9/11 Physics from Non-Experts

[Dr Adequate]

What is it with nutters and thermodynamics?

 

[gumboot]

Modern computers are capable of handling quite impressive arrays (or rather matrices) of numbers, even in the billions. I'm not sure where the practical limits are - we'd have to find a compsci person to probably find that out.

The problem is this - if the assumption is that the upper intact section (UIS) essentially free-falls before striking the lower intact section (LIS) then the following are of concern:

1. What is the shape of the UIS after it breaks free from the supports? Has it deformed under loading?

2. What is the orientation of the UIS as it falls (probably dynamic, as the upper portion rotated)?

3. What is the shape of the LIS in our simplified model? Since we are trying to model free-fall for the UIS, what is left in the interstitial space between LIS and UIS?

We also have to look at how sensitive our model is to our answers to the three questions. Techniques such as Monte Carlo let you examine such sensitivity, so I don't think there's a way around it, but since this is a far less complex model (at least numerically) than the total collapse scenario it will therefore take much less time to run a block of simulations. It's still non-trivial, though, and will require a computer.

Thanks for the info... I suppose in the scenario I was trying to work on (it's quite hilarious, kind of like a blind man trying to build an Ark) in response to those questions...

My simplified scenario is such that the aircraft impact zone essentially is just completely removed, with UIS and LIS completely intact. Given the UIS twisted, I dealign the columns so that the columns of the UIS do not line up exactly with the columns of the LIS (in other words they strike the floor truss instead) however, assuming that the UIS is level at impact thus the force is spread evenly across the entire footprint of all 287 columns.

Hrm, see now I'm thinking maybe it's just that my simplified scenario is too simplified - as in it's so simplified it's not useful as even a starting point.

My head hurts.

(And thank you AZCat for your patience)

-Gumboot

 

[jsiv]

"Each floor held up all the floors above it?"

 

[westprog]

I understand. I wasn't proposing the entire collapse - I imagine the variables in such a scenario would be literally billions, beyond the processing power of modern computers.

I'm simply talking the initial moment of impact, when the upper intact section of each tower came in contact with the first floor of the lower intact section of each tower.

Essentially, I suppose, what I'm referring to is the collapse of the first intact floor, rather than the collapse of the 92 (WTC1) or 76 (WTC2) floors below that.

-Gumboot

The energy calculation is fairly easy. The force calculation isn't. The energy can be calculated using the mgh formula - m is mass, g acceleration due to gravity, and h the height difference. Calculating the mass of the falling portion of the building involves a bit of approximation, but it's not too difficult to get a ballpark figure. (The fact that the bottom part of the building weighed more than the top maens that it's not just a matter of allocating weight to floors).

Once the energy calculation is made, most of the CT objections just vanish. They simply don't understand just how powerful gravity is.

That's not to say that a force or momentum based analysis is pointless, but it's more difficult to do.

 

[AZCat]

Thanks for the info... I suppose in the scenario I was trying to work on (it's quite hilarious, kind of like a blind man trying to build an Ark) in response to those questions...

My simplified scenario is such that the aircraft impact zone essentially is just completely removed, with UIS and LIS completely intact. Given the UIS twisted, I dealign the columns so that the columns of the UIS do not line up exactly with the columns of the LIS (in other words they strike the floor truss instead) however, assuming that the UIS is level at impact thus the force is spread evenly across the entire footprint of all 287 columns.

Hrm, see now I'm thinking maybe it's just that my simplified scenario is too simplified - as in it's so simplified it's not useful as even a starting point.

My head hurts.

(And thank you AZCat for your patience)

-Gumboot

No sweat, Gumboot - this is my equivalent of a "busman's holiday". This isn't my area (I do building thermal stuff) so I can't tell you much more about how we could analyze this, but somebody here probably has the necessary knowledge. It might also be a good topic for someon's Phd. thesis (hint, hint - to any potential prof's).

 

[Quad4_72]

I think the guy in the video just really enjoyed hearing himself say "Force=Net zero". Must make him feel like he understands physics. Not only are there so many other factors that he leaves unaccounted for, he just simply has no grasp of the very basic concepts of physics. I have a feeling that he is the loner at his school and he has became wrapped around conspiracy theories because the people that agree with him make him feel accepted. Its sad really.

