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WTC Towers: The Case For Controlled Demolition
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 |
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WTC Towers: The Case For Controlled Demolition
wrote in message ... WTC Towers: The Case For Controlled Demolition By Herman Schoenfeld This "case" is no more convincing now then when you spammed it out last month... |
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WTC Towers: The Case For Controlled Demolition
On Dec 5, 3:37 am, wrote:
WTC Towers: The Case For Controlled Demolition By Herman Schoenfeld snip lying BS Take it over to alt.conspiracy. Your head will deservedly be handed to you for being an idiot. Harry K |
#4
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WTC Towers: The Case For Controlled Demolition
Over 3000 people died by cowards who took over 4 civilian planes.
I would have more respect for the muslims if they were out it the open and willing to take the west head on... but they can't. They live in a 7th Century morass that will forever keep them socially/technically/ politically backwards. This isn't to say that Christians didn't go through their own 'backwardness'. e.g. Spanish Inquisition, split between Catholic and Protestant churches, and so on. Its just today, while the rest of the world is heading into the 21st Century, most muslim countries want to pretend its the 7th Century redux and the emam in the Wheel is back running around the fields again. So whether its a conspiracy or not, I don't care. What I do care about are muslim extremist trying to kill everyone who doesn't see the universe in the same manner as they. |
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