The 9/11 Forum

OK, another check of scaling. In my copy of the CBS video, frame 260 is the approximate time at which the roofline begins to descend visibly. At about frame 290, a second later, the NW corner begins to drop in a similar fashion. At a time 3.8 seconds later, that would be frames 374 and 414.

These are the four frames:

F260 - http://i38.tinypic.com/ra7t47.png
F290 - http://i38.tinypic.com/2jb7fo0.png
F374 - http://i38.tinypic.com/21b6mmg.png
F414 - http://i35.tinypic.com/vo62w0.png

No need to make measurements on frame 414 because, by this time, the building has disappeared from view.

Code: Select all

NW corner vertical position and delta in pixels
F260   13   --
F290   14   1
F374   272   259


Roofline just to left of kink vertical position in pixels
F260   86   --
F290   94   8
F374   326   240


Just these quick manual measurements are pretty interesting. The NW corner starts a second later than the other roofline point, but ends up moving farther! This might have something to do with the discrepancy.

But, continuing on, time to do (regular) floor height measurements.

Close to NW corner horizontal position: 6 stories is 136 pixels => 22.7 pixels per story
At roofline point horizontal position: 6 stories is 130 pixels => 21.7 pixels per story

The total travel for both points in story units and meters, assuming 3.96m/story, is then:

NW corner = 11.4 stories => 45.1m
Roofline = 11.1 stories => 44.0m

Even less than 52 meters... obviously there is a problem with the scaling! I will figure out what it is and let you know.

Dr. G:

Going back to einsteen's data, which he scaled based on smaller story heights from a 174m total, the values at 0.7 seconds and the end of data are:

0.7, 3.194
4.26, 60.20

giving a difference of about 57m. Correlating to my copy of the video, the end of travel for the NW corner is about frame 390. The position at that time is 372 pixels, giving a difference of 359 px ~ 15.8 stories = 62.6m or 58.5m depending on floor height of 3.96 or 3.7. Close enough, since his video is a different frame rate. And the 62.6m figure matches with my scaling up of einsteen's original data.

The displacements, then, are well within reason. It really did move that distance in that amount of time. What then can be the problem? I suggest it may be the choice of t0, as well as some of the relative timing involved between the two videos, my offsetting and NIST's timeline.

While extrapolating the scaled einsteen curve on my graphs would have the displacement at 3.8 seconds be about 72 meters, the true time from the beginning of einsteen's video would be 4.6 seconds, and there's only 4.26s of data. Taking a different approach, I could find the point where 52m of displacement has occurred and subtract 3.8 seconds from that. This occurs at just under 4.0 seconds after the start of einsteen's video, so the t(0) you're working with must be around 0.2 seconds into it. That's a half second before the NW corner really starts moving and about a half second after the roofline's initial descent.

The curves you have plotted show a drop of about 72 meters at 3.8 seconds in which case the average acceleration is very close to 10 m/s^2 or a tad greater than g.

The problem remains, because now this motion is verified - but only in story height units. It seems to me that 3.96m/story could be too large; though it wouldn't trim much off, it could put it under g. Also, the rest of the roofline is substantially slower than the NW corner, so it's important to keep their respective start times distinct. Beyond that, I have no good explanation.

The rest of the building was moving down for a second before the west face yielded and began its descent. I've avoided suggesting that the rest of the building dragged it down as an entrainment phenomena, because that sounds absurd. Imagine the beams as bungee cords and you'll get the idea: some resistance but some assistance, too. Not something one expects from a building that's disassembling rapidly, but it's a thought.

Naw.

OneWhiteEye wrote:It will take some visuals to support my position but the manner in which the top deforms just prior to the NW corner descent suggests there is no structural integrity left by that time...

Here is the visual to support the idea that it's a rectangular-ish pile of debris by the time the NW corner starts dropping:



It's a difference between frames 260 and 295, a little over a second apart. The later frame is in red underneath the earlier frame in black. If there was no motion, you'd only see red where some of the smoke has been picked up by the mask. Instead, you see a lot of red.

The left side has moved to the left and dropped a little, but the middle has dropped a lot. You can see the sag is less at the two ends. Not only is the roofline sagging but the whole face is too except for the west side, where the red is seen to curve up and join the black, indicating no motion. It's broken completely, though I'd not claim it's an empty shell, not at all.

OneWhiteEye:

Nice work indeed!

Yes, I suspect the selection of t(0) is the problem - always has been! Thus I don't think we need to worry about the floor height,- I believe 3.96 meters is probably pretty accurate.

The sagging of the middle of the building is very interesting and you may be onto something with its influence on the drop of the NW corner. Perhaps the NW side of the building was relatively undamaged and resisted the collapse to the very end. When the NW corner finally gave up the ghost it was quite literally pulled down by the center section. (So Silverstein was right after all: WTC 7 was "pulled"!!!) The pulling action on the west side could give an initial drop acceleration to the NW corner that was faster than free fall for the first 1 - 2 seconds of the collapse, but the interplay of forces would cause the NW corner to quickly "catch up" with the center section which was slowed a little in the process. Eventually, say after 3 seconds, the roofline would be falling more or less horizontally.

