I've been recently made aware of the conspiracy theories sourrounding 9/11. And of course i was sceptic and i still try to remain so, but i must say that i was amazed about how little i actually knew about 9/11. I sure do have some issues with the Loose Change movie/documentary, and perhaps i will stick around here and share my issues, but i suppose it did make its point and i must admit that after looking into this subject for weeks i now doubt the official stories much more.

Recently i've started to discuss 9/11 on another forum. (I'm sorry but i won't link you guys to it as i don't want you all to start crowding that forum). Must say that i've had very little succes as many of the participants in that discussion mostly just neglect any and every point i try to make and result in nothing more than name calling. At the very best all they do is link to some site that attempt to debunk conspiracy theories like the LooseChangeGuide and the likes. And every time i'm forced to point out that these sites, when being generous, are at most 10% about debunking and the other 90% is just immature garabage and invalid debate tactics. So i'm hoping that i'll get more intelligent responses here, even though i realise this might not be the most objective place it strangely enough is the most objective place i can find at this moment.

Anyway, thats my short introduction. On the other forum i've made two posts and i wanted to know what people around here think about them. There are probably a lot of inaccuracies in those posts as they were made in an active topic and i pretty much wrote it down as i thought them up performing the calculations at the same time. There are probably a lot of people who have done something similar as my calculations, but i haven't found them yet. So if any of you got any good links concerning the mathematics of the collapse (no matter what side of the debate they support) then please post them as i would be very interested.

Most people don't know about the other World Trade Centers.



WTC 3 stood directly south of the North Tower and directly west of the South Tower, it did not completely collapse. WTC 6 stood directly north of the North Tower and did not completely collapse. WTC 7 standing over 300 feet away from the North Tower completely collapsed. Also note that the Verizon building was hardly damaged from the collapse of the two twin towers, most of its damage is located at the side caused by the collapse of WTC 7.

Now we should let loose the idea that steel framed buildings are like a house of cards that can collapse straight down. In about 120 years history of skyscrapers it has never happened. If that is an indication of the chance of a skyscraper collapsing on any given day then that gives us a chance of 3 out of 43800. Now for 3 skyscrapers to completely collapse on a certain day that gives us a chance of 1 out of 3,112,136,000,000.

Some other numbers:
If 80 percent of the debris of the north tower fell in a radius of 91.44 metres (or 300 feet) and we estimate that 20% of the mass was pulverized then on every square meter in that 91.44 radius range fell on average 12,182 kg. WTC 6 completely located within this 300 feet radius and estimating a 7900 square meter surface area for that building then about 96 thousand ton of debris fell on that building. Of course this is not completely accurate as more debris would have fallen closer to the tower, and probably more mass was pulverized, but i'm only using this as comparison with WTC 7.

Now if 20% of the debris fell outside the radius of 91.44 metres (distance necessary to hit WTC 7) and within a radius of say 115 metres then about 5,235 kg fell on ever square meter in that range. Estimate that this radius covers about 1000 square metres of WTC 7 (a very high estimate) then that means that only 5.2 thousand ton of debris fell on WTC 7. Looking at the damage on other buildings that were within the radius of 115 metres we have to conclude that the numbers i picked here are extremely generous as in it being much more likely that a much larger percentage of the debris fell within the 91.44 metres radius. (note also the collapse plume not reaching that far, it's more reasonable to consider that at least 95% of the debris did not fall beyond 90 metres from the towers)

So if 18.5 times as much mass from the North Tower fell on WTC 6 compared to WTC 7, then why did WTC 6 not suffer a complete collapse like WTC 7? You can use other numbers for the calculations if you like, but unless you use absurd numbers it will pretty much result in this same ratio.

Steel framed buildings don't just collapse...

...not even this building:

Hiroshima dome, 600 metres away from where the atomic bomb exploded on August 6, 1945. Estimated to have been exposed to temperatures of about 4000 degrees Celcius. To this day the building still stands.

