Dr. G wrote:Greening vs. Chandler and Newton’s Laws:
I note with amusement that someone who calls himself Reprehensor has posted the recent e-mail exchange between myself and Steven Jones on 9/11 Blogger. From the 40-plus comments Reprehensor’s post has generated I see that many Truthers view my opinions on Chandler’s “proof” (that the collapse of WTC 1 must have been a CD) as evidence that I misunderstand the basic rudiments of Newtonian physics. Well, I beg to differ and will now go through Chandler’s arguments one more time just to clarify my position on this issue.
Chandler’s arguement is as follows: During the collapse of WTC 1, an upper portion of the building, (let’s say the top 13 floors), started moving downward relative to the lower, fixed portion of the building, causing the lower portion to be crushed. Let’s call the (initial) mass of the upper block M(upper). For WTC 1, M(upper) was at least 30,000 tonnes and the initiating drop distance was presumably about 3.7 meters or one story height.
Measurements of the motion of the upper block show it dropped many story heights for the first 3 seconds with an approximately constant acceleration of 6.31 m/s^2 or 64 % of g. From this observation Chandler concludes that the block was subject to a net force of 0.64M(upper)g. Prior to the collapse of WTC 1, the lower portion of the building was perfectly capable of holding up the upper block which we know exerted a downward force equal to M(upper)g. So why, once the collapse started, was the lower section of WTC 1 not able to support a load of 0.64M(upper)g? Chandler’s answer to this question: During the collapse of WTC 1, the only way the upper block could have accelerated at 64 % of g was for the lower section of the building to have continuously lost its load-carrying capacity, presumably through the occurrence of column failures ahead of the collapse front. The fact that the downward acceleration was not far below g shows that columns failed without significant resistance. This, concludes Chandler, proves that the destruction of WTC 1 was a controlled demolition.
This all sounds like a very nice exercise in Newtonian mechanics, …. so how could it possibly be incorrect? Well, the main problem with Chandler’s analysis is that he is ignoring what actually happens to a building during collapse. In the collapse of WTC 1, the upper section is not the only part of the building that is set into motion. Evidently the top of the lower section also starts to move downwards, floor-by-floor. This means that some of the potential energy of the upper block is converted into kinetic energy of some portion of the lower block. For example, columns and beams at lower levels of the collapse front are set in motion as they are pushed downwards or sideways by a growing avalanche of debris. This means that we no longer have two distinct masses, M(upper) and M(lower). We have M(upper) = M(Initial upper) + dM/dt, and M(lower) = M(Initial lower) – dM/dt. Here dM/dt is the rate of mass accretion by the descending upper block. And this is without mass shedding ……
Obviously this situation greatly complicates momentum transfer calculations because you have to include a dM/dt term as well as a dv/dt (acceleration) term into your simple M1V1 = M2V2 calculations. I call it the the reverse rocket equation problem...... I challenge Chandler to re-do his analysis with inclusion of a dM/dt term.
Meanwhile, back in the war room, energy balance requires that:
a = g – E1/3.7M(upper)
where E1 is the energy needed to collapse one floor.
The fact that a is observed to be approximately constant means E1/M is also approximately constant. That E1/M should be more or less constant is consistent with the design of WTC 1 & 2, or indeed any tall building.
What a big waste of time all of this is! The lower columns were stronger in proportion to the greater mass they needed to carry. In addition, you don't even have a natural mechanism to deliver the energy you speak of, as the upper block of WTC 1 never decelerates at any time during the first 114 feet of it's drop, through which it was visible and measureable. That is proven now and I showed you what it should have looked like if a kinetic energy transferring impulse had occurred, with the velocity curve of the Balzac-Vitry demolition, which did decelerate after going through it's two story intentional drop.
Have you asked Dr. Bazant if he is going to modify his papers to correct for the lack of deceleration and the errors in column axial stiffness and kinetic energy to energy absorption ratio? It would probably be easier to just withdraw them as we now know there is no energy delivery for a natural collapse. Of course, he could just say that this recently put forward evidence invalidates his papers and that he now realizes the towers had to be demolished and write on how he thinks it was accomplished. He could probably do a good job on that and regain some of the respect he has lost.
