WTC Towers: The Case For Controlled Demolition

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 the "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
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

<> wrote in rec.arts.tv:

>
> WTC Towers: The Case For Controlled Demolition
> By Herman Schoenfeld

Lunatic

--
Brandy Alexandre

The measure of a man's real character is what he would do if he knew he
never would be found out. -- Thomas Babington Macaulay

>>
>>
> Controlled demolition of a skyscraper require miles of trigger wires, beam
> cutting, and careful placement of bombs. Bombs are not stable in high heat
> and wires melt, so guess what happens to the controlled part of the
> demolition? How do you hide this activity from the office workers?
>
> Here is the closer: a controlled demolition requires that the basement and
> first floor of a skyscraper be back filled with cement to control the
> downward forces.

Imagine hundreds of people trying to keep a secret about anything?

In article <1qp7kw778nnwu$.>,
Rocinante <> wrote:


> Here is the closer: a controlled demolition requires that the basement and
> first floor of a skyscraper be back filled with cement to control the
> downward forces.

And most of the support columns have to be cut and weakened.

On Dec 10, 11:05 am, "It's the Principle!"
<brandy...@kittylitternewsguy.com> wrote:
> <schoenfeld....@gmail.com> wrote in rec.arts.tv:

> > WTC Towers: The Case For Controlled Demolition
> > By Herman Schoenfeld
>
> Lunatic

That's true enough.

Of course, Hitler did have the Reichstag fire set, and *if* American
politicians had done such a horrible thing, the American people would
want to know about it.

But the notion is too improbable to be entertained for a moment, and
it is an insult to the families of those who perished that day. And if
the WTC was blown up by explosives, so there were no hijackings... I
suppose all those people who spoke to loved ones by cell phone on
Flight 93 were in on the hoax.

That, I think, pretty much puts paid to these crazy and pathetic
conspiracy theories.

John Savard

> Controlled demolition of a skyscraper require miles of trigger wires, beam
> cutting, and careful placement of bombs. Bombs are not stable in high heat
> and wires melt, so guess what happens to the controlled part of the
> demolition? How do you hide this activity from the office workers?
>
> Here is the closer: a controlled demolition requires that the basement and
> first floor of a skyscraper be back filled with cement to control the
> downward forces.

Now THAT's a good answer!

> > Controlled demolition of a skyscraper require miles of trigger wires, beam
> > cutting, and careful placement of bombs. Bombs are not stable in high heat
> > and wires melt, so guess what happens to the controlled part of the
> > demolition? How do you hide this activity from the office workers?
> >
> > Here is the closer: a controlled demolition requires that the basement and
> > first floor of a skyscraper be back filled with cement to control the
> > downward forces.
>
> Imagine hundreds of people trying to keep a secret about anything?

Another great answer.

> But the notion is too improbable to be entertained for a moment, and
> it is an insult to the families of those who perished that day.

I can't see how its an insult. They were patriotic and gave of
themselves in the best way they knew how. You can't really ask for
anything more than that in a person. The 911 movement is never trying
to belittle that at all. If anything most of them do it FOR those
people. Everyone recognizes their sacrifice. Everyone honors and
respects them.

> And if the WTC was blown up by explosives, so there were
> no hijackings... I suppose all those people who spoke to
> loved ones by cell phone on Flight 93 were in on the hoax.
>
> That, I think, pretty much puts paid to these crazy and pathetic
> conspiracy theories.

Good points. Now how is that SOME, granted not many, but some highly
educated and intelligent people are involved in the 911 movement?
That's what I don't get.

In article <61aeaaf6-81c6-4a4e-b3f7-7be7584bd696
@d21g2000prf.googlegroups.com>, says...
> WTC Towers: The Case For Controlled Demolition
> By Herman Schoenfeld

Hey, didn't he also write that failed stageplay "Santa Claus the
paedophile?"

On Dec 10, 6:32 pm, The New Guy <replytogr...@here.thanks> wrote:
quoting me:

> > But the notion is too improbable to be entertained for a moment, and
> > it is an insult to the families of those who perished that day.
>
> I can't see how its an insult. They were patriotic and gave of
> themselves in the best way they knew how. You can't really ask for
> anything more than that in a person. The 911 movement is never trying
> to belittle that at all. If anything most of them do it FOR those
> people. Everyone recognizes their sacrifice. Everyone honors and
> respects them.

It's certainly true that they're not openly and directly insulting the
victims of the September 11 attacks; no one would stand for that for a
minute, and therefore it would make it impossible for them to be
persuasive. Nor is the insult intentional.

But given that it was al-Qaeda that really *did* pull the trigger, and
the conspiracy theories are pretty far off-base - well, then those
conspiracy theories are a joke in poor taste. And if they're put
together well enough to fool anyone, one might suspect they were put
together by people who should - and perhaps do - know better.

John Savard