WTC Towers: The Case For Controlled Demolition

Discussion in 'Digital Photography' started by schoenfeld.one, Dec 5, 2007.

1. schoenfeld.oneGuest

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.
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)

Simulates a top-down demolition of WTC 1 in SI units.
Simulates a top-down demolition of WTC 2 in SI units.

schoenfeld.one, Dec 5, 2007

2. barnegatdxGuest

barnegatdx, Dec 5, 2007

3. Doctor EvilGuest

The question isn't who destroyed the WTCs...the question is who made
crazy money on investments that day. Remember the investigation
determined that and it was immediately sealed to protect Bush's
pals...

O'ROURKE: I mean, this is lots of fun attacking George Bush, who is an
idiot and obviously screwed up on this completely
BEHAR: Thank you!
MAHER: Oh, thank you!

PJ O'Rourke on Bill Maher show 9/16/2005

Doctor Evil, Dec 5, 2007
4. Mr. StratGuest

You Truthers are really a disgusting lot.

Mr. Strat, Dec 5, 2007
5. On The Highways and Bi-Ways God BuiltGuest

really? where was that reported??? i mean besides on
idonthaveagirlfriendso9-11wasaninsidejob.com?

most sincerely,

GodBuilt

--

On The Highways and Bi-Ways God Built, Dec 6, 2007
6. VengerGuest

Go away, Truther Douchebag!!!

Truthers are dumb people. Don't be dumb.

Venger

Venger, Dec 6, 2007
7. Doctor EvilGuest

The Truth is only disgusting to traitors who hate America. Obviously,
9-11 was a conspiracy between Bush and the Muslims.

