WTC Towers: The Case For Controlled Demolition
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From: schoenfeld.one on 5 Apr 2008 22:52 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. > 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 By Herman Schoenfeld
From: mommycalled on 6 Apr 2008 01:41 <Drivel snipped> I see you flooded just about every newsgroup with your drug induced fantasy yet again. Regardless of how many times people point out the LIES AND DISTORTIONS YOU CREATE to support your conspiracy theory you periodically post your LIES AND DISTORTIONS. What a sad little person you are
From: "TOPposter" TOPposter on 6 Apr 2008 01:44 There is only one truth the media would never lie to us -- Socrates taught his students that the pursuit of truth can only begin once they start to question and analyze every belief that they ever held dear. If a certain belief passes the tests of evidence, deduction, and logic, it should be kept. If it doesn't, the belief should not only be discarded, but the thinker must also then question why he was led to believe the erroneous <mommycalled(a)gmail.com> wrote in message news:4f678d9c-a655-4b53-91d7-3fe5bcd8bb76(a)m3g2000hsc.googlegroups.com... > <Drivel snipped> > > I see you flooded just about every newsgroup with your drug induced > fantasy yet again. Regardless of how many times people point out the > LIES AND DISTORTIONS YOU CREATE to support your conspiracy theory > you periodically post your LIES AND DISTORTIONS. > > What a sad little person you are
From: Dave on 6 Apr 2008 03:28 schoenfeld.one(a)gmail.com wrote: > 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" And what exactly does this have to do with the price of cheese?
From: Fred Hiltz on 6 Apr 2008 06:29
Dave wrote: > schoenfeld.one(a)gmail.com wrote: >> 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" > > And what exactly does this have to do with the price of cheese? It got the poor fellow the attention he craves. -- Fred Hiltz, fhiltz at yahoo dot com |