The 9/11 Forum

You've got it. The location is very close, indeed.

I find Google Maps Street View a little creepy on some level, but it is a useful tool. I put in the address you have and started looking around. Starting from street level on the waterfront side and panning up:





Moving to the other side of the building, the side facing the WTC7 complex, zooming in on the framed area in the WTC7 video:



For comparison, a frame from that video:



And the same thing for a frame from the WTC 1 video, first the street view cap and then a frame:





These views are restricted to ground level, obviously.

...with strange black window pattern...

Yeah, what is that about?

Oops, reread your post; I got the wrong building...

From the WTC side looking back at the building:



Unfortunately, the ground level view is obstructed when looking towards WTC7.

bridgestreet.com

Great resource, Dr. G! I've added that to my toolbox.

I'm a little hesitant to admit that I still have problems distinguishing the buildings in this cluster when viewed from different locations and with different illumination.

I generated 308 smears, corresponding to the vertical slices from this section of the CBS frames:




One of the more interesting ones is on the NW corner:




The horizontal motion measured by NIST can be seen directly.




What does one do with 308 smears? Make a movie, of course. Pretty weird to swap horizontal space and time dimensions.

Dr. G wrote:I believe that NIST has dug a hole for itself with its fitting function and conclusion that the WTC 7 roofline acceleration was precisely equal to g for several seconds during the collapse. I think NIST reached this erroneous conclusion because it tried too hard to fit questionable data points measured early in the collapse.

At this point, I agree. I don't think there's a better fit than the one you just did.

The net result is it's OK to believe in the freefall of WTC7, if you're so inclined. I see the belief systems changing already, but the news hasn't reached everyone yet.

Or in other words, the motion had a constant acceleration of ~ 8.7 m/s^2, or 89 % of g, for the first 4 seconds.

Or, basically what einsteen had first calculated (8.75)! Wow.

Now I believe this is a much more physically appealing result than NIST's, and it is based on two completely independent sets of measurements of the same Camera 3 video.

Pretty solid so far and much more appealing. Given what you know about mass, what does this say about the characteristics of E1/m as a function of displacement?

Consider the smear from pixel column 259, located between the kink and centerline (very left edge of crop above), CBS video:



And column 552, located at the NW corner:



These smears can be reduced to simple regions and overlaid to compare shape. This is something einsteen already did, I just want to examine it in detail. Strictly speaking, the pixel-distance conversions aren't the same, but this is qualitative. With the tops aligned as best as possible, the NW corner is light green and the midroof is purple, and where they overlap is bluish-green. The edge forming the curve is really the only thing of interest.



The midroof starts sooner and drops slower. Zooming in on the early portion only, and giving it a vertical stretch:



The 'elbows' are quite different. We've noted this before, the center moves sooner but ends up with similar or even less displacement than the NW corner. There's no way the early portions of these curves can be fit by the same function. It could be that no parts of these two sets can be fit with the same form.

This got me thinking about the data I took on the big dark rectangle, the data which does not appear to be good in the early stage. When I scale as best as possible and lay a graph of the displacement on top:



A little additional tweaking on the time was done, so I'm not claiming there's a numeric match, though that may be so. The first half of the data has an unexplained drift downward, causing me to question its validity because I can't confirm it visually (may be real, or smoke, etc.); so ignore that, it's the last half that may be OK, and is likely fine at higher velocities.

Zooming in and stretching vertical as before:



A decent enough match to the midroof smear over the last half. Since the smear is from a roofline over the rectangle, it ought to be pretty close but not necessarily match exactly. If the rectangle data is good over the last half, and I have no reason to doubt it, then this should more closely resemble what NIST was trying to fit. Now, this was the data Dr. G said was resistant to polynomial fits, and it looks to be the case.

The fits are giving me fits. I think this is the hole NIST went down.

Dr. G wrote:...for WTC 7 in a simple energy transfer model should fit:

a = g - E1/Mh
...

Since the observed value of a is apparently closer to 8.75 m/s^2 this suggests that E1 is smaller than 0.75 GJ, or possibly that we need to assume there was a larger falling block.

Thank you. Does this seem like a reasonable value, all things considered, or is it too early to ask?

I reprocessed the big rectangle data using 3.89m story heights (taken from NIST's slab-to-slab distances for typical floors) and a scale measurement below the center of the rectangle of 5 stories equal to 114 pixels. This measurement is subject to considerable error, about +/- 5 pixels, because of a lot of distortion over the north face, so I'll start with the nominal figure of 0.171 meters per pixel but later investigate 0.163 and 0.178.

Since the first half is questionable and precedes global initiation, I've trimmed off the first 6.5 seconds. This is still not quite enough to make the data only monotonically increasing in the beginning, but it's a good start. Also, the last eight points were not used in the fits to follow.

The intent here is to interpolate, not provide a functional form that has physical meaning. Unlike NIST, I will use two different functions for the first and last half of the dataset, both simpler than their single function. The first 3.5 seconds are fit to an exponential and the interval 2.8 - 4.35 seconds are fit by a 3rd degree polynomial.

f_1(t) = a0 + a1*exp(a2*t)
f_2(t) = a0 + a1*t + a2*t^2 + a3*t^3

The fits obtained are very good:
f_1(t) = -0.0019275 + 0.0024491*exp(1.9909*t)
f_2(t) = -31.025 + 33.588*t - 12.379*t^2 + 1.5785*t^3

The following graph depicts the dataset points as light green dots and the two interpolating functions as darker green solid lines with their first and second derivatives as broken lines. A constant acceleration of g is indicated by a red dash. Note the ranges of the interpolating functions overlap, by design, and we can see the zeroth, first and second derivatives are all matched at 3.15 seconds.


Large: http://i33.tinypic.com/2hy7w9v.png


Shows acceleration exceeding g starting at just after 3.6 seconds. Let's see, we have the following propositions, all found to be true:

1) The mid-roofline smear has a different shape than the NW corner -- shallower
2) The rectangle data closely follows the shape of the mid-roofline, to within small scale factors in time and distance
3) The pair of interpolating functions match the rectangle displacement data very well
4) The velocity and acceleration derived from the interpolations are well behaved and essentially continuous at 3.15s
5) The derived acceleration from interpolation exceeds g substantially


Adding Dr. G's fit function in as a blue line, after translation by 1 meter up and 2.87 seconds later:


Large: http://i37.tinypic.com/6r21wl.png


Not a perfect match, but amazingly close. Paradoxically, the acceleration obtained from this fit is a constant 8.7 m/s^s, as stated. More to come.

Edit: the label for the blue line says 'f(t) = ...' but erroneously shows powers of x.