# WTC Towers: The Case For Controlled Demolition - Linux

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

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

Why is this posted here? Am I missing something, or does this have
nothing whatsoever to do with Linux?
It looks like someone just posted a load of what is probably
conspiracy theory garbage to a handful of random groups (alt.fan.rush-
alt.gossip.celebrities, microsoft.public.windowsxp.general)

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

"schoenfeld.one@gmail.com" stated in post
1194748691.850612.28350@e34g2000pro.googlegroups.c om on 11/10/07 7:38 PM:

> WTC Towers: The Case For Controlled Demolition

No case needs to be made - unfortunately the towers have already been
demolished.

--
BU__SH__

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

On Nov 10, 8:33 pm, Snit wrote:
> "schoenfeld....@gmail.com" stated in post
> 1194748691.850612.28...@e34g2000pro.googlegroups.c om on 11/10/07 7:38 PM:
>
> > WTC Towers: The Case For Controlled Demolition

>
> No case needs to be made - unfortunately the towers have already been
> demolished.
>

....and "America's Mayor" hastily shipped out all the evidence for
recycling.

> --
> BU__SH__

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

wrote in message
> Why is this posted here? Am I missing something, or does this have
> nothing whatsoever to do with Linux?
> It looks like someone just posted a load of what is probably
> conspiracy theory garbage to a handful of random groups (alt.fan.rush-
> alt.gossip.celebrities, microsoft.public.windowsxp.general)
>

--
A little learning is a dangerous thing, but it still beats total ignorance.

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

On 2007-11-10 22:01:40 -0500, "bmillerjacobson@gmail.com"
said:

> Why is this posted here? Am I missing something, or does this have
> nothing whatsoever to do with Linux?

Because the poster is a highly paranoid conspiratard. Ignore the ****wit.

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

nrballard@gmail.com wrote:
> On Nov 10, 8:33 pm, Snit wrote:
>> "schoenfeld....@gmail.com" stated in post
>> 7:38 PM:
>>
>>> WTC Towers: The Case For Controlled Demolition

>>
>> No case needs to be made - unfortunately the towers have already been
>> demolished.
>>

>
> ...and "America's Mayor" hastily shipped out all the evidence for
> recycling.
>

He had to move it out of the way so new buildings could be erected !

No, wait...

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

[off-topic diatribe snipped]

This belongs in alt.conspiracy, not cola.

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

"bmillerjacobson@gmail.com" writes:

> Why is this posted here? Am I missing something, or does this have
> nothing whatsoever to do with Linux?
> It looks like someone just posted a load of what is probably
> conspiracy theory garbage to a handful of random groups (alt.fan.rush-
> alt.gossip.celebrities, microsoft.public.windowsxp.general)
>

Hey look! There's a new Sheriff in town. Watch out High Plains Borefest
and Mark Kent - you're in danger of being usurped as the group's leading
self righteous gas bags.

--
You can tell how far we have to go, when FORTRAN is the language of
supercomputers.
-- Steven Feiner

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

On Nov 11, 8:34 pm, Hadron wrote:
> "bmillerjacob...@gmail.com" writes:
> > Why is this posted here? Am I missing something, or does this have
> > nothing whatsoever to do with Linux?
> > It looks like someone just posted a load of what is probably
> > conspiracy theory garbage to a handful of random groups (alt.fan.rush-
> > alt.gossip.celebrities, microsoft.public.windowsxp.general)

>
> Hey look! There's a new Sheriff in town. Watch out High Plains Borefest
> and Mark Kent - you're in danger of being usurped as the group's leading
> self righteous gas bags.
>
> --
> You can tell how far we have to go, when FORTRAN is the language of
> supercomputers.
> -- Steven Feiner

If that's how it came across, I would like to apologize. However, that
certainly wasn't my intent.

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

bmillerjacobson@gmail.com wrote:

>On Nov 11, 8:34 pm, Hadron wrote:
>>
>> Hey look! There's a new Sheriff in town. Watch out High Plains Borefest
>> and Mark Kent - you're in danger of being usurped as the group's leading
>> self righteous gas bags.

>
>If that's how it came across, I would like to apologize. However, that
>certainly wasn't my intent.

You should not feel that you need to apologize to a snotty lying

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

On Nov 12, 9:20 am, chrisv wrote:
> bmillerjacob...@gmail.com wrote:
> >On Nov 11, 8:34 pm, Hadron wrote:

>
> >> Hey look! There's a new Sheriff in town. Watch out High Plains Borefest
> >> and Mark Kent - you're in danger of being usurped as the group's leading
> >> self righteous gas bags.