My previous post was only a rough estimate of the amount of mass hitting WTC 6, compared to WTC 7. There are a couple of inaccuracies, for example the tower being considered as a single point, when this point of course is about 63 * 63 metres in size. If we consider half the mass to have fallen in this point (its own footprint), then of course the total amount hitting both WTC 6 and WTC 7 is already halved. This however does not change the ratio, and looking at video evidence it is more reasonable to estimate that 30 - 40 times as much mass fell on WTC 6 compared to the amount that hit WTC 7.

The ammount of stress that WTC 6 received compared to WTC 7 is even much more since the debris impacted on the roof of WTC 6 at an estimated speed around 70 m/s. (I can provide the calculation for this if necessary).

If we consider that debris ejected from the North Tower reached distances of 115 metres, than this debris would only hit the south of WTC 7 with a horizontal speed of about 11.5 m/s (26 mph). Now if we consider that some debris was found ejected about 250 metres away from the towers, then that would imply that the horizontal speed was about 25 m/s at most (56 mph), but this would only apply to a vast minority of the debris. Now this is not the kind of mass + velocity that can penetrate reinforced concrete or steel beams no more than you could throw a rock through a concrete wall. (Note how much of the roof of WTC 6 is still intact and the debris in that case reached about 70 m/s)

It can of course penetrate windows and from there cause substantantial damage to the floors below because of its vertical velocity, but the point is that it simply would not have slammed far into WTC 7. The potential damage that it can do is restricted to only the south and smallest side of the building (as we can also see in photo's from bankers trust a building directly across the street of the South Tower). Again note how far fetched it is that this could cause a symmetrical collapse of the building.

Formula for kinetic energy in case some of you did not pay attention in physics class.

Ek = 0.5 * mass * velocity ^ 2.

Note that velocity is of much greater influence in the formula. Say that 40 thousand ton slammed into WTC 6. Now i'm going to do some interval estimation here to provide some accuracy on the kinetic energy here.
25 % at average speed of 60 m/s.
25 % at average speed of 40 m/s.
25 % at average speed of 20 m/s.
25 % at average speed of 10 m/s.
The sum of the kenitic energy on the entire structure of WTC 6 would then be about 28,500,000 KJ.

Now the kinetic energy of the debris that hit WTC 7 on the south side of the building if we estimate that 1.5 thousand ton hit that side and 25% of the mass managed to penetrate and burry itself inside (which is an extremely generous estimate) then the kenetic energy on that 1 side of the building would be:
Velocity Sqrt(70^2 + 11.5^2) = 71 m/s. (extremely generous assumption)
Ek = 945,188 KJ.

The ammount of energy directed on the roof of WTC 6 even with very generous assumptions would still be 30 times greater then the ammount of energy directed at the south side of WTC 7. Now the difference in terms of stress that the roof received compared to the ammount of stress the entire building of WTC 7 received is even much greater, we are now talking about ranges into the 100 hundreds. That is the roof of WTC 6 was stressed hundreds of times more than WTC 7.

Now we would be absolute fools if we were to believe that WTC 7 collapsed because of debris from the North Tower. And not just a collapse, but a total collapse straight down at or beyond free fall speed, by a building with insignificant impact damage on only 1 side. And don't tell me it was because of (very mysterious) fires, since it clearly was not equally spread over the entire building and even if it was it still isn't remotely plausible that all steal beams give out at the exact same time without showing any indication of significant weakening before the collapse.

But go ahead and try to rationalize this event. If you were to read the official reports you would see that they can be summed up by one line and that is simply: "we have no explanation".

PS.

