More Fatal Flaws in Bazant et al's WTC Analysis

Bazant et al's analysis supporting the official WTC collapse theory can be found here. I have described other fatal flaws in his model here and here.

FIRST-- his entire paper rests on differential equations for the time of the "collapse", notably equation 2-- the "crush down" equation. He gives this equation on page 3, but for some reason it takes him until page 7 to note that "... Eq. (2), the equation of motion, has been set up under the assumption that the accreted mass gets moving after impact with the same velocity as the top part, which implies perfectly inelastic collision (a zero coefficient of restitution)."

A perfectly inelastic collision is where a body A moving at velocity V strikes a body B, typically at rest, then both bodies stick together (the "accreted mass"), and then both bodies move together after that at the same final velocity. If both bodies are similar masses, then the final velocity will be 1/2 of the original velocity. If body A is much larger than body B, then the final velocity will be closer to the original velocity.

So there are three obvious problems with this:

1) a perfect inelastic collision assumes that no mass is lost during the collision, which we know is not the case as, during each "collision", concrete was pulverized and and ejected AND outer columns were ejected -- resulting in a loss of mass for each floor.

2) a perfect inelastic collision assumes that the collided floors stick together, which is highly improbable. Further, we know that this is not the case as, during each "collision", concrete and interior contents were pulverized, creating a significant barrier of debris between floors.

3) most fatally, by its very nature, a perfect inelastic collision model cannot take into account the resistance from the supporting columns below when calculating the final velocity.

Another problem is that Bazant does not show any calculations revealing the mass he is using for the upper colliding mass and what mass he is using for the lower mass. In fact, as far as I can tell, the collapse equations are derived indirectly, by a series of equations that calculate an overall collapse energy balance and that rest on dubious propositions (for example as described in part 2 below).

Now, Bazant should be doing collision calculations using two equal masses, as the two floors that initially collide are similar masses! But as far as I can tell, the model he uses the complete mass of the upper tower here, which will give a much faster final velocity, in order to obtain a rapid collapse time and a complete crush-down.

In reality, floor A colliding with floor B at velocity V should result in a final velocity of V/2-- and this is under perfect conditions! This halving of momentum would slow down any collapse greatly. Now, I should note that for a real world collapse, the analysis would get complicated as, after the initial collision of floors, the floors above the first collided floor will still be moving at the original velocity, which will lead to more floor-by-floor collisions-- particularly in the upwards direction. So there should be a great deal of crush UP during the "crush down" phase-- a fact that Bazant et al completely ignore in their unrealistic analysis that favors a fast collapse time. And of course, "crush up" is what is actually seen in the videos-- the top part of the tower basically completely breaks apart as it moves downwards. So Bazant et al. not only ignore basic logic but as has been pointed out before, ignores the visual record of what happened.

It is worth adding that Judy Wood's "Billiard Ball example" for the WTC collapse was criticized by many people for assuming (essentially) perfect elastic collisions for each floor. In fact, for reasons I noted above, an elastic collision is a much more reasonable assumption than an inelastic collision for floors striking each other. Obviously in the real world, though, a collision is not going to be perfectly elastic or inelastic-- so models need to really take this into account better. But overall, I find it shocking how UNREALISTIC the official collapse models are-- they barely make an attempt at making a reasonable sequence of events for the collapse. Jeesh-- I sometimes think I could do a better job of explaining the official story.

SECOND-- there is a problem with Bazant et al's equation 4, which they claim specifies all the resisting forces to collapse:

Fc = Fs + Fa + Fb

where Fc is the total resisting force, Fs is the energy required to pulverize the concrete, Fa is the energy required to expel air, and Fb is the energy required to buckle all the columns.

The key problem here is that he completely neglects two important energy sources:

1) the energy required to eject outer facade columns hundreds of feet in all directions around the towers.

2) the energy required to expel pulverized concrete for thousands of feet all around the WTC complex.

Considering the masses of the outer wall columns, and the immense mount of concrete that was expelled, no one can seriously argue that these are trivial sources of energy-- particularly when Bazant is saying AIR gave enough resistance to collapse to bother calculating!!!

And, as has been discussed here before, Bazant et al badly under-estimate the energy required to pulverize the WTC concrete (see links above).



The bottom line, again, is that the official analyses of the WTC collapse (such as Bazant et al's) are so fatally flawed that they essentially prove demolition by default!

In other words, if expert scientists must resort to such rigged mathematical models to explain what happened, there can be little doubt they are covering up a very ugly truth.