The 9/11 Forum

OneWhiteEye wrote:Greening's is the best documented.

Greening simply claims:

The potential energy stored in one WTC tower = 1.0  10^12 J
(This result is assuming mass of one WTC tower = 510,000,000 kg)

He doesn't even attempt substantiate his claim any further than that. He's obviously doing the same abstracting of the tower into a ball suspended from a height as Mackey did though, while using much higher mass and center of mass estimates to arrive at more than double Mackey's supposed PE value.

OneWhiteEye wrote:

My interest here is in discussing Psykey's question of "how did the supposed PE of the WTC produce dust hundreds of feet above the ground?"...

Collisions, as I said above.

And as i replied above; collisions are ignored when one abstracts the situation into calculating PE as if describing a ball dangling from a rope.

The figure is disputed by many. Suggest a better one.

How is that figure used? Energy is neither created nor destroyed; the change in potential energy between the initial and final states of the tower must be accounted for. By observing there is excess lost PE energy over and above that calculated to be used in failing supports, it is noted that sufficient energy remains to crush the concrete. When it comes to proposing the actual mechanism, step-wise collisions with successive stories are used. The total potential energy change figure is not used for this.

Greening wrote:Let’s now consider the beginning of the 1st stage of the collapse of each tower. For WTC 1 we will take as an example 14 floors, and for WTC 2, 29 floors impacting the floor below with a maximum velocity of 8.6 m/s. It follows that the kinetic energy on impact was ½ x 14 x (510,000,000/110) x (8.6)^2 joules = 2.4 x 10^9 J for WTC 1, and the K.E. was ½ x 29 x (510,000,000/110) x (8.6)^2 joules = 5.0 x 10^9 J for WTC 2. If we assume 50 % of this energy was available to crush concrete, we have 1.2 x 10^9 J available for WTC 1, and 2.5 x 10^9 J available for WTC 2. This is sufficient to crush the concrete on the impacted floor to 175 µm particles.

Consider now the newly formed mass of (14 + 1) floors of WTC 1, and (29 + 1) floors of WTC 2, impacting on the floor below. Because of momentum transfer, the impact velocities are slightly lower than the 8.6 m/s impact speed for the first floors hit: 8.1 m/s for WTC 1, and 8.3 m/s for WTC 2. The maximum kinetic energy prior to impact is ½ x 15 x (510,000,000/110) x (8.1)^2 joules = 2.3 x 10^9 J for WTC 1, and ½ x 30 x (510,000,000/110) x (8.3)^2 joules = 4.8 x 10^9 J for WTC 2. This is essentially the same result as the previous impact calculation and the kinetic energy released is therefore also sufficient to crush the concrete on the impacted floor to 175 µm particles.

Bolding mine to emphasize the word IMPACT, and these are the collisions of which I spoke. Far cry from ball on a rope, wouldn't you say?


Having said this, I wouldn't necessarily produce the same mechanism if asked; I'm not so well-versed in concrete crushing. I'll give you my crude take on it in a few. The point is collisions are NOT ignored, quite the opposite. Continuum models don't have impacts per se but accrete continuously with infinitesimal impacts which conserve momentum and therefore amount to the same thing as the discrete impacts.

OneWhiteEye wrote:The figure is disputed by many. Suggest a better one.

I suggest Psikey is correct in dismissing efforts to derive such figures as "nothing but mathematical pseudo-intellectual bullshit."

OneWhiteEye wrote:By observing there is excess lost PE energy over and above that calculated to be used in failing supports, it is noted that sufficient energy remains to crush the concrete.

Rather, by abstracting the tower into a ball suspended from a height, he cites that supposed PE value to claim there was more than enough energy to fail the supports and crush the concrete.

OneWhiteEye wrote:When it comes to proposing the actual mechanism, step-wise collisions with successive stories are used.

