I went to 75% of F.R. Greening's document WTCREPORT.pdf and have some serious questions. His excel sheets, values for floor, masses etc will surely be correct. We don't have to reinvent the wheel. I admit that I don't understand everything at the moment (it's been awhile), but if you debug a source code you also don't have to know it completely.
Upper block falls
This is assumed by TV coverage, it does not explain why this happened, apse time you already should take other factors into account, the time could be extremely dependent on these factors or maybe not.
Tacitly assumed that the impulsive delivered by the impact is sufficient to rupture...
Why?
The second stage of collapse
Absolutely relevant for the seismic data, but not really relevant for the speed at which the buildings come down.
For now it is sufficient to note that the collapse times calculated without allowing for E1 are already in reasonable agreement with the observed collapse times.
Of course because this is the theoretical minimum time and that should be near free-fall time because in fact section 3.0 of the paper assumes no resistance in any way, in fact point masses with non-elastic collapses merging into each other without any of the mass moving at an other directory
However, to more precisely model the physics of the WTC collapse events, we need to consider the bending and fracturing energy, E1, that must be expended to collapse each floor
Great but this is still under the assumption of all mass falling down in the same direction to break the next floor.
But the initial kinetic energy Ti is equal to (1/2)Nm_f u^2 so the fractional conversion, fc, of kinetic energy to heat is simply,
fc = Q/Ti = 1/(1 + N)
This is an amazing result IMO, but indeed under the assumption no mass is scattered away from floor N to floor N-1 to ... to floor 1
If we assume 50 % of this energy was available to crush concrete, we have 1.2 x 10^9 J available for WTC 1, and 2.5 x 10^9 J available for WTC 2. This is sufficient to crush the concrete on the impacted floor to 175 micrometer particles. Consider now the newly formed mass of (14 + 1) floors of WTC 1, and (29 + 1) floors of WTC 2, impacting on the floor below.
An amazing amount of energy indeed. Again all crushed concrete is assumed to form a new mass to crush the next floor. Check some videos and detailed pictures, it's absolutely impossible to consider this as a first approximation, the mass scatters in all directions, even upwards. Of course the conservation of mass can't be violated, but the part traveling down together with the initial upperblock is not
(n+1)m_floor
but should be
n m_floor +w m_floor =(n+w)m_floor (**** I wrote it wrong at top)
with w the fraction of the mass traveling downwards. Greening didn't use that, also note that w is not constant, it will be a complicated function (dependent on some variables) for which we only know 0< w<1, it should be estimated.
Further small particles are very sensitive to air resistance and the rest of the crap in the air and the so-called terminal speed is reached very quickly, I'm not sure if the factor w can take that into acount or if another factor is needed for that somewhere. Maybe I'm wrong also now and all these factors seem to have not much influence on the theoretical minimum, but it was just something I thought after reading a little bit.
But now it's time to go out and have some beers, my wife is a little bit angry.. "you should marry with your computer" etc..
