A Fermi problem for C7: Iron spheres mean how much thermite?

[Oystein]

The aim of this thread is to shed some light on a claim made by christopher7 (C7), formulate it as a hypothesis or theory, and make rough predictions from that theory. In particular, I want to formulate this as a Fermi problem to arrive at a rough guess (order of magnitude) for the amount of thermite predicted by the theory.

C7's iron sphere theory to date

As far as I am aware, C7 claims
a) that about 6% (of the mass?) of the dust released in the WTC event of 9/11 consists of iron spheres
b) that such iron spheres could only be formed by extreme temperatures as are released in a thermite reaction, and not at temperatures known to exist in building fires or trash fires.

C7 concludes from this that
c) The presence of iron spheres in such abundance is indicative of the massive use of thermite (or derivatives)


To support a), christopher7 has linked the following paper a few times:

http://www.nyenvirolaw.org/WTC/130 ...ignature.Composition and Morphology.Final.pdf

In this paper, the RJ Lee Group Inc. analysed dust collected from a building near GZ to assess hazards.

Indeed, on page 24 of that paper (page 28 of the PDF), in Table 3, we find confirmation for a):

Fe Sphere 5.87%

I will, for the sake of this thread, accept assumption b) as true. I would, however, like to ask C7 to specify more clearly the chemical and/or physical process that would release iron spheres by using thermite.
C7, do the iron spheres result from the thermitic reaction itself (FeO_x + Al -> Fe + Al_yO_z), or from the melting of structural steel? Or both?


The Fermi problem

If thermite is responsible for the bulk of the iron spheres, then a certain minimum amount of thermite must have burned to create the resulting amount of iron spheres. To estimate that amount, we need to estimate the following numbers:

1. How much dust was created in the event? This would be a portion of the mass of the collapsing buildings. Let's deonte this mass as m_d
2. What is the overall percentage of iron spheres in all of the dust? Is it ok to go with the 6% from the Lee report? Let's denote this number as p_fe
From 1. and 2., the total mass of iron spheres would be estimates as m_{fe =} m_d*p_fe
3. How much thermite is needed to create 1g of iron spheres? Let's denote this proportion as p_t.
From 1.-3. it follows that the minimum amount of thermite in use would be m_t = m_d*p_fe*p_t


So the problem boils down to estimating
- m_{d =} The total amount of dust
- p_t = the amount of thermite needed to create one unit of iron spheres


So christopher, and whoever wants to join in: Bang away with your best estimates!

 

[Oystein]

Oh I should add: It is a bit in the nature of Fermi problems that we don't have to insist too heavily on sources and measurements. If we can source something, great, but if we can't, that need not stop us. Just employ common sense and make some effort to justify your assumptions. The key is really to clearly define your assumptions.

 

[Sabretooth]

The aim of this thread is to shed some light on a claim made by christopher7 (C7), formulate it as a hypothesis or theory, and make rough predictions from that theory. In particular, I want to formulate this as a Fermi problem to arrive at a rough guess (order of magnitude) for the amount of thermite predicted by the theory.

C7's iron sphere theory to date

As far as I am aware, C7 claims
a) that about 6% (of the mass?) of the dust released in the WTC event of 9/11 consists of iron spheres
b) that such iron spheres could only be formed by extreme temperatures as are released in a thermite reaction, and not at temperatures known to exist in building fires or trash fires.

C7 concludes from this that
c) The presence of iron spheres in such abundance is indicative of the massive use of thermite (or derivatives)


To support a), christopher7 has linked the following paper a few times:

http://www.nyenvirolaw.org/WTC/130 ...ignature.Composition and Morphology.Final.pdf

In this paper, the RJ Lee Group Inc. analysed dust collected from a building near GZ to assess hazards.

Indeed, on page 24 of that paper (page 28 of the PDF), in Table 3, we find confirmation for a):



I will, for the sake of this thread, accept assumption b) as true. I would, however, like to ask C7 to specify more clearly the chemical and/or physical process that would release iron spheres by using thermite.
C7, do the iron spheres result from the thermitic reaction itself (FeO_x + Al -> Fe + Al_yO_z), or from the melting of structural steel? Or both?


