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Harry K Harry K is offline
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Default WTC Towers: The Case For Controlled Demolition

On Mar 13, 9:51*pm, wrote:
On Mar 13, 9:41 pm, wrote:





On Mar 13, 9:53 pm, Harry K wrote:


On Mar 13, 1:17 am, wrote:


WTC Towers: The Case For Controlled Demolition
By Herman Schoenfeld


In this article we show that "top-down" controlled demolition
accurately accounts for the collapse times of the World Trade Center
towers. A top-down controlled demolition can be simply characterized
as a "pancake collapse" of a building missing its support columns.
This demolition profile requires that the support columns holding a
floor be destroyed just before that floor is collided with by the
upper falling masses. The net effect is a pancake-style collapse at
near free fall speed.


This model predicts a WTC 1 collapse time of 11.38 seconds, and a WTC
2 collapse time of 9.48 seconds. Those times accurately match the
seismographic data of those events.1 Refer to equations (1.9) *and
(1.10) *for details.


It should be noted that this model differs massively from a "natural
pancake collapse" in that the geometrical composition of the structure
is not considered (as it is physically destroyed). *A natural pancake
collapse features a diminishing velocity rapidly approaching rest due
to the resistance offered by the columns and surrounding "steel mesh".


DEMOLITION MODEL


A top-down controlled demolition of a building is considered as
follows


* * * * 1. An initial block of j floors commences to free fall.


* * * * 2. The floor below the collapsing block has its support structures
disabled just prior the collision with the block.


* * * * 3. The collapsing block merges with the momentarily levitating floor,
increases in mass, decreases in velocity (but preserves momentum), and
continues to free fall.


* * * * 4. If not at ground floor, goto step 2.


Let j be the number of floors in the initial set of collapsing floors.
Let N be the number of remaining floors to collapse.
Let h be the average floor height.
Let g be the gravitational field strength at ground-level.
Let T be the total collapse time.


Using the elementary motion equation


* * distance = (initial velocity) * time + 1/2 * acceleration * time^2


We solve for the time taken by the k'th floor to free fall the height
of one floor


* * * * [1.1] * t_k=(-u_k+(u_k^2+2gh))/g


where u_k is the initial velocity of the k'th collapsing floor.


The total collapse time is the sum of the N individual free fall times


* * * * [1.2] * T = sum(k=0)^N (-u_k+(u_k^2+2gh))/g


Now the mass of the k'th floor at the point of collapse is the mass of
itself (m) plus the mass of all the floors collapsed before it (k-1)m
plus the mass on the initial collapsing block jm.


* * * * [1.3] * m_k=m+(k-1)m+jm =(j+k)m


If we let u_k denote the initial velocity of the k'th collapsing
floor, the final velocity reached by that floor prior to collision
with its below floor is


* * * * [1.4] * v_k=SQRT(u_k^2+2gh)


which follows from the elementary equation of motion


(final velocity)^2 = (initial velocity)^2 + 2 * (acceleration) *
(distance)


Conservation of momentum demands that the initial momentum of the k'th
floor equal the final momemtum of the (k-1)'th floor.


* * * * [1.5] * m_k *u_k *= m_(k-1) *v_(k-1)


Substituting (1.3) and (1.4) into (1.5)
* * * * [1.6] * (j + k)m u_k= (j + k - 1)m SQRT(u_(k-1)^2+ 2gh)


Solving for the initial velocity u_k


* * * * [1.7] * u_k=(j + k - 1)/(j + k) SQRT(u_(k-1)^2+2gh)


Which is a recurrence equation with base value


* * * * [1.8] * u_0=0


The WTC towers were 417 meters tall and had 110 floors. Tower 1 began
collapsing on the 93rd floor. *Making substitutions N=93, j=17 , g=9.8
into (1.2) and (1.7) gives


* * * * [1.9] * WTC 1 Collapse Time = sum(k=0)^93 (-u_k+(u_k^2+74.28))/9.8 =
11.38 sec
* * * * * * * * where
* * * * * * * * * * * * u_k=(16+ k)/(17+ k ) SQRT(u_(k-1)^2+74.28) * * *;/ u_0=0


Tower 2 began collapsing on the 77th floor. Making substitutions N=77,
j=33 , g=9.8 into (1.2) and (1.7) gives


* * * * [1.10] *WTC 2 Collapse Time =sum(k=0)^77 (-u_k+(u_k^2+74.28))/9.8 =
9.48 sec
* * * * * * * * Where
* * * * * * * * * * * * u_k=(32+k)/(33+k) SQRT(u_(k-1)^2+74.28) * * *;/ u_0=0


REFERENCES


"Seismic Waves Generated By Aircraft Impacts and Building Collapses at
World Trade Center ",http://www.ldeo.columbia.edu/LCSN/Eq...C_LDEO_KIM.pdf


APPENDIX A: HASKELL SIMULATION PROGRAM


This function returns the gravitational field strength in SI units.


g :: Double
g = 9.8


This function calculates the total time for a top-down demolition.
Parameters:
* _H - the total height of building
* _N - the number of floors in building
* _J - the floor number which initiated the top-down cascade (the 0'th
floor being the ground floor)


cascadeTime :: Double - Double - Double - Double
cascadeTime _H _N _J *= *sum [ (- (u k) + sqrt( (u k)^2 + 2*g*h))/g | k-[0..n]]
* * * * * * * * * * * where
* * * * * * * * * * * * j = _N - _J
* * * * * * * * * * * * n = _N - j
* * * * * * * * * * * * h = _H/_N
* * * * * * * * * * * * u 0 = 0
* * * * * * * * * * * * u k = (j + k - 1)/(j + k) * sqrt( (u (k-1))^2 + 2*g*h )


Simulates a top-down demolition of WTC 1 in SI units.


wtc1 :: Double
wtc1 = cascadeTime 417 110 93


Simulates a top-down demolition of WTC 2 in SI units.


wtc2 :: Double
wtc2 = cascadeTime 417 110 77- Hide quoted text -


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For the people buying into the 'conspiracy' go over to
alt.conspiracy. *There are many threads there, at least 4 running now
in which all the BS theories are discussed. *Of course none of the
conspiracists will believe any of the debunking but it is good for
laughs.


Harry K- Hide quoted text -


- Show quoted text -


They really are a pathetic bunch, aren't they? * They like to focus on
every little nit separately, completely distort it and make outrageous
claims. * * None of these crackpots has put together a time-line and
story that runs from start to finish explaining what happened that
day. *Forget about controlled demolition. * What about all the planes
that left 3 airports that day and were flown into the buildings? * Who
flew them or is that just a myth too? * And if they were part of the
conspiracy, how would anyone know precisely where the planes would hit
the buildings and that the impact would not disrupt the allegedly pre-
planted explosives?


The official explanation does put together a whole picture that makes
sense. * *For this to have been some govt conspiracy, it would have
had to be the most elaborate one in history. *And the funniest part of
all, is these kooks try to blame it on the Bush administration. *If
they were gonna pull any conspiracy like this, why didn't they just
put some WMD's in Iraq? * That would be child's play compared to what
this alleged 911 conspiracy would have had to entail.


Sure.
If one can't explain every detail then the "official" conspiracy
theory is the truth?
What about the spire?http://youtube.com/watch?v=FWn8QNQWSsY&feature=related- Hide quoted text -

- Show quoted text -


One does not have to explain _everything_ but mosst of it does have to
be. If you are paying attention, the kooks explain absolutely
NOTHING. They make assertions with nothing to back them up, ignore
reams of evidence, what they can't ignore they either distort or lie
about.

You are doing a good job of the latter.

Harry K