WTC Towers: The Case For Controlled Demolition

Discussion in 'UK Motorcycles' started by schoenfeld.one, Nov 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, Nov 5, 2007
    #1
    1. Advertisements

  2. schoenfeld.one

    TOG Guest

    <snip> and follow-ups reset.
     
    TOG, Nov 5, 2007
    #2
    1. Advertisements

  3. schoenfeld.one

    ogden Guest

    From drinking their own shitty lager, I presume.
     
    ogden, Nov 6, 2007
    #3
  4. schoenfeld.one

    Daniel Kolle Guest

    You are a bloody buffoon and ****.
     
    Daniel Kolle, Nov 6, 2007
    #4
  5. schoenfeld.one

    Baldoni Guest

    explained on 05/11/2007 :
    You wouldn't remember the Blitz would you ?
     
    Baldoni, Dec 1, 2007
    #5
  6. **** off. NGs snipped.
     
    The Older Gentleman, Dec 1, 2007
    #6
  7. schoenfeld.one

    marcus Guest

    Jean Charles de Menezes
    I don't see the weight of the aircraft in the calculations, an additional
    quantity the building was not designed to support, particularly after the
    shock of a side impact.
     
    marcus, Dec 1, 2007
    #7
    1. Advertisements

Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.