The Fermi problem

If thermite is responsible for the bulk of the iron spheres, then a certain minimum amount of thermite must have burned to create the resulting amount of iron spheres. To estimate that amount, we need to estimate the following numbers:

1. How much dust was created in the event? This would be a portion of the mass of the collapsing buildings. Let's deonte this mass as m_d
2. What is the overall percentage of iron spheres in all of the dust? Is it ok to go with the 6% from the Lee report? Let's denote this number as p_fe
From 1. and 2., the total mass of iron spheres would be estimates as m_{fe =} m_d*p_fe
3. How much thermite is needed to create 1g of iron spheres? Let's denote this proportion as p_t.
From 1.-3. it follows that the minimum amount of thermite in use would be m_t = m_d*p_fe*p_t


So the problem boils down to estimating
- m_{d =} The total amount of dust
- p_t = the amount of thermite needed to create one unit of iron spheres


So christopher, and whoever wants to join in: Bang away with your best estimates!

My brain hurts today and I don’t feel like doing math…but I can’t help but find this question intriguing.

So we are just estimating? I mean, I don’t even know where to begin figuring the weight of the dust/mass of the WTC7 wreckage.

But let’s say I take a wild estimate and say 1 million tons (2 million lbs).

6% of 2 million lbs = 120,000 lbs.

So…120,000 lbs…of nothing but slag from thermite…from what is probably a gross underestimate of the weight of WTC7…

I’ve hit kind of a brain-blank here, Oystein. How do I translate waste/slag into an amount of thermite needed?

Regardless, I opted to post anyway, because we are venturing into the territory of tens, maybe hundreds, of thousands of pounds of thermite…

 

[Oystein]

sabretooth,

thanks for chiming in.
How did you arrive at your numbers? Wild guess? I think we should do better than that.

We can find upper bounds and lower bounds, I think.
Upper bound would be the mass of the 3 principal buildings taken together. We should be able to find estimates for that in the literature.
A percentage of that mass would have been turned into dust. More than 5%, less than 50%, I would say.
Lower bound ... hmmm I think in the Lee Group report, we can find quotes about how thick the WTC dust was in and on buildings in the immediate vicinity; we can estimate the total area of that vicinity, multiply with thickness and specific weight, and that would give us a lower bound.

The proportion of thermite:iron can also be estimated, One way would be to use figures such as energy density of thermite, the energy needed to melt iron. Another could be looking at the chemical formula for the thermite reaction, and taking into account atomic weights. These two methods would give us lower bounds for melting of steel and iron resulting as reaction product.

 

[R.Mackey]

Something to think about is that an efficient thermite attack would generate relatively little in the way of iron microspheres. Such spheres indicate that the reacted iron was exposed to atmosphere -- while still liquid -- rather than in contact with structural members. It also suggests that heat was wasted in boiling off the surface layers and through convection to the atmosphere rather than being directed anywhere useful.

I've run calculations like this on my own before, and the numbers I get are alarmingly large. You can also eyeball it using known thermite experiments, such as this epic from The Mythbusters:

 

[Oystein]

Some data to work with:

1. Thermite reaction

See http://en.wikipedia.org/wiki/Thermite_reaction

Chemical reaction:
Fe₂O₃ + 2Al → 2Fe + Al₂O₃ + heat

Atomic weights in g/mol: (rounded to full number)
Iron: 56
Aluminium: 27
Oxygen: 16

The reaction above contains, by weight, 112 parts Fe, 54 parts Al and 48 parts O, for a total of 214 parts.

So we need 1,91 parts of thermite to produce 1 part iron.

Heat produced:

Source: http://www.ilpi.com/genchem/demo/thermite/index.html
1 mol Fe₂O₃ + 2mol Al -> 847.6 kJ

Standard thermite releases 847.6 kJ/214g = 3,96 kJ per gram of thermite.

