WTC Towers: The Case For Controlled Demolition

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

  1. 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+74.28))/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/20010911_WTC/WTC_LDEO_KIM.pdf

    APPENDIX A: HASKELL SIMULATION PROGRAM

    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
    #1
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  2. schoenfeld.one

    barnegatdx Guest

    barnegatdx, Dec 5, 2007
    #2
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  3. schoenfeld.one

    Doctor Evil Guest

    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
    #3
  4. schoenfeld.one

    Mr. Strat Guest

    You Truthers are really a disgusting lot.
     
    Mr. Strat, Dec 5, 2007
    #4

  5. 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
    #5
  6. schoenfeld.one

    Venger Guest

    Go away, Truther Douchebag!!!

    Truthers are dumb people. Don't be dumb.

    Venger
     
    Venger, Dec 6, 2007
    #6
  7. schoenfeld.one

    Doctor Evil Guest

    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]

    3. "Mechanics of Possible Bin Laden Insider Trading Scam," Herzlyya
    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,
    <www.suntimes.com/terror/stories/cst-nws-trade20.html>. "Probe of
    options trading link to attacks confirmed," [...] Chicago Sun-Times,
    September 21, 2001,
    <www.suntimes.com/terror/stories/cst-fin-trade21.html>.

    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
    #7
  8. schoenfeld.one

    Mr. Strat Guest

    <more Truther bullshit snipped>

    All of you conspiracy nuts need to get a life *and* a clue.
     
    Mr. Strat, Dec 6, 2007
    #8
  9. 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
    #9
  10. schoenfeld.one

    Al Dykes Guest


    Pure fiction.
     
    Al Dykes, Dec 6, 2007
    #10
  11. schoenfeld.one

    'Key Guest

    "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
    #11
  12. schoenfeld.one

    'Key Guest

    "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
    #12
  13. schoenfeld.one

    'Key Guest

    "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
    #13
  14. schoenfeld.one

    'Key Guest

    "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
    #14
  15. schoenfeld.one

    Beau Blue Guest

    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
    #15
  16. 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
    #16
  17. schoenfeld.one

    RHF Guest

    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
    #17
  18. schoenfeld.one

    barnegatdx Guest

    On Dec 5, 6:38 am, wrote

    Off Off topic;
     
    barnegatdx, Dec 7, 2007
    #18
  19. schoenfeld.one

    Burr Guest

    SO, talk to us!

    Burr
     
    Burr, Dec 7, 2007
    #19
  20. schoenfeld.one

    Nicik Name Guest

    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.
    So get your head out of your ass and start thinking critically.
     
    Nicik Name, Dec 7, 2007
    #20
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