Mathematically debunking 9/11 conspiracy theories

Airfix · 31st December 2020, 02:13 PM

Can someone help me out mathematically, I sometimes argue with conspiracy theorists elsewhere and I could do with a bit more details.

Twin towers were 110 stories, but what did they exactly weigh ?
I've read an approximate mass of 500,000 tons, but is this correct ?

If it is, to divide the weight by it's floors produces an average floor weight of 4545.45 tons.

What is the correct weight of a floor ?

And what was the correct mass above the impact points ?

Taking a 767 200 series jet, and adding 31 tons of fuel to it's weight gives 111.1 tons, that multiplied by it's acceleration in metres per second, gives it's force.

But what was the acceleration of Flight 11 & Flight 175 ?

The Common Potato · 31st December 2020, 02:28 PM

I'd suggest that it's history, not mathematics, that's important.

bknight · 31st December 2020, 03:39 PM

Originally Posted by Airfix

Can someone help me out mathematically, I sometimes argue with conspiracy theorists elsewhere and I could do with a bit more details.

Twin towers were 110 stories, but what did they exactly weigh ?
I've read an approximate mass of 500,000 tons, but is this correct ?

If it is, to divide the weight by it's floors produces an average floor weight of 4545.45 tons.

What is the correct weight of a floor ?

And what was the correct mass above the impact points ?

Taking a 767 200 series jet, and adding 31 tons of fuel to it's weight gives 111.1 tons, that multiplied by it's acceleration in metres per second, gives it's force.

But what was the acceleration of Flight 11 & Flight 175 ?

IIRC there was a Ytube presentation on the collapsing towers giving most of what you need. I don't know about the acceleration, but I suspect it was close to nil, and I'm not sure I have ever seen a representation.

Brainster · 31st December 2020, 03:47 PM

Originally Posted by bknight

IIRC there was a Ytube presentation on the collapsing towers giving most of what you need. I don't know about the acceleration, but I suspect it was close to nil, and I'm not sure I have ever seen a representation.

My physics is a bit rusty but isn't there tremendous force expended in decelerating the jets?

Axxman300 · 31st December 2020, 05:57 PM

Originally Posted by Airfix

Can someone help me out mathematically, I sometimes argue with conspiracy theorists elsewhere and I could do with a bit more details.

Twin towers were 110 stories, but what did they exactly weigh ?
I've read an approximate mass of 500,000 tons, but is this correct ?

If it is, to divide the weight by it's floors produces an average floor weight of 4545.45 tons.

What is the correct weight of a floor ?

And what was the correct mass above the impact points ?

Taking a 767 200 series jet, and adding 31 tons of fuel to it's weight gives 111.1 tons, that multiplied by it's acceleration in metres per second, gives it's force.

But what was the acceleration of Flight 11 & Flight 175 ?

Skeptic Magazine had all of that stuff.

JSanderO · 31st December 2020, 06:47 PM

All of these numbers are available... but what do you need them for?

Long story short... each of the twin towers collapsed because fire along with the mechanical damage caused by the planes led to structural failures in the regions above the plane strike zones. These structural failures led to loss of support for both the steel structure and the floor slabs which were supported by the steel structure. Once support was lost the materials.. steel frame, floor slabs and building contents... collapse down... onto the intact floors below the impact zone. The floors were not capable of supporting these loads especially as they were dynamic loads. This led to a runaway floor collapse from top to bottom which moved at about 65 mph. The intact steel frame/structure below then failed when it lost the bracing required for it to stand. The structural design was a composite and so when any part of the composite was removed or failed... the rest of the composite failed as well.

There has been no conclusive explanation as to how the steel frame above the impact zone failed. It was a progressive process as both towers survived "intact" until the tops began to drop. So from the time of impact... the only "energy input" was the fires which raged and that of dropping slabs or steel most likely related to expansion of steel beams pushing the columns (progressively) destroying the aggregate axial capacity or the frame. The structure DID redistribute loads during the process... but over time few columns remained to support the original load.
We can't see inside the building so we can never know the sequence of failures. But the concept or progressive loss of axial capacity is the only mechanism to explain the drop of the steel above the plane strike zones. NIST proposed a floor truss failure which led to destruction of the axial capacity. It may have been sequential core column which went runaway.

Sound engineering principals explain either scenario.

The weight of the plane or the building were not important.

beachnut · 31st December 2020, 07:20 PM

Flight 11 hit at the equal energy of ~1400 pounds of TNT, enough to break the WTC tower shell and damage about 4 Core Columns.