Other thermite or thermate mixtures may have a somewhat lower or higher energy density. Nano-thermate will have a lower energy density. Reason: Nano-sized particles of Al have a higher surface-to-volume ration than larger particles; the surface of Al will always oxidise before use. The Al-oxides add to the mass of the mixture, but not to its energy release.

 

[9/11 Chewy Defense]

My question to C7 is this: "What the hell does rust (iron oxide) have to do with you proving that thermite was used?"

Rust is rust, does that mean every car/truck that has rust on them carry the "highly explosive" thermite on them?

 

[Oystein]

Something to think about is that an efficient thermite attack would generate relatively little in the way of iron microspheres. Such spheres indicate that the reacted iron was exposed to atmosphere -- while still liquid -- rather than in contact with structural members. It also suggests that heat was wasted in boiling off the surface layers and through convection to the atmosphere rather than being directed anywhere useful.

I've run calculations like this on my own before, and the numbers I get are alarmingly large.

I know you've done it before. But the best excercises are those you do yourself. I hope, christopher 7 will tag along for the educational ride!

You can also eyeball it using known thermite experiments, such as this epic from The Mythbusters:

So.
More than 1000lb of thermite
Took quite a while.
Didn't even cut straight down through the roof of the car.

Should be pretty hard to apply it to large steel columns and make it burn through horizontally within a tightly controlled time frame for a "Controlled" demolition.

But that's not even the point I am going at. Just want to know the bare minimum - and more importantly: Lead christopher7 to spell out and test his theory about iron spheres.

 

[Oystein]

My question to C7 is this: "What the hell does rust (iron oxide) have to do with you proving that thermite was used?"

Rust is rust, does that mean every car/truck that has rust on them carry the "highly explosive" thermite on them?

Please Chewy, not here. this thread is about the theory, that explains iron spheres in dust with use of thermite. Got nothing to do with anyone finding rust anywhere. I think.

 

[R.Mackey]

I know you've done it before. But the best excercises are those you do yourself. I hope, christopher 7 will tag along for the educational ride!

Agreed -- it's a great exercise and you've framed it well. I just wanted to add a little extra to think about for the more methodical readers.

The funny thing about the efficiency issue is that either way it inflates your final thermite estimate. If it was an efficient thermite attack, then we find a very small fraction in the form of microspheres, so given the amount we did find the amount must have been much higher. On the other hand, if it wasn't an efficient attack, first of all "why bother," but that implies much more thermite was needed to cause structural failure.

Unless, of course, there was no thermite attack in the first place. I know it's a radical idea but it's worth considering. Carry on.

 

[Disbelief]

So.
More than 1000lb of thermite
Took quite a while.
Didn't even cut straight down through the roof of the car.

That was probably 1.2 mm thick. If you add in the reinforcements in the front and rear, that would add 2-3 mm more.

 

[9/11 Chewy Defense]

Please Chewy, not here. this thread is about the theory, that explains iron spheres in dust with use of thermite. Got nothing to do with anyone finding rust anywhere. I think.

I said it just in case C7 does come here, if he ever does!

We know that thermite works best if there's a right mixture of aluminum & iron oxide particules. But it would be impossible to bring down a building with the stuff, since it liquifies and burns out within minutes of ignition.

 

[Oystein]

Agreed -- it's a great exercise and you've framed it well. I just wanted to add a little extra to think about for the more methodical readers.

The funny thing about the efficiency issue is that either way it inflates your final thermite estimate. If it was an efficient thermite attack, then we find a very small fraction in the form of microspheres, so given the amount we did find the amount must have been much higher. On the other hand, if it wasn't an efficient attack, first of all "why bother," but that implies much more thermite was needed to cause structural failure.

Unless, of course, there was no thermite attack in the first place. I know it's a radical idea but it's worth considering. Carry on.

