# WTC Towers: The Case For Controlled Demolition - Linux

This is a discussion on WTC Towers: The Case For Controlled Demolition - Linux ; 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. ...

# Thread: WTC Towers: The Case For Controlled Demolition

1. ## WTC Towers: The Case For Controlled Demolition

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

By Herman Schoenfeld

2. ## Re: WTC Towers: The Case For Controlled Demolition

wrote in message

I'll start paying more attention to all of the 9/11 conspiracy theorists
once they come up with something that doesn't distil down to "The Jews did
it".

3. ## Re: WTC Towers: The Case For Controlled Demolition

On Sun, 6 Apr 2008 09:56:02 -0400, MI Wakefield wrote:

> wrote in message
>
> I'll start paying more attention to all of the 9/11 conspiracy theorists
> once they come up with something that doesn't distil down to "The Jews did
> it".

Shalom!

--
Moshe Goldfarb
Collector of soaps from around the globe.
Please visit The Hall of Linux Idiots:
http://linuxidiots.blogspot.com/

4. ## Re: WTC Towers: The Case For Controlled Demolition

> By Herman Schoenfeld

A Jew!

5. ## Re: WTC Towers: The Case For Controlled Demolition

Moshe Goldfarb wrote:

> On Sun, 6 Apr 2008 09:56:02 -0400, MI Wakefield wrote:
>
>> wrote in message
>>
>> I'll start paying more attention to all of the 9/11 conspiracy theorists
>> once they come up with something that doesn't distil down to "The Jews
>> did it".

>
> Shalom!
>

You'd think by now that they could have come up with a better conspiracy
theory than this tired old rubbish.

6. ## Re: WTC Towers: The Case For Controlled Demolition

On Sun, 06 Apr 2008 15:44:47 +0100, SomeBloke wrote:

> Moshe Goldfarb wrote:
>
>> On Sun, 6 Apr 2008 09:56:02 -0400, MI Wakefield wrote:
>>
>>> wrote in message
>>>
>>> I'll start paying more attention to all of the 9/11 conspiracy theorists
>>> once they come up with something that doesn't distil down to "The Jews
>>> did it".

>>
>> Shalom!
>>

>
> You'd think by now that they could have come up with a better conspiracy
> theory than this tired old rubbish.

You'd think by now you would learn to figure out who said what in a thread.

FWIW I didn't write the OP and FWIW I certainly do not agree with it.

Looks like the work of Mark S. Bilk, a nutball extreme.

--
Moshe Goldfarb
Collector of soaps from around the globe.
Please visit The Hall of Linux Idiots:
http://linuxidiots.blogspot.com/

7. ## Re: WTC Towers: The Case For Controlled Demolition

On Sun, 06 Apr 2008 18:29:26 +0000, David Morgan \(MAMS\) wrote:

> "MI Wakefield" wrote...
>
>> I'll start paying more attention to all of the 9/11 conspiracy
>> theorists once they come up with something that doesn't distil down to
>> "The Jews did it".

>
>
> I think very few of these point any fingers at "jews".

What does this have to do with Linux?

8. ## Re: WTC Towers: The Case For Controlled Demolition

On Sun, 06 Apr 2008 18:53:34 GMT, alt wrote:

> On Sun, 06 Apr 2008 18:29:26 +0000, David Morgan \(MAMS\) wrote:
>
>
>> "MI Wakefield" wrote...
>>
>>> I'll start paying more attention to all of the 9/11 conspiracy
>>> theorists once they come up with something that doesn't distil down to
>>> "The Jews did it".

>>
>>
>> I think very few of these point any fingers at "jews".

>
> What does this have to do with Linux?

What do most of the messages in COLA have to do with Linux?
The majority are Microsoft hate messages, Donovan.

--
Moshe Goldfarb
Collector of soaps from around the globe.
Please visit The Hall of Linux Idiots:
http://linuxidiots.blogspot.com/

9. ## Re: WTC Towers: The Case For Controlled Demolition

"alt" wrote in message newsan.2008.04.06.18.53.04@lazyeyez.net...
> On Sun, 06 Apr 2008 18:29:26 +0000, David Morgan \(MAMS\) wrote:
>
>
> > "MI Wakefield" wrote...
> >
> >> I'll start paying more attention to all of the 9/11 conspiracy
> >> theorists once they come up with something that doesn't distil down to
> >> "The Jews did it".

> >
> >
> > I think very few of these point any fingers at "jews".

> What does this have to do with Linux?

It's for people who don't understand the 'operating system' they live in?

;-)

10. ## Re: WTC Towers: The Case For Controlled Demolition

"alt" wrote in message...

> What does this have to do with Linux?

Oh.... what does *anything* have to do whith Linn Knocks ?

12. ## Re: WTC Towers: The Case For Controlled Demolition

Moshe Goldfarb is flatfish (aka: Gary Stewart)

http://colatrolls.blogspot.com/2008/...arb-troll.html
http://colatrolls.blogspot.com/2007/...ish-troll.html

Traits:

Frequently cross posts replies to other non-Linux related newsgroups

13. ## Re: WTC Towers: The Case For Controlled Demolition

On Sun, 06 Apr 2008 18:53:34 +0000, alt wrote:

> On Sun, 06 Apr 2008 18:29:26 +0000, David Morgan \(MAMS\) wrote:
>
>
>> "MI Wakefield" wrote...
>>
>>> I'll start paying more attention to all of the 9/11 conspiracy
>>> theorists once they come up with something that doesn't distil down to
>>> "The Jews did it".

>>
>>
>> I think very few of these point any fingers at "jews".

>
> What does this have to do with Linux?

It's a little-known fact that Tux is Jewish.

14. ## Re: WTC Towers: The Case For Controlled Demolition

On Sun, 06 Apr 2008 16:19:34 -0500, netcat wrote:
>On Sun, 06 Apr 2008 18:53:34 +0000, alt wrote:

>> On Sun, 06 Apr 2008 18:29:26 +0000, David Morgan \(MAMS\) wrote:
>>
>>
>>> "MI Wakefield" wrote...
>>>
>>>> I'll start paying more attention to all of the 9/11 conspiracy
>>>> theorists once they come up with something that doesn't distil down to
>>>> "The Jews did it".
>>>
>>>
>>> I think very few of these point any fingers at "jews".

>>
>> What does this have to do with Linux?

>It's a little-known fact that Tux is Jewish.

what an idiotic response.