World Trade Center Collapse as Inelastic Collision
by Alberto Miatello
Alberto Miatello has published on Academia.edu a preliminary version of his (originally written in Italian) paper
WORLD TRADE CENTER COLLAPSE AS INELASTIC COLLISION,
AND THE “VARIABLE MASS” PROBLEM IN PHYSICS.
WHY — WITHOUT A CONTROLLED DEMOLITION OF BASEMENT —
WTC1 COLLAPSE WOULD HAVE STOPPED 15 STORIES BENEATH.
Reproduced below are the Abstract and Conclusion (both edited for improved readability) from this paper. The author welcomes comments from fellow members of Academia.edu.
In the years since September 11, 2001, many remarkable studies and specialists have correctly criticized and challenged the “official” version and hypothesis that just a “gravity-driven” collapse of the tops of the Twin Towers, after structural weakening by airplane crashes and fires, could have possessed energy enough to totally crush both buildings (and especially WTC1, whose damaged top was only 10% of the total building height) and also WTC7 (which suffered neither an airplane crash nor big fires).
However, no alternative study — as far as known — has yet proposed a physical/mathematical model explaining why, how and where the collapse of the top of WTC1 would have stopped long before the total destruction of building. Therefore, this paper is the first attempt to set out and model the problem of the WTC1 (and WTC2) collapse as an inelastic collision in the frame of “variable-mass” problems of physics, in which a variable initial mass Mi — here the top 12 falling stories — with a known accretion/ablation factor, under two contrary forces (here gravity g against structural resistance η of steel beams, concrete flooring, air, etc.) and thereby receiving a constant “thrust”, gets turned into a final mass Mf.
How powerful and correct this model is, can be known just by recalling that the “variable mass” approach in physics and engineering has been used many times, since the beginning of the 20th century, to calculate precisely the energy needed to send rockets into space and to the Moon (it is thus also known as the “rocket equation”).
Hence the (often suggested) hypothesis of a controlled demolition, i.e., the demolition of the Twin Towers mainly by blasting charges in the basements, can explain their total and quick collapse, whereas the “gravity-driven” total demolition of the buildings by the collapse of the top part of the buildings alone is physically impossible. This model can also explain what really happens, in physical/mathematical terms, both when a controlled demolition succeeds in totally destroying a building, and when it fails with just a resulting partial destruction.
On the thorny and grievous path toward the Truth on one of the most terrible tragedies of contemporary history, a very important contribution can come — once again — from physics and mathematics. After 14 years we can mathematically prove that neither the collapsing top of WTC2 nor (especially) the top of WTC1 could have crushed a mass significantly larger than its own.
The top 30 collapsing floors of WTC2 could destroy — at most — 33 more floors beneath, and the 12 collapsing floors of WTC1 could barely possess the energy to crush 15 more floors beneath.
Dr. Pettit of NASA wrote that the “tyranny” of the rocket equation dictates rigid and insuperable limits to the highest velocities/accelerations a rocket can reach (see www.nasa.gov/mission_pages/station/expeditions/expedition30/tryanny.html).
In the same way that the rocket equation prevents logarithmically an increase in velocities and accelerations by reducing mass or payload of a rocket (even filling it with 10 times more fuel the gain of velocity would be only twice what it was before), even worse, in the situations we have seen above, where a mass is growing while collapsing onto another, the same powerful and precise equation dictates that such “slackening” effect dooms the collapse to stop very soon.
The “tyranny” of the rocket equation is working any time a variable mass is ablating (rockets) or accreting (WTC) under the influence of a positive or negative “thrust”/force (power of ejected propellants, or structural resistance η by steel and concrete structures).
This model is also in total agreement with basic laws of dynamics, i.e., momentum + energy conservation, and the law of decreasing kinetic energy after inelastic collisions with masses at rest.
Finally, our model includes also the structural damage suffered by the Twin Towers as a consequence of airplane crashes and fires reaching (at some points) up to 800°C, as evidenced by reduced structural resistance η. Therefore, the only possible explanation of the WTC1 and WTC2 collapses seems the destruction of the central supporting columns in their basements through blasting charges, which was also the only way to produce the large destructive kinetic energy, rather than through the collapse of the tops of the buildings.
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