# WTC Towers: The Case For Controlled Demolition - Mandrake

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

# Thread: WTC Towers: The Case For Controlled Demolition

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

WTC Towers: The Case For Controlled Demolition
By Herman Schoenfeld

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

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

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

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

( unbeleavable stupid mindles drivell deleted )

You ignoramus!

Its funny how the gov. had this incredibly planned 'Demolition' but was
UNABLE to 'plant' WMDs in Iraq.

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

On Sat, 8 Mar 2008 21:43:43 -0500, "Robo-man" wrote:

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

>
>( unbeleavable stupid mindles drivell deleted )
>
>
>You ignoramus!
>
> Its funny how the gov. had this incredibly planned 'Demolition' but was
>UNABLE to 'plant' WMDs in Iraq.

YHBT.

Note that the rant was completely off-topic for all five of the groups
it was posted to, and that none of the groups have anything to do with
each other (excepting alt.os.linux.mandrake and comp.os.linux.misc) -
this is a sure sign that the poster is posting in order to get
responses...

Followups Set.

--
Rob Kelk Personal address (ROT-13): eboxryx -ng- tznvy -qbg- pbz
"Aggresive killfiling. I highly recommend it. It isn't personal;
there's just a limited number of hours in the day."
- Russ Allbery (), in message

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

Robo-man wrote on [Sat, 8 Mar 2008 21:43:43 -0500]:
>
> wrote in message
>> WTC Towers: The Case For Controlled Demolition
>> By Herman Schoenfeld

>
> ( unbeleavable stupid mindles drivell deleted )

That would be better if spelt correctly.

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

In comp.os.linux.misc Robo-man :

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

> ( unbeleavable stupid mindles drivell deleted )

> You ignoramus!

> Its funny how the gov. had this incredibly planned 'Demolition' but was
> UNABLE to 'plant' WMDs in Iraq.

Seems it worked quite well:

http://www.bushflash.com/pl_lo.html

--
Michael Heiming (X-PGP-Sig > GPG-Key ID: EDD27B94)
mail: echo zvpunry@urvzvat.qr | perl -pe 'y/a-z/n-za-m/'

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

"Max" wrote in message
news:slrnft9gfc.g22.chrismax@debian.dns2go.com...
> Robo-man wrote on [Sat, 8 Mar 2008 21:43:43 -0500]:
>>
>> wrote in message
>>> WTC Towers: The Case For Controlled Demolition
>>> By Herman Schoenfeld

>>
>> ( unbeleavable stupid mindles drivell deleted )

>
> That would be better if spelt correctly.

Probably right.

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

On Mar 8, 6:55*pm, schoenfeld....@gmail.com wrote:
> WTC Towers: The Case For Controlled Demolition
> By Herman Schoenfeld
>
> 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.
>

Actually, it does not, nor does it match with the visual data
(videos),
which show collapse times of significantly longer.

> 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".
>

No it doesn't "rapidly approach rest" until it hits the ground. Why?
Because the amount of matter plowing downward, and hence the
weight, is _increasing_ as more floors pile up.

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

On Mon, 10 Mar 2008 19:51:13 -0700 (PDT), mike3
wrote:

Folks, would you *_please_* take this to a group where it's on-topic?

--
Rob Kelk Personal address (ROT-13): eboxryx -ng- tznvy -qbg- pbz
"When a person can no longer laugh at himself, it is time for others
to laugh at him."
- Thomas Szasz, "The Second Sin", 1973

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

wrote in message