You have never asked me this question, let alone three times. This is what I mean by your inability to communicate with concision and clarity.
I am not agreeing with the calculations, as they are derived working backwards from the facts, in order to fit the facts. Moreover you haven't explained these calculations, you simply posted them.
I am agreeing that the collapse time is probably within 10 - 13 seconds, a time frame that the calculations you provide confirm. Therefore, as I've stated several times already, we both agree that the collapse time of the towers was within 10 to 13 seconds. Therefore, we are not arguing about the collapse time.
If you still don't understand, you might want to try breaking those sentences down into smaller units for understanding.
Science works by looking at the facts and then finding a theory to explain them. You have to work backwards from the facts, and your theory must fit the facts. Why are you stating that this approach is a problem?
You say, "this repeats at increasing velocities" for the subsequent 90 and 77 floors. As you know, the problem is that the descent of the alleged upper block would slow, not increase. The pull of gravity does not overcome 91 and 78 floors presenting normal resistance. If you want to show us your calculations again and actually walk us through it, I'd be interested in seeing how those results are arrived at. We did this in another thread and found that the poster was unwilling to explain the math he posted.
We had calculated the Kinetic Energy (KE) for each upper block of storeys in this post:
Let us focus on one, WTC1, which is the smaller of the two upper blocks, and consequently the one with the least amount of kinetic energy. What this means is that if the WTC1 upper block had enough kinetic energy to overcome the resistance of the lower floors, the upper block of WTC2 which had more kinetic energy, would aslo have had enough kinetic energy to overcome the resistance of the lower floors.
So, right before it hit the lower block, KE (wtc1) = 14 x 1.67 x 10 to the 8 J = 23.4 x 10 to the 8 J
and the velocity was 8.5 m/s.
Now, it takes a certain amount of KE to demolish the structure of the floor. There have been several different estimates made of this number. I will use the highest one I found, from this study:
Greening also uses this number in his energy calculations. I quote:
Thus, based on T. Wierzbicki et al. calculation, we estimate a total of 6.29 x 10 to the 8 J of impact energy was
required to collapse one WTC floor, a value that is remarkably close to Bažant’s estimate
of 5.0 x 10 to the 8 J for the plastic energy dissipated by the collapse of one floor.
So, we will subtract that energy from the kinetic energy, as it has been expended.
So, we have 17.1 x 10 to the 8 J. for the left over kinetic energy at the time of impact.
Now the new mass is equal to the upper block of storeys plus the floor just impacted.
m for one floor = (510,000,000 / 110) kg, so the new mass is 15 times that amount (the 14 upper storeys plus the newly added single lower floor).
Using our equation for kinetic energy:
we can calculate the new velocity by isolating the v variable, which stands for velocity.
v = sqrt of 2KE/m
v = sqrt of 2(17.1 x 10 to the 8)/69,545,454
v = 7m/s
Now, to determine the velocity of an object falling from rest in free fall, we use this equation:
g=9.8 meters per second squared
v = sqrt 2(9.8)(3.7)
v = 8.5m/s
But remember that this i sfor an object falling from rest, or an initial velocity of 0, but our upper storey was actually falling at 7m/s right after impact, so we have to add these 7m/s to our calculated velocity.
This means that the now slightly larger upper block was travelling at 15.5 m/s right before it impacted the second of the lower floors.
Let us now calculate KE for the upper block for the same instant:
KE = (1/2)(m)(v squared)
v = 15.5m/s
KE=167.1 x 10 to the 8 J
Please note that the kinetic energy for the upper block and the velocity for the upper block were faster at the moment of impacting the second lower floor than they were when the upper block impacted the first lower floor.
This shows clearly that the upper block crashed through the lower floors at ever increasing speeds.
You asked for the math, jas. You got it.
A second problem is your wishy-washy statement that "the upper block falls apart somehwat as it falls, but mostly after it has impacted all the lower floors." Does NIST say this?? I don't think they do. Why do you say the upper block falls apart "somewhat"? If it's falling apart, how could it stay intact through the crushing and pulverizing of 90 and 77 intact floors? Why would it, only then, collapse itself?
Do you remember your accreted matter? It ended up on the bottom of the upper block of storeys, cushioning the structure of the upper block of storeys from the impacts. Now, it didn't absorb all the energy, so some energy made it onto the upper block to cause some damage, but relatively little.
A third problem of course is you still haven't provided evidence that this upper block of storeys is present through the collapse sequence in order to provide this piledriving of 90 and 77 intact floors - about one third of a kilometre, or higher, of steel and concrete highrise.
I provided a photo. You even comment on it in this very post that I am responding to.
A fourth problem is the lack of acceptable physics that can explain how a block of storeys that begins tilting to the side could then crush the lower floor in a way that would then cause global, symmetrical collapse of the floors below it--and in the rapid fashion we saw. This defies both common sense and accepted physical principles. What also isn't explained from the picture you provide is how it is the collapse has already begun while the block is tilting--but on the opposite side of where it would be creating pressure.
I highly doubt it was perfectly symmetrical.
It may defy your common sense, but not mine.
It does not defy principles of physics, as I have mathematically demonstrated.
The collapse already begun because a plane crashed into the building, destroying structural elements and fireproofing and scattering burning jet fuel over most of the floor area on those floors where it impacted.
I have no idea how you can say that the picture is showing collpase on the opposite side of the tilt. There is a rather large debris cloud obscuring that area of the building.
Well, I'm sorry, but what you're describing would only produce partial collapse, if at all. And then the tilting block would fall over, in the direction it is tilting, because it has supposedly just crushed those portions of building below it, which then can no longer support it.
But I have a further question: What caused its tilting away from the impact zone in the first place, and why would it not have simply continued its momentum in that direction?
Please provide evidence for the bolded statement.
As for the tilting question, it would depend on the magnitude and direction of whatever force is causing it to tilt. If it is caused by moment force couples (do you know what those are?), the tilting would only get worse if the structure providing the normal force does not collapse under the weight of the upper block. Since we can plainly see it did collapse, this would not be an issue.
You ascribe a lot of power to the fireproofing, as well as to the hypothesis that the planes would have removed it, and only in the impact zone. Are you aware that there are pictures of people standing in the holes of the impact zones, and that these fires were largely smoking black? At the same time, you maintain that the fires in the upper blocks, which burned for 60 and 90 minutes respectively, did nothing to weaken the structural integrity of the upper block. Again, your hypothesis requires several leaps of faith.
From the [url=http://wtc.nist.gov/pubs/NISTNCSTAR1-1D.pdf]NIST report[/url] discussing building code regulations (see page 44/168) the fire resistance rating of the structural members for the WTC towers was 3 hours. This means that the fireproofing around the structure would have protected the steel from temperatures high enough to weaken it for 3 hours. Please note that this is considerably longer than the durations of the fires.
This is why I claim that the fire in the upper block did not weaken the structure.
So, now I will look for those calculations that show that gravity cannot overcome the normal resistance of 91 and 78 intact floors of the WTC and you will look for evidence that the upper blocks did in fact remain intact through the collapse sequence.
I am eagerly awaiting your evidence.