a long enough string and are strong enough, you could pull the kite.

The question at the beginning of the thread states that you would not be able to pull it either, for if you did, then the conveyor belt you are on would actually need to be moving BACKWARDS to account for the amount that you are moving the kite forward, even if your legs are not moving.  In otherwords, to keep it stationary, you would need to account for the thrust.  However, if you do NOT account for the thrust, at some point it WILL in fact move forward, causing airflow over the wings, and a rapid ascent (as is shown on the navy catapults via the naval carriers, except theirs is calculated so that the plane is released when the thrust is at a certain point).

However, if this question is ever proven by physicist that indeed a plane can take off while stationary, we should all be able to own and take off from our own backyards soon, as that will be far cheaper than the runways which we all utilize currently.

The fact that we have NOT done so, to me is bigger evidence of the flaw of the question, rather than the actual details of the science to it.

Link to comment
Share on other sites

1 minute ago, JohnsonJones said:

I mean, in answer to the question he asked.  In it the website NOTATES the problem with the question...the question itself is flawed.

Hence, Mythbusters had to ALTER the question in order for them to even make something that remotely works.

I think the website probably ALSO mentions that it is NOT groundspeed, but the thrust that makes an airplane take off.  Mythbusters, though they accounted somewhat for groundspeed (though they could not do instant matching like you would need to), they did not really account for the thrust.  It is the THRUST that makes the airplane move, due to the equal but opposite properties.

However, if you keep something STATIONARY, the airplane cannot fly.  Even if it gets airborne, it will fall.  It has to move forward through the air.  The only exception, is if it's thrust ratio is greater than the friction (in which case your going to destroy the wheels or the belt), at which point it becomes a rocket and it is that force that propels it upwards.

Imagine a kite.  A kite needs wind against it in order to go up.  If the wind is strong enough, the kite can be stationary (and the same principle applies to aircraft, if you have a strong enough headwind, you can actually take off at a groundspeed of zero miles per hour, but as I've constantly said, the differences between what mythbusters did, and the question that is typically asked is one is based upon the ground effects the other is just mentioning keeping the aircraft stationary).  However, if there is no wind, the kite either falls, or you have to generate someway to provide that wind to the kite (sometimes by running really fast). 

However, if you have no wind, and you have no movement, and simply throw the kite up...the question then is will it go up into the air with no effort?

The answer is typically no.  HOWEVER, the mistake is thinking that the movement is in relation to your legs, when the question asked in this thread is based upon ALL acceleration, rather than simply one form or the other.  In the kite example,  your legs are the primary point of movement in the assumption...however, that does not necessarily need to be true.  If you have a long enough string and are strong enough, you could pull the kite.

The question at the beginning of the thread states that you would not be able to pull it either, for if you did, then the conveyor belt you are on would actually need to be moving BACKWARDS to account for the amount that you are moving the kite forward, even if your legs are not moving.  In otherwords, to keep it stationary, you would need to account for the thrust.  However, if you do NOT account for the thrust, at some point it WILL in fact move forward, causing airflow over the wings, and a rapid ascent (as is shown on the navy catapults via the naval carriers, except theirs is calculated so that the plane is released when the thrust is at a certain point).

However, if this question is ever proven by physicist that indeed a plane can take off while stationary, we should all be able to own and take off from our own backyards soon, as that will be far cheaper than the runways which we all utilize currently.

The fact that we have NOT done so, to me is bigger evidence of the flaw of the question, rather than the actual details of the science to it.

I believe you're operating under the fallacy that we believe the plane will remain stationary.  I do not believe the plane will remain stationary.  

Link to comment
Share on other sites

6 minutes ago, Grunt said:

I'm confused, too.  As I read his statement and that website, I believe he just proved himself wrong.

Sigh...

From the website...

