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Science Forum Index » Physics Forum » WTC Towers: The Case For Controlled Demolition
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| Guest |
 Posted: Thu Dec 20, 2007 4:01 am |
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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+74.2 )/9.8 =
11.38 sec
where
u_k=(16+ k)/(17+ k ) SQRT(u_(k-1)^2+74.2 ;/ 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+74.2)/9.8 =
9.48 sec
Where
u_k=(32+k)/(33+k) SQRT(u_(k-1)^2+74.2 ;/ u_0=0
REFERENCES
"Seismic Waves Generated By Aircraft Impacts and Building Collapses at
World Trade Center ", http://www.ldeo.columbia.edu/LCSN/Eq/20010911_WTC/WTC_LDEO_KIM.pdf
APPENDIX A: HASKELL SIMULATION PROGRAM
This function returns the gravitational field strength in SI units.
Quote: 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)
Quote: 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.
Quote: wtc1 :: Double
wtc1 = cascadeTime 417 110 93
Simulates a top-down demolition of WTC 2 in SI units.
Quote: wtc2 :: Double
wtc2 = cascadeTime 417 110 77 |
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| jcon |
| Posted: Thu Dec 20, 2007 9:30 am |
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Guest
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On Dec 20, 12:34 pm, Front Office <armistead_...@bigfoot.com> wrote:
Quote: Ken Dixon wrote:
Yep, like Rosie O said, "first time in history steel was melted by
fire". Idiot.http://zapatopi.net/afdb/
When were iron and steel first melted?
I would guess it happened in the latter 19th century.
Huh?!? Iron has been smelted since at least 1500 BC, with the
first steel appearing not much later. By about 2000 years ago,
they were making high quality steel.
And of course, no one (except kooks) claim the steel was melted.
The elastic limit of steel goes down significantly well below
the melting point.
-jc
> Surprising how little there is on the Web about this. |
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| CamachoMan |
| Posted: Thu Dec 20, 2007 11:00 am |
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<schoenfeld.one@gmail.com> wrote in message
news:bdfa4fd8-635f-49e4-aee7-5c76f29e8f04@d27g2000prf.googlegroups.com...
Quote: WTC Towers: The Case For Controlled Demolition
By Herman Schoenfeld
Yes, but was a cigar used to light a fuse or was it all done on a board?
And if it was a cigar, what kind/type was it? Monitcristo? Robusto?
Lonsdale? OpusX??
--
CamachoMan
Relax, have a cigar...
The reason congressmen try so hard to get re-elected is that
they would hate to have to make a living under the laws
they've passed.
http://www.joejackson.com/pdf/5smokingpdf_jj_smoke_lies.pdf |
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| Ken Dixon |
| Posted: Thu Dec 20, 2007 12:04 pm |
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| jcon |
| Posted: Thu Dec 20, 2007 12:49 pm |
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On Dec 20, 4:25 pm, Front Office <armistead_...@bigfoot.com> wrote:
Quote: James wrote:
See what happens when Jean/Sue lets their guard down for even a second.
"jcon" <cirej...@yahoo.com> wrote in message
news:1b4fa549-a112-4d58-b8f5-d818d0dcd851@p1g2000hsb.googlegroups.com...
On Dec 20, 12:34 pm, Front Office <armistead_...@bigfoot.com> wrote:
Ken Dixon wrote:
Yep, like Rosie O said, "first time in history steel was melted by
fire". Idiot.http://zapatopi.net/afdb/
When were iron and steel first melted?
I would guess it happened in the latter 19th century.
Huh?!? Iron has been smelted since at least 1500 BC, with the
first steel appearing not much later. By about 2000 years ago,
they were making high quality steel.
Smelted, yes. Melted, I don't think so.
It was all wrought, the steel at least was.
Ancient "bloomeries" could easily reach the melting
point of iron, but were intentionally kept lower to avoid
melting the ore, since there was no practical way to
to cast the iron.
Don't underestimate ancient technology.
-jc
Quote: I had forgot about cast iron, for which the
Wikipedia cites early 18th century dates.
(http://en.wikipedia.org/wiki/Cast_iron) |
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| Front Office |
| Posted: Thu Dec 20, 2007 2:34 pm |
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Ken Dixon wrote:
When were iron and steel first melted?
I would guess it happened in the latter 19th century.
Surprising how little there is on the Web about this. |
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| James |
| Posted: Thu Dec 20, 2007 3:33 pm |
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See what happens when Jean/Sue lets their guard down for even a second.
"jcon" <cirejcon@yahoo.com> wrote in message
news:1b4fa549-a112-4d58-b8f5-d818d0dcd851@p1g2000hsb.googlegroups.com...
Quote: On Dec 20, 12:34 pm, Front Office <armistead_...@bigfoot.com> wrote:
Ken Dixon wrote:
Yep, like Rosie O said, "first time in history steel was melted by
fire". Idiot.http://zapatopi.net/afdb/
When were iron and steel first melted?