 

[MarkyX]

I think the guy in the video just really enjoyed hearing himself say "Force=Net zero". Must make him feel like he understands physics. Not only are there so many other factors that he leaves unaccounted for, he just simply has no grasp of the very basic concepts of physics. I have a feeling that he is the loner at his school and he has became wrapped around conspiracy theories because the people that agree with him make him feel accepted. Its sad really.

You can say that about any internet group such as Furries or Yaoi fanfiction writers. Don't google those two examples.

The owner of the humor site SomethingAwful.com, Rich "Lowtax" Kyanka, was invited into a university talking about online communities and just how messed up they are. A really interesting look at the whole affair.

EDIT: Found it.

http://www.somethingawful.com/d/comedy-goldmine/lowtax-speaks-at.php

 

[stilicho]

This is odd that people think the towers ought to have been still standing. Even the firefighters apparently believed and trusted that the buildings would survive. Otherwise they certainly wouldn't have gone into them. (And, forgotten by the truthers, after seeing what happened to the two towers, would any human being--let alone an emergency worker--have dared entering WTC7 after just seeing the 'impossible' happen to the twin towers?)

But, a total layman on things like structural engineering and physics, I remember watching CNN on SEP 11 and thinking to myself that this was a fascinating yet doomed scenario. Just having known a small bit about those kind of buildings. I worked in one similar to those three buildings, just 34 storeys, but one of the orientation talks was about two potential dangers--an explosion in 'plant' and a plane collision. They never talked about possible collapse but they emphasised evacuation procedures in either case. (The municipal airport was only a couple of kilometres from the building so the risk was definitely there. A Cessna crashed into a hospital closer to the airport once when the pilot lost consciousness on his approach.)

Being a few hours behind New York time, I was able to watch most of the beginning of the scenario, and by the time I got to work, I was told they had collapsed. But it sure didn't surprise me. Why on earth's name do lay people think they ought to have withstood the crashes and fires? I do hope that these 'professors' get their credentials re-examined. Just as I do 'Harvard psychiatrists' who believe in alien abductions.

 

[gumboot]

This is odd that people think the towers ought to have been still standing. Even the firefighters apparently believed and trusted that the buildings would survive. Otherwise they certainly wouldn't have gone into them.

To be fair the FDNY realised the structure's integrity was in serious doubt pretty quickly, and ordered an immediate full evacuation of all FDNY personnel.

Some heard it and decided to continue trying to reach the fires anyway, others never heard it because of problems with the radios. Only a few actually responded and left the buildings.

-Gumboot

 

[defaultdotxbe]

To be fair the FDNY realised the structure's integrity was in serious doubt pretty quickly, and ordered an immediate full evacuation of all FDNY personnel.

Some heard it and decided to continue trying to reach the fires anyway, others never heard it because of problems with the radios. Only a few actually responded and left the buildings.

-Gumboot

or they chose to go into the towers because there were still people inside who needed to be evacuated

 

[gumboot]

or they chose to go into the towers because there were still people inside who needed to be evacuated

Yeah that's what I meant by the first one.

The order came after they were in the towers... so no one went up the stairs (at least in WTC1) after it was issued. But a lot of guys heard it and kept going up anyway.

-Gumboot

 

[T.A.M.]

It makes me cringe every time I hear a truther utter...

"For every action there is an equal, and opposite, reaction..." as if this answers any and every problem regarding the collapses...twirps.

TAM

 

[Myriad]

Gumboot, it is possible to answer your question in a simple way, using only F=ma, if you make lots of simplifying assumptions. Let's start with your already simplified case of simply dropping the upper 1/5 of the tower through 1 storey of open air onto the lower tower.

In order for the lower portion of the tower to arrest the collapse, the upper portion of the tower, already in motion, now has to stop moving. (Even if it were possible for it to "topple to the side" at that point, its vertical motion still has to stop or else it will keep smashing downward through the lower tower instead.)

To go from falling to at-rest, the moving mass must accelerate upward. The structure it falls onto must provide sufficient force for a sufficient amount of time to accelerate the moving mass to zero downward velocity. A lot of force over a short time will do, or a lesser force over a longer time.

