What you're missing is that you're treating impact of a single object, versus impact of a cloud of objects.
The objects in the WTC case are essentially trapped in the WTC structure (unless they actually punch a hole and exit, in which case the damage is done by default). Since they're trapped, they are doomed to deliver all of their kinetic energy to the structure, regardless of how many times it ricochets before it is finally spent.
Also, your equation is just one mechanism. Your equation predicts that jet fuel, having a coefficient of restitution of effectively one, would do no damage at all to steel columns. That is true for small amounts of jet fuel or low speeds, but it is utterly false for 10,000 gallons moving at 0.85 Mach. Indeed, in the case of the Pentagon, which didn't totally collapse and burn and therefore allowed a more detailed inspection of the impact mechanics, the primary mode of deformation is caused by blast and fluid effects, and only in a few cases was blunt impact the dominant factor.
The NIST simulations capture these effects nicely.
By the way, you have it backwards. Hard objects are more likely to collide elastically, not soft objects. That's why billiard balls aren't made of clay.
I can't keep up with all the posts.
I'll try and respond to your group of posts in just this single response.
Regarding my supposed misquotes from your replies, that was not intentional. In the interest of brevity, I only quoted what I thought was the essence of your message. I'm sorry it's so tedious.
Originally Posted by
R.Mackey 
The best guess they constructed does not agree very well with the landing gear observation,
but it's not bad -- while they don't predict landing gear break-through, they do predict a large mass of aircraft breaking through in similar fashion, and with only minor tweaks that are inside the margin of observational error, that mass can be the landing gear.
Your statement was confusing and lacked clarity so I applied it as best I could. To me, "does not agree very well" and "but it's not bad" don't co-exist well and frankly contradict each other. Is a large mass supposed to equate to a unified mass or just a large accumulation of aircraft particles? By saying that with a few tweaks, within the margin of observational error, that the mass could be the landing gear, do you mean it could have the equivalent mass or actually could be physically characteristic of the actual landing gear? It's a very important distinction.
Again I apparently misquoted you about massive chunks of aircraft. You are very easy to misquote unfortunately..or slippery.
Anyway, in the more severe case "chunks" of something, apparently from the aircraft, was comparable in size to the landing gear or a wheel and that for you, this was in excellent agreement.
Well I've looked at the their graphics and see the progression of the aircrafts through the towers. It's not particularly clear to me how they can be sure that what appears to be a small amount of debris exit is actually from the aircraft, or pieces from inside the building when it was impacted by pieces of the aircraft? It's important because particles or groups of particles would not be as significant as a large object known to definitely come from the aircraft. As we know, the only aircraft components capable of remaining relatively intact were the heavy steel components like the titanium engine and landing gear. The rest of the aircraft and it's contents, due to lack of material strength would have become part of the debris cloud.
I think NIST definitely erred in using a homogeneous model. It unfairly describes the aircraft, and when combined with the model failing to confirm the only major observable criteria, the exiting engine and landing gear, it raises justifiable concerns when only their extreme case scenario succeeded in a collapse initiation.
I disagree that the jet fuel, even at 570 mph, as in the extreme case scenario, had enough concentratible momentum to cut the towers steel perimeter columns.
Quote=R.Mackey
No, not really. Exiting the far side of the Tower depends on two things -- trajectory, and whether or not core and perimeter columns were cleared out by something in front. The total energy captured by the tower, and the energy dissipated by the core columns, are the most important features, and energy is a function of m v2 rather than the inherent strength of the components. A stronger component may actually deliver less damage in some situations, because more energy can be dissipated by deforming the component!
That argument may have merit when debating the downward forces acting on the towers at the point of collapse initiation but I feel it is less compelling when dealing with these lateral "slicing" forces.
Yes trajectory of course factors into what lines up with what, and therefore will determine where the relatively clear paths to the exit perimeter wall lay. The major stopper for large, heavy, materially strong objects prior to a clean exit, is of course the heavy steel core columns. Certainly they had the capacity to stop engines and landing gear, while obviously sustaining significant damage to themselves in the process. The fact that a jet engine and landing gear did in fact break through the opposite steel perimeter walls and exit the towers at over 100+ mph indicates a lot of core damaging aircraft components failed to do what the NIST simulation indicates they must have done.
You are arguing energy totals as the key ingredient and I disagree. Certainly the total energy is something to be considered and given a large enough energy budget, the landing gear and the engines could be ruled out as inconsequential in the greater scheme of things. The fact that the less severe and base scenarios failed to create a collapse initiation indicates there wasn't an overwhelming energy budget available. The columns were vulnerable to focused energy and less vulnerable to dispersed energy of the same amount. Think of a karate chop. The same amount of energy delivered with the flat of the hand (large surface area) vs. the side of the hand (small surface area), when striking a board is going to produce two different results. I won't insult your intelligence by explaining that further.
