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David B. Benson
QUOTE (Chainsaw,+Dec 4 2007, 07:24 AM)
Does not matter it is Fe304 from oxygen cutting of steel not molten Iron or molten steel easy to tell the difference.

Right. For you it is easy. But it helps explain reports of pools of molten steel on the part of non-experts.
David B. Benson
Here is the correct results for naive Bayesian factor comparisons of the hypotheses using just pixel column line 447. Several more hypotheses are disconfirmed because the best hypotheses have such a small standard deviation, despite having only about 1/3 of the data. (This wasn't what I expected.)

CODE

BV-Z+ZS+SS-F-pow-stretch  dB= 0.0 sd= 0.076

BV-Z+ZS-F-pow-stretch     dB= 0.0 sd= 0.075
BV-Z+linZS-F-pow-stretch  dB= 0.0 sd= 0.075
BV-lin-F-sq-stretch       dB= 0.2 sd= 0.083
BV-sq-F-sq-stretch        dB= 0.6 sd= 0.091
BV-sq-F-lin-stretch       dB= 0.7 sd= 0.098
BV-Z+ZS-F-exp-stretch     dB= 0.8 sd= 0.098
Sef-Z+ZS+SS-F-pow-stretch dB= 0.9 sd= 0.104
Sef-Z+ZS-F-exp-stretch    dB= 1.2 sd= 0.110
BV-Z+SS-F-exp-stretch     dB= 1.3 sd= 0.113
BV-s-F-s-stretch          dB= 1.8 sd= 0.124
Sef-Z+linZS-F-pow-stretch dB= 2.5 sd= 0.144
BV-s-F-sq-stretch         dB= 2.8 sd= 0.143
Sef-Z+ZS-F-pow-stretch    dB= 3.0 sd= 0.152
BV-Z+ZS+SS-F-exp-stretch  dB= 3.0 sd= 0.152
Sef-Z+SS-F-exp-stretch    dB= 3.1 sd= 0.149
BV-s-F-funny-exp-stretch  dB= 3.7 sd= 0.162
BV-lin-F-lin-stretch      dB= 5.2 sd= 0.190
BV-const-F-sq-stretch     dB= 5.3 sd= 0.197
Sef-Z+ZS+SS-F-exp-stretch dB= 6.7 sd= 0.207
BV-const-F-lin-stretch    dB= 9.5 sd= 0.244
BV-lin-F-const-stretch    dB=32.9 sd= 0.453
const-acc-no-stretch      dB=57.3 sd= 0.604
mB-const-F-no-stretch     dB=74.3 sd= 0.678
BV-const-F-stretch0.14    dB=140.6 sd= 0.899
BV-const-F-stretch0.18    dB=140.7 sd= 0.898
BV-const-F-no-stretch     dB=143.3 sd= 0.914
David B. Benson
But the ground is not flat. So 1560 m north of WTC 1 the ground might be either higher (more likely) or lower (less likely). So my assumption of the camera being 1.25 m above the ground of WTC 1 seems a bit dubious.

Is there a better estimate to use?
Chainsaw,
QUOTE (David B. Benson+Dec 4 2007, 06:22 PM)
Right. For you it is easy. But it helps explain reports of pools of molten steel on the part of non-experts.

Other processes though were undoubtedly at play, there is no doubt that chemical reactions would also cause molten metals in that situation that would also be mistaken for molten steel.

http://www.sciencedirect.com/science?_ob=A...f96c0fd10477159

Interestingly I have found that a lot of materials could have been mistaken for molten metals simply because they can glow.

I have even found that supersonic sound waves generated in the collapse can cause compression wave fronts in air insiting combustion events of hot fuels as the air releases heat as it is being compressed in front of the wave.
This can increase the heat value of the reaction considerably, however I lack the materials and funds to study it any futher until I have a better way of generating the supersonic wave fronts.

Fe 304 is likely to be just one of the materials mistaken for molten steel, however it is not the only one.
David B. Benson
Here is the code for the perspective corrections I have made, which assumes a fixed vertical angle per pixel over the entire camera range. It seems to work very well, but I will certainly listen to altenatives.

CODE

val pixelCount18Stories = 258.67
val roofLine = 417.0 and roofEdge2AntennaTower = 31.0 and darkBandElevation = 27.0
val cameraDistance = 1560.0 and cameraHeight = 1.25
val roofLineLessCameraHeight = roofLine - cameraHeight
val floor106Height = roofLine - WtcUtil.feet2meters(WtcUtil.floor2dropFeet(106.0))
val floor088Height = roofLine - WtcUtil.feet2meters(WtcUtil.floor2dropFeet(106.0-18.0))
val scale = (hypotenuse+roofEdge2AntennaTower)*Math.sin(darkBandAngle)/(roofLineLessCameraHeight+darkBandElevation)
fun metersDrop pixels =
let
val upAngle = darkBandAngle - radians
in
scale*(roofLine+darkBandElevation-cameraHeight-heightMeters)
end

metamars
QUOTE (metamars+Dec 4 2007, 01:06 AM)

Figure 2 in this paper plots both compressive strain vs. time, as well as bending vs. time (stacking the graphs so that their time axes match up.)

http://metamars.i8.com/arigurstrainvstime.JPG

If you click on it, it will render more clearly.

I'm not sure that I understand the bending vs. time graph. Apparently, about 1/4 m sec after the peak compressive impulse passes, the bending strain hits it's first extremum. It then oscillates around 0 bending stress, I would guess due to a "whipsaw" effect that comes from elastic loading in the transverse direction.

If this interpretation is correct, then it implies (I think) that energy is being dissipated in plastic deformation not only downwards, but upwards, also, with the net deflection being downwards.

I would further guess that, in the regime tested, there is almost as much energy dissipated in the 'down-stroke' plastic deformation stages as in the 'up-stroke' plastic deformation stages.

All other things being equal, I would therefore guess that this will almost quadruple the energy sink associated with plastic deformation in the dynamic regime studied, vs. the quasi-static deformation assumed to occur performed during the "usual" calculations as implied by Bazant Zhou and carried out by Newton's Bit (on JREF).

Can anybody enlighten us as to the correct interpretation of the bending vs. time graph?

Sorry, the hotlink above won't work. The following web page will serve up the graphic.

http://metamars.i8.com/index.html
einsteen
QUOTE (David B. Benson+Dec 4 2007, 09:58 PM)
Here is the code for the perspective corrections I have made, which assumes a fixed vertical angle per pixel over the entire camera range. It seems to work very well, but I will certainly listen to altenatives.

CODE

some code

That's impressive. Do you already have conclusions about how it affects the data ?
OneWhiteEye
Intriguing results, for sure. I've many comments but unfortunately I'm going to be tied up with another matter for a while.
metamars
Kevin Ryan of STJ911 on Ryan Mackey's work:

http://journalof911studies.com/letters/b/MackeyLetter

einsteen
QUOTE (metamars+Dec 5 2007, 06:17 PM)
Kevin Ryan of STJ911 on Ryan Mackey's work:

http://journalof911studies.com/letters/b/MackeyLetter

thanks, I saw that post elsewhere, but to read something like this you first have to struggle through MacKey's work (sometimes I think I spend too much time at subjects that are totally irrelevant for my personal life, but what about that guy!) but also then first through DRG's stuff. I've heard about the latter but never read a book or something, I already know that 911 is a product of improbabilities
David B. Benson
QUOTE (einsteen+Dec 5 2007, 04:50 AM)
Do you already have conclusions about how it affects the data ?

Yes. Here are the results for just the not-previously-disconfirmed hypotheses using a slightly improved version of the scaling. (The improved code will be posted separately.)

CODE

darkBandAngle=0.271416839851  Antenna tower scale factor=1.0
meters per foot =0.3048012
zeroTime=3.91991058736

BV-Z+linZS-F-pow-stretch  dB= 0.0 sd= 0.081

BV-Z+ZS-F-pow-stretch     dB= 0.0 sd= 0.080
BV-Z+ZS+SS-F-pow-stretch  dB= 0.1 sd= 0.085
BV-lin-F-sq-stretch       dB= 0.5 sd= 0.098
Sef-Z+ZS-F-exp-stretch    dB= 0.6 sd= 0.102
BV-Z+ZS-F-exp-stretch     dB= 0.7 sd= 0.101
Sef-Z+ZS+SS-F-pow-stretch dB= 0.7 sd= 0.107
BV-sq-F-sq-stretch        dB= 0.7 sd= 0.103
BV-sq-F-lin-stretch       dB= 0.9 sd= 0.108
Sef-Z+ZS-F-pow-stretch    dB= 1.8 sd= 0.136
BV-s-F-s-stretch          dB= 2.2 sd= 0.141
BV-Z+ZS+SS-F-exp-stretch  dB= 2.8 sd= 0.160
Sef-Z+linZS-F-pow-stretch dB= 2.9 sd= 0.160
BV-s-F-sq-stretch         dB= 3.0 sd= 0.157
Sef-Z+ZS+SS-F-exp-stretch dB=12.6 sd= 0.295

which is much better disconfirmation than previously. In effect, the top-grade hypotheses fit the actual data better than the data with the prespective distortions left in, while the opposite appears to be the case for the low-grade hypotheses.
David B. Benson
Here is the SML code to remove the perspective effects, assuming a constant vertical angle per pixel. I think this is now completely correct, but please question whether there is still some mistake.

CODE

val pixelCount18Stories = 258.67
val roofLine = 417.0 and roofEdge2AntennaTower = 31.0 and darkBandElevation = 27.0
val cameraDistance = 1560.0 and cameraHeight = 1.25
val cameraATDistance = cameraDistance + roofEdge2AntennaTower
val roofLineLessCameraHeight = roofLine - cameraHeight
val floor106Height = roofLine - WtcUtil.feet2meters(WtcUtil.floor2dropFeet(106.0))
val floor088Height = roofLine - WtcUtil.feet2meters(WtcUtil.floor2dropFeet(106.0-18.0))
val darkBandAngle =             Math.atan((roofLineLessCameraHeight+darkBandElevation)/cameraATDistance)
fun metersDrop pixels =
let
val upAngle = darkBandAngle - radians
val heightMeters = cameraATDistance*Math.tan(upAngle)
in
roofLine+darkBandElevation-cameraHeight-heightMeters
end
David B. Benson
Here are the results, using just the better hypotheses, for pixel column 448 data. This is to compare the decibans and rank order for stabilty with the previously obtained results for pixel column 447.

