The 9/11 Forum

From features manually extracted by OneWhiteEye from the Sauret DVD video and using iterative improvement from a formula suggested by Dr. G the following angles (b01) and feature displacements were computed. (Roof means the northwest corner feature.)

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Improved angles and displacements (x is to the south, z is drop)
0: roof
1: upper right dish

frame time after formal start: angle (degrees) displacements (meters)
800 t= -3.637 b01=  0.000 xz0=(0.000, -0.000) xz1=(0.000,  0.000)
900 t= -0.300 b01=  0.360 xz0=(0.344, -0.277) xz1=(0.471, -0.081)
910 t=  0.033 b01=  0.547 xz0=(0.523, -0.168) xz1=(0.716,  0.131)
920 t=  0.367 b01=  0.913 xz0=(0.872, -0.177) xz1=(1.190,  0.324)
930 t=  0.701 b01=  1.647 xz0=(1.565,  0.111) xz1=(2.129,  1.027)
940 t=  1.034 b01=  3.381 xz0=(3.194,  0.477) xz1=(4.292,  2.402)
950 t=  1.368 b01=  3.937 xz0=(3.581,  2.501) xz1=(4.837,  4.758)
960 t=  1.702 b01=  5.391 xz0=(4.704,  4.701) xz1=(6.343,  7.845)
970 t=  2.035 b01=  6.091 xz0=(4.916,  8.475) xz1=(6.723, 12.051)
980 t=  2.369 b01=  6.657 xz0=(4.830, 13.156) xz1=(6.765, 17.086)
985 t=  2.536 b01=  7.310 xz0=(4.994, 15.607) xz1=(7.069, 19.947)
990 t=  2.703 b01=  8.797 xz0=(5.755, 17.348) xz1=(8.112, 22.629)
995 t=  2.870 b01=  7.427 xz0=(4.304, 21.528) xz1=(6.402, 25.942)

Sme discussion of error: The feature extraction ought to be good to well within a decimeter, but OneWhiteEye will undoubtedly have more to say about that. In these computations, the assumption is that the upper portion of WTC 1 and its antenna mast were perfectly vertical at frame 800; probably not reality. Another assumption is that the tilt is due to rotation about a perfect hinge on the north wall at floor 98.
Determining such small angles with great accuracy is quite difficult; despite all the decimal places, these angles might be within +-0.1 degrees of arc. This then places limitations on the accuracy of the displacements.

Having stated all that, it is perfectly possible that north wall of WTC 1 did undergo some small negative drop. This also might be true of the antenna mast if in frmae 800 it was still leaning slightly to the north. Such very small angles can (approximately) simply be linearly added to the angles computed and listed above.

DBB:

Yes, that is very interesting data. I still have some questions about the vertical calibration though.

Also, is the maximum in the tilt at 2.7 seconds, ( frame 990), real or an artefact?

Dr. G wrote:I still have some questions about the vertical calibration though.

Ask away.

The xz0 values are the displacements of the northwest corner of the roof from the frame 800 positions.
The xz1 values are the displacements of the upper right dish from the frame 800 positions.

Also, is the maximum in the tilt at 2.7 seconds, ( frame 990), real or an artefact?

Without either extending this series (very hard) or some form of analysis of variance I cannot begin to say. I'm concerned enough about the accuracy of these values to consider doing the latter.

DBB:

I have used OWE's data for the dark band on the antenna to estimate the tilt angle from 0 - 3 seconds and I do NOT see any sign of the tilt passing through a maximum.

Error estimates:

The angles were computed 6 times per frame. For the bottom measurement both the northwest corner and the washer (window washing apparatus) were used. For the top measurement both the upper center and upper right dishes were used as well as the dark band. Here are the averages and standard deviations, both in degrees of arc:

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Angle difference statistics:
800 t= -3.637: mean=  0.000 sigma=  0.000
900 t= -0.300: mean=  0.406 sigma=  0.289
910 t=  0.033: mean=  0.676 sigma=  0.104
920 t=  0.367: mean=  1.153 sigma=  0.174
930 t=  0.701: mean=  1.648 sigma=  0.311
940 t=  1.034: mean=  2.842 sigma=  0.578
950 t=  1.368: mean=  3.897 sigma=  0.095
960 t=  1.702: mean=  4.997 sigma=  0.284
970 t=  2.035: mean=  5.945 sigma=  0.095
980 t=  2.369: mean=  6.642 sigma=  0.215
985 t=  2.536: mean=  7.380 sigma=  0.551
990 t=  2.703: mean=  8.466 sigma=  0.353
995 t=  2.870: mean=  8.347 sigma=  1.078

DBB:

Here is my latest time vs. tilt data for WTC 1:

Time(s); Tilt(deg)
0.33; 0.68
0.67; 1.52
1.00; 1.90
1.33; 2.70
1.67; 4.43
2.00; 5.30
2.33; 6.54
2.67; 7.11
2.83; 7.86
3.00; 8.72
3.17; 9.62
3.33; 10.44

Dr. G wrote:DBB:

Here is my latest time vs. tilt data for WTC 1:

Time(s); Tilt(deg)
0.33; 0.68
0.67; 1.52
1.00; 1.90
1.33; 2.70
1.67; 4.43
2.00; 5.30
2.33; 6.54
2.67; 7.11
2.83; 7.86
3.00; 8.72
3.17; 9.62
3.33; 10.44

Hm, during 3.33 seconds of crush down, >50 meters of WTC 1 below floor 97 should have disappeared, viz become a 12 meters rubble layer of what was 13/14 storeys of structure 3.3 seconds before, according to your BLGB paper. Any sign of that on the videos?

