The 9/11 Forum

So what have we got...

Tower footprint: 63.1*63.1 = 3980.8 m^2
Core footprint: 26.5*41.1 = 1091.1 m^2
Core openings: 0.29*1091.1 = 316.4 m^2

Ignoring multiple floor implications, obstructions and absorbant materials, this increases the percentage of *run off* from 1.868% to (316.4/3980.8 ) 7.948%

Assuming your conversion to/fro gallons/litres is correct, then scaling from 10000 to 7415, gives us...

(7415/10000*15899) = 11789l

7.948% of 11789l is 937l down core openings

Need to gather the areas of C6, C7 & C50 to finalise...

...short-cut...

Assuming proportion of 75.1m^2 as per your values for C6, 7 & 50...

C6 & C7: 30.9/297.1*75.1 = 7.81 m^2
C50: 23.5/297.1*75.1 = 5.94 m^2

...so quantity of fuel going down...

C6 & C7: 7.81/316.4*937 = 23.1 l
C50: 5.94/316.4*937 = 17.6 l

Always worth a cross-check. A little over two thirds of your values.

(Various assumptions made, especially ability for even flow. My opinion is that many factors would obstruct the volume of fuel able to flow, such as physical obstructions, absorbant materials, fuel distribution and flooring damage (holes), all of which would reduce the values imo. A big assumption is that the fuel is not ignited, but as we're just trying to get a handle on the volumes involved...)

iconoclast wrote:42% of the fuel remained after the explosion..?
i understand it was a somewhat enclosed area, but almost half of the fuel remained? can you link or redirect me to those numbers? ty.

Just an estimate. Many different estimates exist, but no-one will know for sure. Several are higher.

A reasonable estimate imo. Perhaps even a little low, but suitable for this purpose.

No-one really looks at what may have been consumed within the *internal* fireball, but we could look at that...

Trippy wrote:Finally, if we apply the ideal gas law, then we can calculate that if the resultant fireball has a temperature of 600-800°C, and a pressure of 17.8 psi (14.7 for 1 standard atmosphere, and 3.1 psi over pressure) then it should have a volume of 32,230-39,611 m^3.

D'oh.
I forgot the Nitrogen.
D'oh.
I woke up this morning (about 10 minutes ago) sat up to turn my alarm off, and realized that I had completely neglected Nitrogen in calculating the volume of the fireball.

Revising the volume of the fireball to include Nitrogen heated to 600-800°C gives us a fireball volume of 140,130-172,221m^3

(PS apologies if anybody has already pointed this out)

femr2 wrote:NIST figures...

Flight 175 impact fuel total
7415 US gallons
991 cubic feet
(31% of capacity)

Initial Fuel Distribution
Flight 175
Floor US Gallons
78 826
79 2072
80 811
81 1996
82 1500
83 210

Did I get my flight numbers mixed up? :Head scratch:

femr2 wrote:

Now, if my estimates are something close to accurate

Need some tweaking, the multi-floor aspect needs to be addressed, and all materials able to absorb fuel (such as the large volumes of gypsum and concrete dust, and soft furnishings) need to be taken into account.

Correct, although furnishings (and such) capable of absorbing the fuel only really affect the amount of fuel available for combustion on each floor, rather than the amount of fuel falling down elevator shafts - unless the furnishings and such have the potential to absorb more than 98% of the fuel, which, to me at least, seems unlikely.
Also, as far as the multi floor aspect goes, I considered this last night, and decided against it. If you multiply the number of floors by 6, you also multiply the number of openings by 6, and the space taken up by them by 6, but the percentage of space taken up by the openings remains the same. It doesn't actually matter (for the purposes of this anyway) if we consider all of the fuel across one floor, or part loads across multiple floors.

femr2 wrote:

then on the 94th floor, elevator shafts occupied a grand total of 75.1 m^2 of floor space

Suggest looking at 83-78 instead...we can assume WTC2 and WTC1 shaft layouts match, and all openings need to be accounted for, not just elevator shafts.

Again. Did I get my flights mixed up?
Correct, Ironically, I considered this lastnight also, all openings do need to be accounted for, however, ultimately, unless you're taking fluid flow paths into account, or unless other openings account for more than 98% of the total floor space, they're not going to affect the amount of fuel getting to the shafts, only the amount of fuel available for combustion on each floor. Another advantage of the percentage based approach.

femr2 wrote:

From here we can treat the fuel in two ways, which, Ironically give us the same ultimate answer. We can assume that the fuel remains in a single lump, and has a probability of all going down an elevator shaft, or, we can assume that the fuel spreads out evenly,and that which occupies the same floor space as the elevator shafts falls into them.

Only in a virtual environment with perfectly flat frictionless flooring, no obstructions and no absorbant materials. Not trying to overcomplicate, just clarify.

