The 9/11 Forum

Just e-mailed this to NIST (for what it's worth, since NIST have never responded to anything I have sent them on WTC 7.....

Dear Sir,

I am writing to seek clarification on an issue raised in the Final Report on NIST’s investigation of the Collapse of WTC 7. The issue of concern appears on pages 597 to 599 in Chapter 12 of NCSTAR 1-9, and includes a Figure 12-74 that deals with the kinetic energy of the global collapse of Building 7. The figure in question is a graph of the evolution of the global kinetic energy of WTC 7 over the 30-second interval covered by NIST’s computer simulation of the initiation and early propagation of the collapse.

Although the precise instant of collapse initiation of Building 7 is difficult to define, NIST states in its Final Report that significant downward motion of the entire roofline of WTC 7 started approximately 23 seconds into its computer simulation of the collapse. NIST also states that 24.5 seconds into the simulation, the roof of WTC 7 was falling with a velocity of approximately 10 to 15 m/s. This claim is consistent with Figure E-4 of NCSTAR 1-9A that shows the roofline of WTC 7 had descended about 3 stories 24.6 seconds into the simulation, or 1.6 seconds after collapse initiation. In addition, the expected rise in the global kinetic energy of WTC 7 during the first few seconds of the building’s collapse is clearly visible in the time interval from 23 to 27 seconds of NIST’s Figure 12-74. Evidently this rapid increase in the kinetic energy of the building was brought about by the sudden downward motion of a large block of floors – a well known, and much debated characteristic of the collapse of WTC 7.

The reason for my concerns about Figure 12-74 is that the global kinetic energy curve plotted in this figure passes through a maximum value of only 4.13 x 10^9 Joules. This apparently occurs approximately 4.5 seconds after collapse initiation or 27.5 seconds into NIST’s computer simulation. As I intend to show:

An energy of a little over 4 GJ is far too small to represent the kinetic energy created by the collapse of a structure as large as WTC 7.

To estimate the kinetic energy of the collapse of WTC 7 requires a precise evaluation of two terms:

(i) The mass, M, of that portion of the building that is in motion at time, t, which may be represented by a function M(t).

(ii) The instantaneous velocity, V, of this mass.

Thus we may write:

K.E. = ½ M(t) V^2

We will assume that the mass that is in motion after time, t, started as a large upper block of mass M(0) which lost mass as each lower floor struck the ground. If we also assume that the building had a uniform mass, m, per unit height and had dropped a distance, s, in time t, we may write:

M(t) = M(0) - ms

Video analysis of the collapse of WTC 7 reported by NIST and other researchers has shown that the collapse of the building proceeded, at least for the first 4 seconds, with a relatively constant acceleration, a, that was close to, but smaller than, g. Thus we may write:

V = at, and s = ½ at^2

Substituting in the equation for the kinetic energy of the descending mass yields:

K.E. = ½ [M(0) - ½ m.a.t^2] a^2.t^2

or,

K.E. = ½ M(0).a^2.t^2 - 1/4 m.a^3.t^4

and differentiating this equation yields:

d(K.E.)/dt = M(0). a^2.t - m.a^3.t^3

Now the kinetic energy will pass through a maximum value when d(K.E.)/dt is equal to zero, or when:

M(0). a^2.t = m.a^3.t^3

Thus,

t = Sqrt{ M(0)/m.a }

Studies of the collapse of WTC 7 show that an upper block of about forty-two floors moved downwards at collapse initiation. If we assume that each floor had a mass m(1), and the inter-floor height was h, we may take M(0) to be 42m(1) and m, the mass per unit height, to be m(1)/h so that:

t = Sqrt{ 42h/a }

For WTC 7, h is ~ 4 meters and the acceleration is measured, (over the first 4 seconds of collapse), to be ~ 8 m/s^2. Thus the time for the kinetic energy to reach its maximum value is calculated to be about 4.6 seconds. After this time interval at a constant acceleration of 8 m/s^2, the velocity of descent will be 36.7 m/s.

With this value of V we are in a position to calculate the mass of the upper block of forty-two floors using NIST’s previously quoted maximum kinetic energy of 4.13 x 10^9 Joules, (See Figure 12-74). Thus we calculate the mass of 42 floors of WTC 7 to be ~ 6 x 10^6 kg so that the mass of the entire building is estimated to be 47/42 times this value, or a mere 7,000 tonnes. This is considerably smaller than NIST’s own estimate of the mass of WTC 7, which is about 100,000 tonnes.

I am really at a loss to explain this significant discrepancy in the mass of WTC 7 derived from a kinetic energy calculation – a mass, I should emphasize that was inferred from NIST’s Figure 12-74. One possibility is that the inferred mass is low because NIST’s kinetic energy calculation only considered “falling debris”, implying that only material that had become detached from the remaining, intact structure, was included in NIST’s analysis. If this is indeed the case, the use of the phrase “global kinetic energy” would appear to be entirely misleading and inappropriate.