Ah yes, of course, I forgot to acknowledge that efficiency issue. Thank you! So far, I am only looking for the amount of thermite needed to melt the total amount of iron spheres. Yes, of course we then need to add thermite for every chunk of steel that was melted but not turned to dust, and for all the energy that was lost due to such things as radiation, convection, kinetic whatever etc. etc.

Maybe, for starters, we can guess that between an optimistic 5% and a super-optimistic 50% of the thermitik heat actually goes into melting the spheres - to keep this within one order of magnitude

 

[Oystein]

Some more data to work with

2. Mass of the Twin Towers

See http://www.journalof911studies.com/volume/200703/GUrich/MassAndPeWtc.pdf

The Journal of 9/11 Studies is, as we know, the journal run be the thermite champions Steven Jones and Kevin Ryan.

Gregory H. Urich estimates the mass of one of the twin towers to be
288,100 metric tons
or
2.881 x 10¹¹g

Two Towers then have a mass of
5.762 x 10¹¹g


3. Mass of WTC7

Ok I have not found a quote for the mass of WTC7 after a quick search. Acknowledging that it shares basic properties of the twin towers (tube in tube design, steel frame), a first estimate might compare volumes:

Volume of a twin tower is 415x63x63 m³ = 1.65 x 10⁶ m³
WTC7's long sides are 247ft and 329ft, respectively, that's an average of 288ft = 87.78m
It's 140ft = 42,67m deep and 186m tall
Volume of WTC7 is 87.78 x 42.67 x 186 m³ = 6.96709 x 10⁵ m³ or 42% of the volume of WTC1

Let's assume further that WTC7, on account of being smaller, would be 25% lighter per volume unit that the larger towers.

That gives a mass for WTC7 of
2.881 x 10¹¹g x 42% x 75% = 9 x 10¹⁰g




Total mass of the 3 collapsing towers is approximately
6,6 x 10¹¹g



(I'll ignore the other buildings that were destroyed; shouldn't affect the order of magnitude too much.)

 

[alienentity]

Estimates will assume that thermite was present in all the affected buildings - is there any reason to exclude WTC5 and 6, for example?

Or for that matter any way to exclude either WTC 1, 2 or 7?

 

[Oystein]

Even more data to work with

4. Energy needed to melt iron

Let's take the values from Wikipedia:
http://en.wikipedia.org/wiki/Iron
(For the sake of simplification, I'll consider pure iron. The properties of steel vary. For example, the melting point may be higher or lower. But for the sake of estimating values of a Fermi problem, I think looking at pure iron will not yield results that are vastly off-target. If anybody better verses in metallurgy begs to differ, please do so).

The physical properties we need are
Standard atomic weight: 55.845(2) g/mol
Melting point: 1538 °C
Heat of fusion: 13.81 kJ/mol
Specific heat capacity at 25 °C: 25.10 J/(mol K)

The following is probably pretty bad material physics, but hey...

To heat one mol (56g) of iron from ambient temperature to melting point, you need approximately
25.1J * (1538-18) = 38.152kJ
In addition, to transition that mol to liquid phase, you need 13.81kJ for a total of 52kJ.
Actually, for droplets of that iron to stay liquid long enough to break free from a larger mass, we would have to heat it to somewhat above melting point. So let's say, to melt iron from which to form iron spheres, we need to expend

56kJ/mol = 1kJ/g

 

[Oystein]

Estimates will assume that thermite was present in all the affected buildings - is there any reason to exclude WTC5 and 6, for example?

Or for that matter any way to exclude either WTC 1, 2 or 7?

You are right. I am excluding 5 or 6, which means I am excluding both their contribution to the dust amount and to the thermite needed. 5 and 6 are only a few percent of the mass of 1, 2, 7, so they are not significant. Our estimates are much too rough for that.

You are right, the amount of thermite that we compute might have been distributed among the 3 buildings. But then we can break down that amount and estimate how much thermite they might have used on each single building.