Sure, by abstracting the upper mass in his assumed successive collisions as a ball suspended from a height, and subtracting PE from that by accounting for the difference between the observed acceleration of the destruction and that of free fall. Put simply, his whole line of argument is a textbook example of reverse scientific method.

{deleted}

I'm going to take a more exploratory approach to bound certain aspects of the problem, rather than be assertive with disputable figures. The computations use unit masses for each story, therefore all energy values on graph axes are scaled down by the appropriate order of magnitude. The first case examines a classic WTC1 split at the 96th floor, rigid block above. No support fail energy is supplied in the first two cases, they are momentum-only to show how much energy is dissipated solely through the action of inelastic collision. The first case matches Greening's momentum-only y(t),v(t) result for WTC1.

By assuming inelastic collision between slabs (a very defensible assumption), the model requires a certain amount of KE to be dissipated at each collision according to conservation of momentum. Dissipated does not mean disappeared. This energy is precisely what goes into deformation and pulverization of material. Since the components presenting the vast majority of collision surface area are the floors and office contents, it is not only reasonable but mandatory that the majority of energy dissipated through inelastic accretion be in those items.

Empirically it can be seen that the bulk of the perimeter and a substantial amount of core did not participate in the interior collapse and only a small percentage of columns were significantly buckled. This corroborates the prior observation that the bulk of energy dissipated in collision went into crushing the interior, because it had to go somewhere and it didn't go into deformation of columns and couldn't go into descent speed. There are other independent sinks like gas expulsion, of course, but let's look at what's mandated by the assumption of inelastic collision, mindful that other incidental sinks will reduce the figures somewhat. (these can be revisited later)


Kinetic energy dissipation at each impact story due to inelastic collision only

12 story block


Because a 12 story rigid block is not a realistic scenario, this is a single story upper block (no stories 98 - 110) plotted alongside the prior:

12 and 1 story block



The one story upper block case has a lower potential energy change over collapse because it has 11 fewer stories mass up top, so a direct comparison of dissipated kinetic energy will naturally be lower for the structure with smaller mass. Neither, incidentally, do those floors need to be crushed since they don't exist!

Both examples show how the energy dissipated in inelastic collision rises linearly with position after a short time. Position, though, is proportional to a power of time (approximately squared). This is an increasingly brutal pounding on essentially similar floors going all the way down.

In a physics engine simulation which allows crush up and down, a rigid top versus crushing top with all else equal shows the two cases have nearly identical kinetic energies over time, now showing the nearly parabolic increase of KE as a function of time:



This indicates the overall energy distribution over time differs little with respect to rigidity of the upper block. The physics engine simulation has been specifically validated against the test case shown above. The prior examples then should serve as a reasonably good indicators of the energy distribution over time regardless of rigidity, and have already shown similar energy dissipation in collision with a miniscule upper block of one story. Notice the immediate loss of much kinetic energy at the moment of final compaction. It's dissipated quickly by slamming into the ground - the seismic signal - and it is tremendous.

How does this dissipated energy compare to other energies involved?

From the physics engine, a comparison of dissipated energies for multiples of support fail energy show dominant loss is to inelastic collision:



Except for the arresting case, the vertical upswings at the end are the counterpart to the KE curve vertical downswings when at full compaction. Conservation of energy requires this accumulation to go into the partitions of bouncing, dispersal, pulverization, heat, sound.

Finally, while there is ample reasoning to show pulverization in air is plausible, I'd like to point out that the assumption that it occurred in large quanities early on is just that - an assumption. Dust clouds are observed immediately but the actual concrete contribution in air is not known. Wallboard was present in abundance, it pulverizes easily. Large amounts of smoke was expelled quickly at the same time. The final distribution of dust is the result of the totality of collapse. It's apparent from the mechanics of this model that KE can become very large. It is most reasonable to believe that a significant amount of pulverization and dispersal resulted from the end of collapse.

Pavlovian Dogcatcher wrote:I suggest Psikey is correct in dismissing efforts to derive such figures as "nothing but mathematical pseudo-intellectual bullshit."