CODE

Sef-Z+ZS-F-pow-stretch    dB= 0.0 sd= 0.092

BV-Z+ZS+SS-F-exp-stretch  dB= 0.0 sd= 0.093
BV-Z+linZS-F-pow-stretch  dB= 0.0 sd= 0.094
BV-Z+ZS-F-pow-stretch     dB= 0.0 sd= 0.095
BV-lin-F-sq-stretch       dB= 0.0 sd= 0.091
BV-Z+ZS+SS-F-pow-stretch  dB= 0.1 sd= 0.101
BV-sq-F-lin-stretch       dB= 0.1 sd= 0.103
BV-sq-F-sq-stretch        dB= 0.2 sd= 0.103
Sef-Z+ZS+SS-F-exp-stretch dB= 0.3 sd= 0.111
Sef-Z+ZS-F-exp-stretch    dB= 0.6 sd= 0.129
Sef-Z+ZS+SS-F-pow-stretch dB= 0.6 sd= 0.134
BV-Z+ZS-F-exp-stretch     dB= 0.9 sd= 0.150
Sef-Z+linZS-F-pow-stretch dB= 1.0 sd= 0.153
BV-s-F-s-stretch          dB= 1.1 sd= 0.156
BV-s-F-sq-stretch         dB= 1.2 sd= 0.159

The really bad case is hypothesis Sef-Z+ZS+SS-F-exp-stretch which (surprisingly) faired badly on the 447 data and does rather well on this data. I suspect that the problem is that the parameter estimation technique bacme trapped in a poor local minimum on the 447 data.

Also note that the winner with this data, Sef-Z-ZS-F-pow-stretch, places eighth on the 447 data. Again, the parameter esimation technique is suspect.
newton
QUOTE (einsteen+Dec 5 2007, 07:56 PM)
I already know that 911 is a product of improbabilities

QUOTE (metamars+Dec 5 2007, 01:17 PM)
Kevin Ryan of STJ911 on Ryan Mackey's work:

http://journalof911studies.com/letters/b/MackeyLetter

Nothing he has EVER written has been worth reading.

All of his articles are persuasive if you don't actually check out his assertions.

THEN you find his interest is only to further his agenda that NIST is IN ON IT.

Take this from his last:

QUOTE
Mackey claims that Griffin and I “err” in an energy argument in which I point out that there was no kinetic energy remaining from the aircraft impacts to affect fireproofing loss.
Mackey says this is a “mystification of the NIST summary of findings”, when, in fact, my point that no energy was available was not taken from NIST at all, but from calculations done by Tomasz Wierzbicki and other engineers at MIT.[3] These calculations show that all of the kinetic energy available from the impact of the aircraft was consumed in the crushing of the floors and columns in the WTC towers, and in destruction of the aircraft itself. Mackey would have known this if he had referred to the references of the book he was criticizing.

This of course is a TOTALLY ERRONEOUS conclusion from the MIT study.

The MIT study SIMPLIFIED the energy formulas to get a reasonable ESTIMATE of how many core columns were damaged, thus they didn't even include ANY of the building interior contents.

This is CLEARLY not the same as Ryan's moronic conclusion that "there was no kinetic energy remaining from the aircraft impacts to affect fireproofing loss".

His paper is only worth lining the bottom of the bird cage with.

Arthur
newton
but, NIST is on it, arthurs. not all the scientists, just the public relations bottleneck.
OneWhiteEye
QUOTE (David B. Benson+Dec 4 2007, 06:47 PM)
But the ground is not flat.  So 1560 m north of WTC 1 the ground might be either higher (more likely) or lower (less likely).  So my assumption of the camera being 1.25 m above the ground of WTC 1 seems a bit dubious.

Is there a better estimate to use?

There is a lot more building footprint than street in the area where the camera had to be located. I've always entertained the possibility that the camera elevation is a fair bit above ground level. Until I spend some time studying satellite photos and tweaking the rendered scene, I can't say... except the biggest open space at 'ground' level (within a considerable margin of lateral placement) is a couple of small city blocks further away. Since I haven't tried that location yet, I can't rule it out; it may be necessary to analyze the audio track to assist in radial distance determination.

Thanks for the results. I see the perspective corrections made a big difference, I can only believe that's a good thing.

With error due to view angle reduced, the next fish to fry is the data itself. There's clearly a sensitivity to the input data, something I did expect, as you can see from many previous posts. This, too, is a good thing; any hypothesis selection mechanism worth its salt ought to spit out different results when fed data with and without a perspective correction. Fifteen degrees doesn't qualify for small angle approximation.

As to the use of column data from smear-o-grams and the merging thereof, I'd hoped to be able to pull a dog-and-pony show out of my assuredly large bag of tricks, but there's another 'product of improbabilities' that's pressing me hard right now and I actually have to solve this one. Hopefully soon. But it does pay.

In light of that, something else that's less work.

The DBB dB DB model:

http://i14.tinypic.com/729pkc1.png

No joke. Whaddya expect for 10 minutes, a star schema? Haven't populated the database... truth is, I haven't generated it yet. The Parametrics table could use some work, maybe starting with a better name? In any case, without normalization (in the relational sense), I'm limited to applications that treat text like 'BV-Z+linZS-F-pow-stretch' as elements of an enumeration; that is to say, I'm ******. Oh, there are a few decent apps, but another day.
David B. Benson
Here are the results from pixel column 449. The rank ordering was a complete surprise to me.

CODE

aveNegs=0.0482242745662 aveWeight=0.414918918919
zeroTime=3.92492523983

BV-sq-F-sq-stretch        dB= 0.0 sd= 0.056

BV-sq-F-lin-stretch       dB= 0.0 sd= 0.061
BV-Z+ZS-F-exp-stretch     dB= 0.1 sd= 0.057
BV-Z+linZS-F-pow-stretch  dB= 0.2 sd= 0.064
Sef-Z+ZS-F-exp-stretch    dB= 0.5 sd= 0.072
BV-Z+ZS+SS-F-pow-stretch  dB= 0.8 sd= 0.080
BV-s-F-sq-stretch         dB= 1.3 sd= 0.090
Sef-Z+ZS+SS-F-pow-stretch dB= 1.5 sd= 0.104
BV-lin-F-sq-stretch       dB= 1.8 sd= 0.104
BV-s-F-s-stretch          dB= 2.2 sd= 0.117
BV-Z+ZS-F-pow-stretch     dB= 2.8 sd= 0.125
Sef-Z+linZS-F-pow-stretch dB= 2.9 sd= 0.132
Sef-Z+ZS-F-pow-stretch    dB= 3.5 sd= 0.137
BV-Z+ZS+SS-F-exp-stretch  dB= 5.3 sd= 0.165
Sef-Z+ZS+SS-F-exp-stretch dB=10.6 sd= 0.232
Sef-Z+SS-F-exp-stretch    dB=28.4 sd= 0.367
BV-Z+SS-F-exp-stretch     dB=61.9 sd= 0.494
David B. Benson
einsteen --- While this came up over on JREF, this forum is much easier for me to use. So I'll reply here.

The concept of a constant resistive force, equivalently a constant energy consumption, per story is now decisively disconfirmed in favor of a constant percentage of the available kinetic energy being consumed in each instant of the collapse. This is vastly in excess of the approximately 33 MJ needed to disconnect all the trusses of one story. Hence most of the energy consumption went towards crushing other portions of each story, such as (most of) the core.
David B. Benson
This paper seems vaguely related to the question of a physically motivated equation for the stretch of crushed trusses, but you'll have to go web trawling on the search term

Emerald FullText Article: Crashworthiness of helicopter subfloor structural components

since I don't seem to be able to copy the URL...
NEU-FONZE
David:

I have been looking at the column load data in NCSTAR 1-6D for WTC 1 and WTC 2. It is most interesting to follow the available load data down the towers and compare this result with core column AREA data to get the average stress state of the columns on each WTC floor. It's a HELL of a lot of work to plough through this type of data, (see wtcmodel.wikidot.com), especially if you try to do it for ALL the core AND the perimeter columns. But there are legitimate short cuts that lead you to the important conclusions that the loads were approximately 50 % core to 50 % perimeter all the way down the towers, AND, the stress was approximately constant all the way down the towers as well, because the load, (which is the local downwards force), was (by design!) proportional to the core column area all the way down. Example, the total core column area was 3.1 m^2 at floor 80 and 1.9 m^2 at floor 95 and the corresponding loads were 300 MN and 180 MN. Hence the stress at the 80th and 95th floors was about the same - ~ 95 MPa. (By the way, the core column area was about 9 m^2 at floor 18 and the load was ~ 800 MN). Now stress represents stored elastic energy, so when this "potential" energy was released during the collapse, since it was stored as a constant function of height, it was released as a constant function of height. The design of the Twin Towers really was amazing!
David B. Benson
QUOTE (NEU-FONZE+Dec 6 2007, 05:44 PM)
I have been looking at the column load data in NCSTAR 1-6D for WTC 1 and WTC 2. ... conclusions that the loads were approximately 50 % core to 50 % perimeter all the way down the towers,

... so when this "potential" energy was released during the collapse, since it was stored as a constant function of height, it was released as a constant function of height.

Here are the percentages of load on the core (undamaged structure) that I obtained from NCSTAR1-6 and NCSTAR1-6D.

WTC 1:
floor 105 41%
floor 098 46.5%

WTC 2:
floor 105 35.1%
floor 083 49.5%

=============
The release of the elastic strain would cause the top ends of columns to rise a bit. I'm not sure I fully see the consequences of this...
lozenge124
Interesting article about scale model building:

The science of how buildings fall down

It's good to see some work going on in this area at least.
newton
here's a link to a PDF of a somewhat SUSPICIOUSLY motivated study....

Head Skull: Astaneh, we need a study on something that's never happened before, so we can avoid it in the future.
Astaneh: another whitewash? like OKC?

Astaneh Theorizes on Progreesive Collapse of Steel Buildings

....published in august 2001.
David B. Benson
A plausible resistive force function is

F(S) = cSS

where S is the speed and c is some parameter. This is the appropriate force function for a mass moving through a fluid. Therefore, it is also correct for moving the air out of the tower and also for concrete comminution.

While reasonable to try this hypothesis, it fails on the pixel column 449 data (but not the other two). Carl Hauser, over a pleasant, just concluded lunch, suggests discarding this hypothesis on the grounds that it is too sensitive to the particular data, and hence cannot represent the physical phenomenon of the collapse of WTC 1.

On these grounds, the only simple hypothesis for the resistive force function is that due to a constant consumption of some of the available kinetic energy,

F(Z,S) = kZS

for some constant parameter k. (I still have no reason to offer to explain this.)