Correct.

femr2 wrote:

1.868% of 15,899l is 297.1 l of fuel down the elevator shafts.
Of which, 211.7 l would have gone down the local elevators.
30.9 l would have gone down the 6 and 30.9l would have gone down 7
23.5 l would have gone down 50.

These need to be reconsidered, and lowered.

Probably, but the only real way of doing so would seem to require more detailed information than we have available, but, bear in mind that i've also ignored the space occupied by the core columns. Removing that space from the total floor space increases the percentage of space occupied by elevator shafts. Considering the internal footprint instead of the external one will also increase the percentage of floor space occupied by the elevator shafts.
I've assumed a minimum percentage of fuel entering the building.
I've calculated a minimum percentage of floor space occupied by elevator shafts.

femr2 wrote:I'll post an updated openings area as soon as I get around to it. I currently have 29% of core area set within my spreadsheet model, which also accounts for things like stairways, which should obviously be included.

Quite, but again, this only reduces the fuel available for combustion.

iconoclast wrote:

This implies that a maximum of 58% of the fuel could have remained outside the building, and an absolute minimum of 42% of the fuel could have entered the building - in otherwords.

sorry, please tolerate a question from someone uninformed.
i pretty much read the whole thread so i'm sorry if i missed it, but....
42% of the fuel remained after the explosion..?
i understand it was a somewhat enclosed area, but almost half of the fuel remained? can you link or redirect me to those numbers? ty.

No, this was my (independant) guestimate as to the minimum percentage of the fuel load availble to enter the building, using an 'end case' scenario - IE that the perimeter columns behaved like perfect rigid bodies and did not fail during the impact, which, as I pointed out.

This isn't the fuel available after the fireball. This is the fuel available for the fireball.
In order to calculate the fuel consumed by the fireball, I need information about the size of the fireball.

femr2 wrote:...short-cut...

Assuming proportion of 75.1m^2 as per your values for C6, 7 & 50...

C6 & C7: 30.9/297.1*75.1 = 7.81 m^2
C50: 23.5/297.1*75.1 = 5.94 m^2

These numbers look identical to the ones that I used.

femr2 wrote:...so quantity of fuel going down...

C6 & C7: 7.81/316.4*937 = 23.1 l
C50: 5.94/316.4*937 = 17.6 l

Always worth a cross-check. A little over two thirds of your values.

Thanks for the independent verification!!!!!
11789/15899 = 0.7414
17.6/23.5 = 0.7489
The difference in the third decimal place is due to rounding errors. You've made my day .
The reduced fuel going into the shafts is solely because of the reduced fuel load that you've used.

femr2 wrote:(Various assumptions made, especially ability for even flow. My opinion is that many factors would obstruct the volume of fuel able to flow, such as physical obstructions, absorbant materials, fuel distribution and flooring damage (holes), all of which would reduce the values imo. A big assumption is that the fuel is not ignited, but as we're just trying to get a handle on the volumes involved...)

Some of these, most importantly, ability for even flow would reduce these numbers, other would have little or no effect (although obviously hole location combined with flow paths is a BIG factor).

Trippy wrote:

femr2 wrote:NIST figures...

Flight 175 impact fuel total
7415 US gallons
991 cubic feet
(31% of capacity)

Initial Fuel Distribution
Flight 175
Floor US Gallons
78 826
79 2072
80 811
81 1996
82 1500
83 210

Did I get my flight numbers mixed up?

Dunno. What tower are you looking at ? As 175 was mentioned, I've assumed WTC 2 for subsequent values.

If WTC 1, then the fuel volumes go up a bit (but still less than your initial 10000 figure)...

Flight 11 impact fuel total
8684 US gallons
1161 cubic feet
(36% of capacity)

furnishings (and such) capable of absorbing the fuel only really affect the amount of fuel available for combustion on each floor, rather than the amount of fuel falling down elevator shafts - unless the furnishings and such have the potential to absorb more than 98% of the fuel, which, to me at least, seems unlikely.

I'm pointing more towards flow ability than volume.

If you multiply the number of floors by 6, you also multiply the number of openings by 6, and the space taken up by them by 6, but the percentage of space taken up by the openings remains the same. It doesn't actually matter (for the purposes of this anyway) if we consider all of the fuel across one floor, or part loads across multiple floors.

It'll affect timings, and fuel distribution across each floor could seriously affect the volume able to *reach* the appropriate locations, but it's not too critical, depending upon subsequent conclusions

all openings do need to be accounted for, however, ultimately, unless you're taking fluid flow paths into account

Might account for path a bit later, but thought it useful to show the increased *loss* from impact zone. Haven't accounted for flow through holes in the OOS flooring.

Considering the internal footprint instead of the external one will also increase the percentage of floor space occupied by the elevator shafts.

