On 9/11 not only the two main towers of the World Trade Center collapsed after terrorists flew planes into the buildings. Another huge building, WTC7, came down later that day. The collapse of this building has become one of the main issues that *truthers *see as proof that the official story is fabricated by the US government to conceal that the buildings were in fact brought down with explosives in a controlled demolition.

Truthers dispute the official explanation, given by NIST, that the building collapsed after fires had raged uncontrolled over several floors during the day after the building was hit by debris from the North Tower. One argument that has dominated the discussion is ‘the fact’ that WTC7 came down at free fall speed. Truthers claim that this cannot be explained by the NIST models, but only by controlled demolition (even though usual controlled demolition doesn’t show free fall for several seconds either).

In their preliminary report NIST had stated that based on the visible evidence it had found that when the exterior facade came down, 18 floors descended in 5.4 seconds, implying an acceleration about 40% lower than free fall acceleration. After questions were raised they had another look and in the final report they acknowledged that for a period of 2.25 seconds (within the 5.4 seconds) there appeared to be acceleration “equivalent to the acceleration of gravity *g*“. But they also wrote that this was still “consistent with the results of the global collapse analysis” (for a discussion on whether that makes sense I refer the reader to Metabunk).

Let’s see how this came about from the viewpoint of David Chandler, who showed that there seems indeed to be a short period of time during which the northern facade of the building came down at an acceleration equal to the free fall acceleration (9,81 m/s^{2}).

Occasionally this issue has come up in discussions I had with people who are quite sceptical about the official explanation for the collapse of WTC7. Although I had some doubts about the approach NIST used to calculate the acceleration, I didn’t really have a close look and limited my criticism to

### The NIST approach

NIST explains what they did in paragraph 12.5.3 of the final report. You can download the full report or just the pages that I will be talking about.

Like Chandler, NIST picked a point from a video (a different one than Chandler used) showing the collapse, followed that point going down and measured time and height. How they did this exactly and how accurate that was done is also not entirely clear. But I’ll focus on what they did tell us.

The data points are given in the following graph:

NIST fitted a curve through these points using a formula that

Without much ado, NIST tells us that they see three stages by cutting this 5.4-second period (during which the fall of the North facade is visible) at 1.75s and 4s: “The slope of the velocity curve is approximately constant between about 1.75 s and 4.0 s.” Just by eyeballing the graph it seems, and the cuts seem quite arbitrary to me.

Now they assume that Stage 2 has a constant acceleration and approximate this by performing a linear regression on the *velocity data points*. In this way, they find an acceleration of 32.196 ft/s^{2} (= 9.81 m/s^{2}) which is pretty close to the gravitational acceleration *g* indeed.

Those *velocity data points*, however, are not directly measured velocities. They are calculated by *using a central difference approximation*. In other words, for every two neighbouring points in Figure

Why not do a polynomial curve fitting on the actual measurements in Figure 12-76, I wondered? If we assume a constant acceleration *a* for a certain period, the height is given * y(t)=x _{0}+v_{0}(t)+1/2a t*

^{2}with

*x*and

_{0}*v*the height and velocity at t=0. So that’s what I started to work on next.

_{0}### Doing it better than NIST

If we stick to the stages NIST has identified I think it is reasonable to take the 11 data points that lie in the period from 1.6s till 4.1s because those are used to calculate the 10 *velocity data points* in Figure 12-77.

I used Figure 12-76 and Photoshop to read off the values of the data points. The values I found this way you can see on the right.

First I used these values to replicate the linear regression NIST did and found a slightly different value for the acceleration: 32.237 ft/s^{2} . This is pretty close and I think it is fair to assume that the values I read off Figure 12-76 are close enough to the real values of the data points NIST used.

Now I used these data points for a polynomial curve fitting and found as acceleration the value 31,974 ft/s^{2} (=9.75 m/s^{2}), a little lower than in the approach used by NIST. I think this can be understood because in my approach stage 2 is a bit longer. But remember that we actually used the same data points. To me, my approach seems more logical.

When I plotted the found approximation over the data points I noticed that the first point seems quite a bit off the curve.

Now I did the same curve fitting exercise leaving this first point out and found an acceleration of 31,024 ft/s^{2} (=9.46 m/s^{2}). And an argument can be made that this is a more reasonable fit when you look at the differences between the curves and the data points. The sum of squared residuals divided by the number of data points is for the 10-point curve about half of the 11-point curve.

