The 9/11 Forum

David B. Benson wrote:Nope. This is not a zero-G situation.

As I just said: Gravity will assist part C to damage A, but the reaction forces produced by gravity will also assist A to damage C.

In any situation/collision of two object C and A - zero-G (??) or not - you cannot assume (sic) that one part, C!, only suffers 'negligible damages', while A is crushed into small pieces.

OneWhiteEye wrote:
The equivalent is make the lower block go inside the upper. Here, I'd expect exclusive crush-up.


DDB replied: Nope. No (significant) early crush-up.

And that is all that this sort of demonstrator is intended to show.



OWE answered:Ah, then, it makes the experiment all the more interesting, because I believe it will go the other way. Beware experimenter bias !! haha



It will work the other way if the top perimeter slips outside the lower perimeter.

We are seeing that the 2 large perimeter sections leading all others in the fall were from the top section in a different thread.

If the top perimeter sheet falls outside the lower sheet the top floor-to-perimeter connections will be destroyed by the lower sheet. Debris will build inside the tube but large chunks of the perimeter are now broken off from the building altogether and are in freefall.

And this is what we are seeing happen.

Evidently, if the upper part C slips inside lower part A and inside the strong elements (columns) of part A and only encounters weak elements (floors) of part A, then part C will just crush the weak parts/floors and the part A columns will remain. It seems Benson is trying to develop a model to this effect. It proves nothing.
On the other hand, if upper part C slips outside lower part A, the strong elements of part A will destroy the weak elements of part C,&c,

However, the Björkman axiom is:

You cannot crush a structure A by a part C of itself (C = 1/10 A) by dropping part C on A using gravity. Part C either bounces on A or gets damaged in contact with A and is stopped by A that is also damaged a little. It is quite basic and all due to gravity. Materials and particulars of the elements of the structure A doesn't matter the least.

It is applicable to both alternatives above.

Björkman axiom is false in this universe. See Bazant & Verdure or Keith Seffen for an alternative development of a crush-down equation.

Major_Tom --- Not appreciably; what you have discovered, even if correct, agrres with Bazant & Le.

David B. Benson wrote:Major_Tom --- Not appreciably; what you have discovered, even if correct, agrres with Bazant & Le.

Could you elaborate?

OneWhiteEye wrote:Could you elaborate?

Yes, I could, but it would help if you could amplify on what you are wondering about.

David B. Benson wrote:

OneWhiteEye wrote:Could you elaborate?

Yes, I could, but it would help if you could amplify on what you are wondering about.

How does having a large sheet of perimeter wall ripped away from the upper block very early on, and falling outside the lower perimeter, agree with Bazant & Le? (And which paper is B&L? I know BZ, BV, BVreply and BLGB...)

OneWhiteEye B&L = BVreply.

First of all, the BV crush-down equation depends upon four simplifying assumptions, one of which is homogeneity and another is one dimensionality. Neither assumption holds well at the start when the kinetic energy of the moving portion is small. I have no disagreement with Major_Tom about the segment of zone C from the west wall, his analysis seems correct if he can actually identify the blackened portions of the exterior walls. The more recent attempt regarding NE corner could be based at floor 90 just as well as floor 96; a timing analysis might help to distinguish the two possiblities.

I suppose all of this happens with 1.5 seconds of collapse initiation,although I would like some timings! Thereinafter the collapse is closer to "pure" crush down. In any case, B&L indicate the possiblity of some early crush-up and so even having two sections of exterior wall ripped out is only a quite modest portion of zone C. Much the same happens to zone C of your crush-down simulation.

David B. Benson wrote:OneWhiteEye B&L = BVreply.

Thanks for clearing that up. Let me think on what you've said.

Regarding the east and west perimeters of WTC1.

Upper goes into lower, with most of the perimeter tucked inside. Does the upper get squeezed, the lower expanded, or both? At least 14 inches (?) total needs to be accounted for.

OneWhiteEye wrote:Regarding the east and west perimeters of WTC1.

Upper goes into lower, with most of the perimeter tucked inside. Does the upper get squeezed, the lower expanded, or both? At least 14 inches (?) total needs to be accounted for.

From Major_Tom's work, it looks like much of both east and west zone A perimeter walls simply fell off. This suggests that the remaining portions were pulled outwards, enabling zone C to fit into zone A.

The Sauret video offers a high resolution view of the NE and NW corners, and a bit of the E wall plane. It doesn't look like there's any accommodation of the rather significant intrusion the upper block (in its entirety) would represent. While I can certainly imagine the S wall tucking in and forcing out the lower perimeter all the way down, and I can accept the idea the N wall might end up inside, the E and W are a bit more of a problem. By the way, it still appears to me the NW corner and lower tip of the N wall go outside, the corner being sheared off early.

There are other things. I haven't brought it up yet but recently released videos, plus a closer examination of the old ones, reveal a greater percentage and height of core remaining after the crush passes than previously believed. And, the severe angle of the antenna mast - either something jarred it off early or the (bigger than believed) spire punched as much through the N wall as the hat truss.