One other very interesting observation is the motion of the NE edge of the north facade -it moves a considerable distance to the east during the collapse, (i.e. to the left in the Camera 3 video images). This motion gives the illusion of the building stretching horizontally during its descent because the NW edge does not show an equivalent shift! I suspect this effect is caused by the NE side of the building tipping towards the camera as it fell, ..... remember, the Camera 3 (CBS) footage was taken from a location that was about 38 degrees off perpendicilar to the north face.

Edited to add:

I just realized that NIST has a series of images showing the motion of the NE edge of WTC 7 in its Draft Report on page 279 of NCSTAR 1-9.

To all readers of this particular thread may I recommend that you take a look at C. M. Beck's paper on the collapse of WTC 7 available at:

http://arxiv.org/abs/0806.4792

This link actually takes you to the abstract but you can find a pdf of the full paper there too.

I have not finished studying this paper but I already have a few comments:

(i) The paper actually exists in three versions all of which may be accessed at the arXiv site. The first version is dated Jun 29, 2008; the second version was issued on Jul 20, 2008, and the third version is very recent - Oct 23, 2008.

(ii) The paper uses collapse data taken from the 911research.wtc.net website. Interestingly this gives a drop of 51.94 meters at a time of 4.0 seconds. I recently posted some of my "best" WTC 7 collapse curve estimates which included a drop distance of 52 meters at 3.8 seconds.

(ii) Beck concludes from the 911research data set that the collapse was faster than g at the very start of the motion. However, he offers a theory that is very similar to the ideas that have been kicked around on this thread over the last couple of days, namely that the outer frame of the building was initially pulled down by an inner "core" section which began to fall before the rest of the building. This leads to the possibility of an initial collapse acceleration greater than g.

(ii) Beck's explanation for this behavior is that the vertical columns were "eliminated" in the middle part of the inner core at a height of ~ 21 meters. He is very cautious in how he says this, but it's pretty clear he's talking about a controlled demolition!

strange, greater than G?
how can that be?
doesnt have the "core" that seem to pull down the rest of the building, have to be faster than G in order to pull down the rest faster than G?

This leads to the possibility of an initial collapse acceleration greater than g.

Not sure how.

The key phrase seems to be "pulled down". If pulled down by yet another falling object it wouldn't lead to faster than g.

Illusion of of the mind is to think that an object is falling near g and is being "pulled down" by yet more downward force, leading to possibly of faster than g acceleration.

What he really means is that the objects are still somewhat attached. If the piece is viewed as a whole, It is just 2 loosely coupled objects (pulling object and pulled) falling together at ....g or less..


Can't make a local acceleration greater than g unless forces external to the collapsing objects as a whole is applied.

(Like a massive underpressure created by an external source (thermobaric bombs, for instance) that gives some extra pulling.)

Some external source.

I know it sounds crazy but, before we call the men in white coats, hear me out. I don't really have a detailed mechanism for this but I hope to show you how I believe it is possible in principle. First, I hope I was kind to you, Major_Tom, when you first inquired about faster than g; if not, I may have a come uppance due.

Can't make a local acceleration greater than g unless forces external to the collapsing objects as a whole is applied.

Exactly. It was the business of determining the initial velocity and trying to sort out the scaling problem when I realized the following:

1) The bulk of the mass begins dropping a second before the NW corner which is the location of the measurements
2) The upper block is not rigid; in fact, there's stuff falling down in the center independently
3) All the stuff that's dropping in advance of the NW corner has got a chance to get speed up before the initial descent of the corner
4) That means, in some sense, we are talking about multiple bodies, so bodies distinct from the NW corner are indeed external
5) If sufficient sustained but brief force, or even an impulse, can be transmitted by the already moving mass to the mass of the NW corner, it can give it an additional downward kick
6) While I can't elaborate a means, I cannot in principle rule it out

Think of the normal, vertical pancake progressive collapse. Upper floors impacting lower floors provide an impulse such that the result of the collision is a non-zero initial velocity for the newly entrained floor. The difference here is the horizontal nature of the propagation. Imagine you are standing on a beam supported at both ends and a load, sufficient to easily break the supports, is dropped from a small height. The beam flexes, the supports break, and they displace downward faster than g. If you are glued to the beam (you are the relatively light NW corner), you drop faster than g, too, for a short bit.

OneWhiteEye, Daniel & Major Tom:

Have you all read Charles Beck's paper? So we are at least "on the same page"......

Beck considers WTC 7 as two masses - one mass is the building's core that is no longer supported at its base, (the columns have been blown out!), the other mass is the building's outer frame - still connected to the top of the core by an imaginary spring, (See his Figure 7). Suppose the core mass is oscillating, sometimes pulling down on the inside of the top of the frame, but the frame is able to resist - perhaps it just bows a little. Now suppose that the frame fails near its base at the same moment that the spring is fully extended. What would be the motion of the frame?