I've done the calculations here myself, i didn't choose numbers to represent my belief. In fact when in doubt i choose numbers that would be very generous against the conspiracy theories. After that i cross referenced my assumptions that i derived from those numbers with photographic evidence, not the other way arround. For example when assuming impact damage was only resistriced to one side in WTC 7, i checked the impact damage on WTC 6 and the impact damage on Bankers Trust. I don't guarantee that the numbers for kinetic energy are exactly correct as it deals with estimations on the total mass and estimations of the velocity measured with intervals. However they do represent a comparison between the stress that some buildings endured during the collapse of the towers. Which concludes my entire point that it goes directly against logic that WTC 7 collapsed because of debris from the Twin Towers where WTC 6 did not suffer a complete collapse.

my brain hurts :P very intersting though

Nice job....even though I couldn't understand half of it lol. Math is my weakness =P

I got the basic gist of what you were saying and it made sense to me.

I can't take credit for figure 2-1, i got that somewhere from another topic in this forum. I'll try to locate that topic again and then give credit to that person, i apologize for any confusion regarding this.

The reason i'm interested in the maths behind 9/11 is because mathematics isn't just numbers, it is impeccable logic (that is if the formula's and the calculations are correct). Where logic assumptions can be wrong, we can cross reference them with mathematics to show wether the logic is either correct or flawed. Now by cross referencing the mathematics with photographic evidence we can with fair certainty say that the formula's aren't far off and thereby conclude that the logic is correct. In this particular scenario that implies that if WTC 7 collapsed because of debris from the North Tower, than nothing of WTC 6 should be left standing. By same analogy if you drive a fully loaded truck straight through an entire building and the building does not completely collapse, then how much chance do you think a tiny Ford would have in bringing the same type of building down by driving it into just 1 wall on 1 side of the building?

That said my calculations so far are nothing more to just a couple of poor sketches, i didn't take enough time to gather the most accurate data, i didn't use enough intervals for example in the kenetic energy formula (being a software engineer i'm going to write a program who does the interval calculations for me so i can calculate anything using intervals as close as 0.001 seconds), so as of now still to much estimation is involved, and thats not saying that i think my estimations are way off, but only that it would provide a stronger argument when i have invested a little more time into this.

Something else i'm looking at is this:

James H Fetzer in 9/11 revisted stated that the twin towers collapsed in approximately 10 seconds and that if you were to drop a biljart bal from the top of one the towers it would hit the ground in about 8 to 10 seconds without any resistance.

Well not to disagree with him since he is far more educated than i am, but i found his statement a bit odd since without resistance the biljart ball would have hit the ground in 9.2247 seconds each time. That might not be 100% correct since this is assuming a gravitational constant of 9.8 where the gravitational constant is slightly higher close to ground (about 9.81) and slightly lower with considerable distance from the ground. But even then the time would be between 9.2200 - 9.2341 seconds. I'm just not sure why he would say 8 - 10 seconds in his presentation.

But anyway i found the concept to be quite interesting seeing that the towers fell in i believe somewhere between 10 - 12 seconds. So i went on to figure out what the influence of air would be on the biljart bal.

A smooth sphere has a drag coefficient of 0.1. This is an object which is very aerodynamic. There are objects that are more aerodynamic, for example a golf bal which shape is designed to reduce the drag behind the bal.

the first part of the formula ::: sqrt(2mg / pCdA) ::: equals the terminal velocity of the object. Terminal velocity is the velocity where the resitance of air equals the force of the gravity on the object, which causes the acceleration to reach 0. Lets calculate this part first for the biljart bal.

This is also the reason why a coin falling off the Eifel tower (myth) can not kill a person, because it can't exceed terminal velocity that combined with the weight doesn't cause critical injuries. Our biljart bal however could be far more damaging.

Lets calculate the speed of the biljart ball falling at a number of intervals:

Now lets estimate the travelled distance over the intervals

Because the towers were about 417 metres in height then the time for the biljart ball to travel this distance in air would be somewhere around 9.5 seconds. We see that air resitance on this object doesn't have that much influence in the first 417 metres drop, but that is because we are talking about a very aerodynamic shape. If an object the same width, height and mass of the biljartbal but in the shape of brick had fallen down then that object would have a drag coefficient of 2.1. It's terminal velocity would then be a mere 23.45 m/s. The time for this object to drop 417 metres would be well above 20 seconds.

