I did something similar, trying to estimate the amount of dust based on reports of how thick the layer of dust was after it settled out.
http://www.internationalskeptics.com/forums/showthread.php?t=65850
I know others have done similar calculations, so it might be worth looking for them.
ETA: here's some more detailed work:
http://www.internationalskeptics.com/forums/showthread.php?t=71857 Scroll down for the good stuff.
These discussions never came to a close and I think had some numbers wrong or missing.
Mass of concrete in towers
I generally suspect that many authors overestimate the mass of the towers. For example, one often reads 500ktons per tower total, yet the only painstaking tallying I have seen so far of all materials, done by G. Urich, came up with less than 300ktons.
Frank Greening estimated (on page 2) that the twin towers had 627 tons of concrete per office floor, and most of it was lightweight (1500kg/m
3). His numbers for volume per floor work out to (109.5 + 289.4)m
3 = 398.9m
3
So the 2 towers had a total amount of concrete above basements of (multiplying by 220 floors) about
with an average density of about 1570kg/m
3.
--------------------------------------
Density of dust
I think one consideration that the previous discussions did not mention or assess (though I may be mistaken, I only scanned the threads) is the fact that the Manhattan dust, estimated by Horatius to consist of 25% concrete on average, was 75% other materials, with fibers being quite dominant by volume, such that the density of the dust would not be dominated by the density of the concrete, but by fibers. 1500kg/m
3 is almost certainly too much, even though pure concrete dust could conceivably be denser than intact concrete slabs on account of light-weight concrete slabs having inclusions of air on purpose (that's why they are light-weight).
But since I have no better number (does anybody have better numbers?), it is still safe to go with the density of intact concrete. Which is less than the previous discussions assumed.
-------------------------
Distribution function not linear
The previous discussions seemed to assume that all the dust settled only outside of the tower footprints, or that its thickness inside the foorprint was a linear extrapolation of the thickness outside - which is modelled as a cylinder; Horatius also hints at a cone. I think this is wrong; There is probably quite a disproportionate amount of dust inside the footprints and the debris field (mixed with larger particle and fragment sizes, of course), with layer thickness decreasing not linearly but according to some convex function that's asymptotic to zero as distance increases. Not sure I have the mind to model this mathematically.
I also think that cutting the distribution function off at r=800m or some such random choice carries the risk of underestimating the amount of dust that settled even further, or got airborne altogether.
--------------------------------
Particle size and dust volume
Greening estimates (page 10) that 50% of the concrete (by weight) would have been crushed to particles larger than 1mm (that's not dust and would have settled nearly entirely within the debris field), 25% to particles between 10µm and 1mm (coarse dust, mostly settled "close" to GZ) and 25% to particles <10µm (fine dust). So up to half of the concrete could have settled outside of the main debris field.
This particle size distribution is predicted from applying 15% of the available potential energy of the towers to just crtushing concrete. Greening argues convincingly that this amount of energy is a practical limit, more energy would not effectively crush the concrete much further.
On page 15, Greening estimates a volume of the total dust (not only concrete) outside the main debris field of 100,000m
3, having a mass of 120,000,000kg. Deviating from Greening now and using Horatius' previous numbers, the concrete dust then is 25% of that or 40,000 tons - just under 30% of the total amount of concrete in the twin towers. Seing that the available potential energy would be more than sufficient to crush 50% of the dust to particle size small enough for them to travel away from the footprint, this is a good fit under a theory that nuthing but gravitaional collapse produced all the dust.
-----------------------------------
Airborne dust: A back-of-the-envelope calculation
Only dust particle <10µm remain airborne minutes after the collapse. If we assume that 25% of the concrete (34,500,000 kg) was crushed this finely, and that 1% of this remained airborne for a while, and that average density of airborne dust is up to 100mg/m
3 - make that 30mg/m
3 on average, then this dust could have filled up to 1,035,000,000m
3 of air, or a block 400m high (approx. height of the towers were) and 1 mile square. I certainly overestimate the dust density quite massively, but we do get the idea that indeed the dust that was observed, both on the ground and in the air, is absolutely compatible with what to expect when only a minor part of the availabe potential energy comes crushing down on 220 floors of concrete.
-------------------------------------
Don't forget WTC7
In all those calculations we disregarded the buildings other than the twin towers. WTC7 had a
volume of about 700,000m3 which is 21% the volume of both twin towers combined (above ground). Assuming that concrete had a distribution in building 7 similar to that of WTC1 and 2, we can thus increase all our estimates of concrete available for dusting Manhattan by 20%.
-------------------------------------
ETA
Conclusion:
Meticulous calculations of the available amount of concrete, the available potential energy, the expected particle size distribution from applying a modest portion of that energy, and the volume and mass of the dust observed on the ground in Manhattan and in the air above New York suggest that 30-50% of the concrete settled around GZ according to both observation and the prevailing theory of gravitational collapse caused by fire and plane impacts.
