In article <ae5e9eff178816ece4b9fff4b162ed27@[EMAIL PROTECTED]
>,
Bush Sux Clinton Sux <bush.sux@[EMAIL PROTECTED]
> wrote:
> On Sat, 8 Mar 2008, schoenfeld.one@[EMAIL PROTECTED]
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 sup****t columns.
> >This demolition profile requires that the sup****t columns holding a
> >floor be destroyed just before that floor is collided with by the
> >upper falling m*****. 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 a "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 dimini****ng velocity rapidly approaching rest due
> >to 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 sup****t 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.
> >
> >> 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
>
> Yes, we know 9/11 was Der Fuehrer's Reichstag fire, and there's not
> a damned thing anyone can do about it. Michael Moore came out with
> a movie about it, but nobody gave a damn. Bush sux, Clinton sux,
> and quite frankly America sux, because they always buy into their
> ****. Besides, the World Trade Center was an old, ugly building. I
> just wish they'd demolish the UN building. Talk about butt-ugly!
>
> Why post to echostar? This is a group for Dish Network subscribers.
>
> Mike
Same reason as he posts to alt.pantyhose, I suppose.
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