Edited to add: On similar grounds, I am eliminating from furth consideration the four (complex) hypotheses of the form

x-Z+ZS+SS-F-y-stretch

where x is either BV or Sef and y is either exp or pow.
wcelliott
QUOTE
The release of the elastic strain would cause the top ends of columns to rise a bit. I'm not sure I fully see the consequences of this...

It may be academic, if the loads on the columns were released slowly, but if they were released *instantaneously*, the elastic force on the top remaining attached floor would start out the same as the prior total load, so if the supports for 30 floors were instantly severed, the floor beneath the released load would be accelerated at 30g's, initially, assuming the floor brackets could transfer that amount of force to the floor.

That doesn't seem like a realistic assumption, so the conclusion (academic though it may be) would be that the top remaining supported floor would, due to the sudden elastic recoil, sever the brackets supporting *that* floor, too.

And so on, down the tower's structure.

IIRC, your previous consideration of this effect assumed that the net elastic force in the remaining structure would be distributed equally among the remaining floors, but I don't think you really gave the matter much consideration.

Transected columns seldom fail *that* suddenly, that they drop their loads instantaneously, so even the falling sections still exerted *some* load on the remaining columns, even if they were no longer in perfect alignment. It'd still take some time for them to get out of each others' way.
NEU-FONZE
Here is an interesting coincidence!

The elastic strain energy capacity of steel in compression is about 40 Joules/kg.

The energy released by lowering 1 kg of steel 1 m in the earth's gravity field is...

you guessed it,

QUOTE (newton+Dec 7 2007, 04:01 PM)
here's a link to a PDF of a somewhat SUSPICIOUSLY motivated study....

Head Skull: Astaneh, we need a study on something that's never happened before, so we can avoid it in the future.
Astaneh: another whitewash? like OKC?

Astaneh Theorizes on Progreesive Collapse of Steel Buildings

....published in august 2001.

Never happened before?

Hardly.

From the study:

QUOTE
Since 1980’s, a large number of buildings throughout the world have been the target of car bomb attacks. As a result, more than 3200 innocent people have lost their lives and thousands more have been injured. During past car bomb attacks, partial or full “progressive” collapse of the building has been the main cause of deaths and injuries. In many cases, the effect of car bomb explosion has been to knock-out one critical column on the perimeter of the building. After a column was removed, the load supported by the removed column could not be redistributed to other columns and the structure or part of the structure has collapsed in a progressive manner. A very tragic example of this case was the partial collapse of the Murrah Federal Building in Oklahoma City shown in Figure 1.

Sheesh.

Arthur
OneWhiteEye
QUOTE (David B. Benson+Dec 6 2007, 07:30 PM)
Here are the results from pixel column 449.  The rank ordering was a complete surprise to me.

Entirely unsurprising to me.

QUOTE
Carl Hauser, over a pleasant, just concluded lunch, suggests discarding this hypothesis on the grounds that it is too sensitive to the particular data.

Don't be too quick to throw the baby out with the bathwater.

Isn't discarding the data also an option?
OneWhiteEye
David B. Benson, I've adjusted the data model for modeling the data modeling you're doing.

http://i8.tinypic.com/739vp13.png

That's more like it. The lookup values:

http://i7.tinypic.com/6oo0co7.png

My apologies to Al Khwarizmi - step-by-step for embedding all this 'nothinG' in the page.
OneWhiteEye
The information contained in David B. Benson's last posts of fitness tests against individual pixel column data (447-449) can be summarized graphically with brightly colored easter eggs:

http://i16.tinypic.com/71f6s5j.png

The graph is partitioned into three regions for each of the datasets (the upper right quadrant is unused). Starting in the lower left and working counter-clockwise are columns 447, 448, and 449. Each small ellipse represents one result from a test, a record in one of the tables provided. The fill color of the ellipse corresponds to choice of force function, likewise the colors of the bars inside represent a form of stretch. The size of the bars represent SD (top) and dB (bottom) magnitudes. A small constant has been added to these to ensure bars display at least a thin slice for zero values, since the color of the bars can't otherwise be seen. Finally, the border color of the ellipse - not so easily seen - indicates the origin of the hypothesis, BV or Seffen.
newton
QUOTE (adoucette+Dec 8 2007, 03:35 AM)
Never happened before?

Hardly.

From the study:

Sheesh.

Arthur

QUOTE
Since 1980’s, a large number of buildings throughout the world have been the target of car bomb attacks. As a result, more than 3200 innocent people have lost their lives and thousands more have been injured. During past car bomb attacks, partial or full “progressive” collapse of the building has been the main cause of deaths and injuries. In many cases, the effect of car bomb explosion has been to knock-out one critical column on the perimeter of the building. After a column was removed, the load supported by the removed column could not be redistributed to other columns and the structure or part of the structure has collapsed in a progressive manner. A very tragic example of this case was the partial collapse of the Murrah Federal Building in Oklahoma City shown in Figure 1.

okay it happens when there are BOMBS used to make it happen.

between the two studies, it is shown that buildings fall when there is a VIOLENT removal of support on a critical support column.

so, which critical column(s) was(were) car bombed at wtc7?

what caused the instant removal of all support at wtc1 and wtc2? the plane damage was done, and the buildings stood. in fact, they barely noticed the loss of 15% of the support columns, when 50+% could have been removed, and the building still would have stood.

the OKC bombing was another example of a shadow government 'chess move' designed to usher in totalitarianism. there was more than one bomb.

that building after the bombing(s) was missing an entire half, and was supported by ONE COLUMN. yet, it stood.

steel is incredibly strong.
All buildings are different.

Not ALL buildings have a "critical support column".

The WTC 1 & 2 towers for instance had a very symmetrical construction where the loads were fairly equally distributed, about half to the core and half to the exterior columns. The loads on the exterior columns were not exactly the same, but in general varied more by floor than within a floor. The core columns had larger columns in the outer layer, with the largest being the exterior corner columns, but still the loads were fairly evenly distributed across a lot of columns.

But then the flying BOMBS hit.

I'd say that resulted in VERY VIOLENT removal of support columns.

And now the loading on the columns changed and some took on the role of critical support columns, meaning their loads increased, while indeed, the loads on other columns decreased.

It was the now asymmetrical forces that played the biggest role in the towers destruction.

The reason WTC 2 fell first was because the damage and fires were more asymmetrical than in WTC 1.

Which is why your "50% could be removed and the building still stood" is true but not relevant. 50% of the support could be removed ONLY if done in a manner such that the remaining loads were EQUALLY supported by the remaining structure.

But such was NOT the case in EITHER of the towers.

As to what took out the instant support?

Fire and Gravity.

As the fire side bowed in due to the asymmetric loads the long span of laterally unsupported exterior columns began to fail at the point of the highest loads. As the columns failed the loads they were carrying spread to adjacent columns causing them to fail.

As the side failed the interior columns exceeded their limits and also buckled.

Essentially once the bowing of one wall started the collapse had begun and simply accelerated as the loads shifted back and forth between the failing wall and the failing core.

(A better description is found in the NIST report)

As far as OKC, total bovine poo (about the second bomb), but as to the destruction of the building, clearly it suffered a progressive collapse where the truck bomb took out a key HORIZONTAL beam, but since there was no widespread fire (as in the WTC towers), once the collapse of the front center was over there was nothing to cause the collapse to spread to the rear and sides of the building.

Yes, steel is incredibly strong, but designers take advantage of that and load it up to a significant percent of its ability to withstand loads. The remaining ability is related to the temp of the steel. Designers know this and thus steel buildings are protected by sprinkler systems and the steel is fireproofed.

When you introduce a multifloor fire and let it burn but make no effort to fight the fire and the sprinkler system is not working and when much of the CRITICAL insulation is gone, and then when the loads on much of the structure are much higher than anticipated due to massive asymmetrical structural damage. Well then the strength of the steel can be exceeded.

Arthur
newton
i know the official lie, arthur.
it's still a lie.

there is no repeatability in the 'science' put forth in the NIST report. it is an untested, unreproducible THEORY.

there is no proof fireproofing was removed.
there is no evidence suggesting the fires released enough heat to affect even unprotected steel.
fire effects are not 'instant' the way bombs are.
there is no proof of the 'inevitability' of total collapse.

the handwaving from the OCT camp is THE ONLY LEG the official story stands on.
that's a critical column that IS being gradually weakened by the minute.

[poetry]
i think there's a good possibility anthrax knocked down wtc7.
it sure as heck knocked the constitution into the ground.[/poetry]
QUOTE (newton+Dec 8 2007, 01:42 PM)
i know the official lie, arthur.
it's still a lie.

Apparently you wish it were so.

You wish even more that you had something more than handwaving to support your inane assertions.

QUOTE (newton+)
i'm just thinking a micro-muke fits the 'how' bill better than anything else.

It would help support your world view.

But you are most clearly wrong.

Arthur
David B. Benson
QUOTE (OneWhiteEye+Dec 8 2007, 12:54 AM)
Isn't discarding the data also an option?

No.

When new, better data arrives, then of course all the hypotheses need to be tested against that. Doubt it will change much for the actual progressive collapse (as opposed to the collapse initiation phase).
einsteen
QUOTE (David B. Benson+Dec 6 2007, 10:29 PM)
einsteen
The concept of a constant resistive force, equivalently a constant energy consumption, per story is now decisively disconfirmed in favor of a constant percentage of the available kinetic energy being consumed in each instant of the collapse. This is vastly in excess of the approximately 33 MJ needed to disconnect all the trusses of one story. Hence most of the energy consumption went towards crushing other portions of each story, such as (most of) the core.

If I understand this well then the 33MJ is the expected theoretical value for detaching the floors from the colums ? But the 396 MJ is the effective energy ? I think it is clear that this most favourable value is the lower limit, the complete core didn't stand after the collapse. It also then proves that the funneling theory or wedge theory is false.
David B. Benson
QUOTE (einsteen+Dec 8 2007, 12:40 PM)
If I understand this well then the 33MJ is the expected theoretical value for detaching the floors from the colums[sic] ?

But the 396 MJ is the effective energy ?

I think it is clear that this most favourable value is the lower limit, the complete core didn't stand after the collapse.

It also then proves that the funneling theory or wedge theory is false.

Yes, around 33 MJ suffices to detach the floor from both the core and the exterior walls.

Not exactly. If one assumes a constant resistive force, then about 400 MJ would be consumed per story. However, that assumption agrees with OneWhiteEye's data decisively less well than the hypothesis that a constant fraction of the available kinetic energy is consumed per unit time (or per unit height, it is the same).

