The 9/11 Forum

Just to finish a point:

It is easy to graphically see how the building resists collapse as a function of time.


Taking Einsteens graph of a(t) above and remembering that this is the same as the magnitude of F(g)-F(c) (same shape with a different scale), and knowing that F(g) is constant....


We can see the shape F(c) takes just by flipping Einsteens graph upside down. In other words, just mirroring Einsteen's graph around any line a= constant for all t shows us the exact shape of the graph of how the sum total of the forces within the building resist collapse over time.

It crossed F(c)= 0 at two points: The two moments of time when a=g. And when t=0, F(c)=F(g).


If you imagine Einsteen's graph flipped upside down, you can see how building resistance held pretty well during the first few moments and then dropped like a roller coaster.


The sum total of building resistance quickly drops to absolute 0 and than some. F(c) strangely temporarily dips into the negative, baffling adherents of the Newtonian physical world view the world over.

But in our simplified model, We suspect that F(c) has at least two separate recognizable components

F(c)= F(r) + F(s)

Where the vector F(r) is the general resistance of the building to being crushed

and F(s) is a transcient spring force directed downwards.


the vector F(r) always acts upwards because it is inherently resistive.

The vector F(s) only acts downwards and is only considered to exist during a certain interval of the collapse, peaking as a(t) peaks (hence transient).

So, as vectors, they cancel one another.


We can then graphically see how the building resistance then increases rapidly, reaching a point of peak resistance. But then, yet again, resistance to crushing seems to weaken.


The confusion over an F(c) temporarily pulling the building downwards is in not recognizing it is not a purely resistive force.

The negative number may just mean that, when the "spring" was fully loaded, the magnitude of F(s) exceeded that of F(r). It doesn't mean F(r) completely disappears.

Major_Tom:

I have trouble with the fact that the acceleration apparently peaks at about 3 seconds which is well into the collapse and when the building had already dropped about 15 meters. If there was some sort of "loaded" spring surely it would have acted immediately after the roofline started its downward motion. Although I guess it's possible the "spring" gave the roof an initial downward kick and it took a few seconds for the resistance of the lower part of the building to retard the descent....., who knows?

I have also (as a last resort!) been looking at other possible ways to explain accelerations that are equal to or above g - that is assuming NIST's data set is reasonably accurate. One thing worth looking at is the possibility that WTC 7 tilted as it fell. This is discussed by NIST in Chapter 5 of NCSTAR 1-9. NIST estimate that the northeast corner of Building 7's roof was displaced about 11 meters to the north about 3 seconds into the collapse when the vertical drop was only about 15 meters! However, even though the eastern side of WTC 7 was tilted to the north at this point in time, the western side was not! But to make matters worse, if you look at the newly released WTC 7 collapse video, (apparently taken from a highrise building on River Terrace), after about 4.5 seconds of collapse the western roof corner of WTC 7 tilted markedly to the south!
This can only be explained by the building undergoing a twisting motion somewhere near the center of the north face. Very strange!

Anyway, if you factor in tilting effects you can reduce the vertical drops of the center of the roofline by no more than 1 meter at the 3 second mark. This only has a minor effect on the calculated accelerations, but it would be helpful for someone to confirm these preliminary conclusions.

The bottom line is I am still having a lot of trouble with accelerations greater than or equal to g; but I dont see how pre-planted explosives resolves this issue.....

Major_Tom wrote:But in our simplified model, We suspect that F(c) has at least two separate recognizable components

F(c)= F(r) + F(s)

Where the vector F(r) is the general resistance of the building to being crushed

and F(s) is a transcient spring force directed downwards.

Earlier, you'd had a question about some comment I'd made... "maybe it was dragged down" (or pulled, I don't remember). I didn't answer, but that's because I had to think about it.

The relation you give above is exactly what I had in mind, in its naked form. A resistance force and another force that may be oppositely directed, at least transiently (if so is an assistance force). I didn't want to specify if it comes by way of a restoring force from a deflected spring, or the more fluid phenomena of entrainment into already falling interior mass, or something else. Some sort of assistance force may come into play but how long and over what distance could this force be applied?

This argument applies independent of magnitude, if it applies. Faster than freefall is not a requisite condition for there to be an 'assistance' force. That there is already net momentum directed downward prior to global collapse means it will be difficult to unravel the forces acting on the part measured.

What needs to happen first is collection of reliably accurate numbers, and to develop a proper geometric interpretation of the pixel motion. Then, and only then, can there be any hope to resolve this.