How much time does the lower structure have to decelerate the upper mass? Actually that's not quite the right question yet. Let's look at the moment the masses come in contact. The lower mass starts resisting, and the upper mass starts decelerating. But it can't decelerate instantly, that would take infinite force. So the upper mass is still moving after it comes in contact with the lower. The greater the resistive force, the faster the moving mass will accelerate (slow down), and the less distance it will therefore move before it comes to rest. If the resistive force is less, the moving mass will accelerate to zero over a greater distance. (If the resistive force is less than or equal to the gravitational force acting on the falling mass (that is to say, its weight), the moving mass won't slow down at all, it will keep going and possibly accelerating downward. But we expect the resistive force to be greater than the falling mass's weight, because the lower tower was designed to support that weight.)

But as long as the upper mass is still moving, the lower structure that's providing the force to slow it down is also being deformed by that movement. That deformation is going to weaken the lower structure, reducing the force with which it acts against the moving upper mass. So we can transform the question of how much time does it take for the lower structure to bring the upper portion to rest, into over what distance (amount of deformation) can the resistive force continue to act upon the upper mass? This is where it gets complicated, because different kinds of deformation (buckling, fracturing, etc.) will affect the resistance in different ways over different amounts of time and distances. But we can look at ultra-simplified models of this.

Let's say, for instance, that when the upper mass smashes into the next floor down, that next floor will fail completely, cease to offer any resistance, once it is deformed (pushed downward) by half a meter. And let's also say that until then, it resists with its full designed strength. So, the floor must resist with sufficient force to bring the upper mass to a stop in half a meter or less, or else the collapse will continue to the next floor.

In your floor-removed scenario, the upper mass accelerates freely at g for 3 meters. It must decelerate at 6g to come to rest again in .5 meters. (For any given change in velocity, the acceleration needed to cause that change in velocity over a given distance is inversely proportional to that distance.) Therefore the floor it lands on must provide a force of 6 times the (static) weight of the upper mass -- actually 7 times, because it also must resist the gravitational force that's still acting on the upper mass as it falls.

The structures, of course, were not built with 7x redundancy in the amount of upward force they could exert (that is, weight they could bear). The best estimates of their excess capacity seem to be about 1.6x. So, the floor cannot bring the upper mass to rest within .5 meters of deformation. Not even close.

In fact, over the .5 meter distance, in this scenario, the falling mass only is accelerated upward (that is, slowed down) by .6g over a distance of half a meter. Of the velocity it's attained by falling 3 meters at g, it loses only 1/10th of that velocity as a result of the floor's resistance -- after which it has another 3 meters to accelerate at g before hitting the next floor.

I find this a useful mental model to look at the collapses, because it's easy to examine what happens when you change some of the parameters. For instance, you can ask questions like "how far would each floor of the lower structure have to be able to deform, without losing any strength, in order for the falling mass to get progressively slower and eventually stop -- assuming that none of the mass in the lower tower gets added to the falling mass along the way? For a floor-floor distance of 3.5 meters and a "deformation at full strength" distance d, the increase in velocity is proportional to the square root of (g *(3.5 - d)) and the decrease in velocity is proportional to the square root of (.6 * g * d). The decrease becomes greater when the deformation distance is greater than ~2.2 meters.

Of the two biggest assumptions in this model, one works unrealistically in favor of collapse and the other against it. The one that's biased in favor of collapse is the assumption that the upper mass is able to accelerate at g for nearly a whole storey before meeting any resistance. The one that's biased against collapse is that the lower tower is able to resist the force of the falling mass with its full designed load strength, when the upper mass is actually displaced horizontally and tilting, concentrating forces instead of evenly distributing them.

While far short of adequate for any real engineering analysis, this kind of calculation does help me understand why structural engineers are so sure that "collapse is inevitable" once entire upper storeys of a tower start moving. If the structure were strong enough to arrest (literally, bring to rest) the collapsing floors, it would have been strong enough for the floors to not start moving in the first place, even as damaged as they were. (Which probably would have been way too over-buit for any practical economic use.)

That, of course, is why NIST focused on collapse initiation as the key engineering issue here.

Respectfully,
Myriad

 

[qarnos]

Gumboot, it is possible to answer your question in a simple way, using only F=ma, if you make lots of simplifying assumptions. Let's start with your already simplified case of simply dropping the upper 1/5 of the tower through 1 storey of open air onto the lower tower.