Quote
  1. The first goes like this (as depicted on the image above): “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 plane take off?
    Answer: preassumptions cause this situation to be physically impossible.
  2. The second – as shown in Mythbusters – is a little different: “An airplane cannot take off from a runway which is moving backward (like a treadmill) at a speed equal to its normal ground speed during takeoff“.
    Answer: the plane will takeoff
Quote

To take off the airplane needs speed (airspeed, airflow). So it needs to accelerate. In this text I will discuss how it can accelerate on the conveyor belt (accelerate in relation to air and the outside world – not only in relation to the conveyor belt).

Thrust

Thrust is a mechanical force, so the propulsion system must be in physical contact with a working fluid to produce thrust. Thrust is generated most often through the reaction of accelerating a mass of gas. Since thrust is a force, it is a vector quantity having both a magnitude and a direction. The engine does work on the gas and accelerates the gas to the rear of the engine; the thrust is generated in the opposite direction from the accelerated gas. The magnitude of the thrust depends on the amount of gas that is accelerated and on the difference in velocity of the gas through the engine.

Source: NASA

What you need to remember from this part is that the thrust is a force coming from the acceleration of gas (air surrounding the plane).

Quote

This is the problem! The wording of this quiz is wrong and makes it physically impossible.

Divide this situation to several steps. At first, everything is just the same as in my explanation above. We apply thrust and we run the conveyor belt in the opposite direction. The wheel starts turning. As the plane moves forward – the conveyor belt accelerates. Keep in mind the preassumption “conveyor belt is designed to exactly match the speed of the wheels”.

When the aircraft moves forward then its wheels have to travel further than the conveyor belt has moved back. But this is impossible in this situation. The conveyor belt is designed to match the speed of the wheel – so it will increase the speed. But the plane still moves forward – there is again a difference between the speed of the wheel and the speed of the conveyor belt. But we do not allow such situation! So we increase the speed of the conveyor belt!

Actually, this is not a process that happens in steps – all of this happens simultaneously – the plane tries to accelerate and the conveyor accelerates to keep up with the wheels. Adding to the speed of wheels. And the wheels accelerate even more. So the conveyor belt…

It lasts until wheels and conveyor belt speed reaches infinity. Or until they reach the speed of light. If you wish to know what happens then – consult the screenwriters of Start Treck or Star Wars.

The wording of this quiz is wrong! This case is impossible. It is impossible right from the very beginning where the preassumption is that the speeds will always match. If we know (and we know!) the forces applied on the plane we know that during the takeoff there is a huge imbalance of forces. So quoting the Newtonian law:

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

The object will not stay motionless because we have unbalanced forces. So we can not design the conveyor belt to move at the same speed as wheels.

it then goes on to say that Mythbusters modified the question (To what people many times understand it's asking, rather than what it is actually asking) to actually  be able to do something in regards to that question.

The thing is, the question everyone THINKS it is asking is not the question that IS being asked.  Instead, they are understanding it to be the question that Mythbusters is asking.  Mythbusters works because groundspeed is NOT the same thing as AIRSPEED (which is something I've repeated several times now) or thrust.

Edited by JohnsonJones
Link to comment
Share on other sites

10 minutes ago, Grunt said:

I believe you're operating under the fallacy that we believe the plane will remain stationary.  I do not believe the plane will remain stationary.  

The question asked relies on the plane being stationary.  When accounting for thrust, this should be impossible.  if you accounted for thrust, in order to act upon it, the plane would need to move backwards (not all the power of the airplane is transferred to the wheels of the said airplane).  However, as per the question this is not allowed, thus it needs to remain stationary.  Furthermore, this would be in reaction to the ENGINES, not the wheels of the airplane.  It would be in response to the aircraft, and NOT the groundspeed.  Hence the problems with the question itself.  It would in essence, perhaps create an infinite loop.

What many seem to think it is asking, is what Mythbusters changed it to instead.  That is, if a plane is on a runway going at the same speed of it's groundspeed in the opposite direction, would it be able to take off...but groundspeed is NOT airspeed.