Put that together with Major_Tom's recent work. The suggestion is a fairly entangled arrangement, like clasped hands, at the very least. While it's true the perimeter piece in question is a minor portion of the upper block, it removes substantial integrity from the upper block. It's another point towards the argument that debris in a chute more accurately characterizes the propagation than a rigid upper block riding a debris zone B.

That doesn't detract from the model assuming 1D, homogeneity, and dynamic equilibrium in accord with d'Alembert's principle. But there's no reason in my mind a non-equilibrium system formulation, say from fluid mechanics and using rubble instead of a rigid block, would give a solutions that differ much. Does your avalanche form require a rigid body upstairs through a drop of more than 0.5m?

Heiwa wrote:You cannot crush a structure A by a part C of itself (C = 1/10 A) by dropping part C on A using gravity. Part C either bounces on A or gets damaged in contact with A and is stopped by A that is also damaged a little.

In my domino system, an upper block destroyed a lower block 9x bigger, in a variety of circumstances. What about these simulations, in your opinion, fails to capture physical reality accurately? I showed a zero-g case where damage was equivalent. Does this one seem realistic to you? If so, and knowing the difference was absence of uniform force field, why do you suppose one result is realistic and the other not?

As I mentioned, there are results I haven't posted. Such as equal crush up/down and total arrest, even bounce, all under gravitational force. These correspond very well to what you're asserting. If you are correct, those sims are also correct. Why are these correct and not the ones that correspond to what Dr. Benson asserts? Is it merely random happenstance and all the sims are worthless, except twice a day - like a broken clock?

Just curious.

Very nice work, Mr. Eye. Awesome is an understatement.
One question: in your gravity-driven model, with the 2 stories falling (a page or so back), what is it in your engine that creates the off-centeredness (or flip-flopping) that occurs early on? I can see this happening in reality, where no parts are truly identical and alignments cannot ever be perfect, but what causes this in your simulations? Some random imperfection inserted as directed by you?

Un-hyphenated wrote:Very nice work, Mr. Eye. Awesome is an understatement.

Thank you very much.

One question: in your gravity-driven model, with the 2 stories falling (a page or so back), what is it in your engine that creates the off-centeredness (or flip-flopping) that occurs early on?

Very good question. Short answer, I don't know. I'd guess the usual suspects, in combinations: floating point error, order of evaluation, sensitivity to initial conditions and dealing with singularities like edges and vertices. The engine I have uses 32-bit floats so will be susceptible to even a small error accumulation at the beginning, when things are most sensitive. Moreover, floating point numbers leave 'holes' in the number line within their range, not all decimal numbers are represented. Most numerical simulations suffer from these things to one degree or another. Exact precision math mitigates some, not all, of the problems but is slow and not widely employed.

Consider the difference between this and writing a program to compute the values from Greening's ET paper then render them in graphic format in an animation. If that were the case, all of the slabs would always stay lined up, nothing would go off-axis or rotate. At the completion of the collapse, there would be a neat stack of motionless slabs, perfectly aligned. Most important, the collapse would proceed according to the assumptions dictated by the model and represent the solution over time - to within the floating point error of a single step (negligible).

In contrast to an animated visualization of solutions to specific equations, a general simulation will attempt to construct dynamic evolution according to a set of rules and formulae independent of any particular configuration, e.g, identical slabs stacked on one another.* These are configuration details that are provided as input. If the input matches some real physical system, if the simulator is accurate and simulation appropriate in scope, the results should resemble the behavior of the physical system. But it will only resemble, not match. Whether the top falls off this way or that doesn't matter so much as whether or not it falls, which doesn't matter as much as total collapse time, etc.

Some random imperfection inserted as directed by you?

This is a way to average the differences in runs due to sensitivity. Since an object cannot be sized, massed, or placed with perfect precision, a little random variation about the target value can give solutions in a neighborhood, each equally valid. Haven't done it yet.

I can see this happening in reality, where no parts are truly identical and alignments cannot ever be perfect.

So now you see that, in a peculiar way, it is like reality because things are not perfect in this world, either. What's interesting are the non-repeatable runs. Simple stacks like the 20 story jobs are mostly repeatable, down to the distribution of pieces on the final pile. The more complex ones, like some 110 story structures, are not always repeatable. In one case, back to back runs, the first acquired a small early tilt and crushed up 7 of the 10 upper stories simultaneous with crush down. The second run maintained better alignment and only crushed up 2 stories. The displacements differed a fair bit, but the collapses (total) finished 1/10th second apart, out of a total duration of over 9 seconds. In one way, they were very similar; in another, radically different.

Hope that wasn't too much answer.


* [edit] another example: a tipping pencil would stand forever on its point in a perfect simulation. See http://www.mathpages.com/home/kmath259/kmath259.htm, especially towards the bottom

On the other hand, if we imagine that the initial pencil position is just theta_0 = 10^-100 degrees, then the time to tip over is 27.469838205... seconds.

This idealized pencil would take 1 year = 31557600 seconds to tip over (theoretically) if its initial stationary position is theta_0 = 10^-117498396 degrees from vertical.

This explains why anything in my sims that will tip, does so within about 27 seconds!