In order for the lower portion of the tower to arrest the collapse, the upper portion of the tower, already in motion, now has to stop moving. (Even if it were possible for it to "topple to the side" at that point, its vertical motion still has to stop or else it will keep smashing downward through the lower tower instead.)

To go from falling to at-rest, the moving mass must accelerate upward. The structure it falls onto must provide sufficient force for a sufficient amount of time to accelerate the moving mass to zero downward velocity. A lot of force over a short time will do, or a lesser force over a longer time.

How much time does the lower structure have to decelerate the upper mass? Actually that's not quite the right question yet. Let's look at the moment the masses come in contact. The lower mass starts resisting, and the upper mass starts decelerating. But it can't decelerate instantly, that would take infinite force. So the upper mass is still moving after it comes in contact with the lower. The greater the resistive force, the faster the moving mass will accelerate (slow down), and the less distance it will therefore move before it comes to rest. If the resistive force is less, the moving mass will accelerate to zero over a greater distance. (If the resistive force is less than or equal to the gravitational force acting on the falling mass (that is to say, its weight), the moving mass won't slow down at all, it will keep going and possibly accelerating downward. But we expect the resistive force to be greater than the falling mass's weight, because the lower tower was designed to support that weight.)

But as long as the upper mass is still moving, the lower structure that's providing the force to slow it down is also being deformed by that movement. That deformation is going to weaken the lower structure, reducing the force with which it acts against the moving upper mass. So we can transform the question of how much time does it take for the lower structure to bring the upper portion to rest, into over what distance (amount of deformation) can the resistive force continue to act upon the upper mass? This is where it gets complicated, because different kinds of deformation (buckling, fracturing, etc.) will affect the resistance in different ways over different amounts of time and distances. But we can look at ultra-simplified models of this.

Let's say, for instance, that when the upper mass smashes into the next floor down, that next floor will fail completely, cease to offer any resistance, once it is deformed (pushed downward) by half a meter. And let's also say that until then, it resists with its full designed strength. So, the floor must resist with sufficient force to bring the upper mass to a stop in half a meter or less, or else the collapse will continue to the next floor.

In your floor-removed scenario, the upper mass accelerates freely at g for 3 meters. It must decelerate at 6g to come to rest again in .5 meters. (For any given change in velocity, the acceleration needed to cause that change in velocity over a given distance is inversely proportional to that distance.) Therefore the floor it lands on must provide a force of 6 times the (static) weight of the upper mass -- actually 7 times, because it also must resist the gravitational force that's still acting on the upper mass as it falls.

The structures, of course, were not built with 7x redundancy in the amount of upward force they could exert (that is, weight they could bear). The best estimates of their excess capacity seem to be about 1.6x. So, the floor cannot bring the upper mass to rest within .5 meters of deformation. Not even close.

In fact, over the .5 meter distance, in this scenario, the falling mass only is accelerated upward (that is, slowed down) by .6g over a distance of half a meter. Of the velocity it's attained by falling 3 meters at g, it loses only 1/10th of that velocity as a result of the floor's resistance -- after which it has another 3 meters to accelerate at g before hitting the next floor.

I find this a useful mental model to look at the collapses, because it's easy to examine what happens when you change some of the parameters. For instance, you can ask questions like "how far would each floor of the lower structure have to be able to deform, without losing any strength, in order for the falling mass to get progressively slower and eventually stop -- assuming that none of the mass in the lower tower gets added to the falling mass along the way? For a floor-floor distance of 3.5 meters and a "deformation at full strength" distance d, the increase in velocity is proportional to the square root of (g *(3.5 - d)) and the decrease in velocity is proportional to the square root of (.6 * g * d). The decrease becomes greater when the deformation distance is greater than ~2.2 meters.

Of the two biggest assumptions in this model, one works unrealistically in favor of collapse and the other against it. The one that's biased in favor of collapse is the assumption that the upper mass is able to accelerate at g for nearly a whole storey before meeting any resistance. The one that's biased against collapse is that the lower tower is able to resist the force of the falling mass with its full designed load strength, when the upper mass is actually displaced horizontally and tilting, concentrating forces instead of evenly distributing them.