Edited by JohnsonJones
Link to comment
Share on other sites

2 minutes ago, JohnsonJones said:

The question asked relies on the plane being stationary.  When accounting for thrust, this should be impossible.  if you accounted for thrust, in order to act upon it, the plane would need to move backwards (not all the power of the airplane is transferred to the wheels of the said airplane).  However, as per the question this is not allowed, thus it needs to remain stationary.  Furthermore, this would be in reaction to the ENGINES, not the wheels of the airplane.  It would be in response to the aircraft, and NOT the groundspeed.  Hence the problems with the question itself.  It would in essence, perhaps create an infinite loop.

What many seem to think it is asking, is what Mythbusters changed it to instead.  That is, if a plane is on a runway going at the same speed of it's groundspeed in the opposite direction, would it be able to take off...but groundspeed is NOT airspeed.

I didn't read it that way at all.  It can't remain stationary, so even though the question said it was designed to I found that to be irrelevant.

Link to comment
Share on other sites

26 minutes ago, Grunt said:

I didn't read it that way at all.  It can't remain stationary, so even though the question said it was designed to I found that to be irrelevant.

Well, there IS the simpler answer. 

Right now the question is something similar to...If I put a car in outerspace, would it be able to move? 

By itself, it's sort of ridiculous because there are a bunch of quantifiers that are missing.

However, there IS a simple answer.  Without the engines operating to provide thrust and providing that power, the wheels do not move.  The conveyor belt is not moving.  Hence the plane goes no where, because it isn't providing thrust.  When I first do engine start on the jet, it's only providing electrical power to the aircraft.  Even if I do move forward, unless I provide enough thrust to move the plane forward, it isn't going to take off.

The question asked in the original part of this topic is read as if it's relating to groundspeed (the question Mythbusters tried to present, but even then, it was flawed as you see the pilot actually built power above what he should have, which builds the question whether it was staged...it's not noticeable unless you know what to look at, but he builds power farther and has greater acceleration eventually than what they are driving it seems...but even then, once airborne, is no longer stationary...as it's no longer groundspeed being answered).

Unfortunately, THIS is the question everyone actually THINKS is being asked.  In this scenario, yes, the plane takes off, but that is because the takeoff is not reliant upon the groundspeed.  It is reliant upon the thrust of the airplane.  The reason for this is because the wheels are not a good measure of the forward momentum of the aircraft.  It is an intermediary of that power when it is on the ground.  The entirety of the power of the aircraft is behind it, as it is being thrust forward by the engines.  The wheels are merely a reflection of that power upon the ground, when it is in contact with the ground.  Hence, the do not receive nor reflect the entire power of the aircraft.

This is one of the laws of Physics, that when a force acts, and equal but opposite force also reacts.  The reason the aircraft can take off is that the ground is not providing an equal but opposite force to that of the wings or the thrust of the aircraft caused by the engines.  The wheels are not translating that force, and hence the aircraft, even if you think it is stationary, is actually, via it's force, moving forward.  It is not acted upon by an equal and opposite force, because it's wheels are not transferring the entirety of that force. 

This is the question people typically think is being asked, and the one Mythbusters answered...but that's NOT what is actually being stated.

However, the original question was...

Quote

An airplane sitting on a conveyor belt.  The airplane has either propellers or jet engines - it doesn't matter.  The airplane's wheels are just wheels - no brakes or motors on the wheels at all.

For purposes of this thought experiment, assume the airplane has sufficient gas and the conveyor belt has sufficient power, to reach a conclusive end to the experiment and arrive at a clear answer.

The conveyor belt is perfectly programmed to roll the opposite direction the plane wants to move, in order to keep it stationary.  The conveyor belt is large, wide, and long enough to remain under the airplane and fully functional no matter what the airplane does. 

The airplane's engines start working, and begin to do their thing, and the conveyor belt begins to do it's thing.  Does the airplane fly?