Clearly more than 33 MJ was consumed per story. Most of the core was crushed, the exterior wall sections were ripped apart at the bolts, etc.

I am most unsure what this 'theory' or 'theories' might be, so I cannot comment. Apologies.
einsteen
I remember that I also used maple once in the exact discrete model, I'm going to look if I can create some plots, similar as for wtc7, but then for several E/M values
Chainsaw,
QUOTE (newton+Dec 8 2007, 06:42 PM)
i know the official lie, arthur.
it's still a lie.

there is no repeatability in the 'science' put forth in the NIST report. it is an untested, unreproducible THEORY.

there is no proof fireproofing was removed.
there is no evidence suggesting the fires released enough heat to affect even unprotected steel.
fire effects are not 'instant' the way bombs are.
there is no proof of the 'inevitability' of total collapse.

the handwaving from the OCT camp is THE ONLY LEG the official story stands on.
that's a critical column that IS being gradually weakened by the minute.

[poetry]
i think there's a good possibility anthrax knocked down wtc7.
it sure as heck knocked the constitution into the ground.[/poetry]

I think it is a good possibility that structural overloading took down World Trade Center 7, along with other effects caused by a building falling on it.

Cause and effect are know to exist, in this universe!
David B. Benson
QUOTE (newton+Dec 8 2007, 11:42 AM)
it's still a lie.

there is no evidence suggesting the fires released enough heat to affect even unprotected steel.

No, a lie is an in tensional falsehood, usually with the intent to mislead. Check OED.

But there is. Photographic evidence. In great quantities. You might care to start with NCSTAR1-5A, but also see NCSTAR1-2A & B.

Instead of just MSU (Making Stuff Up).
einsteen
I get indeed problems fitting a curve with constant acceleration for the first 3.8 seconds (roughly 12 stories) but for the first 4 stories (15.1 meter) or 2.15 seconds it works better.

The discrete model can be solved exactly as v=v(k), with k the amount of stories collapsed. For wtc1, k=96 gives the famous 52 m/s end speed

If we plot this curve for several E/M values we have to compare it with the fact that the initial acceleration for the first 3.8 seconds or roughly 12 stories is (2/3)g. It is not easy to write the discrete model directly as a v=v(t) function, Shagster's java program will be able to do it, but if we have a=(2/3)g we can eliminate the t in the equation and find

L=v^2/2a, further if we divide it by 416/110=3.78 we have another velocity as function of k, i.e. sqrt(2*a*k*416/110)

I get this plot

http://i19.tinypic.com/85lbxo0.gif

what I also tried is comparing the E1/M=0 plot with several acceleration functions and it looks like in this discrete fitting an effective acceleration 0.8g fits approx with the momentum transfer model. It is really a very fine tuning job (0.8g or 0.66g differs a lot!) In the discrete model in theory it can be done modifying the E values as function of the floor, it will be hard to do.
David B. Benson
Here are three new hypotheses (run with two of the older ones), unsing pixel column 447 data.

CODE

BV-Z+ZS-F-pow-stretch     dB= 0.0 sd= 0.080

BV-ZS-F-exp-pow-stretch   dB= 1.1 sd= 0.114
Sef-ZS-F-exp-pow-stretch  dB= 1.6 sd= 0.131
Sef-Z+ZS-F-pow-stretch    dB= 1.8 sd= 0.136
BV-K+Z-F-const-stretch    dB=38.5 sd= 0.515

exp-pow-stretch is another attempt to find a functional form for the stretch function which has some kind of basis in physics:

s(Z,S) = s0*exp(-s1(ZS)^(s2))

where s0 is about 0.54, s1 is about 24 and s2 is about 1.5, all these being best fitting parametr values for the BV case.

For the last one, the force is

F(Z) = k0 + k1*Z

and the best fitting values are k0 = k1 = 0, which was not expected!
OneWhiteEye
QUOTE (David B. Benson+Dec 8 2007, 07:09 PM)
No.

QUOTE
When new, better data arrives, then of course all the hypotheses need to be tested against that.

Fair enough, I understand you can only work with what you have at the time.

QUOTE (->
 QUOTE When new, better data arrives, then of course all the hypotheses need to be tested against that.

Fair enough, I understand you can only work with what you have at the time.

Doubt it will change much for the actual progressive collapse (as opposed to the collapse initiation phase).

That may be the case. Initiation is peculiar because of rotation of the subject.

To what do you attribute the differences between results from individual columns 447, 448 and 449?

QUOTE
...and the best fitting values are k0 = k1 = 0, which was not expected!

In a hypothesis described as being introduced in an "attempt to find a functional form for the stretch function which has some kind of basis in physics" the resistance force is found to be zero? As in, fell without resistance? Interesting.
newton
QUOTE (Chainsaw,+Dec 8 2007, 09:02 PM)
I think it is a good possibility that structural overloading took down World Trade Center 7, along with other effects caused by a building falling on it.

Cause and effect are know to exist, in this universe!

the same building 'fell' on wtc6 first. .......leaving storeys deep perfectly round, cylindrical, black holes through the roof.

IF the tower 'fell' on wtc7, there would be a clear path of perimeter columns leading up to it, like we see lying on the ground towards the winter garden theatre.

no such thing is observed, therefore you have either skyscapaer-destroying debris being ejected 600ft.(IIRC) through open air, OR you have NO TWIN TOWER DEBRIS capable of doing any real damage to wtc7.

and don't show me the few pictures of towers falling on the other side of wtc, where a simple trick of perspective deceives the eye. pictures and videos from other perspectives show ZERO debris reaching as far as tower seven.

what caused the media to ignore the anthrax story once no more was being mailed?
what caused the media to never show the footage of wtc7 falling perfectly symmetrically at freefall acceleration?

cause and effect, indeed.
David B. Benson
QUOTE (OneWhiteEye+Dec 8 2007, 04:01 PM)

To what do you attribute the differences between results from individual columns 447, 448 and 449?

In a hypothesis described as being introduced in an "attempt to find a functional form for the stretch function which has some kind of basis in physics" the resistance force is found to be zero? As in, fell without resistance? Interesting.

No, I still have it.

As long as a hypothesis maintains its dB at less than 5, the differences are not very interesting, (so far). But if a hypothesis fairs poorly on any one of the three, either it is just bad, or else so sensitive to data differences that it cannot be a stable description of the collapse. (That's how I am treating the matter, but I have never run into a comparable situation before.) Does that answer your question?

No! The second and third best are the exp-pow-stretch cases. The last hypothesis assumes a simple force function and a constant stretch, and is decisively disconfirmed! And yes, the resistive force function, for best fit (not very good), is no resistive force. But, of course, the inertial effect of momentum conservation is still there...
David B. Benson
QUOTE (newton+Dec 8 2007, 04:07 PM)
no such thing is observed, ...

Untrue.

Evidence was posted on this thread by Grumpy.
David B. Benson
Here is one more new hypothesis, using pixel column 447:

CODE

BV-Z+ZS-F-pow-stretch     dB= 0.0 sd= 0.080

BV-K+Z-F-lin-stretch      dB= 7.3 sd= 0.232

Again the force function is

F(Z) = k0 + k1*Z

and the best fitting values are k0 non-zero and k1 = 0. The stretch starts at about 0.3 and declines linearly. At 7.3 dB down, this hypothesis is substantially disconfirmed.
QUOTE (newton+Dec 8 2007, 06:07 PM)
the same building 'fell' on wtc6 first. .......leaving storeys deep perfectly round, cylindrical, black holes through the roof.

IF the tower 'fell' on wtc7, there would be a clear path of perimeter columns leading up to it, like we see lying on the ground towards the winter garden theatre.

no such thing is observed, therefore you have either skyscapaer-destroying debris being ejected 600ft.(IIRC) through open air, OR you have NO TWIN TOWER DEBRIS capable of doing any real damage to wtc7.

More delusions and disinfo.

Why am I not surprised?

newton hasn't stopped this garbage since he claimed that something was fired from a helo into the tower.

He simply goes from one implausible explanation to the next, as he has no interest in the TRUTH, just in trying to make people BELIEVE HIM.

Let's look at REALITY though.

The North face of WTC 1 was ~ 300 ft from WTC 7.

To put the magnitude of newton's error in perspective, WTC 2 was ~ 600 ft from WTC 7.

Interestingly though, when WTC 2 fell, from 600 ft away, it caused quite a bit of damage to the WTC 7 lobby.

And then there is the newton strawman: but no one said the whole side of a tower had to fall on WTC 7.

But imagine what just ONE OR TWO of the ~7 ton perimeter trees could have done as they fell from, oh, 1,000 ft or so.

Coupled with a fire that goes on for almost 7 hours.

Arthur

OneWhiteEye
QUOTE (David B. Benson+Dec 8 2007, 11:12 PM)
No, I still have it.

But you're not using it.

QUOTE
To a large degree, yes, it does.

Do you remember how close the Landmark and WTC1 curves were? Not as close as these pixel columns but really quite close in both shape and magnitude for two such dissimilar buildings and circumstances. The Landmark's initial descent was a slow creep when we looked closely at the initial values, even more than the WTC. NEU-FONZE provided a reference and explanation for why the descent could be expected to look like that, which happens to be the way the WTC1 is expected to appear (at least by some).

For any two videos of the WTC1, the combined error in perspective adjustment could equal or exceed the difference between the WTC1 and Landmark, similarly NOT in a random but systematic fashion. I'm not saying that means the method would therefore fail to distinguish between them, neither am I saying there SHOULD be a difference, though now we're getting into the realm of my surprise if, by coincidence, the maths and parametric inputs should all happen to work out that way.

How useful is any hypothesis that doesn't discriminate between WTC1 and the Landmark, UNLESS the math coincidentally works out that way for the two buildings?

QUOTE (->
To a large degree, yes, it does.

Do you remember how close the Landmark and WTC1 curves were? Not as close as these pixel columns but really quite close in both shape and magnitude for two such dissimilar buildings and circumstances. The Landmark's initial descent was a slow creep when we looked closely at the initial values, even more than the WTC. NEU-FONZE provided a reference and explanation for why the descent could be expected to look like that, which happens to be the way the WTC1 is expected to appear (at least by some).

For any two videos of the WTC1, the combined error in perspective adjustment could equal or exceed the difference between the WTC1 and Landmark, similarly NOT in a random but systematic fashion. I'm not saying that means the method would therefore fail to distinguish between them, neither am I saying there SHOULD be a difference, though now we're getting into the realm of my surprise if, by coincidence, the maths and parametric inputs should all happen to work out that way.