To this minute, I'm still having problems getting good data, reducing it to a fitted function, and forget about interpretation. If these curves never went above g , no one would ever look twice. NIST's formula for y and v shine a spotlight on these problems. The glaring reality is that acceleration is a second order quantity; the underlying position dataset must be incredibly accurate and properly interpreted to give meaningful results. Across these threads, constant ~8.7 m/s^2 crops up again and again, but it is also possible to hit 15 m/s^2 with a fairly justifiable interpolation!

My feeling right now is that NIST is not doing this correctly, there's no reason to get to involved with any of the consequences if the work is flawed. I've just been hit with the same thing only worse with some of my data. Decent interpolations can give nonsense, and a pair of equally viable strategies can diverge wildly. The main difference is, I post my stuff on a forum as informal, tentative works in progress. I don't have any attachments to any stage yet, nor is there a timeline. It gets worked until it gets right.

Dr. G wrote:OneWhiteEye:

Additional research will be undertaken to make these results more ambiguous

i still think, any way you slice it, it's TOO fast to be unassisted.
the bottom has to disappear out from underneath the descending mass for anything NEAR freefall to be 'natural'.

I've still not read a line concerning the final function in the report but what about the function v(t) itself and x(t)


http://i33.tinypic.com/102uk2v.gif

With maple it is a simple matter of pasting

Code: Select all

v:=247.52*(0.18562*t)^2.5126*exp(-(0.18562*t)^3.5126);
plot(v,t=0..10);
x:=int(v,t=0..t1);
plot(x,t1=0..10);


The latter one (if the function is correct, which I doubt) should in fact be the smearogram. The fact that a number like 3.5126 is given with four digits after the dot implies that the error is less than 0.0001, could a<g be obtained taking that into account for all numbers...? Well, first I should RTFR of course...

I have trouble with the fact that the acceleration apparently peaks at about 3 seconds which is well into the collapse and when the building had already dropped about 15 meters. If there was some sort of "loaded" spring surely it would have acted immediately after the roofline started its downward motion. Although I guess it's possible the "spring" gave the roof an initial downward kick and it took a few seconds for the resistance of the lower part of the building to retard the descent....., who knows?

I agree. I was only painting a picture.

The generic equations I gave are still valid in any case if we consider F(s) not as a spring force but as a general downward mystery force, the origin of which we are trying to discover.

Or perhaps their mapping and equation is just wrong.

My point is I am not here to take on classical mechanics, just the bastards attempting to manipulate a gullible humanity into a further dwindling spiral of greed and hate.

We'd all agree that if a=>g, there must have been an additional generic downward force which I call F(s).

i still think, any way you slice it, it's TOO fast to be unassisted.
the bottom has to disappear out from underneath the descending mass for anything NEAR freefall to be 'natural'.

I agree. And I must once again stress that, even more important than this, it is the SYMMETRY and SIMULTANEITY of column failure which strongly suggests this was planned and intentional.

This is more important than any numbers we can produce.

The following questions refer to the part of WTC7 that we can see in the collapse videos; we can only see the north facade in most videos, and the north and west in one video. The videos obviously do not show the other facades or the interior.
Does everyone agree with NIST that the visible part of WTC7 dropped at near free fall for about 2.25 seconds or 25 meters? Is anyone surprised that there is uncertainty in this value of maybe 5 or 10 percent? Do we all agree the data would have been better had there been an IMAX camera recording the collapse from a few blocks away?
Give the data we have, can we conclude that a roughly 25 meter segment was suddenly removed from most of WTC7's vertical support columns, at least the vertical support columns for the facade we can see? Do we all agree that this happened at nearly the same time, within maybe half a second, all over the base of WTC7, or at least the base of the facades?
Do we agree that the final part of WTC7's descent did not happen at free fall because relatively undamaged vertical beams hit the ground after WTC7 dropped 25 meters at free fall?
Does anyone rule out sabotage, arson, or controlled demolition based on the videos we have?
Does anyone rule them out on OTHER evidence?
Thanks!
-Richard

But if we accept this result I have to ask:

What is going on?

resulting acceleration as measured at floor 47:

During frame 150 and 180 the west penthouse dropped at (near) free fall. The north wall either kinked down for about 0.3 meters or just kinked south***. When the tolerance of the floor slaps was reached the already accelerated core catapulted the outer shell down. For a short time the entire outer shell achieved an acceleration of about 11.5m/s².

***probably the the north wall was pulled towards south by the falling core. The video NIST used for measurements is a low perspective. A movement towards south would look like a downwards movement. There is no way to decide either the one way or the other without additional measurements or using different perspectives.

more about the measurements here:
http://the911forum.freeforums.org/wtc-7-trace-data-t353.html#p9790

Major_Tom wrote:Just to finish a point:

It is easy to graphically see how the building resists collapse as a function of time.