To be precise, NIST’s Figure 12-74 does show a small secondary peak in kinetic energy supposedly caused by the early collapse of the area below the East Penthouse centered on columns 79, 80 and 81. However, NIST’s discussion of Figure 12-74 makes it clear that this pre-collapse of the eastern part of Building 7 was a minor contributor to the “global” collapse kinetic energy. The only other way I can see to partially correct the confusion embodied in Figure 12-74 is for the patient reader of NIST’s Final Report to assume that this figure is a plot of the kinetic energy of only the interior columns. Unfortunately, however, the mass of the exterior columns would be quite insufficient to account for the “missing mass” apparent in NIST’s global collapse kinetic energy plot.

Thus to summarize: NIST’s collapse analysis discussed on pages 586 to 598 of NCSTAR 1-9, indicates that interior column buckling started at 15 seconds into the computer simulation and was complete at the 20 second mark; exterior column buckling started at 21.5 seconds and was complete within 2 seconds at the 23.5 second mark. Hence, the major kinetic energy production depicted in Figure 12-74, which starts at about 23 seconds of the computer simulation and peaks at 27.5 seconds, covers a time interval when, according to NIST: “the entire building moved downward as a single unit”. It is therefore very difficult to imagine how, during this phase of the global collapse of WTC 7, NIST is able to make a distinction between “attached” and “detached” steel and/or concrete structural elements in the chaos of a building undergoing self-destruction. Hopefully, one day, NIST will explain how it accomplished such a remarkable feat of scientific analysis; but until that day this feature of the NIST Final Report - the curious Figure 12-74 - will remain unverified and little more than an object of extreme skepticism and puzzlement.

Sincerely, etc, ......

(EDITED on Dec 7th to correct a small error in my maths.)

Sensational, Dr. G! Very lightweight building, it was. Marvel of engineering. Maybe they need to go back and run the sim with the lower mass? Haha...

Whatever the mass of WTC7 is/was, it was safely carried by 24 inner columns and a much larger number of wall perimeter columns.

According NIST WTC7 Final Report (20 November 2008) page 90:
"WTC7 was prone (sic) to classic progressive collapse in the absence of debris impact and fire-induced damage when a section of Column 79 between Floors 11 and 13 was removed (sic). The collapse sequence demonstrated a vertical and horizontal progression of failure upon removal (sic) of the Column 79 section, followed by buckling of exterior columns, which led to the collapse of the entire building."

So according NIST by removing one little part between floors 11/13 of an inner column (no. 79) remaining 23 inner columns and all wall perimeter columns fail simultaneously and the mass above the failures drop free fall.

I wonder who or what removed the column 79 piece! Gravity does not remove steel columns. To remove a piece of a column you have to cut it in two places and then shift it out of the way. Did fire do that? Or thermal expansion?

The NIST software to do the FEA and then to establish and analyse all structural failures and finally, to keep track of all loose parts flying around is a mystery. Does such software exist?

In my view the software used to create the pictures in the report is the same that is used to design disaster films in Hollywood and to attempt to simulate such destructions.

Again an inconsistency, although there is only one error needed to reject a complete theory you found a whole list of them.

Heiwa, brute force methods also fail in chaotical situations like this, the propagation of the error goes at least exponentially, perhaps you need computers larger than the universe to model that, but I'm sure that you know much more about that.

I know this has been discussed to death before, .... for WTC 1 & 2, .....
but now it's building 7's turn .....

If we buy NIST's collapse theory we have the "inside" of the building falling first, followed by the collapse of the "outside" shell.

So I am interested in the relative masses of the core vs. the exterior of WTC 7.

Does anyone know anything about the mass of WTC 7?

And not just the total mass, but the mass distribution!

Hambone, I know you're out there .......

NIST has some limited info on this, but it's very sketchy. And, as I will show, NIST is very vague about the specifications for the exterior columns of building 7.

However, one interesting thing about WTC 7 compared to WTC 1 & 2 is the number and mass of the core vs. exterior columns.

And remember, all these buildings shared the structural loads more or less equally between the core and the exterior columns. However WTC 1 & 2 had 47 core and 240 exterior columns, while WTC 7 had 24 core and only 57 exterior columns.

However, as I already mentioned, all NIST has to say about the exterior columns of WTC 7 is a one- liner in NCSTAR 1-9 on page 29 of Chapter 2:

"Exterior columns were nominally 14 in. W shapes (W14) of ASTM A36 steel."

From a rough comparison with WTC 1 & 2, I would guess there was about 3500 tonnes of exterior columns in WTC 7. I also estimate that there was 2500 tonnes of granite plates, 1000 tonnes of glass and insulation plus 1500 tonnes for the roof.

Thus the exterior "shell" of WTC 7 weighed only about 8500 tonnes, or am I missing something?

Anyway, if the exterior of WTC 7 really was this light compared to the total mass of the building, the exterior would have relatively little inertia and would follow the motion of the core like a jacket on a man hit by a bullet.

When the wounded man falls, he does not leave his jacket behind, ......... except in cartoon land!

The fact that the exterior of WTC 7 did NOT distort as it fell, just bend a little at the "kink", tells me the core did NOT fall first but the upper section fell largely as an intact, undamaged, structure.

Hi Dr. G,

I have think the mass (and distribution) of WTC 7 could not have been much different from the top 47 floors of WTC 1. The core falling first is nonsense. The expulsion of dust would have been visible much earlier and the windows would get blow out.