"The fact that $2.5 million of the put options remained unclaimed is not explained at all by market pessimism, and is evidence that the put option purchasers were part of a criminal conspiracy." The Bloomberg News reported that put options on the airlines surged to the phenomenal high of 285 times their average. Over three days before terrorists flattened the World Trade Center and damaged the Pentagon, there was more than 25 times the previous daily average trading in a Morgan Stanley "put" option that makes money when shares fall below$45. Trading in similar AMR and UAL put options,
which make money when their stocks fall below $30 apiece, surged to as much as 285 times the average trading up to that time. 6 When the market reopened after the attack, United Airlines stock fell 42 percent from$30.82 to $17.50 per share, and American Airlines stock fell 39 percent, from$29.70 to $18.00 per share. 7 http://911research.wtc7.net/sept11/stockputs.html Insider Trading Pre-9/11 Put Options on Companies Hurt by Attack Indicates Foreknowledge Financial transactions in the days before the attack suggest that certain individuals used foreknowledge of the attack to reap huge profits. 1 The evidence of insider trading includes: Huge surges in purchases of put options on stocks of the two airlines used in the attack -- United Airlines and American Airlines Surges in purchases of put options on stocks of reinsurance companies expected to pay out billions to cover losses from the attack -- Munich Re and the AXA Group Surges in purchases of put options on stocks of financial services companies hurt by the attack -- Merrill Lynch & Co., and Morgan Stanley and Bank of America Huge surge in purchases of call options of stock of a weapons manufacturer expected to gain from the attack -- Raytheon Huge surges in purchases of 5-Year US Treasury Notes In each case, the anomalous purchases translated into large profits as soon as the stock market opened a week after the attack: put options were used on stocks that would be hurt by the attack, and call options were used on stocks that would benefit. Put and call options are contracts that allow their holders to sell and buy assets, respectively, at specified prices by a certain date. Put options allow their holders to profit from declines in stock values because they allow stocks to be bought at market price and sold for the higher option price. The ratio of the volume of put option contracts to call option contracts is called the put/call ratio. The ratio is usually less than one, with a value of around 0.8 considered normal. 2 Losers American Airlines and United Airlines, and several insurance companies and banks posted huge loses in stock values when the markets opened on September 17. Put options -- financial instruments which allow investors to profit from the decline in value of stocks -- were purchased on the stocks of these companies in great volume in the week before the attack. United Airlines and American Airlines Two of the corporations most damaged by the attack were American Airlines (AMR), the operator of Flight 11 and Flight 77, and United Airlines (UAL), the operator of Flight 175 and Flight 93. According to CBS News, in the week before the attack, the put/call ratio for American Airlines was four. 3 The put/call ratio for United Airlines was 25 times above normal on September 6. 4 This graph shows a dramatic spike in pre-attack purchases of put options on the airlines used in the attack. (source: www.optionsclearing.com) The spikes in put options occurred on days that were uneventful for the airlines and their stock prices. On Sept. 6-7, when there was no significant news or stock price movement involving United, the Chicago exchange handled 4,744 put options for UAL stock, compared with just 396 call options -- essentially bets that the price will rise. On Sept. 10, an uneventful day for American, the volume was 748 calls and 4,516 puts, based on a check of option trading records. 5 The Bloomberg News reported that put options on the airlines surged to the phenomenal high of 285 times their average. Over three days before terrorists flattened the World Trade Center and damaged the Pentagon, there was more than 25 times the previous daily average trading in a Morgan Stanley "put" option that makes money when shares fall below$45. Trading in similar AMR and UAL put options,
which make money when their stocks fall below $30 apiece, surged to as much as 285 times the average trading up to that time. 6 When the market reopened after the attack, United Airlines stock fell 42 percent from$30.82 to $17.50 per share, and American Airlines stock fell 39 percent, from$29.70 to $18.00 per share. 7 Reinsurance Companies Several companies in the reinsurance business were expected to suffer huge losses from the attack: Munich Re of Germany and Swiss Re of Switzerland -- the world's two biggest reinsurers, and the AXA Group of France. In September, 2001, the San Francisco Chronicle estimated liabilities of$1.5 billion for Munich Re and $0.55 bilion for the AXA Group and telegraph.co.uk estimated liabilities of £1.2 billion for Munich Re and £0.83 billion for Swiss Re. 8 9 Trading in shares of Munich Re was almost double its normal level on September 6, and 7, and trading in shares of Swiss Re was more than double its normal level on September 7. 10 Financial Services Companies Merrill Lynch and Morgan Stanley Morgan Stanley Dean Witter & Co. and Merrill Lynch & Co. were both headquartered in lower Manhattan at the time of the attack. Morgan Stanley occupied 22 floors of the North Tower and Merrill Lynch had headquarters near the Twin Towers. Morgan Stanley, which saw an average of 27 put options on its stock bought per day before September 6, saw 2,157 put options bought in the three trading days before the attack. Merrill Lynch, which saw an average of 252 put options on its stock bought per day before September 5, saw 12,215 put options bought in the four trading days before the attack. Morgan Stanley's stock dropped 13% and Merrill Lynch's stock dropped 11.5% when the market reopened. 11 Bank of America showed a fivefold increase in put option trading on the Thursday and Friday before the attack. A Bank of America option that would profit if the No. 3 U.S. bank's stock fell below$60 a share had more than 5,900 contracts traded on
the Thursday and Friday before the Sept. 11 assaults, almost five
times the previous average trading, according to Bloomberg data. The
bank's shares fell 11.5 percent to $51 in the first week after trading resumed on Sept. 17. 12 Winners While most companies would see their stock valuations decline in the wake of the attack, those in the business of supplying the military would see dramatic increases, reflecting the new business they were poised to receive. Raytheon Raytheon, maker of Patriot and Tomahawk missiles, saw its stock soar immediately after the attack. Purchases of call options on Raytheon stock increased sixfold on the day before the attack. A Raytheon option that makes money if shares are more than$25 each
had 232 options contracts traded on the day before the attacks, almost
six times the total number of trades that had occurred before that
day. A contract represents options on 100 shares. Raytheon shares
soared almost 37 percent to $34.04 during the first week of post-attack U.S. trading. 13 Raytheon has been fined millions of dollars inflating the costs of equipment it sells the US military. Raytheon has a secretive subsidiary, E-Systems, whose clients have included the CIA and NSA. 14 US Treasury Notes Five-year US Treasury notes were purchased in abnormally high volumes before the attack, and their buyers were rewarded with sharp increases in their value following the attack. The Wall Street Journal reported on October 2 that the ongoing investigation by the SEC into suspicious stock trades had been joined by a Secret Service probe into an unusually high volume of five-year US Treasury note purchases prior to the attacks. The Treasury note transactions included a single$5 billion trade. As the Journal
explained: "Five-year Treasury notes are among the best investments in
the event of a world crisis, especially one that hits the US. The
notes are prized for their safety and their backing by the US
government, and usually rally when investors flee riskier investments,
such as stocks." The value of these notes, the Journal pointed out,
has risen sharply since the events of September 11. 15