Nope.

Rather, by abstracting the tower into a ball suspended from a height, he cites that supposed PE value to claim there was more than enough energy to fail the supports and crush the concrete.

He simply did the physics according to reasonable assumptions, and there was.

Sure, by abstracting the upper mass in his assumed successive collisions as a ball suspended from a height, and subtracting PE from that by accounting for the difference between the observed acceleration of the destruction and that of free fall. Put simply, his whole line of argument is a textbook example of reverse scientific method.

Wrong again, and too many times I'm afraid. It's called doing physics. You don't know how to do it, so don't know how to criticize it. It shows. Very much. There's a reason why damn few people get the degree; I'm not sure why people not versed in the subject always seem to feel free to dabble. It's like correcting native Japanese on their inflection when the only Japanese you've been exposed to is "Domo arigato, Mr. Roboto."

I've presented a fairly brief argument. The results of Greening's work, my independent derivation and computations, AND a game engine (for chrissakes) ALL agree to a fine level of detail on the scenarios in which they can be compared, despite the considerable differences in approach and means of achieving dynamic solutions for motions. The odd one out is you, with your protestations that anti-science is being done but no physics, no models, no calculations, no experiment (either!) to back your arguments.

It's time to put up or shut up.

femr2 wrote:{deleted}

Dude, why the **** did you do that? I LOVED it. Do you remember it? Please.
It's a wonderful opportunity to post theory and observation. But the debate? What debate? I was about to seriously climb on PD because this has gotten insane. I was glad to see someone else thought so, too.

OneWhiteEye wrote:

femr2 wrote:{deleted}

Do you remember it?.

Pretty much.

PD,

It's clear that you do not understand basic physics principles. It's clear that you do not understand that, in order for the mass of the towers to move from its original location to its post descent location, all of its PE MUST be converted into other forms, regardless of any simplification (relative to ground for instance).

It's time for this nonsense to stop.

If you were capable of losing the attitude I'm sure you would have learned much by now, but it is clear that is not going to happen.

We could really do without this nonsense here.

OneWhiteEye wrote:He simply did the physics according to reasonable assumptions...

Do you consider it reasonable to assume that, in the scenarios depicted bellow; when replacing the steel beam connecting the bricks in scenario A with the a spring of the same mass as shown in scenario B, both will do equal crushing to the blocks of dirt bellow them?:



If you do believe such simplification is reasonable, I suppose I could arrange an experiment to demonstrate otherwise.

This has nothing to do with crushing. it has all to do with the floors being overloaded being the yield strength of the weakest component.

The columns did not collapse nor vaporize. Something fell and what it was was mostly the floors and finally the core fell afterwards.

The floors fell because either all their connections to the columns or channels supporting them were destroyed or the live load increased on the top most undamaged floor to the point of causing it to collapse. And then the one below it collapsed and so on. The facade fell because it had no lateral support. It was not crushed by the top columns. The collapse was slower than free fall, but it reached a terminal velocity and it tool about 14 seconds... fast but not what a free falling object would take. Tens and then hundreds of thousands of tons of rubble falling is not going to be arrested by a 4" slab on bar truss joists.

Pavlovian Dogcatcher wrote:Do you consider it reasonable to assume that, in the scenarios depicted bellow; when replacing the steel beam connecting the bricks in scenario A with the a spring of the same mass as shown in scenario B, both will do equal crushing to the blocks of dirt bellow them?:

No, they are not equivalent. The impulse is short and high for the rigid case, and the impulse for the other is long and low magnitude. The total impulse will be the same, but the effects on an impacted object below will not be.

SanderO wrote:This has nothing to do with crushing. it has all to do with the floors being overloaded being the yield strength of the weakest component.

The subject had drifted to pulverization...

Me: Things collided before hitting the ground.
PD: Most definitely, yet that is ignored when one abstracts the situation into to calculating PE as if describing a ball dangling from a rope.