Flight 175 hit with the equal energy of 2093 pounds of TNT, like a 2000 pound bomb but in Kinetic Energy, breaking the shell, and damaging about 7 core columns.

There is a study which shows the WTC tower shell would have stopped an aircraft going 180 mph to 250 mph or so... the study is out there, Conspiracy Theorists can't find real studies, facts, evidence, or reality.

The towers failed because of fire, and a floor in the WTC only holds up itself and fails when overloaded past 29,000,000 pounds, and less if the mass above the impact zone is falling.

https://www.nist.gov/topics/disaster...-investigation
search for 29,000,000 pounds... etc

bknight · 31st December 2020, 10:40 PM

Originally Posted by Brainster

My physics is a bit rusty but isn't there tremendous force expended in decelerating the jets?

The energy is transferred from the moving object to the "stationary" object. I guess what I meant to say was that the jets weren't accelerating or decelerating just prior to impact, but you are right there would a lot of energy transferred at the impact and post impact movement.

Airfix · 1st January 2021, 03:27 AM

Originally Posted by JSanderO

All of these numbers are available... but what do you need them for?

I'm interested in providing mathematical figures to debunk a rather persistent and annoying conspiracy theorist extremist on another forum who has it in his head that the towers were able to cope with anything.

By showing the actual forces involved, I'm hoping to give that person pause for thought.

GlennB · 1st January 2021, 03:33 AM

Originally Posted by Airfix

I'm interested in providing mathematical figures to debunk a rather persistent and annoying conspiracy theorist extremist on another forum who has it in his head that the towers were able to cope with anything.

By showing the actual forces involved, I'm hoping to give that person pause for thought.

As has been mentioned, you won't get far without considering the weakening effect of the fires. After all, the towers did withstand the plain initial structural damage.

Airfix · 1st January 2021, 03:35 AM

Originally Posted by beachnut

Flight 11 hit at the equal energy of ~1400 pounds of TNT, enough to break the WTC tower shell and damage about 4 Core Columns.

Flight 175 hit with the equal energy of 2093 pounds of TNT, like a 2000 pound bomb but in Kinetic Energy, breaking the shell, and damaging about 7 core columns.

There is a study which shows the WTC tower shell would have stopped an aircraft going 180 mph to 250 mph or so... the study is out there, Conspiracy Theorists can't find real studies, facts, evidence, or reality.

The towers failed because of fire, and a floor in the WTC only holds up itself and fails when overloaded past 29,000,000 pounds, and less if the mass above the impact zone is falling.

https://www.nist.gov/topics/disaster...-investigation
search for 29,000,000 pounds... etc

Already tried explaining how fire can reduce steel below 1 tenth of it's room temperature strength and also cause expansion and buckling.

Anyway thank you!

bknight · 1st January 2021, 09:01 AM

Originally Posted by Airfix

Already tried explaining how fire can reduce steel below 1 tenth of it's room temperature strength and also cause expansion and buckling.

Anyway thank you!

I wouldn't spend too much effort, (s)he is convinced that there is a great conspiracy(US Government probably) that brought down the towers. I've tried on different forums debating these hard core CTs, on many different subjects. All have been in vain. I keep trying so that if there are any fence sitters out there can become educated.

Oystein · 2nd January 2021, 05:24 PM

Gregory Urich did a detailed tally of the mass distribution and summary of the twin towers more than 13 years ago:

http://www.journalof911studies.com/v...ssAndPeWtc.pdf

On page 23, Section 5.2, you find links to tables (PDF, XLS, HTML) with all the details. The XLS allows you to find the mass of each floor, and more.

In summary, Urich estimated the North Tower to have had a mass of 288,000 metric tons above ground level (so ignoring basement levels), with an associated Potential Energy of 480,600 MJ. If you take those numbers and do a little physics equations, you find that this implies the center of mass was at a height of about 170 m, or 41% of total height.

---

As for the deceleration of the planes: The easiest way to go about it would be to estimate the distance it took them to go from original speed (450 mph or whatever it was) to 0 and assume constant deceleration. This is easier said than done, as some of the mass was stopped within inches (consider wingtips), while some of the mass (at least one engine; a percentage of the fuel; ...) shot out the other side of the tower at some residual velocity.
So what would we say - on average, the mass penetrated to the center of the tower, or 100 feet?

However, if your "adversary" claims that the steel perimeter ought have stopped the planes right away, without them entering the building, the distance is real short: Just a couple of meters for the wings, for example.