The SEC's Investigation
Shortly after the attack the SEC circulated a list of stocks to
securities firms around the world seeking information. 16 A widely
circulated article states that the stocks flagged by the SEC included
those of the following corporations: American Airlines, United
Airlines, Continental Airlines, Northwest Airlines, Southwest
Airlines, US Airways airlines, Martin, Boeing, Lockheed Martin Corp.,
AIG, American Express Corp, American International Group, AMR
Corporation, AXA SA, Bank of America Corp, Bank of New York Corp, Bank
One Corp, Cigna Group, CNA Financial, Carnival Corp, Chubb Group, John
Hancock Financial Services, Hercules Inc., L-3 Communications
Holdings, Inc., LTV Corporation, Marsh & McLennan Cos. Inc., MetLife,
Progressive Corp., General Motors, Raytheon, W.R. Grace, Royal
Caribbean Cruises, Ltd., Lone Star Technologies, American Express, the
Citigroup Inc., Royal & Sun Alliance, Lehman Brothers Holdings, Inc.,
Vornado Reality Trust, Morgan Stanley, Dean Witter & Co., XL Capital
Ltd., and Bear Stearns.

An October 19 article in the San Francisco Chronicle reported that the
SEC, after a period of silence, had undertaken the unprecedented
action of deputizing hundreds of private officials in its
investigation:

The proposed system, which would go into effect immediately,
effectively deputizes hundreds, if not thousands, of key players in
the private sector.
....
In a two-page statement issued to "all securities-related entities"
nationwide, the SEC asked companies to designate senior personnel who
appreciate "the sensitive nature" of the case and can be relied upon
to "exercise appropriate discretion" as "point" people linking
government investigators and the industry. 17

Michael Ruppert, a former LAPD officer, explains the consequences of
this action:

What happens when you deputize someone in a national security or
criminal investigation is that you make it illegal for them to
disclose publicly what they know. Smart move. In effect, they become
government agents and are controlled by government regulations rather
than their own conscience. In fact, they can be thrown in jail without
a hearing if they talk publicly. I have seen this implied threat time
and again with federal investigations, intelligence agents, and even
members of the United States Congress who are bound so tightly by
secrecy oaths and agreements that they are not even able to disclose
criminal activities inside the government for fear of incarceration.
18

Interpreting and Reinterpreting the Data
An analysis of the press reports on the subject of apparent insider
trading related to the attack shows a trend, with early reports
highlighting the anomalies, and later reports excusing them. In his
book Crossing the Rubicon Michael C. Ruppert illustrates this point by
first excerpting a number of reports published shortly after the
attack:

A jump in UAL (United Airlines) put options 90 times (not 90 percent)
above normal between September 6 and September 10, and 285 times
higher than average on the Thursday before the attack.
-- CBS News, September 26
A jump in American Airlines put options 60 times (not 60 percent)
above normal on the day before the attacks.
-- CBS News, September 26
No similar trading occurred on any other airlines
-- Bloomberg Business Report, the Institute for Counterterrorism
(ICT), Herzliyya, Israel [citing data from the CBOE] 3
Morgan Stanley saw, between September 7 and September 10, an increase
of 27 times (not 27 percent) in the purchase of put options on its
shares. 4

Merrill-Lynch saw a jump of more than 12 times the normal level of put
options in the four trading days before the attacks. 5

--------------------------------------------------------------------------------
[Excerpted ENDNOTES]

International Policy Institute for Counter Terrorism (ICT), September
22, 2001. Michael C. Ruppert, "The Case for Bush Administration
Advance Knowledge of 9-11 Attacks," From the Wilderness April 22,
2002. Posted at Centre for Research and Globalization
<www.globalresearch.ca/articles/RUP203A.html>.

