#### Oystein

##### Senior Member

A Contribution to Analysis of Collapse of High-Rise Building Inspired by the Collapses of WTC1 and WTC2: Derivation of Simple Formulas for Collapse Upper Speed and Acceleration

This is fresh, and I have not even browsed the paper, only the e-mail, which claims:

I have to admit, this work eluded me so far. A search for "Němec" or "Nemec" in this sub-forum came up empty....we have derived the limit acceleration of progressive collapse of a high-rise building from its top. We have found that the theoretical upper limit of acceleration of falling mass, omitting any resistance of columns, and assuming that all the falling mass hit the lower floors, is one third of the gravitational acceleration. When assumed that half of the falling mass fell outside the building perimeter, the limit acceleration is one fifth of the gravitational acceleration. The acceleration limits were derived independently from both pertinent laws of mechanics, i.e. conservation of energy and conservation of momentum. The observed acceleration was faster than the theoretical limit. The needed energy was bigger than the potential energy of gravity of the buildings. The source of additional energy needed was not officially explained.

Earlier we have derived a general differential equation of progressive collapse of high-rise buildings and solved it for the case of the WTC 1 tower. We have shown that with regards to the basic laws of physics, the collapse, when started, for probable input parameters should arrest after 80-100 meters, or for a less realistic parameters the whole building could fall, but much more slowly than it was observed. We have described this in detail it in the book

Dynamics of Collapse of a High-Rise Building: Inspired by the Collapse of the Twin Towers of the WTC.

https://www.amazon.de/Dynamics-Coll...ert487p7i1tNjZV4pXqb7RZLP3nh_jmE78yGY3jaKJuIk

In the conclusion we declared that the official explanation of the WTC 1 and WTC 2 collapses is in contradiction with the fundamental laws of mechanics. ...

The result of the paper, that acceleration derived from Conservation of Momentum, and ignoring resistance from columns, is 1/3 of g, is actually the same result that I got years ago when I modeled the WTC1/2 collapses as a series of collisions between falling accumulated upper floor slabs and static (magically suspended in air until hit) individual lower floor slabs. Except that my model only

*approached*1/3 g after a number of floors had already collasped and the collapse front had gained considerable speed. Before that, acceleration started at almost g and decreased from there.

So my model was, for a few suitably chosen floors early in the collapse, roughly in line with Chandler's measured "2/3 of g" during some time interval early in the collapse.

I wonder if the same is true for Němec's analytical model.