Let THEM do the calculation of what deceleration, and then force, that translates to. It's their theory, after all.

It's not straightforward to figure out what force the impacted perimeter structure could withstand, though. Again, let THEM do the calculations. You will find that they just don't have any - they are merely guessing, imagining, making stuff up.

---

There is a concept called "Unevaluated Inequality Fallacy" popularized (and possibly coined) by member Dave Rogers:

It applies when a claim can be expressed in the form "A > B", but claimant has not actually evaluated (found values for) A or B, and so has not, in fact, proven that the value for A is indeed greater than the value for B.
(Note: it is not strictly necessary to find exact values for A and B, it suffices to find a lower bound for A and an upper bound for B).

In your example: The claim that the planes could not have penetrated the perimeter wall can be expressed as "A > B", where

A is (a lower bound for) the force that the perimeter wall can exert against the shape of an impacting 767
B is (an upper bound for) the force that an impacting 767 would exert on the perimeter wall when it decelerates from original velocity to zero without penetrating.

You will find that your adversary has neither evaluated A nor B, and thus has committed the Unevaluated Inequality Fallacy.

Allen773 · 2nd January 2021, 07:50 PM

9 out of 11 times, 9/11 Truthers are mistaken.

The other 2, they're lying.

31st December 2020, 02:13 PM	#1
Airfix Graduate Poster Join Date: Aug 2016 Posts: 1,030	Mathematically debunking 9/11 conspiracy theories Can someone help me out mathematically, I sometimes argue with conspiracy theorists elsewhere and I could do with a bit more details. Twin towers were 110 stories, but what did they exactly weigh ? I've read an approximate mass of 500,000 tons, but is this correct ? If it is, to divide the weight by it's floors produces an average floor weight of 4545.45 tons. What is the correct weight of a floor ? And what was the correct mass above the impact points ? Taking a 767 200 series jet, and adding 31 tons of fuel to it's weight gives 111.1 tons, that multiplied by it's acceleration in metres per second, gives it's force. But what was the acceleration of Flight 11 & Flight 175 ?
Airfix Graduate Poster Join Date: Aug 2016 Posts: 1,030

31st December 2020, 03:47 PM	#4
Brainster Penultimate Amazing Join Date: May 2006 Posts: 18,358	Originally Posted by bknight IIRC there was a Ytube presentation on the collapsing towers giving most of what you need. I don't know about the acceleration, but I suspect it was close to nil, and I'm not sure I have ever seen a representation. My physics is a bit rusty but isn't there tremendous force expended in decelerating the jets?
	__________________ My new blog: Recent Reads. 1960s Comic Book Nostalgia Visit the Screw Loose Change blog.

31st December 2020, 05:57 PM	#5
Axxman300 Illuminator Join Date: Mar 2012 Location: Central California Coast Posts: 4,959	Originally Posted by Airfix Can someone help me out mathematically, I sometimes argue with conspiracy theorists elsewhere and I could do with a bit more details. Twin towers were 110 stories, but what did they exactly weigh ? I've read an approximate mass of 500,000 tons, but is this correct ? If it is, to divide the weight by it's floors produces an average floor weight of 4545.45 tons. What is the correct weight of a floor ? And what was the correct mass above the impact points ? Taking a 767 200 series jet, and adding 31 tons of fuel to it's weight gives 111.1 tons, that multiplied by it's acceleration in metres per second, gives it's force. But what was the acceleration of Flight 11 & Flight 175 ? Skeptic Magazine had all of that stuff.
	__________________ Disingenuous Piranha

31st December 2020, 06:47 PM	#6
JSanderO Illuminator Join Date: Mar 2013 Location: nyc Posts: 3,089	All of these numbers are available... but what do you need them for? Long story short... each of the twin towers collapsed because fire along with the mechanical damage caused by the planes led to structural failures in the regions above the plane strike zones. These structural failures led to loss of support for both the steel structure and the floor slabs which were supported by the steel structure. Once support was lost the materials.. steel frame, floor slabs and building contents... collapse down... onto the intact floors below the impact zone. The floors were not capable of supporting these loads especially as they were dynamic loads. This led to a runaway floor collapse from top to bottom which moved at about 65 mph. The intact steel frame/structure below then failed when it lost the bracing required for it to stand. The structural design was a composite and so when any part of the composite was removed or failed... the rest of the composite failed as well. There has been no conclusive explanation as to how the steel frame above the impact zone failed. It was a progressive process as both towers survived "intact" until the tops began to drop. So from the time of impact... the only "energy input" was the fires which raged and that of dropping slabs or steel most likely related to expansion of steel beams pushing the columns (progressively) destroying the aggregate axial capacity or the frame. The structure DID redistribute loads during the process... but over time few columns remained to support the original load. We can't see inside the building so we can never know the sequence of failures. But the concept or progressive loss of axial capacity is the only mechanism to explain the drop of the steel above the plane strike zones. NIST proposed a floor truss failure which led to destruction of the axial capacity. It may have been sequential core column which went runaway. Sound engineering principals explain either scenario. The weight of the plane or the building were not important.
	__________________ So many idiots and so little time.