This is not possible.  It cannot roll the opposite direction the plane wants to move in order to keep it stationary.  It would constantly need to accelerate and move to counter the ENGINES which would then continue to accelerate in an infinite loop.  In order to keep it stationary, it needs to react to the ENGINES, not the wheels, and thus is a reaction to the airspeed and thrust rather than the groundspeed (which has nothing to do with the aircraft).  Hence, you would never get the thrust for the airflow and the aircraft would remain stationary...if you could even get something like that to work.  In reality, this should be impossible to even do (and if it did react to the engines the aircraft might actually start to move backwards which means the engines would need more thrust to move forward...and you get an infinite loop as it repeats this ad nauseum).  Hence, the question itself is really asking about something that is pretty much impossible.

 

PS: Just to be clear, I am WAAAY open to having someone post evidence (physical evidence, Mythbusters was actually a flawed one, for more than what I said, some have noted it appeared that the pilot applied x2 the amount of acceleration normally needed which matches the 2x=x idea meaning he was actually going faster than the groundspeed stated...but even with that said, the principles of force should say he might be able to take off, but ultra lights are a very BAD example as they can take off on a dime in the right conditions already...we need a heavier aircraft for a good example...if they could get a way to work it) that shows the principles in action.  I'd love to see physical evidence which shows the plane can take off in this situation, if it were at all possible.  As per Bernoulli's principals, I think it is effectively null and void in some purposes though, but I'd love to see that scientific idea proven false by someone, though simply using a rocket probably isn't what I'm looking for.

The US military may be interested in it also, considering they still use Catapults on the Naval Carriers.

Edited by JohnsonJones
Link to comment
Share on other sites

33 minutes ago, Vort said:

Just curious: Did you actually read anything I wrote? Because I specifically addressed this issue.

If you are referring to your first post in this thread...I didn't see anything.

I saw you state that your answer was in the text below, and then it just showed up as a big blank space on my screen.  If it was in there, I did not read it.  I thought it was a joke or something (the blank space) in regards to the answer.  If there was actual writing there, for some reason it did not show up...so I did not read it.  Sorry.

 

PS: If there was something there, did you post it in a different way or something?  I'd be curious as to what you wrote.

Edited by JohnsonJones
Link to comment
Share on other sites

Guest MormonGator
2 minutes ago, Vort said:

Just curious: Did you actually read anything I wrote? Because I specifically addressed this issue.

I think @JohnsonJones is too busy writing his own answers rather than reading ours. 

(Just playing JJ!) 

Link to comment
Share on other sites

As I said, I'm all up for anyone who can post physical evidence.  Now, model airplanes and ultralights probably are VERY BAD examples...

The basic principals of flight rely on Newton and Bernoulli, which normally are thrust and airspeed plus lift via the air movement.  With enough thrust, a many a model airplane or an ultralight need a foot or less to take off, of, if it is really the right conditions, zero distance (the same holds true for bigger aircraft, but that normally only happens when a strong headwind hits, like during a hurricane or something similar).

Here are examples of planes taking off with our current understanding of physics...

 

 

I await the videos that show the planes taking off of a conveyor belt...

Afterall, if you can show me the physical evidence (and as I said, planes that require very low or 0 distance with very low thrust are probably bad examples...especially as the original question that the question in this thread came from utilized asking about a heavy in the first place) of this occurring, I'd be very curious, and probably want to know how in the world it worked or how they figured it out (physics without math or science is magic afterall). 

PS:  Changing this to be more kindly - I'm probably more invested in this than I should, because, while I can show hundreds of examples of planes taking flight from how we understand the physics and the principles of flight to work, I don't see anything showing the opposite to be true in practice.

But at the same time, I'm fascinated at the prospect, if there really IS something that shows that the idea is plausible without any other explanation (light aircraft that could take off on a dime for example is NOT what I'd be looking at for an example...but something which absolutely shows it as hard evidence, I'd be absolutely fascinated by it and wanting to learn more about how they did it or pulled it off with the science behind it rather than...magic).