This doesn't really proof anything yet, but i'm just attempting to give an indication of what kind of resistance would be needed in order for the buildings to not collapse within 12 seconds. This is just a first small step i have taken into this. I'm currently trying to figure out if an object, neglecting structural resistance of the object itself, with the dimensions of the twin towers can in theory collapse within 12 seconds. There is something here that needs to be considered, and in fact i'm amazed that i haven't found any sites that go into great detail with this, but another law of nature states that energy must be conserved. Now we know that a lot of energy is lost by ejecting large quantities of debris outward and the pulverization of energy. Also meaning that the towers had weight unloading as mentioned somewhere else on this forum as well. But what most sites don't mention is that even if object A slams into object B then object A can't continue to move with the same speed as it did before impact since the combined kinetic energy of both A and B must remain the same.

Kinetic energy can be calculated with the following formula:

E = 0.5 * mv^2

Now say object A has the same mass as object B and then Object A crushes into object B with a speed of 20 m/s then if both objects continue to travel as if it was just 1 object (meaning object B provided no resistance whatsover) then the speed at which they continue to travel would only be 14.14 m/s. Again what this means in relation to the collapse is that as each floor collapses it loses velocity even under the absurd notion of the building not providing any resistance.

a site like debunking911.com claims wtc7 was built differently than wtc6, that's why wtc6 did not collapse.

What do you guys think?

Sure it was different, i think it was only 22 stories high. Difficult to imagine that building being many times stronger than WTC 1, WTC 2 and WTC 7 combined.

Today i saw a documentary here in Holland where two university students claim that the collapse of the towers was possible, but of course they did not show how these students came to their conclusions or what exactly their conclusion consisted of. These students went on to say how their numbers matched up (how convenient) and then continued by saying how duped they felt by Loose Change.

This is of course complete nonsense. Here are these students claiming that their numbers are evidence that the official story is correct, however that is impossible since nobody has that data. You need to make a terrible ammount of assumptions on how much energy and mass is lost in ejecting the debris and pulverizing steel and concrete. Then you need to make more assumptions on how much weight each floor could hold. Hell we only have estimates about how much mass each tower was. Now if they had said something along the lines of: "under our assumptions we conclude that the possibility exists that the towers collapsed in 10-12 seconds" then i wouldn't have a problem with their personae, but instead they said: "our calculations are proof that the official story is correct.. oh yeah and Loose Change is dishonest". These kind of things just infuriate me, and the problem is that people actually believe them and don't do the research themselves.

Btw they did air Loose Change directly after that "documentary". I'm glad that it also gets aired here as the people here now even less than what most Americans do. I just wished they hadn't aired such a piece of crap before it. Must say that the producers of Loose Change know a lot better what they are doing.

Oh my Gosh. Can I just nod and say, you're right? Will you take my math classes for the next two terms? It's the only thing holding me back from graduation, hehe.

That's probably why those people sent you to web pages because they couldn't figure any of that out.

Interesting calculations.

I can comment on this part in particular. You are correct in stating that velocity will be lost as an object strikes another. If it is one object striking another object of equal mass which then combine, the initial velocity of the combination will be about half the final velocity of the first object.

As I am sure you know, this is down to conservation of momentum where you would adjust the final velocity by V*(b/b+1), where B represents the ball, so the first calculation would be V*(1/2), so indeed the velocity is cut in half.
But if you have more than one ball falling, say 15 of them, the calculation is V*(15/16), the 16 combined balls would move off with a velocity of 93% of the original 15. If you have 50 balls falling, the 51 would move off with a velocity of 98% of the original 50.

I suggest you read this paper on WTC momentum transfer by Dr Frank Greening, it is interesting.


And a comment on peripheral WTC buildings.

WTC3 did not stand, it was 22 floors high, crushed to a pulp.