31st December 2020, 07:20 PM	#7
beachnut Penultimate Amazing Join Date: Oct 2006 Location: Dog House Posts: 25,852	Flight 11 hit at the equal energy of ~1400 pounds of TNT, enough to break the WTC tower shell and damage about 4 Core Columns. Flight 175 hit with the equal energy of 2093 pounds of TNT, like a 2000 pound bomb but in Kinetic Energy, breaking the shell, and damaging about 7 core columns. There is a study which shows the WTC tower shell would have stopped an aircraft going 180 mph to 250 mph or so... the study is out there, Conspiracy Theorists can't find real studies, facts, evidence, or reality. The towers failed because of fire, and a floor in the WTC only holds up itself and fails when overloaded past 29,000,000 pounds, and less if the mass above the impact zone is falling. https://www.nist.gov/topics/disaster...-investigation search for 29,000,000 pounds... etc
	__________________ "Common sense is the collection of prejudices acquired by age eighteen" - Albert Einstein "... education as the means of developing our greatest abilities" - JFK https://folding.stanford.edu/ fold with your computer - join team 13232

31st December 2020, 02:28 PM	#2
The Common Potato Critical Thinker Join Date: Apr 2019 Location: The Scunthorpe Problem Posts: 410	I'd suggest that it's history, not mathematics, that's important.

31st December 2020, 03:39 PM	#3
bknight Master Poster Join Date: Apr 2017 Location: Houston, Texas Posts: 2,380	Originally Posted by Airfix Can someone help me out mathematically, I sometimes argue with conspiracy theorists elsewhere and I could do with a bit more details. Twin towers were 110 stories, but what did they exactly weigh ? I've read an approximate mass of 500,000 tons, but is this correct ? If it is, to divide the weight by it's floors produces an average floor weight of 4545.45 tons. What is the correct weight of a floor ? And what was the correct mass above the impact points ? Taking a 767 200 series jet, and adding 31 tons of fuel to it's weight gives 111.1 tons, that multiplied by it's acceleration in metres per second, gives it's force. But what was the acceleration of Flight 11 & Flight 175 ? IIRC there was a Ytube presentation on the collapsing towers giving most of what you need. I don't know about the acceleration, but I suspect it was close to nil, and I'm not sure I have ever seen a representation.

31st December 2020, 10:40 PM	#8
bknight Master Poster Join Date: Apr 2017 Location: Houston, Texas Posts: 2,380	Originally Posted by Brainster My physics is a bit rusty but isn't there tremendous force expended in decelerating the jets? The energy is transferred from the moving object to the "stationary" object. I guess what I meant to say was that the jets weren't accelerating or decelerating just prior to impact, but you are right there would a lot of energy transferred at the impact and post impact movement.

1st January 2021, 03:27 AM	#9
Airfix Graduate Poster Join Date: Aug 2016 Posts: 1,030	Originally Posted by JSanderO All of these numbers are available... but what do you need them for? I'm interested in providing mathematical figures to debunk a rather persistent and annoying conspiracy theorist extremist on another forum who has it in his head that the towers were able to cope with anything. By showing the actual forces involved, I'm hoping to give that person pause for thought.
Airfix Graduate Poster Join Date: Aug 2016 Posts: 1,030

1st January 2021, 03:33 AM	#10
GlennB Loggerheaded, earth-vexing fustilarian Join Date: Sep 2006 Location: Usk, Wales Posts: 26,548	Originally Posted by Airfix I'm interested in providing mathematical figures to debunk a rather persistent and annoying conspiracy theorist extremist on another forum who has it in his head that the towers were able to cope with anything. By showing the actual forces involved, I'm hoping to give that person pause for thought. As has been mentioned, you won't get far without considering the weakening effect of the fires. After all, the towers did withstand the plain initial structural damage.
	__________________ "Even a broken clock is right twice a day. 9/11 truth is a clock with no hands." - Beachnut