That said, once again, I AM open to physical evidence that shows why planes do not need runways, airlift, or airspeed to take off on. Also adding, if Vort did write something I didn't see in his first posting, interested in seeing what it actually said...I don't know why it shows up as a blank space on my screen on that post, but I would be interested in what it said if it could be written down in a manner that I can see it to read it.

Edited by JohnsonJones
Link to comment
Share on other sites

Okay so I just read the article that @JohnsonJones posted, as well as some of the comments.  Are people just not understanding each other on this?

My understanding is thus:

1)  It is physically impossible to accurately produce the experiment because it there is no conveyor or wheels that exist or can be created to produce such a situation.  However, if it were physically possible to create the situation as described, then the plane would not fly.

2)  Because it is physically impossible to accurately produce this experiment as worded, the forces involved in attempting it would result in the plane overcoming the conveyor belt and accelerating into eventual flight.

Perhaps I am missing something, but while one could say that the plane taking flight is the only correct answer, this seems to be only because of the impossibility of the experiment, therefore being correct by technicality.

Link to comment
Share on other sites

3 minutes ago, person0 said:

Perhaps I am missing something, but while one could say that the plane taking flight is the only correct answer, this seems to be only because of the impossibility of the experiment, therefore being correct by technicality.

Ah ha!  So because it's impossible for a plane to fly under these circumstances, it's possible for the plane to fly under these circumstances? :crackup:

Link to comment
Share on other sites

11 hours ago, Vort said:

The question is phrased in order to guide you to making a wrong assumption; that the airplane speed is controlled by the conveyor belt speed. This is false. If the wheels roll with negligible friction, the airplane speed will have nothing to do with the conveyor belt speed.

Note that this assumption would be true with an automobile or any vehicle powered by driving its wheels. In that case, if the conveyor belt matches the speed of the wheels but in the opposite direction, the vehicle remains stationary with respect to the ground. But an airplane is not powered by driving the wheels; it is powered by a propeller or jet engine, which acts on the air, not on the ground.

Once the airflow over the wings is sufficient, the plane will take off. How fast the wheels are or or not rolling is irrelevant. Consider the same situation, but with the plane on a sheet of ice and fitted with ice blades on the bottom. (And pretend the ice is on some kind of conveyor belt or some such thing.) It doesn't make any difference how fast the ice is moving; as a frictionless surface, it will not hold back the airplane. Same with the treadmill idea.

Awe, I finally figured out what you did there.  I had to hit the quote button and make it all black to see it though.  Is there an easier way (I am an individual that is not quite as tech literate as many younger individuals may be, or even some older ones that are my age perhaps!)

That isn't the answer to the question asked though.  That's the answer to the Mythbusters question in regards to ground speed....

It is correct, once the airflow over the wings is sufficient, the plane will take off, but if the airflow is stationary, as in regards to the thrust which causes it, then it will remain on the ground.  Of course, the problem is that as per the questions wording, this is actually impossible.  The question has it worded so the conveyor belt is responding to the engines and airflow rather than the wheels, which as explained, means that this would move the plane backwards...thus meaning the plane needs to continually accelerate which makes it stationary, which creates an infinite loop.  Normally, the wheels or the belt would burst into flame or erode or something, but that isn't possible as per the question.  It's like asking...if a car could accelerate at one mile per hour on an endless highway, could it go an infinite speed?

Caution, that car question is more tricky than it may first appear.

 

PS: That said, I would be delighted to be shown that my thoughts are wrong.  I'd love to see the physical evidence of this idea working on a heavy (or even a fighter jet which can require a lot less runway with enough thrust).  The closest thing are the Navy catapults, but they require a LOT of thrust and at least a little runway to takeoff.  I'd love to see a living example rather than claims.

Edited by JohnsonJones
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...