How useful is any hypothesis that doesn't discriminate between WTC1 and the Landmark, UNLESS the math coincidentally works out that way for the two buildings?

No!  The second and third best are the exp-pow-stretch cases.  The last hypothesis assumes a simple force function and a constant stretch, and is decisively disconfirmed!

Yes, I see exp-pow is a bit down the grade, not a prime contender... for C447. But not sharply rejected, either.

QUOTE
And yes, the resistive force function, for best fit (not very good), is no resistive force.  But, of course, the inertial effect of momentum conservation is still there...[/i]

Yes, but this hypothesis then indicates the only things resisting collapse are the inertia and crushing of the materials in the way, something not even predicted for a building like the Landmark, where an efficient demolition would use as much potential energy to do the work as feasible.
newton
QUOTE (adoucette+Dec 8 2007, 11:35 PM)
More delusions and disinfo.

To put the magnitude of newton's error in perspective, WTC 2 was ~ 600 ft from WTC 7.

Interestingly though, when WTC 2 fell, from 600 ft away, it caused quite a bit of damage to the WTC 7 lobby.

And then there is the newton strawman: but no one said the whole side of a tower had to fall on WTC 7.

But imagine what just ONE OR TWO of the ~7 ton perimeter trees could have done as they fell from, oh, 1,000 ft or so.

Coupled with a fire that goes on for almost 7 hours.

Arthur

perimeter columns are like thirty-something feet long.
what force could possibly push them sideways 600, or even 300 ft.?
this is where the tipping/banana peel argument is seen for what it is... ie. pure BS.

"interestingly, though, when wtc2 EXPLODED, from 600 ft. away, it caused quite a bit of damage to the wtc7 lobby."

keep those delusions and disinfo alive, arthurs.
David B. Benson
QUOTE (OneWhiteEye+Dec 8 2007, 04:44 PM)
But you're not using it.

To a large degree, yes, it does.

Do you remember how close the Landmark and WTC1 curves were?

How useful is any hypothesis that doesn't discriminate between WTC1 and the Landmark, UNLESS the math coincidentally works out that way for the two buildings?

Yes, I see exp-pow is a bit down the grade, not a prime contender... for C447. But not sharply rejected, either.

Yes, but this hypothesis then indicates the only things resisting collapse are the inertia and crushing of the materials in the way, something not even predicted for a building like the Landmark, where an efficient demolition would use as much potential energy to do the work as feasible.

Not just now. I'll have to ponder further various ways in which that data can be used in conjunction with yours.

Good. Feel free to ask more when you are of a mind to do so.

Yes. I am quite confident that a top-grade hypothesis should be able to distinguish the two.

Useful to the structural engineering community in designing tall buildings which meets FEMA's building safety criterion, i.e., the building does not collapse due to high magnitude earthquake, for example.

As long as any hypothesis is less than 5 dB down, it remains a contender.

Exactly. Since that is certainly not what was observed, this combination of force function and stretch function is decisively disconfirmed. However, this is what most modelers have been using up until now, although with non-zero parameters.
David B. Benson
QUOTE (newton+Dec 8 2007, 04:54 PM)
perimeter columns are like thirty-something feet long.
what force could possibly push them sideways 600, or even 300 ft.?

Three stories, 36 feet.
A big enough one to break the bolts at the top of the section and start the whole thing leaning further out. Gravity would then do the rest.

The source for this force was probably the pressure of all the crushed materials inside. Visuals of such materials pouring out the side through a hole left by a some departed exterior wall sections has been posted on this thread. A very nice one by metamars, for example.
wcelliott
QUOTE
Three stories, 36 feet.
A big enough one to break the bolts at the top of the section and start the whole thing leaning further out. Gravity would then do the rest.

That would probably be sufficient, but there are a couple other phenomena that make it even more likely.

First, the "trees" weren't merely *released* at 1000', they were under tension from the sagging floors when the brackets failed, so they didn't merely fall, but were *flung* outward by their stored elastic energy.

Second, and it's less a factor (but it's still a factor) is that those trees had aerodynamic properties, unintended, definitely, but everything has some sort of lift-to-drag ratio, and those trees would've had a non-zero glide slope.
QUOTE (newton+Dec 8 2007, 06:54 PM)
perimeter columns are like thirty-something feet long.
what force could possibly push them sideways 600, or even 300 ft.?

Shirley, you jest?

I mean WHAT in the world could POSSIBLY release enough energy to give an acceleration of ~ 20 mph to an exterior column piece during that collapse?

hmmmm, I wonder??????

Arthur
David B. Benson
Here is the newest run using the pixel column 449 data:

CODE
BV-ZS-F-exp-pow-stretch   dB= 0.0 sd= 0.072

Sef-ZS-F-exp-pow-stretch  dB= 1.4 sd= 0.125
BV-Z+ZS-F-pow-stretch     dB= 1.4 sd= 0.125
Sef-Z+ZS-F-pow-stretch    dB= 1.9 sd= 0.137
BV-K+Z-F-lin-stretch      dB=14.2 sd= 0.315
BV-K+Z-F-const-stretch    dB=43.7 sd= 0.593

No surprises.
newton
QUOTE (adoucette+Dec 9 2007, 04:52 AM)

Shirley, you jest?

I mean WHAT in the world could POSSIBLY release enough energy to give an acceleration of ~ 20 mph to an exterior column piece during that collapse?

hmmmm, I wonder??????

Arthur

i haven't seen any video of perimeter trees going 300 ft. sideways at 20 mph.
i wonder why?

i'll give you holiday brownie points for calling me shirley.
David B. Benson
Here is a confirmation that there was little (or no) constant component to the resistive force, using pixel column 449 data:

CODE
BV-K+ZS-F-exp-pow-stretch dB= 0.0 sd= 0.116

Sef-K+ZS-F-exp-pow-stretch dB= 0.2 sd= 0.130

In the BV case, the constant parameter is 0.0032 and the ZS parameter is 1.4856. In the Seffen case, the constant parameter is zero.
wcelliott
QUOTE
I mean WHAT in the world could POSSIBLY release enough energy to give an acceleration of ~ 20 mph to an exterior column piece during that collapse?

hmmmm, I wonder??????

newton seems to be better at grokking Japanese Godzilla-movie physics than that stuffy kind taught in college physics courses.

You know, tall buildings are supposed to fall *over*, steel is, after all, what the Man of Steel is compared to (therefore invulnerable, unbreakable, bulletproof...), every cloud of dust is proof of explosions, and the silent explosives are the result of government scientists working in secret labs, bald guys in white coats working on mind-control weapons, etc.

newton lives in a much more interesting universe than the rest of us.
David B. Benson
Here is a variation in which the t0 time parameter is adjusted for best fit, again using the pixel column 447 data:

CODE
BV-K+ZS-F-exp-pow-stretch dB= 0.0 sd= 0.100

Sef-K+ZS-F-exp-pow-stretch dB= 0.7 sd= 0.131

There is no substantial change in the Seffen case, but in the BV case, starting a mere 1.7 milliseconds later, also slightly different other parameters, reduces the sd from 0.116 to 0.100.

For both, K=0 was forced to hold.
David B. Benson
Another variation in which only constant force is used. (ZS parameter forced to be zero.)

CODE
BV-K+ZS-F-exp-pow-stretch dB= 0.0 sd= 0.252

Sef-K+ZS-F-exp-pow-stretch dB= 0.6 sd= 0.329

Notice how much poorer the fit is. I take this as further confirming evidence against a constant resistive force.

By the way, notice that a resistive force of

F(Z,S) = kZS

is the constant k time the momentum, ZS. Dunno why...
OneWhiteEye
QUOTE (David B. Benson+Dec 9 2007, 12:03 AM)
Good.  Feel free to ask more when you are of a mind to do so.

Thanks for all the info.

QUOTE
Yes.  I am quite confident that a top-grade hypothesis should be able to distinguish the two.

Certainly seems reasonable.

QUOTE (->
 QUOTE Yes.  I am quite confident that a top-grade hypothesis should be able to distinguish the two.

Certainly seems reasonable.

Useful to the structural engineering community in designing tall buildings which meets FEMA's building safety criterion, i.e., the building does not collapse due to high magnitude earthquake, for example.

I wasn't too clear in what I said. I meant any hypothesis which is unable to distinguish between WTC1 and Landmark is no good... with the one exception where the proper assignment of parameters (E1, h, whatever) for the respective buildings, BY PURE CONCIDENCE, call for nearly identical displacement data.

QUOTE
Exactly.  Since that is certainly not what was observed, this combination of force function and stretch function is decisively disconfirmed.  However, this is what most modelers have been using up until now, although with non-zero parameters.

Interesting.

What are your thoughts on error due to rotation of the antenna? And what is the stance of BV equations wrt rotational energy in the 1-D model? I mean specifically as it relates to making measurements which have both rotational and translational components.
newton
QUOTE (wcelliott+Dec 9 2007, 08:32 PM)
newton lives in a much more interesting universe than the rest of us.

yes. i don't know everything, which means life is still full of wonder for me.

i'd hate to be as omniscient as some of you OCTs seem to be.
einsteen
QUOTE (OneWhiteEye+Dec 10 2007, 12:41 AM)
What are your thoughts on error due to rotation of the antenna? And what is the stance of BV equations wrt rotational energy in the 1-D model? I mean specifically as it relates to making measurements which have both rotational and translational components.

That is a very interesting remark. If I understand everything well, it is your data from the antenna measurements. The perspective effect has been corrected, but the rotation is still a problem. And even if it is possible to correct for rotation then we get an other problem, i.e.

1) Does the data corrected for rotation represent a model in which a non-tilted block falls perfectly straight down.

2) Does the data corrected for rotation represent a tilted block falling perfectly straight down.

From the smear-o's that I posted not much difference could be seen although we have two totally different situations. I made them quick and dirty, but even if you do it precisely there is a high chance that also not much difference will be seen. On the one hand we are dealing with a large mass that needs to be accelerated and I made the remark that they therefore should look the same, but on the other hand we can wonder what the value of the data is if there is really no difference with the Landmark.
einsteen
QUOTE (David B. Benson+Dec 9 2007, 11:59 PM)

By the way, notice that a resistive force of

F(Z,S) = kZS

is the constant k time the momentum, ZS.  Dunno why...

That's indeed strange. I guess this is based on the first 3.8 seconds, how does something like this work out if you use it for the whole collapse ?