Heiwa --- That's off-topic on this thread, but yup.

Using a different algorithm based on the assumption that the north wall of WTC 1 is hinged at floor098, which then drops without translation, rather larger angles are obtained:

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Geom angles
0: roof   0': washer
1: upper right dish   1': upper center dish
2: dark band

frame: angles (degrees)
800 b01= 0.000 b01'= 0.000 b0'1= 0.000 b0'1'= 0.000 b02= 0.000 b0'2= 0.000
900 b01= 0.728 b01'= 1.071 b0'1= 0.408 b0'1'= 0.408 b02= 1.800 b0'2= 1.185
910 b01= 1.077 b01'= 1.305 b0'1= 1.342 b0'1'= 1.342 b02= 1.688 b0'2= 1.771
920 b01= 1.736 b01'= 2.248 b0'1= 2.234 b0'1'= 2.234 b02= 2.689 b0'2= 2.745
930 b01= 2.921 b01'= 3.396 b0'1= 2.538 b0'1'= 2.538 b02= 4.123 b0'2= 3.297
940 b01= 5.316 b01'= 5.433 b0'1= 3.625 b0'1'= 3.625 b02= 6.291 b0'2= 4.435
950 b01= 5.993 b01'= 6.163 b0'1= 5.303 b0'1'= 5.303 b02= 7.332 b0'2= 6.617
960 b01= 7.658 b01'= 7.571 b0'1= 6.244 b0'1'= 6.244 b02= 8.973 b0'2= 7.706
970 b01= 8.513 b01'= 8.513 b0'1= 7.409 b0'1'= 7.409 b02=10.238 b0'2= 9.263
980 b01= 9.215 b01'= 9.346 b0'1= 8.543 b0'1'= 8.543 b02=10.770 b0'2=10.076
985 b01=10.027 b01'= 9.662 b0'1= 9.503 b0'1'= 9.503 b02=11.360 b0'2=11.318
990 b01=11.696 b01'=11.665 b0'1=10.464 b0'1'=10.464 b02=13.387 b0'2=12.307
995 b01=10.279 b01'=10.583 b0'1=11.685 b0'1'=11.685 b02=12.039 b0'2=13.516

Note the general tendency for the higher of 1, then 1', then 2 to have larger angles. This might be especially noticable after 2.2 seconds, when the visable guy wire snaped. At that point the antenna mast was certainly free to flex.
No, b0'1 and b0'1' are not duplicates! I checked this for the first algorithm and the values are not precisely equal as long floating point numbers. It just appears, so far, to be a remarkable coincidence.

The statistics also demonstrate that the angles are quite varied depending upon the measured features used for the lower and upper points.

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Angle difference statistics:
800 t= -3.637: mean  0.000 sigma=  0.000
900 t= -0.300: mean  0.866 sigma=  0.631
910 t=  0.033: mean  1.383 sigma=  0.289
920 t=  0.367: mean  2.233 sigma=  0.437
930 t=  0.701: mean  3.056 sigma=  0.720
940 t=  1.034: mean  4.768 sigma=  1.101
950 t=  1.368: mean  6.088 sigma=  0.825
960 t=  1.702: mean  7.409 sigma=  1.020
970 t=  2.035: mean  8.553 sigma=  1.098
980 t=  2.369: mean  9.393 sigma=  0.905
985 t=  2.536: mean 10.273 sigma=  0.843
990 t=  2.703: mean 11.670 sigma=  1.112
995 t=  2.870: mean 11.584 sigma=  1.157

femr2 ---- From OneWhiteEye's earlier data, maybe posted on the WTC 1 collapse initiation thread, it is clear that the W->E of the antenna mast is so small as to be neglected for at least my purposes. This agrees with NIST's assessment in NCSTAR1--6D of no observed tilt to the east..
Dr. G and I are just considering the fairly substantial tilt to the south.

femr2 --- I'm satisfied I can stop at frame 995, OneWhiteEye's data goes on much longer. Go check it to confirm that W->E is insignificant. For example the dark band only moves 2.3 pixels to the east at frame 980 relative to frame 800. That's less than 0.575 meters, not worth my considering.

Even the Sauret video, not shot from exactly due north, can be visually misleading. Measure pixels and correct for perspective.