I would guess it happened in the latter 19th century.
Huh?!? Iron has been smelted since at least 1500 BC, with the
first steel appearing not much later. By about 2000 years ago,
they were making high quality steel.
And of course, no one (except kooks) claim the steel was melted.
The elastic limit of steel goes down significantly well below
the melting point.
-jc
Surprising how little there is on the Web about this.
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| Ken Dixon |
| Posted: Thu Dec 20, 2007 3:51 pm |
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| Jordan |
| Posted: Thu Dec 20, 2007 4:26 pm |
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On Dec 20, 6:01 am, schoenfeld....@gmail.com wrote:
Quote: WTC Towers: The Case For Controlled Demolition
The case against controlled demolition:
http://www.debunk911myths.org/topics/Controlled_demolition
The collapse of the World Trade Center twin towers initiated where the
planes hit the buildings. Controlled demolitions always are initiated
at the bottom of a building, to take advantage of maximum gravity
forces.
If the World Trade Center collapsed due to controlled demolition, as
the theory goes, the explosive charges would have had to survive the
crash of airplanes into the buildings. (at ~500 miles per hour)
When a controlled demolition occurs, you hear the very loud and very
distinct sound of the charges going off. These will repeatedly go off,
in a quick, regular pattern, for 10+ seconds prior to the structure
collapsing. While some people heard what "sounded like an explosion"
at the World Trade Center, this is not what they heard or described.
Nor is any such sound of demolition charges going off heard in any
videos of the collapse.
The detonations in a controlled demolition go off in a very regular
pattern, not at all like the random squibs seen on 9/11. Those squibs
are the result of pockets of air (the building is ~70% air in volume)
being collapsed, with pulverized gypsum (drywall) and other material
being forced out.
Blasting caps, detonating cord, and other such evidence were not found
in the World Trade Center debris.
How long does it take to prepare for a building implosion?
It takes months to prepare a building for implosion. It's not
something that can be done over a weekend.
The demolition of the Washington DC Convention Center in 2004 involved
preparations that went on for months. Massive crews were at work,
placing explosives around ~500 columns and doing other preparation
work. The crews and activity were highly noticeable to people in the
area.[7]
The demolition of Kodak Park's Buildings 9 and 23 in Rochester, New
York took months of preparation. Setting up the explosives involved
cutting torches to slice through metal pipes and heavy equipment to
drill holes in the forest of thick concrete support beams, and placing
sticks of dynamite into the holes. When they go off, the explosions
cause the buildings to implode, or collapse inward.[8]
Absolutely zero chance that an effort like that could go unnoticed in
large office buildings full of workers. Given the nature of stock and
bond trading in a global marketplace, with places like Japan, Hong
Kong, and London, people were there at all hours. Such preparations
would definitely be noticed. |
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| Front Office |
| Posted: Thu Dec 20, 2007 6:25 pm |
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Guest
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James wrote:
Quote: See what happens when Jean/Sue lets their guard down for even a second.
"jcon" <cirejcon@yahoo.com> wrote in message
news:1b4fa549-a112-4d58-b8f5-d818d0dcd851@p1g2000hsb.googlegroups.com...
On Dec 20, 12:34 pm, Front Office <armistead_...@bigfoot.com> wrote:
Ken Dixon wrote:
Yep, like Rosie O said, "first time in history steel was melted by
fire". Idiot.http://zapatopi.net/afdb/
When were iron and steel first melted?
I would guess it happened in the latter 19th century.
Huh?!? Iron has been smelted since at least 1500 BC, with the
first steel appearing not much later. By about 2000 years ago,
they were making high quality steel.
Smelted, yes. Melted, I don't think so.
It was all wrought, the steel at least was.
I had forgot about cast iron, for which the
Wikipedia cites early 18th century dates.
(http://en.wikipedia.org/wiki/Cast_iron) |
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| SHaKeY STeVe |
| Posted: Fri Dec 21, 2007 1:25 am |
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On Dec 20, 9:26 pm, Jordan <lu...@earthlink.net> wrote:
Quote: snip
The demolition of Kodak Park's Buildings 9 and 23 in Rochester, New
York took months of preparation. Setting up the explosives involved
cutting torches to slice through metal pipes and heavy equipment to
drill holes in the forest of thick concrete support beams, and placing
sticks of dynamite into the holes. When they go off, the explosions
cause the buildings to implode, or collapse inward.[8]
Absolutely zero chance that an effort like that could go unnoticed in
large office buildings full of workers. Given the nature of stock and
bond trading in a global marketplace, with places like Japan, Hong
Kong, and London, people were there at all hours. Such preparations
would definitely be noticed.