>
> >If that's how it came across, I would like to apologize. However, that
> >certainly wasn't my intent.

>
> You should not feel that you need to apologize to a snotty lying

I'm kind of new, so I don't know who has the troll nature yet. I had
given him about a 75% chance of being a troll. One good thing about
that sort of apology is if someone is not a troll, it is acceptable,
and if they are, it denies them the opportunity to... well... troll
(can I use that as a verb?).

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

bmillerjacobson@gmail.com wrote:

>On Nov 12, 9:20 am, chrisv wrote:
>> bmillerjacob...@gmail.com wrote:
>> >On Nov 11, 8:34 pm, Hadron wrote:

>>
>> >> Hey look! There's a new Sheriff in town. Watch out High Plains Borefest
>> >> and Mark Kent - you're in danger of being usurped as the group's leading
>> >> self righteous gas bags.

>>
>> >If that's how it came across, I would like to apologize. However, that
>> >certainly wasn't my intent.

>>
>> You should not feel that you need to apologize to a snotty lying

>
>I'm kind of new, so I don't know who has the troll nature yet. I had
>given him about a 75% chance of being a troll. One good thing about
>that sort of apology is if someone is not a troll, it is acceptable,
>and if they are, it denies them the opportunity to... well... troll
>(can I use that as a verb?).

Of course it can be used as a verb. Other worthless trolls to look
out for are cc (Hadron's leg-humper), clogwog, Tim Smith, Erik
FUDenbusch, amicus curious, John Bailo, the nym-shifting idiot who
likes names like heather.banger@gmail.com and dont.pullout@yahoo.com,
and the nym-shifting idiot who likes names that start with "Dr." or a
military rank.

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

On Nov 12, 3:57 pm, chrisv wrote:
> bmillerjacob...@gmail.com wrote:
> >On Nov 12, 9:20 am, chrisv wrote:
> >> bmillerjacob...@gmail.com wrote:
> >> >On Nov 11, 8:34 pm, Hadron wrote:

>
> >> >> Hey look! There's a new Sheriff in town. Watch out High Plains Borefest
> >> >> and Mark Kent - you're in danger of being usurped as the group's leading
> >> >> self righteous gas bags.

>
> >> >If that's how it came across, I would like to apologize. However, that
> >> >certainly wasn't my intent.

>
> >> You should not feel that you need to apologize to a snotty lying
> >> asshole like "Hadron" Quirk.

>
> >I'm kind of new, so I don't know who has the troll nature yet. I had
> >given him about a 75% chance of being a troll. One good thing about
> >that sort of apology is if someone is not a troll, it is acceptable,
> >and if they are, it denies them the opportunity to... well... troll
> >(can I use that as a verb?).

>
> Of course it can be used as a verb. Other worthless trolls to look
> out for are cc (Hadron's leg-humper), clogwog, Tim Smith, Erik
> FUDenbusch, amicus curious, John Bailo, the nym-shifting idiot who
> likes names like heather.ban...@gmail.com and dont.pull...@yahoo.com,
> and the nym-shifting idiot who likes names that start with "Dr." or a
> military rank.

Thanks. That's good to know.

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

Didja use Excel for these figures?

--
Paul Hovnanian mailto:Paul@Hovnanian.com
------------------------------------------------------------------
mv Windows /dev/null

16. ## Re: chrisv adds nothing as usual

On Nov 12, 4:03 pm, "bmillerjacob...@gmail.com"
wrote:
> On Nov 12, 3:57 pm, chrisv wrote:
>
>
>
>
>
> > bmillerjacob...@gmail.com wrote:
> > >On Nov 12, 9:20 am, chrisv wrote:
> > >> bmillerjacob...@gmail.com wrote:
> > >> >On Nov 11, 8:34 pm, Hadron wrote:

>
> > >> >> Hey look! There's a new Sheriff in town. Watch out High Plains Borefest
> > >> >> and Mark Kent - you're in danger of being usurped as the group's leading
> > >> >> self righteous gas bags.

>
> > >> >If that's how it came across, I would like to apologize. However, that
> > >> >certainly wasn't my intent.

>
> > >> You should not feel that you need to apologize to a snotty lying
> > >> asshole like "Hadron" Quirk.

>
> > >I'm kind of new, so I don't know who has the troll nature yet. I had
> > >given him about a 75% chance of being a troll. One good thing about
> > >that sort of apology is if someone is not a troll, it is acceptable,
> > >and if they are, it denies them the opportunity to... well... troll
> > >(can I use that as a verb?).