If we only look at a discrete model in vacuum, ignore stretch and all stuff then it is hard to explain. I would say that something like k0+k1*Z makes sense for a building. Could it be that ejection of mass plays a role?
shagster

Einsteen,

I plotted the crush-up collapse duration for various values of E1/m. I used ODE Toolkit and the continuous diffeq crush-up model that I posted about on p542 to obtain the values of crush-up duration vs. E1/m. This is for a tower height of 174 m (WTC7).

I'm not sure where the squiggles came from in your t vs E1/m graph. Perhaps it is artifact from a numerical solver if you were using one. I don't see it in my results.

Graph (y = collapse duration; x = E1/m):

Larger graph:

http://i134.photobucket.com/albums/q91/sha...rushupe1m-1.jpg

Here are the results from ODE Toolkit
(E1/m in J/kg and collapse duration in seconds)

0, 5.96
1, 6.06
2.5, 6.26
4, 6.48
5, 6.66
6, 6.86
7, 7.06
7.5, 7.17
8, 7.28
8.5, 7.39
9, 7.51
10, 7.74
11, 7.97
12.5, 8.3
14, 8.66
15, 8.88
16, 9.12
17.5, 9.45
19, 9.78
20, 10.0
21, 10.22
22.5, 10.54
24, 10.85
25, 11.1

shagster
QUOTE (einsteen+Dec 3 2007, 08:00 AM)

I found something interesting, if I use the maple discrete calculation I get

E1/M,  t(s)

0, 5,96
5, 6.63
10, 7.73-0.23i
15, 8.90-1.04i
20, 10.00 - 2.33i
25, 11.07 - 4.21i

The real part then is the collapse time, which is almost the same as your values.

The crush-up solution has an imaginary component when E1/m is higher than the critical value where the collapse no longer goes to completion.

Here is a graph of the results of the ODE solver for a crush-up. This is the same as the graphs I posted on p542 but the time axis extends out to 30 seconds. Note that the solutions are oscillatory when E1/m is higher than the critical value (E1/m = 10,15,20,25). The imaginary component in your solution stems from that oscillatory behavior.

larger graph:

http://i134.photobucket.com/albums/q91/sha...up/crushup1.jpg

It's important to not make an erroneous conclusion that the collapse duration for a crush-up can't be higher than the duration associated with the critical E1/m. The duration can be higher. The portions of the x vs t curves past the first minimum that show the oscillatory behavior aren't physically meaningful for the collapse phenomenon that is being modeled (i.e., the resistive force doesn't make the top of the building rise up into the air after it reaches a minimum height). The portions of the curves up to the first minimum in the x vs. t curve are meaningful and give the collapse duration.
shagster
As an exercise, it might be useful to try to model the first few seconds of the WTC1 collapse using the antenna drop data and the continuous crush-up model instead of crush-down. Parameters such as resistive force and stretch as a function of height could be adjusted to see how small the standard deviation could be made.
OneWhiteEye
QUOTE (einsteen+Dec 10 2007, 09:43 AM)
1) Does the data corrected for rotation represent a model in which a non-tilted block falls perfectly straight down.

2) Does the data corrected for rotation represent a tilted block falling perfectly straight down.

Exactly. If only looking at the one video, it would be easy to assune the total rotation of the upper block remains quite small. But, even in that case, what impact does it have on interpretation of data? Small angle but a massive body, while pure translation during the same interval is also small (or zero); neglecting rotation due to small angle cannot or should not give a correct result.

But, if you look at other videos, you see the antenna rotates to a substantial angle, not apparent in the one video because rotation is away from the camera. In real measurements, two points very close on the antenna appear to get about two percent closer in the first few seconds, an effect of the projection of rotation.

A rotation about an abitrary origin is equivalent to a rotation and translation about different body-centered coordinates. If all or most of the translation of a measured feature comes from rotation about another point, would it even be reasonable to expect any sort of match from a 1-D model? Particularly one that excludes rotation entirely as opposed to having a corrective term in the canonical coordinate?
David B. Benson
I'll eventually answer questions, but just now I have to state that the differential equation I have been using is only correct for constant stretch. For other stretch functions there are corrective terms to be added. I suspect (or maybe just hope) that the correction is small. We'll have to see.

As it stands, all results to date, except those for constant stretch, have to be thrown out.
OneWhiteEye
Unfortunate. I'm sorry to hear that, but it's much better it be caught now than later.
OneWhiteEye
C447 data (raw) is roughly the frame range 800-1032. This is the C447 smear-o-gram with the curve that was digitized for that data:

http://i15.tinypic.com/820vdz9.png

The net vertical displacement over this time is measured to be 177 pixels. First appreciable apparent vertical motion occurs around frame 895, as reflected in the numeric data.

Look at the feature which the smear-o-gram of pixel column 447 tracks, at least initially:

http://i5.tinypic.com/733jmm8.png

It is the left edge of the dark band, marked by a green star. Where is this feature in frame 1032?

http://i19.tinypic.com/71vukie.png

Well, the feature isn't really visible anymore (!!!) but the once-bright thing to the right still is, so it can be determined from direct inspection of these initial and final frames that the dark band as a whole has moved about 6 pixels to the left while going 179 down. A two pixel discrepancy exists between the vertical displacement in the C447 data and a more reliable observation, not too bad but still a 1% correction upwards (faster).

The discrepancy can be explained and, in the process, more insight gathered as to the nature of errors and differences between C447 and the next two columns. I explained the mechanics of the distortion in a previous post but the effect will now be examined for the real data. In a blow up of the dark band taken from frame 800, the measurement point for C447 data (green star) can be followed through its migration 6 pixels over to the right, likewise C448 and C449 (blue and red):

http://i6.tinypic.com/8228lds.png

The dark point being measured in C447 has shifted up two pixels, so the discrepancy is fully explained, as was expected all along. Geometric considerations evident from the very beginning have finally been quantified in the most rudimentary fashion: up to 2 pixels of non-random error exists in all three datasets.

It's obvious the measurement points of the three columns migrate at the same horizontal rate but suffer artificial vertical displacement at different times, due to geometry. Column 449, in particular, is seen to get its 'boost' well before C447, whenever that is. The horizontal rate itself cannot be taken to be constant or even linearly increasing, the initial motion is not known, so it's impossible to say where these shifts occur in the data without further measurement.
OneWhiteEye
Such measurements are not that difficult and I will do them soon. I believe that these corrections should not only be applied to the data, but done first as depicted in this diagram:

http://i12.tinypic.com/81hmr29.png

The reasons are simple. This is a systematic error that is known to exist and can be accurately quantified and corrected. It introduces unnecessary discrepancies between the three datasets. Once corrected, the three datasets will probably agree so well the +/- 1 pixel accuracy claimed will seem quite modest. I would then totally support merging C447-449 into one set; it would be the right thing to do.

Some predictions (I wrote this before DBB's revelation above but it's worth saying still):

- this correction would make a substantial difference to the results of a Bayesian analysis, not unlike perspective correction despite smaller magnitude
- much better agreement between individual runs of the column data which would, in turn, make an even stronger justification for merging the data
- the results of analyzing the merged data will agree more strongly with the results from individual columns
- I'd be surprised if there was much if any change in rank between runs of individual or merged columns
- the measure of discrimination as a dependency on quantity of points (posted by DBB) will be satisifed as the sets are merged one by one

That's a pretty specific set of predictions for someone shooting from the hip, isn't it? Audacious, considering I've never done such an analysis and barely understand it. Wouldn't it be incredible if I were right? Could I claim the \$1M challenge prize from the Randi people?

I could be completely wrong. It wouldn't matter, the justification is that it's the right thing to do.

The work is not done so naturally the corrections are pending. Preliminary data such as this, though, is provisional. There are no things that can be refuted with confidence by the current data.

David B. Benson, I've got great respect for what you're trying to do with your analyses, that's why I'm working to provide you with data. I don't see anyone else (except maybe einsteen) who is or will be doing anything with it. You understand your process better than I could hope to, but I have familiarity with this data and I'm no stranger to the acquisition, reduction and analysis of data in the general sense. I just want to be sure the best possible results are obtained from data I provide, and no premature conclusions are reached.

Added thought: In light of the need to re-run everything, it seems an opportune time to bring this up, even if the issues in previous runs could be attributable to modeling error.

frater plecticus: If you happen to be driving by again, THIS is what I mean by GOOD data.
David B. Benson
Whew! Here is the first run with the correct equation, using again the pixel column 447 data:

CODE
BV-K+ZS-F-exp-pow-stretch dB= 0.0 sd= 0.120

Sef-K+ZS-F-exp-pow-stretch dB= 1.0 sd= 0.167

Notice that the standard deviations are somewhat worse, but not a lot. Above has K=0 forced. Below has parameter for ZS term forced to be zero.

CODE
BV-K+ZS-F-exp-pow-stretch dB= 0.0 sd= 0.262

Sef-K+ZS-F-exp-pow-stretch dB= 1.4 sd= 0.391

So, once again, a constant resistive force is disconfirmed in comparison to a force function of

F(Z,S) = kZS.
chris lz
Hi. New here. Don't know if this has been answered, or if this is the place to ask.

From the PM 9/11 book, pp46-7

QUOTE
"The explosives configuration manufacturing technology [to bring down those buildings]  does not exist," [Mark] Loizeaux says. "If someone were to attempt to make such charges, they would weigh thousands of pounds apiece.  You would need forklifts to bring them into the building."

The biggest commercially available charges, Loizeaux tells Popular Mechanics, are able to cut through steel that is three inches thick. The box columns at the base of the World Trade Center towers were 14 inches thick on a side. If big enough charges did exist, Loizeaux says, for each tower it could hypothetically take as long as two months for a team of up to 75 men with unfettered access to three floors to strip the fireproofing off the columns and then place and wire the charges.

I'm having a discussion on this point in another forum. The poster writes

QUOTE (->
 QUOTE "The explosives configuration manufacturing technology [to bring down those buildings]  does not exist," [Mark] Loizeaux says. "If someone were to attempt to make such charges, they would weigh thousands of pounds apiece.  You would need forklifts to bring them into the building."The biggest commercially available charges, Loizeaux tells Popular Mechanics, are able to cut through steel that is three inches thick. The box columns at the base of the World Trade Center towers were 14 inches thick on a side. If big enough charges did exist, Loizeaux says, for each tower it could hypothetically take as long as two months for a team of up to 75 men with unfettered access to three floors to strip the fireproofing off the columns and then place and wire the charges.