 

[Oystein]

Data to work with, continued

5. How much dust was airborne?

The RJ Lee Group sampled dust from WTC that had settled in and on the Deutsche Bank building at 130 Liberty Street (see Google Maps)

This building had 1500 of its windows broken (Lee report, page page 1). Inside, they found on average 8.62g/m² of dust.
The building has 42 stories, each having an area of approximately 2500m², so total amount of dust would be
42 x 2500m² x 8,62 g/m² = 9 x 10⁵g of dust inside that one building


130 Liberty Street was about 200m away from the "center of gravity" of the WTC collapses (south tower much closer, north tower farthe, WTC7 even farther). A circle of radius 200m has a circumference of 1256m. The Facade of 130 Liberty Street had at most a total width of 50m of windows facing the WTC, that is 4% of that perimeter. If we estimate that a great amount of dust never made it to that 200m perimeter, or blew above the height of the building, or did not enter the building, I am fairly confident that at most 1% of all the WTC dust landed inside 130 Liberty Street to be found there months later by the Lee group.

Hence, a lower bound of the mass of airborne dust from WTC is 100 x 9 x 10⁵g = 9 x 10⁷g

 

[Mikemcc]

Some more data to work with

2. Mass of the Twin Towers

See http://www.journalof911studies.com/volume/200703/GUrich/MassAndPeWtc.pdf

The Journal of 9/11 Studies is, as we know, the journal run be the thermite champions Steven Jones and Kevin Ryan.

Gregory H. Urich estimates the mass of one of the twin towers to be
288,100 metric tons
or
2.881 x 10¹¹g

Two Towers then have a mass of
5.762 x 10¹¹g


3. Mass of WTC7

Ok I have not found a quote for the mass of WTC7 after a quick search. Acknowledging that it shares basic properties of the twin towers (tube in tube design, steel frame), a first estimate might compare volumes:

Volume of a twin tower is 415x63x63 m³ = 1.65 x 10⁶ m³
WTC7's long sides are 247ft and 329ft, respectively, that's an average of 288ft = 87.78m
It's 140ft = 42,67m deep and 186m tall
Volume of WTC7 is 87.78 x 42.67 x 186 m³ = 6.96709 x 10⁵ m³ or 42% of the volume of WTC1

Let's assume further that WTC7, on account of being smaller, would be 25% lighter per volume unit that the larger towers.

That gives a mass for WTC7 of
2.881 x 10¹¹g x 42% x 75% = 9 x 10¹⁰g




Total mass of the 3 collapsing towers is approximately
6,6 x 10¹¹g



(I'll ignore the other buildings that were destroyed; shouldn't affect the order of magnitude too much.)

According to this source 185,101 tons(I'm assuming that means ye olde worlde Imperial/standard measurement) of steel was removed from the site:

http://911research.wtc7.net/wtc/groundzero/cleanup.html

That works out at 907185g/ton, so 1.68E11 g of steel removed from the site.

Now this site guesstimates the mass of steel in WTC1 and 2 to be 9.6E10g per tower, giving 1.92E11 g for both WTC1 & 2. Assuming your 42% ratio is correct then total steel mass will be 2.42/2 * 1.68E11 = 2.03E11 g.

http://www.physforum.com/What-was-the-weight-of-a-WTC-Tower_4299.html

Therefore the 'missing steel' is 3.53E10g (only 35kt of steel there folks!)

This would mean that 1760t of steel ended up as this 'dust'.

Anybody that's ever seen a thermite reaction will attest that most of the product ends up as a slag, rather than a dispersed dust (that's why it's used to weld railway joints). So a thermite reaction is extremely inefficient at generating this 'dust', probably only a few percentage points. I'll take a probable over-estimate (WAG) of 10% of the reaction producing these dust particles, that gives an effective end result of 17600t of steel undergoing a thermite reaction.

Next problem - thermite assumes a finely ground iron oxide / aluminium mix - not solid steel objects. I don't know how this affects the reaction.

 

[femr2]

Don't think there is much value in the thread, but...

Something to think about is that an efficient thermite attack...

Mythbusters need to work on their efficiency I reckon...


1000lbs/Plant pot.