>
> > Of course it can be used as a verb. Other worthless trolls to look
> > out for are cc (Hadron's leg-humper), clogwog, Tim Smith, Erik
> > FUDenbusch, amicus curious, John Bailo, the nym-shifting idiot who
> > likes names like heather.ban...@gmail.com and dont.pull...@yahoo.com,
> > and the nym-shifting idiot who likes names that start with "Dr." or a
> > military rank.

>
> Thanks. That's good to know.

I'd like to submit to the court every post chrisv has ever written.
Take a look and decide for yourself.

17. ## Re: chrisv adds nothing as usual

cc writes:

> On Nov 12, 4:03 pm, "bmillerjacob...@gmail.com"
> wrote:
>> On Nov 12, 3:57 pm, chrisv wrote:
>>
>>
>>
>>
>>
>> > bmillerjacob...@gmail.com wrote:
>> > >On Nov 12, 9:20 am, chrisv wrote:
>> > >> bmillerjacob...@gmail.com wrote:
>> > >> >On Nov 11, 8:34 pm, Hadron wrote:

>>
>> > >> >> Hey look! There's a new Sheriff in town. Watch out High Plains Borefest
>> > >> >> and Mark Kent - you're in danger of being usurped as the group's leading
>> > >> >> self righteous gas bags.

>>
>> > >> >If that's how it came across, I would like to apologize. However, that
>> > >> >certainly wasn't my intent.

>>
>> > >> You should not feel that you need to apologize to a snotty lying
>> > >> asshole like "Hadron" Quirk.

>>
>> > >I'm kind of new, so I don't know who has the troll nature yet. I had
>> > >given him about a 75% chance of being a troll. One good thing about
>> > >that sort of apology is if someone is not a troll, it is acceptable,
>> > >and if they are, it denies them the opportunity to... well... troll
>> > >(can I use that as a verb?).

>>
>> > Of course it can be used as a verb. Other worthless trolls to look
>> > out for are cc (Hadron's leg-humper), clogwog, Tim Smith, Erik
>> > FUDenbusch, amicus curious, John Bailo, the nym-shifting idiot who
>> > likes names like heather.ban...@gmail.com and dont.pull...@yahoo.com,
>> > and the nym-shifting idiot who likes names that start with "Dr." or a
>> > military rank.

>>
>> Thanks. That's good to know.

>
> I'd like to submit to the court every post chrisv has ever written.
> Take a look and decide for yourself.

I would second that. But I am still convinced that bmillerjacobsmusheln
or whatever his name is, is a sockpuppet for someone like HPT and is
still very much in the "nurture trust" phase. Time will tell. But there
are too many giveaways like the schizophrenic changes of mood and the
amazing knowledge, for someone new, of supposed flatfish nyms. It could
even be Mark Kent or Roy, but frankly they are too stupid to carry it
off for more than a post before they revert to form.

Lets face it, anyone with an ounce of common sense would not be cozying
up to such an obvious loony tunes as "chrisv".

18. ## Re: chrisv adds nothing as usual

news:fk0hp2\$r4j\$4@registered.motzarella.org...
> cc writes:
>
>> On Nov 12, 4:03 pm, "bmillerjacob...@gmail.com"
>> wrote:
>>> On Nov 12, 3:57 pm, chrisv wrote:
>>>
>>>
>>>
>>>
>>>
>>> > bmillerjacob...@gmail.com wrote:
>>> > >On Nov 12, 9:20 am, chrisv wrote:
>>> > >> bmillerjacob...@gmail.com wrote:
>>> > >> >On Nov 11, 8:34 pm, Hadron wrote:
>>>
>>> > >> >> Hey look! There's a new Sheriff in town. Watch out High Plains
>>> > >> >> Borefest
>>> > >> >> and Mark Kent - you're in danger of being usurped as the group's
>>> > >> >> self righteous gas bags.
>>>
>>> > >> >If that's how it came across, I would like to apologize. However,
>>> > >> >that
>>> > >> >certainly wasn't my intent.
>>>
>>> > >> You should not feel that you need to apologize to a snotty lying
>>> > >> asshole like "Hadron" Quirk.
>>>
>>> > >I'm kind of new, so I don't know who has the troll nature yet. I had
>>> > >given him about a 75% chance of being a troll. One good thing about
>>> > >that sort of apology is if someone is not a troll, it is acceptable,
>>> > >and if they are, it denies them the opportunity to... well... troll
>>> > >(can I use that as a verb?).
>>>
>>> > Of course it can be used as a verb. Other worthless trolls to look
>>> > out for are cc (Hadron's leg-humper), clogwog, Tim Smith, Erik
>>> > FUDenbusch, amicus curious, John Bailo, the nym-shifting idiot who
>>> > likes names like heather.ban...@gmail.com and dont.pull...@yahoo.com,
>>> > and the nym-shifting idiot who likes names that start with "Dr." or a
>>> > military rank.
>>>
>>> Thanks. That's good to know.