I'm having a discussion on this point in another forum. The poster writes

If anyone thinks about it, the "14" on a side" explanation for why "tons of explosives" would have been needed to cut the supports in the Towers, that one would easily see that the supports, being hollow (for reasons of strength, reduced weight, and cost) would invalidate the explanation. And I don't care how poor an "expert" one is, anyone even remotely acquainted with the way steel high rises are constructed would never have come up with THAT zinger.

David B. Benson
QUOTE (einsteen+Dec 10 2007, 06:46 AM)
That's indeed strange. I guess this is based on the first 3.8 seconds, how does something like this work out if you use it for the whole collapse ?

If we only look at a discrete model in vacuum, ignore stretch and all stuff then it is hard to explain.

I would say that something like k0+k1*Z makes sense for a building.

Could it be that ejection of mass plays a role?

Yes, just the first 3.82 seconds. I haven't attempted extrapolating to the entire collapse, so I'll just guess that it makes the collapse take somewhat longer.

However, the stretch is an important component of progressive collapse.

Naively, yes. Indeed, up until now that is what modelers have been using, modified in BLGB to include an additional term for air movement and another for concrete comminution. What makes this so puzzling, in part, is that at 3.8 seconds the collapse is proceeding at about 25 m/s. That should be plenty to comminute concrete.

I assume uniform mass distribution. About 17 floors are crushed in the 3.82 seconds. At that elevation each story massed about 6% more that at the collapse starting elevation. But I also ignore mass ejection. If that is about the same as the increase in mass, it evens out. So I currently think that mass ejection does not explain the resistive force function.
OneWhiteEye
QUOTE (chris lz+Dec 10 2007, 08:09 PM)
Hi. New here. Don't know if this has been answered, or if this is the place to ask.
From the PM 9/11 book, pp46-7
I'm having a discussion on this point in another forum. The poster writes
...

Greetings, chris lz, welcome to the forum. Opinions, but no comments except that Loizeaux would certainly be aware of the hollow nature of the supports in the comment he made. Whether or not his observation is accurate - no comment.
David B. Benson
QUOTE (chris lz+Dec 10 2007, 01:09 PM)
... if this is the place to ask.

Certainly is!

While the box core columns were indeed hollow, the ones at the bottom levels contained an additional bar through-welded in the center, running the long dimension of the column. So the short dimension, about 14 inches, was about 9--10 inches of mild steel and the remainder air.
einsteen
QUOTE (shagster+Dec 10 2007, 02:46 PM)
Einsteen,

I plotted the crush-up collapse duration for various values of E1/m. I used ODE Toolkit and the continuous diffeq crush-up model that I posted about on p542 to obtain the values of crush-up duration vs. E1/m. This is for a tower height of 174 m (WTC7).

I'm not sure where the squiggles came from in your t vs E1/m graph. Perhaps it is artifact from a numerical solver if you were using one. I don't see it in my results.

Graph (y = collapse duration; x = E1/m):

Larger graph:

http://i134.photobucket.com/albums/q91/sha...rushupe1m-1.jpg

Here are the results from ODE Toolkit
(E1/m in J/kg and collapse duration in seconds)

0, 5.96
1, 6.06
2.5, 6.26
4, 6.48
5, 6.66
6, 6.86
7, 7.06
7.5, 7.17
8, 7.28
8.5, 7.39
9, 7.51
10, 7.74
11, 7.97
12.5, 8.3
14, 8.66
15, 8.88
16, 9.12
17.5, 9.45
19, 9.78
20, 10.0
21, 10.22
22.5, 10.54
24, 10.85
25, 11.1

As far as I know it is only a summation and on a larger scale it looks smooth, it must have an explanation, I'll check tomorrow.
David B. Benson
QUOTE (einsteen+Dec 10 2007, 02:43 AM)
If I understand everything well, it is your[OneWhiteEye's] data from the antenna measurements.

The perspective effect has been corrected, but the rotation is still a problem.

1) Does the data corrected for rotation represent a model in which a non-tilted block falls perfectly straight down.

2) Does the data corrected for rotation represent a tilted block falling perfectly straight down.

... on the other hand we can wonder what the value of the data is if there is really no difference with the Landmark.

Yes.

Yes, although the effect will be minor for WTC 1 with a tilt of only about 11 degrees of arc.

Yes, close enough.

Yes, close enough for WTC 1.

But there is a difference in the data between WTC 1 and Landmark. In either case, I am after a model which is fast to run and can be used to aid in calibrating the ASI (and others) global progressive collapse software.
David B. Benson
QUOTE (OneWhiteEye+Dec 9 2007, 05:41 PM)
What are your thoughts on error due to rotation of the antenna?

And what is the stance of BV equations wrt rotational energy in the 1-D model?

I mean specifically as it relates to making measurements which have both rotational and translational components.

This is a perspective error which needs to be compensated for. The equations are easy to derive, but we need some estimate of the magnitude of the tilt at each time. I have some data measured by NEU-FONZE and I plan to use this as a first approximation to make this (small) correction.

The crush-down equations are one-dimensional only.

Just make the best possible measurements. If the measurements are taken both on the antenna tower and also towards the left (east) end of the roofline, it should be possible to use that to calculate the tilt away from the camera. (The small movement to the left can be ignored.)
OneWhiteEye
Thanks for your response. I'll refrain from making too many comments until you've had a chance to digest some of the later remarks.

QUOTE (David B. Benson+Dec 10 2007, 09:59 PM)
This is a perspective error which needs to be compensated for.  The equations are easy to derive, but we need some estimate of the magnitude of the tilt at each time.  I have some data measured by NEU-FONZE and I plan to use this as a first approximation to make this (small) correction.

Sounds good.

QUOTE
The crush-down equations are one-dimensional only.

Yes, I understand, but even a 1-D equation of motion can account for effects introduced by other degrees of freedom. An example would be a fictitious force such as centrifugal force when doing calculation along a single axis of a 2+ dimensional rotating coordinate frame. Or, if your bend is more Lagrangian or Hamiltonian, an additional energy term expressed as a function of the single canonical coordinate.

I haven't looked at the papers in a while, but I don't remember seeing such a term, so I thought I'd ask.

I honestly don't know whether or not it is a significant correction term, but it seems like a significant action in the early displacement data I took. Empirically, it would seem that it could only be ignored if it were shown to be truly decoupled.

QUOTE (->
 QUOTE The crush-down equations are one-dimensional only.

Yes, I understand, but even a 1-D equation of motion can account for effects introduced by other degrees of freedom. An example would be a fictitious force such as centrifugal force when doing calculation along a single axis of a 2+ dimensional rotating coordinate frame. Or, if your bend is more Lagrangian or Hamiltonian, an additional energy term expressed as a function of the single canonical coordinate.

I haven't looked at the papers in a while, but I don't remember seeing such a term, so I thought I'd ask.

I honestly don't know whether or not it is a significant correction term, but it seems like a significant action in the early displacement data I took. Empirically, it would seem that it could only be ignored if it were shown to be truly decoupled.

Just make the best possible measurements.  If the measurements are taken both on the antenna tower and also towards the left (east) end of the roofline, it should be possible to use that to calculate the tilt away from the camera.

Yes. As I've pointed out, it's quite likely that it can be calculated from the other manual data I've posted, based on the difference over time of positions of points on the antenna together with the camera angle and the known initial antenna tilt angle of zero. The difference gradually reaches an easily observable 2%. Working with the differentials strictly determines the tilt angle over time, to the measurement accuracy.

QUOTE
(The small movement to the left can be ignored.)

In general, yes, from the view of deviation from vertical. The Y component of an (x,y) measurement will not care about the X. But, as I've demonstrated above, the small movement makes a significant difference in the C447-449 data, a one dimensional measurement that does NOT directly account for 2D motion.
David B. Benson
Pixel column 449 data with corrected equation:

CODE
BV-ZS-F-exp-pow-stretch   dB= 0.0 sd= 0.118

Sef-ZS-F-exp-pow-stretch  dB= 0.4 sd= 0.148
BV-K+Z-F-exp-pow-stretch  dB= 1.8 sd= 0.201
Sef-K+Z-F-exp-pow-stretch dB= 6.5 sd= 0.328

The last two have force functions of the form einsteen suggested,

F(Z) = k0 + k1*Z

and in both cases neither k0 nor k1 is zero. But only the last is substantially disconfirmed.
David B. Benson
QUOTE (OneWhiteEye+Dec 10 2007, 03:43 PM)
I haven't looked at the papers in a while, but I don't remember seeing such a term, so I thought I'd ask.

... the known initial antenna tilt angle of zero.

The difference gradually reaches an easily observable 2%.

Working with the differentials strictly determines the tilt angle over time, to the measurement accuracy.

There isn't one in the equations as they are written. I don't think it an important correction term for such a massive structure.

The tilt angle at t0 is about 1.1 degrees of arc, according to NEU-FONZE.

Sorry, what difference reaches 2%?

Can you amplify on this remark. I'm not following.

========================================
More later...
OneWhiteEye
QUOTE (David B. Benson+Dec 10 2007, 11:19 PM)
There isn't one in the equations as they are written.  I don't think it an important correction term for such a massive structure.

Energy scales with mass so the importance of such a term is independent of the mass. Big mass, big moment of inertia, big rotational kinetic energy. The tipping begins first and continues for some time... it represents less and less total energy rapidly as the descent progresses, but I'm not so confident it can be totally ignored in the first few seconds.

This, obviously, is a statement towards the accuracy of the theory as applied to this specific instance, not an observation about the data analysis.

QUOTE
The tilt angle at [I]t0p/I] is about 1.1 degrees of arc, according to NEU-FONZE.

Thanks for that correction. I do need to relate that to my t0, though, because I see the slow creep to the side. At my t0, I don't think the tilt is as much as 1.1 degrees, but I can't be sure without further observation. What matters for the solutions, though, is your t0, so this isn't a big deal.

QUOTE (->
 QUOTE The tilt angle at [I]t0p/I] is about 1.1 degrees of arc, according to NEU-FONZE.

Thanks for that correction. I do need to relate that to my t0, though, because I see the slow creep to the side. At my t0, I don't think the tilt is as much as 1.1 degrees, but I can't be sure without further observation. What matters for the solutions, though, is your t0, so this isn't a big deal.

Sorry, what difference reaches 2%?

The difference in position values between the dark band and the average antenna dish position, in the manual data I posted some time back. I could see the difference in the curves easily by visual inspection; when overlaying the graphs it was very obvious. I've spoke of this several times.

These points are physically close together on the antenna. Given the accuracy of the measurement (quite good), there is no way the disagreement between the two displacements can be explained as measurement error. A physical explanation is necessary, and crushing of the few feet of antenna between them is not it.