While far short of adequate for any real engineering analysis, this kind of calculation does help me understand why structural engineers are so sure that "collapse is inevitable" once entire upper storeys of a tower start moving. If the structure were strong enough to arrest (literally, bring to rest) the collapsing floors, it would have been strong enough for the floors to not start moving in the first place, even as damaged as they were. (Which probably would have been way too over-buit for any practical economic use.)

That, of course, is why NIST focused on collapse initiation as the key engineering issue here.

Respectfully,
Myriad

But F_net = 0!
It's a constant! It doesn't change!

Nice work, BTW! It may be oversimplified, but it demonstrates the tremendous forces involved.

 

[gumboot]

Gumboot, it is possible to answer your question in a simple way, using only F=ma, if you make lots of simplifying assumptions.

...

While far short of adequate for any real engineering analysis, this kind of calculation does help me understand why structural engineers are so sure that "collapse is inevitable" once entire upper storeys of a tower start moving. If the structure were strong enough to arrest (literally, bring to rest) the collapsing floors, it would have been strong enough for the floors to not start moving in the first place, even as damaged as they were. (Which probably would have been way too over-buit for any practical economic use.)

That, of course, is why NIST focused on collapse initiation as the key engineering issue here.

Respectfully,
Myriad

Thank you, that's certainly enough for me to fill in that "hole" in my understanding. And I can see entirely why it would be difficult to do a serious calculation.

One thing that jumped out at me - based on the single floor fall, the force involved is already significant. If you consider that in reality a number of floors failed simultaneously, the initial impact force becomes even greater (unless I'm mistaken, in WTC1 you're talking 36g's and for WTC2 you're talking 52g's).

In regards to the particular assumption that the initial collapsing floors offer no resistance, it is an over simplification, but I don't think it's an enormous one. Bear in mind, the floors in the aircraft impact zone were severely damaged and sagging prior to collapse initiation. The only thing really keeping them up was the exterior core columns (indeed if the 9-1-1 calls are anything to go by some of these floors were already starting to collapse before the exterior columns buckled). Once the bowing inwards caused the columns to fail, the only thing left between the upper mass and the intact floor below the aircraft impact zone was the core columns. As the building twisted as it fell, it's likely none of the core columns lined up, thus there was literally nothing resisting the upper mass for a distance of 18m (WTC1) and 26m (WTC2).

Actually, scratch that, that's not true. The first intact floor truss in the UPPER mass would have met resistance from the core columns after a fall of one floor (assuming it was still intact).

-Gumboot

 

[Miragememories]

This is what happens when an incomplete education prevents someone from being able to scientifically understand something. I'm no physics expert, but it's painfully easy to see what mistakes he's making.

I'm curious Totovader what exactly are you an expert at?

Hopefully mine and other future responses can prevent you from suffering pain in whatever field of endeavour it is that you think you have some expertise in?

MM

 

[beachnut]

I'm curious Totovader what exactly are you an expert at?

Hopefully mine and other future responses can prevent you from suffering pain in whatever field of endeavour it is that you think you have some expertise in?

MM

It only takes a rational mind to discover the physics lesson from that truther is below the 1st grade level. I have seen ants capable of better understanding of physics in action then the rant of the video physics dolt.

Do you agree? What did the truther physics guy get right? What did he get wrong? Please explain why most have a problem with his WTC model and if you agree or disagree that most engineers would give him a poor grade for being wrong?

 

[Totovader]

I'm curious Totovader what exactly are you an expert at?

Hopefully mine and other future responses can prevent you from suffering pain in whatever field of endeavour it is that you think you have some expertise in?

MM

Your curiosity is none of my concern.

 

[AZCat]

Wow. I just watched about 2/3 of the first part and couldn't take anymore. I'm not going to fault anyone for not knowing this stuff - it's not like everyone needs to understand it - but if you don't have a very good grasp of an area why in the world would you make a YouTube video of yourself trying to explain something in that area, especially when there are thousands of other people out there, all more knowledgeable than you, who disagree with your conclusions?

 

[Horatius]

....but if you don't have a very good grasp of an area why in the world would you ...

That's just it. These guys think they do have a good grasp of physics. They insist it's everybody else who has it wrong.

I have no idea how to fix this.