### Conclusion

Although it is true that NIST ‘admitted’ that for 2.25 seconds the exterior facade of WTC7 came down at an acceleration equal to free fall acceleration, I think it is fair to state that this was based on a questionable calculation. In my view, an acceleration of 9.46 m/s^{2} can be defended with arguments that are at least as good as those of NIST.

Of course, the importance of this all is rather limited as it has no consequences for the models used by NIST to get a grip on why the building collapsed.

*NB In my experience discussions on posts about anything related to 9/11 tend to sprawl rapidly in all directions. Please stay on topic. Comments that discuss other issues than the calculation of the acceleration of the descent of WTC7 will probably be deleted by me.*

One more thing, the duration of freefall is clearly 2.5 seconds when viewed horizontally as it should be measured. The missing quarter second in NIST’s measurement is part of the gradual transition deception due to NIST’s intentionally chosen bad camera angle coupled with the choice of a point midway along the roofline where the anomalous motion would be maximized. I say intentionally chosen because they had all the same videos I have. I got my videos from NIST as part of a FOIA release.

By the way, there are other videos that show the west face of the building, and neither the west face nor the southwest corner show any sign of deformation before or during the freefall part of the collapse. Furthermore, the ejections of smoke and debris from the windows when they do break after collapse initiation is straight out, which is what you would expect if channeled by the floors being intact, but not what you would expect if there were no material behind the supposedly freestanding wall. Where is all that coming from if there is nothing there?

First off, “Truther” is a derogatory, demeaning term and should not be used in rational discourse.

You don’t need to use second generation data via photoshop. I have the original videos, calibration data, and a link to the free downloadable Tracker software assembled as a “kit” on my web site here: http://911speakout.org/physics-tutorial/ The measurements are repeatable and I urge you to repeat them.

This is better software than I had access to originally, and I am offering a better video than the one I originally used. This one is tilted because it is from a camera that was not leveled, but also allowed to run with no human contact, so there is no zooming or camera motion to contend with. The effect of the tilt can be removed by tilting the coordinate system to match.

NIST’s measurement is worse than you suggest. They state that they used Camera 3, as they labeled it, which is a view looking up at the building from West St. Near the onset of downward motion the building flexes laterally, but by choosing a point near the center of the roofline they conflate this lateral motion with the later downward motion. This is the source of the gradual transition seen in Stage 1 of their graph. Any competent scientists would know that to take good measurements you need to eliminate parallax, and since the guys at NIST are competent scientists, they knew what they were doing. They clearly intended to fudge the data to suggest a gradual transition, which they could pass off as some kind of natural process. If you do the measurement using the view that is level with the roofline you will see there is no initial sagging of the roofline and the transition from full support to full freefall is essentially instantaneous. The exact value you get when you fit a straight line to the linear portion of the descent will vary by a percent or so, depending on your choice of points to include in the regression, but your measurement, like mine, should be at or very near 9.8 m/s^2.

The idea that the interior had already collapsed is not supportable. A small area under the east penthouse collapsed, or was imploded, early, and some of the windows beneath it for a limited number of floors show window breakage due to that event. This was clearly a localized event. There is no further window breakage anywhere on the building until after the entire roofline starts to come down. The interior is not isolated mechanically from the exterior surface, so collapsing beams would reveal themselves in deformations on the surface and, as we saw in the case of the east penthouse collapse, window breakage. Furthermore, note that the air conditioning units and west penthouse on the roof were fully supported until a fraction of a second before the global collapse of the building. In fact when the west penthouse started to collapse, it did not even descent its full height before the entire roofline started down and the top of the west penthouse remained visible throughout the freefall part of the collapse. Therefore claims by NIST that we are only looking at the north facade of the building are unsupported. They are postulating events in the interior that are not evidenced on the exterior in any way. By contrast, if you look at the modeling NIST did for the collapse of the building you will see the models are characterized by severe deformations of the exterior. The model does not fit the reality.

I looked at your “kit” but as far as I could see there is nothing in there that can be seen as a basis for Figure 12-76 of NIST. I don’t think it is publically known what point exactly they have chosen to follow in the video, neither has NIST provided a table with the values they found (which I’ve tried to reconstruct by reading those values off from Figure 12-76). If you do know these values, that would be interesting.

I’m well aware that there are other videos that could be used in to estimate the acceleration (I mentioned in this post that you used another video), but that’s not the subject of this analysis. My post is just about the calculation by NIST as presented in their final report.

Maybe you missed the last paragraph of the post. I didn’t delete your comments, but they do mostly relate to issues that I don’t want to discuss here at this moment. Not that those are not interesting, but they have been discussed in detail on fora like internationalskeptics.com and metabunk.org.