Tens and then hundreds of thousands of tons of rubble falling is not going to be arrested by a 4" slab on bar truss joists.

It's also probably a lot more efficient concrete pulverization mechanism than explosives placed for maximal effectiveness in bringing the building down.

OneWhiteEye wrote:No, they are not equivalent. The impulse is short and high for the rigid case, and the impulse for the other is long and low magnitude. The total impulse will be the same, but the effects on an impacted object below will not be.

Actually, since you didn't specify the spring constant, the two cases could be equivalent stiffness. I just assumed a soft spring compared to the steel column.

My statement about total impulse being the same is not correct in the general case.

The initial potential energies of the two cases are the same, but the drop heights and therefore change of PE at impact is not the same. It would be better, I think, to make the elastic and rigid connectors the same length as well as mass, and make the drop heights the same.

I made them so different to exemplify the fact that two objects of the same mass and same center mass heights won't necessarily even come close to producing the same destruction when dropped, demonstrating how unreasonable assumptions to the contrary are.

OneWhiteEye wrote:It's also probably a lot more efficient concrete pulverization mechanism than explosives placed for maximal effectiveness in bringing the building down.

Surely you aren't suggesting that a system absent explosives would have more energy to accomplish pulverization than the same system with them? Also, why would you stipulate "placed for maximal effectiveness" when a covert operation would be unlikely to have the luxury to do that?

Pavlovian Dogcatcher wrote:I made them so different to exemplify the fact that two objects of the same mass and same center mass heights won't necessarily even come close to producing the same destruction when dropped, demonstrating how unreasonable assumptions to the contrary are.

OK. Agreed. Does it result in a quantifiable deficit for observed pulverization in the context of collapse? Using the entire upper block mass is a questionable assumption made for expediency. How much does it affect the energy available for pulverization if there's individual slab-slab contact during collapse instead of a rigid block against single slabs?

Surely you aren't suggesting that a system absent explosives would have more energy to accomplish pulverization than the same system with them?

No. I'm saying the system without them still has an abundance of energy from PE loss, and collision/ recrushing at fairly high density is probably a very good mechanism for pulverization. Compared to incidental blast effects, unless charges were in a grid on the floor pans or even embedded in the slabs and then it wouldn't be incidental, it would be a primary mechanism of pulverization.

Also, why would you stipulate "placed for maximal effectiveness" when a covert operation would be unlikely to have the luxury to do that?

Placement suboptimal for taking the building down will increase the incidental effects, for sure, including pulverization. It isn't the same as placement optimal for pulverization, with the exception mentioned above. Increasing the energy dissipated into global incidental effects increases the visible evidence of such effects in an open floor plan. On another thread, you argue that perimeter trees can be propelled by explosive blast without incurring deformation but here you seem to be arguing that concrete will be pulverized incidentally but small fragments will not propelled at high speed in all directions? I was trying to minimize the amount of obvious blast effects to the relatively low velocity objects observed.

Make it as inefficient as you want and add as much chemical energy needed to achieve the desired result. Eventually, there will be concrete pulverization on a large scale, independent of any collapse effects. The question really is whether the observed pulverization is unexplained by a gravity-driven mechanism. Greening's already done the heavy lifting. You could go back through and re-do the calculations for a single slab on slab initiation and work from there. The notion of discrete slabs for collisions could replaced by rubble stream against intact slab, and the 'cushion' of office contents to spread out the impulse (but which also cause localized pressure inhomogeneities...) could be factored in.

Is there a deficit with a more accurate mechanistic description? I don't know, but I don't think so. The models I work with indicate the overall energy partitioning is similar whether the top is rigid or not, so I don't see the addition of inefficiently applied chemical energy as making a lot of difference. If someone worked through it convincingly to show there's a significant energy deficit, beyond uncertainty, and further showed this deficiency is addressed by additional chemical energy in some specific scenario that estimated pulverization efficiency, I'd check it out.

Do you want to pursue it further?