And WTC6 suffered major damage, WTC1 debris smashed right through to the ground floor of this building, I believe it did not fully collapse because there really wasn't much left to collapse anyway. It was a squat 8 storey block, very different to WTC7.

Thanks for the link.

I think the calculations however are incomplete, i looked quickly through it and it seems that the writer assumes all the mass stays focused downward and does not consider weight unloading (mass ejected outward). If that is the case then the numbers are way off.

wtc3 got smashed and it was closer to the towers, wtc6 didn't get smashed, and it was closer to the towers and yes it must've had some fires, and wtc7 got incinerated yet was the farthest away and fires cannot bring down steel towers, and only one side of the wtc7 was "heavily" damaged (yet no visible proof of 20 story hole or whatever, only pics of smoke).

Does this make sense or what?

Yes it did. WTC6 was left as a gutted shell.

http://www.911myths.com/WTCREPORT.pdf

That sure was an interesting read.
I have to ask though how did you read it? Did you study the report or just skip to the conclusion?

Speaking about the conclusion, lets take a look at their own statements.

Now their entire calculations are based on the assumption that mass stays concentrated (1) focused downward (2) and all mass stays involved in the collapse, e.a no ejected debris (3). Since assumption 1, 2 and 3 are clearly false i have to agree with this part of the conclusion: they must involve an unknown additional source of energy

E1 being the resistance considered that is needed to overcome to collapse a single floor. Now because their calculation of available kinetic energy is incomplete E1 is actually a much larger fraction.

Also some things worth noting about the report.
They based E1 on the energy needed to collapse the top floors of the towers. I find it highly unlikely that the bottom floors would not be any stronger than the top floors.
They calculated weight of each floor by taking the mass of the building and deviding it with the number of floors. Again it is much more likely that the bottom floors were heavier than the top floors.

And thus resulting in a symetrical collapse of the buildings, umm no.. wait... :unsure:

Indeed they went to great lengths to support the official theory.

No paper could account for every variable, it's clear that this paper tries to keep things as basic as possible, but the conclusions are of worth though I have not said that I agree with all of them. And yes, I have read it.

Personally I think this is a very good collapse model for the floorslabs, as they would not have been ejected like the perimeter columns were, and had no other choice but to go downward. The very quick possible collapse times that he calculated were the interesting part, and make the observed times seem entirely possible.

Taking perimeter columns and the core into account is the tricky part, as a collision between a falling piece of core and an intact piece would be very messy indeed. The perimeter columns would not have been involved in any progressive collapsing action(aside from those in the top sections, perhaps) and would have simply peeled away.

Anyway, I've realised this a WTC7 thread, so I'll shut up now.

I'm stunned at this comment...

The whole explanation is that it fell because of the buildings own potential energy being converted to kinetic energy. Now if your total sum of kinetic energy is completely off because you simply neglect that the entire mass did NOT stay concentrated (1) focused downward (2), and involved in the collapse (3) then the only worth of the conclusions is that the actual time to collapse should be well above the times that they calculated.

This isn't just one variable they forgot. It is the MAIN variable.

I'll redo the calculations when i got the time, but you are right about this not being the right forum section.

mdm - welcome to the forums, good to have your perspective on things. [cheers]

I Hope that you find this community approaches discussions with a little more class than your past experiences have offered.

I also hope to hear more from you!


- A *

Greening's paper is a meandering exercise in deception. It's not clear whether Greening himself was deceived by it or not. Nonetheless, it is below the level of bad science. It is simply not scientific at all. It builds conjecture upon speculation built upon negligence.

For merely one example, he fails to take into consideration the portion of the aircraft's weigh represented by its fuel when calculating the energy involved in stopping the collective mass. Recall that much of that fuel ended up outside of the towers and should therefore not be considered as part of the total mas brought to rest by exchanging momentum with the building structure.

I agree, however, that the point about his egregious failure to consider that a large fraction of the collapsing mass did not fall directly onto the original footprint of the building is far more significant.