Quote=R.Mackey
To clarify my issues with the NIST model: The key differences between the modeled impact and reality are the disposition of engine fragments and landing gear. These differences are pretty minor, but worth discussion. The components have three things in common -- they are relatively solid, they are likely to detach as a unit, and they are round.
"Aircraft debris external to the towers (landing gear for WTC 1 and landing gear and engine for WTC 2) as documented by photographic evidence."
xc NIST NCSTAR 1-2B, WTC Investigation
NOT engine fragments but the whole heavy titanium steel engine!
Quote=R.Mackey
If I was conducting this investigation from scratch, I would be leery of using a homogeneous material assumption, but to do otherwise might be too complex to actually compute.
Which only serves to support my contention that NIST over compromised their Model!
Quote=R.Mackey
Both engines and wheels would be more damage resistant than the rest of the aircraft structure, the first by virtue of its high-strength alloys, the second due to its shape and rubber coating. In the model this could be included as a ballistic "fudge factor," or if treated as independent objects, they could be granted a higher component strength.
I agree.
Quote=R.Mackey
The engine fragments, on the other hand, are tricky. As NIST notes in their report, all three cases could plausibly eject engine fragments, because -- not captured in their model -- the engine starts with considerable rotational momentum. They treated it as static. They didn't know how to deal with this, and I don't either. The best I can think of is to flag engine core components and add a centripetal velocity once any piece gets detached.
A complete heavy titanium steel engine in the case of WTC2, not just fragments which only lessens the apparent significance!
Quote=R.Mackey
In the end, though, neither of these concerns is such a big deal, except to malcontents looking for any trace of uncertainty upon which to build a tirade. The global results of the NIST simulation are surprisingly accurate, and even more surprisingly, not overly sensitive to changes in input conditions. I am impressed with the quality of their answers, even though I had some doubts based on their approach.
Not a big deal? Malcontents? Excuse me for not rolling over and accepting every word of the NIST conclusions. The global results of the NIST simulations are surprisingly accurate? I guess accuracy is based on the fact that sure enough, NIST tweaked the extreme case scenario and sure enough the towers fell. just like in reality..case closed. I am impressed by NIST's beautifully presented final report. It looks sweet doesn't it? 10,000 marvelous pages of professional excellence! Who could not love text that looks so good? Well I hate to tear the wrapping paper but the bottomline is the content.
I'm sorry, it doesn't matter if 9,999 pages of the report are true, if one page of critical flaws remain.
Quote=R.Mackey
It bears repeating that the simulations NIST conducted are (were) at the cutting edge of research in computational dynamics, not just in impact but in fluid and fire dynamics as well. Ten years ago, such an approach would have been unthinkable. Naturally it's not going to be perfect, but it's still well done.
Which makes their results and conclusions all the more subject to question!
Quote=R.Mackey
MirageMemories, before quoting me again, please read for content.
I hope I haven't distorted your quotes this time.
Quote=R.Mackey
And let me refresh my latest question, since you seem to have ignored the previous formulation:
In your opinion, which of the three cases is the best fit to all the observed evidence? The less severe, baseline, or more severe case? Choose only one.
NONE!
I place more importance on the only proven observable than you do!
Regarding NIST and pdf page numbers, I know the difference and I always reference to the NIST page numbers which are clearly marked. If I was in error in saying you didn't do this, I apologize.
Yes I made a typo on elastic/inelastic.
I am well aware that there was a "cloud" of objects moving at high velocity inside the towers once the aircraft disintegrated after punching through the perimeter wall.
Just because I isolated the effect of one object, does not negate my point about deformation damage as invalid.
Some of the objects were trapped inside the WTC and some of the objects punched the perimeter walls, making high velocity exits, carrying their remaining destructive potential with them.
Diffused energy due to a high velocity spread of small, relatively soft particles is not going to have the potential for deformation damage that large relatively intact titanium steel jet engines and landing gear will.
Focused energy is more damaging to the core than distributed energy.
I won't argue that liquid moving at high speed carries significant mass and thus significant force, momentum and transferable energy. Since the bulk of fuel is carried inside the wings, it's impact force will be significantly spread out while being further lessened by contact with office components and interior walls. I really question how much impact damage the jet fuel had on critical building structural members.
I have no wish to go off on a tangent by including the Pentagon in this discussion.
No doubt in the volume of posts I have omitted replys to some of your questions. If my answers are important to you, I suggest you re-ask or move on.
MM