Taking Einsteens graph of a(t) above and remembering that this is the same as the magnitude of F(g)-F(c) (same shape with a different scale), and knowing that F(g) is constant....


We can see the shape F(c) takes just by flipping Einsteens graph upside down. In other words, just mirroring Einsteen's graph around any line a= constant for all t shows us the exact shape of the graph of how the sum total of the forces within the building resist collapse over time.

It crossed F(c)= 0 at two points: The two moments of time when a=g. And when t=0, F(c)=F(g).


If you imagine Einsteen's graph flipped upside down, you can see how building resistance held pretty well during the first few moments and then dropped like a roller coaster.


The sum total of building resistance quickly drops to absolute 0 and than some. F(c) strangely temporarily dips into the negative, baffling adherents of the Newtonian physical world view the world over.

But in our simplified model, We suspect that F(c) has at least two separate recognizable components

F(c)= F(r) + F(s)

Where the vector F(r) is the general resistance of the building to being crushed

and F(s) is a transcient spring force directed downwards.


the vector F(r) always acts upwards because it is inherently resistive.

The vector F(s) only acts downwards and is only considered to exist during a certain interval of the collapse, peaking as a(t) peaks (hence transient).

So, as vectors, they cancel one another.


We can then graphically see how the building resistance then increases rapidly, reaching a point of peak resistance. But then, yet again, resistance to crushing seems to weaken.


The confusion over an F(c) temporarily pulling the building downwards is in not recognizing it is not a purely resistive force.

The negative number may just mean that, when the "spring" was fully loaded, the magnitude of F(s) exceeded that of F(r). It doesn't mean F(r) completely disappears.

This description of F(c) is very generic. I can remove the word "spring" and nothing in the reasoning changes.

For the moment I'll consider the case that the greater than g period really happened. Therefore F(s) exists. Are there explanations for F(s) that do not require elastic spring loading?

The simplest explanation for F(s) is a pull-down force on the outside wall caused by the core leading the collapse.

1) Core pulls on perimeter to the point of perimeter "release"

2) Released perimeter could fall close to g once released even if no core is pulling down on it. Released perimeter uncoupled to core would experience forces F(g)-F(r) which may be close to g for a 47 story building. But if the core is pulling downward during and just after the release, the forces are

F(g) -F(r)+F(s)

Where F(s) is not a spring force but just a pull-down force.

An easier way to explain the movement:

Consider Newton's apple ripe on the tree. When the stem breaks the apple goes into free-fall. We know to expect a constant acceleration g.

Now imagine someone ties a string to the apple and pulls it downward the whole time the stem breaks.

The string is F(s) but the string is not elastic. The apple without the spring experiences downward force F(g)=mg. The apple with the string experiences F(g)+F(s).

Slight adjustment. The hand pulling the apple down applies a sustained external force. In this sense it's like a spring attached to ground or a rocket attached to the apple. I'd argue that neither of these types of forces are applicable. While the stationary portion is coupled to the ground, the external force is limited to reaction force of the ground which clearly is never directed downward! Thus all forces which act to accelerate the building downward, besides gravity, must be internal forces. (edit: I screwed this up a bit, as if the hand were attached to a body fixed to the ground, it's all internal forces, but see next post)

Key to this is the force must continue to be applied at least over the interval of over-g, which for WTC7 is of the order of a second-ish. A short impulse doesn't count, no matter how large. A series of impulses can do it. The building can deform elastically, but over no significant distance can it do so in tension through any axis - the string does not stretch. From the cited study by Vlassis, it's prudent to assume there is a small limit on connection rotation before plastic failure as well.

The choices to precede discrete failure of the observed stationary portion , as I see it, are these:

1) strain potential accumulation from debris pile-up
2) rotation about a pivot on the stationary portion

and concurrent/post global release are these:

3) sustained momentum transfer from debris impact
4) lateral pull-in at the bottom from sustained debris stream impact on floor slabs and beams
5) lateral push-out at the bottom from sustained horizontal debris pressure

#1 - #3 have all been suggested by various parties; can't say I've seen 4 and 5 anywhere. Any mix is possible - except the last two are exclusive, of course. The second and fourth are distinct but likely to occur together, if either does at all.

Analogy-wise, a barrel or dumpster instead of apple is sufficient to make it internal.

1) Strain potential: load-up-to-failure-and-release. A sticky stream impacts the apple, accumulating, deforming it (not the branch or stem) elastically, until such time as the stem fails and the apple becomes a free body. The apple rebounds in shape and a portion of it descends at over g and the rest under g, such that the center of mass is in freefall. Depending on the damping, the apple might continue the oscillation so that the previously over g portion becomes the under g portion.