Sure. There's lots of other thing taking up space too, but all other simplifications and assumptions will tend to even it all out.

I've assumed a minimum percentage of fuel entering the building.
I've calculated a minimum percentage of floor space occupied by elevator shafts.

Aiii.

Trippy wrote:These numbers look identical to the ones that I used.

I did a short cut and used your values. I need to confirm them, but there's not likely to be any difference. I'm sure your shaft area values are fine.

The reduced fuel going into the shafts is solely because of the reduced fuel load that you've used.

Absolutely. Slight difference in floor areas used though, which *should* sort out the third decimal place if accounted for (Same methods used otherwise)

Revising the volume of the fireball to include Nitrogen heated to 600-800°C gives us a fireball volume of 140,130-172,221m^3

The size of the external fireball can be estimated using spheres of 63m diameter (width of the building). One of those spheres represents a volume 130924m³. I would estimate the external fireball of WTC2 as 400000-500000m³ (3-4 spheres) and the WTC1 fireball as 250000-300000m³.
Probably we have to add about 40000-50000m³ for the fireball inside the impact zone.

If you multiply the number of floors by 6, you also multiply the number of openings by 6, and the space taken up by them by 6, but the percentage of space taken up by the openings remains the same.

Not at all because 6 floors have 6 rows of windows and therefore the sixfold window area but the open area of the shafts wouldn't change. Only the top and bottom levels are relevant - the open area of the outer shell of that cuboid. The shaft openings of the floors between the top and bottom of the IZ just lead "back" into the IZ.

Does it really matter ?

We have a *rough* estimate for a fuel volume which *may* have entered each relevant shaft...

Not a lot.

achimspok wrote:

Revising the volume of the fireball to include Nitrogen heated to 600-800°C gives us a fireball volume of 140,130-172,221m^3

The size of the external fireball can be estimated using spheres of 63m diameter (width of the building). One of those spheres represents a volume 130924m³. I would estimate the external fireball of WTC2 as 400000-500000m³ (3-4 spheres) and the WTC1 fireball as 250000-300000m³.
Probably we have to add about 40000-50000m³ for the fireball inside the impact zone.

This part of where things start getting complicated, because the volume changes, the pressure changes, and the temperature changes, all the meanwhile you've got work being done by the system, and heat energy being added by the system.

Consider the fireball volumes I posted as being like a starting point.
It's the volume occupied by the combustion products of C8-C-13 mass fraction of the available fuel, assuming a stoichiometric air/fuel mixture, at 17.8 psi (14.7psi ambient + 3.1psi over pressure) and at a temperature of 873-1073k if the combustion products are behaving as an ideal gas.

I have a number of other things running through my head, but I need some time to get them organized and down on paper (a process not made easier by a headcold).

achimspok wrote:

If you multiply the number of floors by 6, you also multiply the number of openings by 6, and the space taken up by them by 6, but the percentage of space taken up by the openings remains the same.

Not at all because 6 floors have 6 rows of windows and therefore the sixfold window area but the open area of the shafts wouldn't change. Only the top and bottom levels are relevant - the open area of the outer shell of that cuboid. The shaft openings of the floors between the top and bottom of the IZ just lead "back" into the IZ.

They also have 6 fold perimeter colum area, so the percentage of space occupied by the windows remains the same.

I should also point out that the context of that post is discussing openings in the core. I've avoided addressing the scenario where fuel flows back out through the hole in the impact zone, but, realistically if you consider the fact that in order to slosh back out of the building, the fuel must first travel into the building until it's deccelerated (either by encountering the core, an opposing wall, or flowing up hill, as I understand it), and therefore had the opportunity to flow down the elevator shafts, so it would seem at least somewhat reasonable to deduct that from the fuel available for the fireball, rather than the fuel available for the shafts.

But as femr2 points out, it's a rough estimate.
It's an 'end case' scenario.
And it demonstrates that it's not much (Probably no more than 1.8% of what makes into the building).

femr2 wrote:Does it really matter ?

We have a *rough* estimate for a fuel volume which *may* have entered each relevant shaft...

Not a lot.

I'm not at all sure of the relevance of the fireball, except to refine the prior fuel *run off* estimates.

My thought now tends towards...

How much damage throughout the entire tower could the estimated volumes of fuel have caused.

C6 & C7: 23.1 l each
C50: 17.6 l

63.8 liter = 16.854 176 94 gallon [US, liquid]

~17 gallons.

Can this fuel volume account for all of the various reports of damage, fireballs and *explosions* ?

1 gallon [U.S.] of kerosene type jet fuel = 142.2 MJ (Converter)

IF converted directly into energy...if we actually have that volume of fuel available...(which I personally doubt for prior stated reasons...)

A fair bit of potential, but can we find an environment within which it could do more than *be on fire* ?

We need to make sure that the multiple events are not overlooked...