psikeyhackr, you seem to be convinced that any use of PE in calculations is somehow borrowing against something that hasn't happened yet. I get that. I understand why you misunderstand, believe it or not, and it's quite frustrating to not be able to communicate this most simple idea to you after untold posts back and forth. Your ridicule is misplaced and, I swear, if you ever come around to understanding this you are going to be embarrassed.
It can be a tad confusing when presented with calculations which compare the PE loss from a given drop to the energy required to "crush" (or more accurately simply "fail") the same distance. It looks like the energy required to fail the supports is taken from the PE which hasn't been lost yet. Sometimes, this is exactly what people do (such as above) because they intend to. They want to see what the energy numbers are IF there's a total collapse.
Let's suppose the towers were taken down by having devices of some sort placed at each and every connection - not even a secret operation, think public demolition in 2050 - so that it ended up in a big heap like what was seen on 9/11. The PE change is the same going from intact structure to debris pile in BOTH cases. It doesn't matter HOW the tower comes down for PE calculations: progressive collapse, demolition, incremental disassembly, even melting in the sun. What matters is the sum of the products
migΔhi where
mi and
Δhi are the mass and total change of height of the
ith mass element. There's nothing in there about HOW the mass got from point A to point B.
When a calculation is done that says a particular amount of PE is lost by the mass dropping X amount, that calculation is applicable
no matter how the condition came to be. Unless you are denying the towers actually came down at all (is this really your position? I'm beginning to wonder...) there is a valid calculation for the PE change regardless of, and independent from, the cause. Once you determine the total PE change, you've determined what energy was available from that source to drive collapse. Unless there were other sources of energy, that's it.
A single, global calculation can't really address the issue of arrest or not even if it were somehow possible to exactly specify all the masses and all the sinks. Arrest is a question of power, not energy. Step-wise and continuum approximations are much better, though hardly perfect. In fact, I'd argue they are (at the current state of the art) way off the mark. Better than your paper loop and washer model, though, just to put it into perspective. Why? Because it's a poor physical analog to the analytical models which are in turn a poor representation of the tower collapses. Irrelevancy heaped on top of irrelevancy.
What a single global calculation of PE change can do, if it's accurate, is specify the total PE change from beginning to end. Of course, it's impossible for such a calculation to be accurate. Once you find the as-built TONS of STEEL and TONS of CONCRETE specified to your satisfaction, you still won't know the final distribution in the pile. Right? It's only ever going to be an approximation based on estimates, whether global or piecewise.
The value of an estimate is in getting a rough idea of what's possible, no more no less. If the estimate is from the energetic perspective, it speaks only to energy and nothing else. In this case, crude estimates indicate an enormous PE loss per unit distance of drop. The
only way it is even possible to arrest is if the sinks per unit distance exceed the PE loss rate. Bazant presents a limiting case based on a good engineering estimate of the MAXIMAL energy dissipation per unit distance of an actual tower, not short paper loops and washers on a dowel, and the conclusion is there is no arrest in that circumstance.
You refuse to speculate on why the towers came down, but reject a natural progression. Thus far, you've not once presented a rational reason for your belief, though the few reasons given are repeated endlessly in this forum and perhaps
hundreds of others. You've encountered the best and the worst of responses and treated them exactly the same, no hint of the slightest discrimination between a good argument and a bad one. It feels like arguing with a chat-bot, I'm sorry to say. Cut and paste argumentation is sooooo tiresome.
Your crusade against PE calculation is quixotic, and you haven't the slightest interest in moving beyond personal misconception and incredulity to more compelling issues. Why?
by 
So why tie their genuine political wish to the dead set loser of lying claims about demolition?