The real explanation is that the antenna tips away during this time, making the projected distance between the two features on the image plane shorter. The effect is the same as if the camera theta angle were to gradually increase. Think dot product of the antenna long axis vector and any vector on the plane normal to the optical axis.

QUOTE
Can you amplify on this remark.  I'm not following.

The two measured points on the antenna start at a fixed apparent distance. As collapse progresses, both of these points displace downward, but at different rates. The apparent decrease in distance can be used to calculate the angle required to produce the difference. The differences from each frame can be used to map the antenna tilt over time.
David B. Benson
Here are the same four hypotheses using the C447 data:

CODE
BV-ZS-F-exp-pow-stretch   dB= 0.0 sd= 0.133

Sef-ZS-F-exp-pow-stretch  dB= 0.3 sd= 0.153
BV-K+Z-F-exp-pow-stretch  dB= 2.6 sd= 0.246
Sef-K+Z-F-exp-pow-stretch dB= 6.0 sd= 0.343

Only the last hypothesis can be excluded as (twice over) substantially disconfirmed.
QUOTE (chris lz+Dec 10 2007, 03:09 PM)
Hi. New here. Don't know if this has been answered, or if this is the place to ask.

From the PM 9/11 book, pp46-7

QUOTE
"The explosives configuration manufacturing technology [to bring down those buildings]  does not exist," [Mark] Loizeaux says. "If someone were to attempt to make such charges, they would weigh thousands of pounds apiece.  You would need forklifts to bring them into the building."

The biggest commercially available charges, Loizeaux tells Popular Mechanics, are able to cut through steel that is three inches thick. The box columns at the base of the World Trade Center towers were 14 inches thick on a side. If big enough charges did exist, Loizeaux says, for each tower it could hypothetically take as long as two months for a team of up to 75 men with unfettered access to three floors to strip the fireproofing off the columns and then place and wire the charges.

It's kind of a strawman argument in that both towers failed at the FIRE/IMPACT floors.

He DOES have a point about the difficulty of unfettered access.

Also, since the collapse began in both towers with an outside wall on a fire floor bowing in, there is no explosive that is capable of a slow sustained force.

Arthur
David B. Benson
QUOTE (OneWhiteEye+Dec 10 2007, 04:54 PM)
... big rotational kinetic energy.

What matters for the solutions, though, is your t0, so this isn't a big deal.

I've spoke of this several times.

The effect is the same as if the camera theta angle were to gradually increase.

The differences from each frame can be used to map the antenna tilt over time.

Yes, it is an energy sink for the first second. I'll think more on this.

The antenna tower would begin to tilt to the south no later than the observed bowing-in of the south wall, 20 minutes before collapse. So for your begin time, there is already some small tilt to the south.

Yes, but it took until now to sink in. This is not a high bandwidth communication medium.

Err, decrease? No, you have it right.

That would be impressive!
OneWhiteEye
QUOTE (David B. Benson+Dec 11 2007, 12:26 AM)
The antenna tower would begin to tilt to the south no later than the observed bowing-in of the south wall, 20 minutes before collapse.  So for your begin time, there is already some small tilt to the south.

I really wish the camera had not been disturbed just prior to collapse. I must remember how fortunate we are the shake stopped when it did.

QUOTE
Yes, but it took until now to sink in.    This is not a high bandwidth communication medium.

True, it's not. Sometimes my explanations are not so good, either. I'm glad we connected on that. The measurements are already very accurate, and will get more so. So good that every measurable point will need individual perspective correction for the dynamics of the rigid body. Sort of a catch 22, but not really. You see we can derive motion in a 3rd dimension from just one 2D video... My feeling is that other videos will add little or no information content to the descent tracking, but rather a fair bit to the dynamic perspective corrections required for features on the upper block in motion.

QUOTE (->
 QUOTE Yes, but it took until now to sink in.    This is not a high bandwidth communication medium.

True, it's not. Sometimes my explanations are not so good, either. I'm glad we connected on that. The measurements are already very accurate, and will get more so. So good that every measurable point will need individual perspective correction for the dynamics of the rigid body. Sort of a catch 22, but not really. You see we can derive motion in a 3rd dimension from just one 2D video... My feeling is that other videos will add little or no information content to the descent tracking, but rather a fair bit to the dynamic perspective corrections required for features on the upper block in motion.

That would be impressive!

It's on the list. And it will work.
David B. Benson
The following C447 run temds to confirm the resistive force is very close to

F(Z,S) = kZS

for constant parameter k:

CODE
BV-linZS-F-exp-pow-stretch dB= 0.0 sd= 0.120

BV-ZS-F-exp-pow-stretch   dB= 0.0 sd= 0.120
Sef-linZS-F-exp-pow-stretch dB= 0.6 sd= 0.151

The linZS hpotheses add a small angle so that, in effect, the parameter k grows slightly with (Z-Z0). But this is only about a half a degree of arc and doesn't fair much better.
chris lz
QUOTE (adoucette+Dec 10 2007, 07:08 PM)

It's kind of a strawman argument in that both towers failed at the FIRE/IMPACT floors.

He DOES have a point about the difficulty of unfettered access.

Also, since the collapse began in both towers with an outside wall on a fire floor bowing in, there is no explosive that is capable of a slow sustained force.

Arthur

Arthur, does it seem to you that Loizeaux's comments are so off base as to be obvious disinformation? This is the contention of the poster I quoted above. I'm trying to get a feel for the accuracy of Loizeaux's assertion. Is the fact it's actually 9-10 inches at that point the deciding factor?

(PS, it's "limo" from ad.com. Hope you'll make a re-appearance there someday. Regards, Chris.)
QUOTE (chris lz+Dec 10 2007, 11:09 PM)

Arthur, does it seem to you that Loizeaux's comments are so off base as to be obvious disinformation? This is the contention of the poster I quoted above. I'm trying to get a feel for the accuracy of Loizeaux's assertion. Is the fact it's actually 9-10 inches at that point the deciding factor?

(PS, it's "limo" from ad.com. Hope you'll make a re-appearance there someday. Regards, Chris.)

Hi Chris,

As to your question about Loizeaux. No, I don't think its disinfo, I just think he was responding to many of the CT'ers who claim that there were explosions at the base of the tower and his comments make it pretty clear that it would have been a FORMIDABLE task to take out sufficient columns at the ground level to affect the towers.

Its interesting to note that in the bombing in 93 not a single column was severed and since the bomb was not under the tower itself, those columns were FAR smaller than these massive core columns.

Arthur

PS, I was thinking about AD just the other day. I'm sure that one of these days I'll come back.

einsteen
Shagster,

Here is your continuous result together with the discrete model:

http://i4.tinypic.com/6lv2wyu.gif

They don't differ really much, I don't think the artifacts are numerical errors, if we zoom in at the point of maximum E1/M for a total collapse we get

http://i16.tinypic.com/8e6la2u.gif

But it is still hard to explain precisely. The first edge is the point where the collapse is barely complete. When E1/M is higher the collapse will not be complete and the same kind of function is expected but then a story before the 47th, but if I create a larger graphic there are even curves going back in time a little bit. I guess it has to do with the discrete model, if it is a pure numerical error it should appear also in the beginning because the collapse time summarizes over all stories. But since the collapse was complete, we don't have to worry about that...
David B. Benson
As above, using C449 data:

CODE
BV-linZS-F-exp-pow-stretch dB= 0.0 sd= 0.110

BV-ZS-F-exp-pow-stretch   dB= 0.0 sd= 0.112
Sef-linZS-F-exp-pow-stretch dB= 0.5 sd= 0.145

The up-angles vary between one and three degrees of arc, in both this run and also the previous one (where I slipped a decimal poiint).

These two runs suggest that a resistive force function of the form

F(Z,S) = k*Z*S

is only approximately correct.
David B. Benson
However, this run using C449 suggests that the assumption of a constant is ever so slightly better:

CODE
BV-ZS-F-exp-pow-stretch   dB= 0.0 sd= 0.103

BV-linZS-F-exp-pow-stretch dB= 0.1 sd= 0.109
BV-K+Z-F-exp-pow-stretch  dB= 2.3 sd= 0.200
David B. Benson
Using C449, have hypotheses which attempt to capture, directly, concrete comminution:

CODE
BV-ZS-F-exp-pow-stretch   dB= 0.0 sd= 0.103

BV-K+Z+ZSS-F-exp-pow-stretch dB= 2.1 sd= 0.192
BV-K+Z+SS-F-exp-pow-stretch dB= 2.8 sd= 0.230
Sef-K+Z+SS-F-exp-pow-stretch dB= 4.6 sd= 0.281
Sef-K+Z+ZSS-F-exp-pow-stretch dB= 5.1 sd= 0.287

K+Z+SS refers to a force function of the form

k0 + k1*Z + k2*S*S

while K+Z+ZSS refers to a force function of the form

k0 + k1*Z + k2(Z-Z0)S*S,

this assuming continual re-crushing of already crushed materials occured.

Again we see that the B&V form is ok, but the Seffen form is substantially disconfirmed.
shagster
QUOTE (einsteen+Dec 11 2007, 05:21 PM)

But it is still hard to explain precisely. The first edge is the point where the collapse is barely complete. When E1/M is higher the collapse will not be complete and the same kind of function is expected but then a story before the 47th, but if I create a larger graphic there are even curves going back in time a little bit. I guess it has to do with the discrete model, if it is a pure numerical error it should appear also in the beginning because the collapse time summarizes over all stories. But since the collapse was complete, we don't have to worry about that...

I tried using my discrete algebraic crush-up model for determining collapse duration vs. E1/m and see artifacts similar to what you describe.

I'll try to post some details later if I have time.
shagster
Einsteen,

I don't know all the details of your discrete model. But if you were using 47 stories in the model, you can try using more stories, such as 470 but with the same building height, and see what happens to that scalloped effect. The higher the number of stories, the more the model should approach a continuous type of model.

einsteen
Indeed Shagster, for each point the difference could be made arbitrarily small if we choose sufficient points. I'm glad you also had that error in your discrete setup.

What I did was calculating the time to go from i -> i+1 with the formula that follows from conservation of energy, the E1 was taken uniform, it could also be due to a peak force, i think this gives a larger collapse time.

for constant E1 I used

t_i=2h/(v_i+V_{i+1})

which is also similar to [V_{i+1}-v_i]/averageAcceleration

It could also be done with g, but then just before and after a floor
reaches ground zero the velocity changes stepwise. The result should be