Dr. G

yes i did read it, it is interesting, but falling objects that fall faster than G are confusing me.

but i am propably just close minded in that aspect

5) If sufficient sustained but brief force, or even an impulse, can be transmitted by the already moving mass to the mass of the NW corner, it can give it an additional downward kick

I mean external to the entire structural system of the building.

There is a way to have momentary local accelerarations faster than g. If you consider this movement as OHE describes as "2 parts , 2 bodies of the same building", the initial movement of 1 without the other may create a type of spring via the coupling between the 2 parts.

The initial movement would put tension in the spring (a stored potential energy).

These internal "stretched springs" actually increase the momentary PE of the building as a whole. It is not merely gravitational potential energy but "tense spring" PE as well.

At any local point like the NW corner (perfect candidate, actually), it is subject the acceleration of falling and a momentary additional acceleration by the downwardly directed tense string.

Hence a can be >g locally and temporarily. ???

Major_Tom wrote:I mean external to the entire structural system of the building.

I know you did, but I wanted to get you thinking inside the box, so to speak, to the internal degrees of freedom of this non-rigid body.

There is a way to have momentary local accelerarations faster than g.
...
Hence a can be >g locally and temporarily. ???

Yes! That's it in a nutshell. The only problem I have is how such potential energy to accelerate even one face can be stored in a relatively intact structure, let alone one that's breaking apart. The roofline may look a like a giant downward pointing crossbow, but I wouldn't carry the analogy too far. You and Dr. G are both talking about modes of oscillation, a different and probably better thing than my multibody internal collision and entrainment scenario.

Edit: Dr. G's reference to the seismic effects studies does suggest that even a disintegrating building can transmit some high amplitude waves...

OK, I've read it. Pretty impressive on the first pass, actually. Following along with the mathematical specifics, on the much slower second pass, will come later. I doubt I'll ever be able to evaluate the structural engineering components.

Quick observations:

- His choice of parameterization of the resistive force may be open for debate

- A quantitative comparison with crush down of the lower block could be done to see if it differs from his free-fall phase by a magnitude exceeding the error range; his treatment appears to appeal to qualitative arguments exclusively

- I'd mused out loud lately about whether the crush-up equations had properly accounted for the pile-up of debris at the bottom, leading to an upward displacement of the crush zone over time. As best I can tell, Beck claims that the equations did not account for it and the introduction of his kappa term does so. Correct me if I'm wrong, please.

- But then, later, when he goes to solve, he sets kappa to zero for simplicity! (not that I blame him)

- He treats the upper motion as a rigid unit in 1D whereas we know it to be differential and complex; specifically he states there was no prior motion to that recorded in the data he uses- that would only be true if the data came from the center roofline and I'm betting it didn't

- I want to examine his fitting method more closely; as we know, we've seen plenty of sensitivity to even the most minor tweaking and he has a paucity of data to work with

- He use a 12ft floor height with his data

- More and better data would only help clarify everything

I find this section hand-wavey at best:

Beck wrote:Next few seconds is the period over which “additional columns buckle,” which we translate at that the top section slows down considerably - in few, say two, seconds it does not cover more than a fraction, say 1/2, of the 12th floor.

We thus have a sequence: possible crawl (failure of the named column) followed by a free fall, both together for 1 floor height, duration of which is at most
t = p2
H/g = 0.86 s. This is followed by a 2-seconds crawl at velocity v ≃ 0.5 ·
H/(2 s)) = 1 m/s. In total, after 3 s of fall the top section may have moved at most floor and a half, ∼ 6 m.

As I stated above, I'm not sure a crush down or simultaneous crush up/down involving the lower section would produce much retardation of displacement from freefall. This is the 'wham' thing all over again; if it's not expected for WTC1 or 2 then I can't imagine it would be for WTC7 with a much larger initial block (that also appears to be disintegrating).

All in all, though, much food for thought. I like his treatment of the momentary excesses of g; I think I may owe some people a note of conciliation. Maybe.

I still want better data.

Daniel:

Let's take the mass of the core to be Mc and the mass of the frame to be Mf. Let's assume the core is disconnected from the ground and is pulling down on the inside of the frame with a spring force kx. This means it is displaced from its equilibrium position by a vertical distance x. The downward force acting on the frame is (Mf + Mc).g + kx which must be balanced by an equal and opposite reaction force to keep the building standing.

Now, suppose the frame suddenly fails at its base so the reaction force -> 0. The new net force acting on the frame is now:

F = (Mf + Mc)g + kx = (Mc + Mf).a

Hence a = g + kx/(Mc + Mf) which is greater than g!

Does this help?

P.S. Not quite a derivation of Beck's equation 21 unfortunately .....but getting there!

The man is a real pro of course, but first of all is it not the data that matters? To start with a table of values from wtc7.net is great but if that is not reproducible, etc we cannot conclude it fell with more than g. As we have seen here there are very much things involved with determining a good a(t). I've not read it (maybe later...) but a faster than g acceleration is for example possible by momentum transfer, when a wtc1,2 floor is detached by the falling mass that floor will also accelerate faster than g a small time interval.. If the inward structure of wtc7 failed first then that is in fact a same kind of effect.