In article . com>,
trijcomm > wrote:
> On Nov 7, 4:11 am, wrote:
> > 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...C_LDEO_KIM.pdf
> >
> > APPENDIX A: HASKELL SIMULATION PROGRAM
> >
> > 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- Hide quoted text -
> >
> > - Show quoted text -
>
> Yep, I'm sure two huge planes filled with fuel had nothing to do with
> it. How stupid.
Millions of us saw airliners used as missles... not lazers or holograms.
It goes to show you how the 'unbelievableness' of the Inevitable Event
goes around and around in our collective unconscious.
The REAL CONSPIRACY is in the botched 'intelligence' and the botched
'response' to that Inevitable Event, not to mention any names. (snicker)
Coffee in Chi-Na