>>
>> I'd like to submit to the court every post chrisv has ever written.
>> Take a look and decide for yourself.

>
> I would second that. But I am still convinced that bmillerjacobsmusheln
> or whatever his name is, is a sockpuppet for someone like HPT and is
> still very much in the "nurture trust" phase. Time will tell. But there
> are too many giveaways like the schizophrenic changes of mood and the
> amazing knowledge, for someone new, of supposed flatfish nyms. It could
> even be Mark Kent or Roy, but frankly they are too stupid to carry it
> off for more than a post before they revert to form.
>
> Lets face it, anyone with an ounce of common sense would not be cozying
> up to such an obvious loony tunes as "chrisv".

I'm a well respected assistant shift manager at Burger King for 40 years
now! So get a life Hadron.

19. ## Re: chrisv adds nothing as usual

news:fk16oe\$oqh\$3@registered.motzarella.org...
>
>> news:fk0hp2\$r4j\$4@registered.motzarella.org...
>>> cc writes:
>>>
>>>> On Nov 12, 4:03 pm, "bmillerjacob...@gmail.com"
>>>> wrote:
>>>>> On Nov 12, 3:57 pm, chrisv wrote:
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> > bmillerjacob...@gmail.com wrote:
>>>>> > >On Nov 12, 9:20 am, chrisv wrote:
>>>>> > >> bmillerjacob...@gmail.com wrote:
>>>>> > >> >On Nov 11, 8:34 pm, Hadron wrote:
>>>>>
>>>>> > >> >> Hey look! There's a new Sheriff in town. Watch out High
>>>>> Plains > >> >> Borefest
>>>>> > >> >> and Mark Kent - you're in danger of being usurped as the
>>>>> group's > >> >> leading
>>>>> > >> >> self righteous gas bags.
>>>>>
>>>>> > >> >If that's how it came across, I would like to
>>>>> apologize. However, > >> >that
>>>>> > >> >certainly wasn't my intent.
>>>>>
>>>>> > >> You should not feel that you need to apologize to a snotty lying
>>>>> > >> asshole like "Hadron" Quirk.
>>>>>
>>>>> > >I'm kind of new, so I don't know who has the troll nature yet. I
>>>>> > >given him about a 75% chance of being a troll. One good thing about
>>>>> > >that sort of apology is if someone is not a troll, it is
>>>>> > >acceptable,
>>>>> > >and if they are, it denies them the opportunity to... well... troll
>>>>> > >(can I use that as a verb?).
>>>>>
>>>>> > Of course it can be used as a verb. Other worthless trolls to look
>>>>> > out for are cc (Hadron's leg-humper), clogwog, Tim Smith, Erik
>>>>> > FUDenbusch, amicus curious, John Bailo, the nym-shifting idiot who
>>>>> > likes names like heather.ban...@gmail.com and
>>>>> > dont.pull...@yahoo.com,
>>>>> > and the nym-shifting idiot who likes names that start with "Dr." or
>>>>> > a
>>>>> > military rank.
>>>>>
>>>>> Thanks. That's good to know.
>>>>
>>>> I'd like to submit to the court every post chrisv has ever written.
>>>> Take a look and decide for yourself.
>>>
>>> I would second that. But I am still convinced that bmillerjacobsmusheln
>>> or whatever his name is, is a sockpuppet for someone like HPT and is
>>> still very much in the "nurture trust" phase. Time will tell. But there
>>> are too many giveaways like the schizophrenic changes of mood and the
>>> amazing knowledge, for someone new, of supposed flatfish nyms. It could
>>> even be Mark Kent or Roy, but frankly they are too stupid to carry it
>>> off for more than a post before they revert to form.
>>>
>>> Lets face it, anyone with an ounce of common sense would not be cozying
>>> up to such an obvious loony tunes as "chrisv".

>>
>>
>> I'm a well respected assistant shift manager at Burger King for 40
>> years now! So get a life Hadron.
>>

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

On Dec 15, 1:03 pm, "Paul Hovnanian P.E." wrote:
> Didja use Excel for these figures?

See Appendix A. The compiler used was WinHugs 98.

> --
> Paul Hovnanian mailto:P...@Hovnanian.com
> ------------------------------------------------------------------
> mv Windows /dev/null