1st January 2021, 03:35 AM	#11
Airfix Graduate Poster Join Date: Aug 2016 Posts: 1,030	Originally Posted by beachnut Flight 11 hit at the equal energy of ~1400 pounds of TNT, enough to break the WTC tower shell and damage about 4 Core Columns. Flight 175 hit with the equal energy of 2093 pounds of TNT, like a 2000 pound bomb but in Kinetic Energy, breaking the shell, and damaging about 7 core columns. There is a study which shows the WTC tower shell would have stopped an aircraft going 180 mph to 250 mph or so... the study is out there, Conspiracy Theorists can't find real studies, facts, evidence, or reality. The towers failed because of fire, and a floor in the WTC only holds up itself and fails when overloaded past 29,000,000 pounds, and less if the mass above the impact zone is falling. https://www.nist.gov/topics/disaster...-investigation search for 29,000,000 pounds... etc Already tried explaining how fire can reduce steel below 1 tenth of it's room temperature strength and also cause expansion and buckling. Anyway thank you!
Airfix Graduate Poster Join Date: Aug 2016 Posts: 1,030

1st January 2021, 09:01 AM	#12
bknight Master Poster Join Date: Apr 2017 Location: Houston, Texas Posts: 2,380	Originally Posted by Airfix Already tried explaining how fire can reduce steel below 1 tenth of it's room temperature strength and also cause expansion and buckling. Anyway thank you! I wouldn't spend too much effort, (s)he is convinced that there is a great conspiracy(US Government probably) that brought down the towers. I've tried on different forums debating these hard core CTs, on many different subjects. All have been in vain. I keep trying so that if there are any fence sitters out there can become educated.

2nd January 2021, 05:24 PM	#13
Oystein Penultimate Amazing Join Date: Dec 2009 Posts: 17,034	Gregory Urich did a detailed tally of the mass distribution and summary of the twin towers more than 13 years ago: http://www.journalof911studies.com/v...ssAndPeWtc.pdf On page 23, Section 5.2, you find links to tables (PDF, XLS, HTML) with all the details. The XLS allows you to find the mass of each floor, and more. In summary, Urich estimated the North Tower to have had a mass of 288,000 metric tons above ground level (so ignoring basement levels), with an associated Potential Energy of 480,600 MJ. If you take those numbers and do a little physics equations, you find that this implies the center of mass was at a height of about 170 m, or 41% of total height. --- As for the deceleration of the planes: The easiest way to go about it would be to estimate the distance it took them to go from original speed (450 mph or whatever it was) to 0 and assume constant deceleration. This is easier said than done, as some of the mass was stopped within inches (consider wingtips), while some of the mass (at least one engine; a percentage of the fuel; ...) shot out the other side of the tower at some residual velocity. So what would we say - on average, the mass penetrated to the center of the tower, or 100 feet? However, if your "adversary" claims that the steel perimeter ought have stopped the planes right away, without them entering the building, the distance is real short: Just a couple of meters for the wings, for example. Let THEM do the calculation of what deceleration, and then force, that translates to. It's their theory, after all. It's not straightforward to figure out what force the impacted perimeter structure could withstand, though. Again, let THEM do the calculations. You will find that they just don't have any - they are merely guessing, imagining, making stuff up. --- There is a concept called "Unevaluated Inequality Fallacy" popularized (and possibly coined) by member Dave Rogers: It applies when a claim can be expressed in the form "A > B", but claimant has not actually evaluated (found values for) A or B, and so has not, in fact, proven that the value for A is indeed greater than the value for B. (Note: it is not strictly necessary to find exact values for A and B, it suffices to find a lower bound for A and an upper bound for B). In your example: The claim that the planes could not have penetrated the perimeter wall can be expressed as "A > B", where A is (a lower bound for) the force that the perimeter wall can exert against the shape of an impacting 767 B is (an upper bound for) the force that an impacting 767 would exert on the perimeter wall when it decelerates from original velocity to zero without penetrating. You will find that your adversary has neither evaluated A nor B, and thus has committed the Unevaluated Inequality Fallacy.
	__________________ Thermodynamics hates conspiracy theorists. (Foster Zygote) Last edited by Oystein; 2nd January 2021 at 05:26 PM.

2nd January 2021, 07:50 PM	#14
Allen773 Graduate Poster Join Date: Jun 2008 Location: Cali Four Neea Posts: 1,370	9 out of 11 times, 9/11 Truthers are mistaken. The other 2, they're lying.