4. ICT, op. cit, citing data from the Chicago Board of Options
Exchange (CBOE). [...] "Terrorists trained at CBPE." Chicago
Sun-Times, September 20, 2001,
September 21, 2001,

5. ICT, op. cit.

19

Ruppert then illustrates an apparent attempt to bury the story by
explaining it away as nothing unusual. A September 30 New York Times
article claims that "benign explanations are turning up" in the SEC's
investigation. 20 The article blames the activity in put options,
which it doesn't quantify, on "market pessimism," but fails to explain
why the price of the stocks in the airlines doesn't reflect the same
market pessimism.

The fact that \$2.5 million of the put options remained unclaimed is
not explained at all by market pessimism, and is evidence that the put
option purchasers were part of a criminal conspiracy. 21

O'ROURKE: I mean, this is lots of fun attacking George Bush, who is an
idiot and obviously screwed up on this completely
BEHAR: Thank you!
MAHER: Oh, thank you!

PJ O'Rourke on Bill Maher show 9/16/2005

Doctor Evil, Dec 6, 2007
8. Mr. StratGuest

<more Truther bullshit snipped>

All of you conspiracy nuts need to get a life *and* a clue.

Mr. Strat, Dec 6, 2007
9. On The Highways and Bi-Ways God BuiltGuest

hell, i'd be happy if they'd just lose their ISP password.

most sincerely,

GodBuilt

--

On The Highways and Bi-Ways God Built, Dec 6, 2007
10. Al DykesGuest

Pure fiction.

Al Dykes, Dec 6, 2007
11. 'KeyGuest

"Doctor Evil" <> cross-posted, off-topic in
message
---snip the cross-posted, off-topic message---

get a clue "Doctor Evil" you are cross-posting
off-topic to some groups that don't give a crap about your
subject !

'Key, Dec 6, 2007
12. 'KeyGuest

"Mr. Strat" <> cross-posted,
off-topic in message
---snip the cross-posted, off-topic message---

get a clue "Mr. Strat" you are cross-posting
off-topic to some groups that don't give a crap about your
subject !

'Key, Dec 6, 2007
13. 'KeyGuest

"On The Highways and Bi-Ways God Built"
<> cross-posted, off-topic in message
---snip the cross-posted, off-topic message---

get a clue GodBuilt1999 you are cross-posting
off-topic to some groups that don't give a crap about your
subject !

'Key, Dec 6, 2007
14. 'KeyGuest

"Al Dykes" <> cross-posted, off-topic in
message
---snip the cross-posted, off-topic message---

get a clue"Al Dykes" you are cross-posting
off-topic to some groups that don't give a crap about your
subject !

'Key, Dec 6, 2007
15. Beau BlueGuest

We do so like policeman, they keep the streets so clean
dealing with the riff-raff so the rest of us can scheme
short wave politicians with photographic style
drop poems into useless threads all jumbled in a pile.

Surely keys are needed here, stop threading on his turf
all you trolls (and you kooks too) you're one damned silly curse
Can't you leave a copper down must you always spoil the day
and call the fiesty keyper out, scent gland ready for a spray.

yeah, HAVE some respect! ya net ya net ya net ... Right, we believe
THAT!

-blue

~ Beau Blue Presents ~ <> http://members.cruzio.com/~jjwebb
Bill Minor * Robert Sward <> Internet Broadsides
Morton Marcus * Renay <> Contemporary American Poetry
~ Blue's Cruzio Cafe ~ <> http://members.cruzio.com/~cafe

Beau Blue, Dec 6, 2007
16. On The Highways and Bi-Ways God BuiltGuest

but then again so are you. so who holds the moral high ground now, huh,
spunk-monkey?

as always, i do!!!

now go away before i get mad.

most sincerely,

GodBuilt

--

On The Highways and Bi-Ways God Built, Dec 6, 2007
17. RHFGuest

Get a Clue "Mr. Straight-Gay" You are Cross-Dressing
and Top-Ic-Less to Groups that Don't Give a Clap about
How You Look in 'other' Words.
.

RHF, Dec 7, 2007
18. barnegatdxGuest

On Dec 5, 6:38 am, wrote

Off Off topic;

barnegatdx, Dec 7, 2007
19. BurrGuest

SO, talk to us!

Burr

Burr, Dec 7, 2007
20. Nicik NameGuest

America was attacked by the United States government.....
What other State in the world would dare do such a thing knowing full well
they would be non extant in a heartbeat by US retalitation?
So whoever set this up made damn sure the attack seemed like it was not from
a world state so there would be no retalitation issues.