This is the floor assemblies bowing down in the center, then when the wall breaks down low they straighten out a bit dragging some portions of the perimeter a little faster, perhaps aided by a fulcrum from laterally asymmetric support. Probably what most people have in mind, from what I gather.

2) Rotation: Couldn't translate this into apple terms. This is also very popular in one form or another but to me is a little harder to fit. I've stopped clicking on the videos depicting top-loaded meter sticks falling with an initial angle near 45 degrees. I get it. While nothing so gross can be observed in WTC7's early motion, there is the possibility that there was some internal rotation of floor slabs about a small angle and subsequent connection failures at the wall occurred over a period of time, each providing a short discrete impulse. Which is really a variant of #3.

The problems are basically...

- the building is not observed to deform substantially in and around the spatial and temporal regions of interest
- likewise, no significant global rotation in these regions
- likewise, no significant external evidence of catastrophic connection failures in these regions
- low expectation of floor connections surviving large rotations

3) Sustained momentum transfer: the firehose effect. The faster stream continues impinging on the apple, transferring momentum. A tank of water is dumped on the apple from above, breaking it free and accelerating it downward until either the stream and apple velocities are the same, or the stream ends before that time.

This is not something which is usually stated explicitly, but some hand-waving propositions basically seem to rely on or imply something like this. A bunch of debris is moving down through the interior exerting a sustained rubble-driven force. Integrity of either component need not be maintained in collisions, but there must be ongoing collisions over the entire interval for this to work. While somewhat aesthetically pleasing, this mechanism is hampered by erosion if there is failure (where do the new contact points, debris stream vectors, and load paths arise?), and degenerates to one of the other modes if there is not.

4) Cascading collapse of interior portions above result in floor assemblies pulling lower wall inward rapidly, as the slabs are pushed down. Here, the downward forces applied by debris impacting lower sections causes the lateral span of the assemblies to decrease (catenary-ish in the loosest sense), imparting horizontal force to rapidly pull wall sections inward. This in turn transmits a downward force due to shortening of the projection of the wall surface onto the vertical axis.

This is, shape-wise, similar to NIST simulation but cause-wise entirely different. The constraint is the floor connections must be very strong in tension. Dont know if that counts as a problem but I'd think so. Advantage is, by moving the mechanical coupling through a horizontal phase, there is no longer a need to drive vertical motion collinearly. Mechanical advantage can exist with fixed length members directly coupled.

A single large (perhaps diffuse) debris impact could bow one or more floors, pinching the perimeter which fails immediately in terms of providing measurable vertical support but also gets yanked in. Now all that's required to sustain the force is to continue to have the floor bow downward more and stay connected to the perimeter, no additional momentum transfer needed because geometry is involved in adding a vertical component of force to something which is now freely falling anyway.

5) Debris pressure pushing outward: opposite of #4. So much stuff falls down the inside that, when it hits bottom, it spreads and forces the walls outward, dragging the perimeter and all attached downward. I used to fancy this one, but it would take a lot of debris to fan out like that. The wall would have to remain attached and not fracture. Seems awfully imaginative.

May have missed something. There are days when all of them seem plausible, and others where none seem possible.

The hand can pull the string and therefore apple down because it's mass capable of generating internal forces. Even if it's just a disembodied arm, it can draw the apple down closer to it as both fall. An isolated hand can draw the apple down in the same way by curling its fingers, but now the magnitude of effect is correspondingly less, just as a free arm will not be able to sustain force of high magnitude like a free whole body could.

I get the impression some would prefer to think of it as an elastic string. Or Wile E. Coyote's neck after stepping off a cliff. No. No such components.

2 quick points:

1) I am glad you mentioned Wile E. Coyote because he is one of my favorite engineers. I could teach a course in university physics 101 by using scenes from "Road Runner" cartoons and having students identify what is physically impossible. With a character as inventive as the coyote, filling a 16 week course would be no problem

If you know who Wile E. Coyote is then you probably are familiar with Mr Magoo.

If you say "yes" I will refer to these two colorful, lovable characters in future posts.



2) I didn't specify but I was considering the perimeter wall at eh point measured as the body and the core pulling as an outside force acting on the body.

I never intended F(s) to be an internal force. We are literally measuring the movement of a mass dm in the region dx*dy*dz of a large complex body. I was thinking the body can be seen as 2 coupled bodies, core and perimeter. Measuring NW is measuring point on perimeter body. Core body is outside object, core pulling is an external force.

I suggest a variation of this...

...is a likely candidate.

Core first, still attached, pulling perimeter.

Over-g is in action after a few feet. Within bounds of multiple floor assemblies being still attached ? I'd say yes given the connection strength, but no given the lack of facade distortion.

Food for thought ?

Implies Northward motion of the core OR pulled southward motion of the North facade