Exactly. Concise and to the point. I guess Shoenfeld also believes the
Pyramids were built by aliens...and he has the quirky math to prove
it... |
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| Rob Kleinschmidt |
| Posted: Fri Dec 21, 2007 10:10 am |
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P. Roehling wrote:
Quote: In Hen3ry's Bizarroland, killfiling netloons is "cowardly" -he actually
thinks his rants should be required reading for the rest of us- while at the
same time he also believes that his constant lies, distortions, and insults
are both brave and patriotic.
In short: you already knew he was nuts, so the sort of wild rationalization
that concludes that anyone who refuses to read his trash is a "coward"
shouldn't surprise you one bit.
Actually, the MI5 dude makes way better reading than Henry.
After deleting about 10,000 of his spams, I got curious and
read one.
The guy actually says that he has schizophrenia, though
he assures us that it is mild and easily treatable with meds.
It was apparantly this schizophrenia though which he says
made MI5 decide to begin persecuting him after somebody
denounced him to them.
As far as the WTC goes, who but the government would
have access to explosives which leave no traces ?
Do you deny that there were no traces of explosives ?
Well do ya ? I think that proves the conspiracy rather nicely. |
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| MLF |
| Posted: Fri Dec 21, 2007 11:55 am |
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<schoenfeld.one@gmail.com> wrote
Quote: WTC Towers: The Case For Controlled Demolition
Geez, I thought these wackos had put their tin foil hats back on and gone
back to playing Dungeons and Dragons in their dark, pizza box strewn hovels
somewhere. Isn't there some "special school" we can lock them up in?
Michael
New Orleans, Louisiana USA fermanis@REMOVEsprynet.com
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| Winston Castro |
| Posted: Fri Dec 21, 2007 12:00 pm |
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On Fri, 21 Dec 2007 09:55:38 -0600, "MLF" <fermanis@sprynet.com>
wrote:
Quote:
schoenfeld.one@gmail.com> wrote
WTC Towers: The Case For Controlled Demolition
Geez, I thought these wackos had put their tin foil hats back on and gone
back to playing Dungeons and Dragons in their dark, pizza box strewn hovels
somewhere. Isn't there some "special school" we can lock them up in?
I went to see that movie Flight 93 when it was playing in theaters
last year. Big mistake, although a great film, it was traumatic as
hell since it was like basically reliving that day all over again.
I have never watched the WTC movie with Nicholas Cage for that reason. |
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| BDK |
| Posted: Fri Dec 21, 2007 1:13 pm |
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In article <fhn3ks$q5i$1@ruby.cit.cornell.edu>, 911@insidejob.gov
says...
Quote: Born a Delusional Kook wrote:
911@insidejob.gov says...
That pretty much confirms that Petie "I'm not psychotic at all"
Roehling, the older clown, and "animal" are lying sacks of shit,
doesn't it? Told ya. <g
Rather than a janitor or bottle washer, kinda looks like I'm a
wealthy Landlord and a technician at Cornell University's prestigious
Elementary Particle Physics Department. Although it pays well with
great benefits, I don't even need the Cornell job, as I live exclusively
off rental income and save my paychecks. I don't need the excellent
retirement benefits, either, as my rental properties will be paid off
in about seven years and I'll own at least a couple of million dollars
worth of income producing real estate free and clear. I keep the Cornell
job because I enjoy it and I do it well. My life is almost too good and
too easy.
And Ithaca - what a great little city. Low crime, clean air, clean
water, a highly educated, progressive populace, incredible natural
beauty, more restaurants per capita than damn near anywhere, world
famous wineries, and awesome State Parks with breath taking gorges,
one of which is only about a mile from my house.
http://www.people.cornell.edu/pages/hhh3/hood.html).
It's one of the best places to live on the Planet, and I'm blessed
with excellent health, a great home in the country, and a beautiful,
kind, and loving young woman who, deserving as I am, still makes me
feel very fortunate to be sharing my life with her.
So I do wonder what sort of crippling mental disability can force shit
brained, no life, usenet kooks and imbeciles to start arguments with
people who are obviously far more intelligent and better informed than
themselves, get their asses handed to 'em, but then instead of learning
from the experience and walking away bruised but with dignity, they
degrade themselves further by spewing silly childish lies while cowering
behind their killfiles. As someone who is used to interacting with
highly educated and respectable professionals, the psychotic, self
deprecating, childlike behavior of self loathing misfits like Petie
and the older clown is really quite a sight to see. Would that we
all could have such impotent, shit brained, cowardly critics. <chuckle
BWHAHAHA, you started out ok
Yup, and finished ever better.
I'll could never be forced to disgrace myself by hiding and cowering
behind a killfile while spewing childish lies about my betters. Why,
that'd be downright pitiful. A man has to like what he sees in the
mirror. Either Petie and the older clown are fond of cowardly, simple
minded, disgraced, self deprecating liars, or they're ashamed of the
"man" they see in the mirror. Neither of those options would work for me...
Better? Funnier for sure. I don't know what the killfile spew is all
about, since I don't killfile any of you kooks, no matter how obnoxious
you are, or how egotistical.
BDK |
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