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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 |
WTC Towers: The Case For Controlled Demolition
Sorry, you lost me at "t_k=(-u_k+(u_k^2+2gh))/g "
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WTC Towers: The Case For Controlled Demolition
On Nov 5, 7:39 pm, wrote:
WTC Towers: The Case For Controlled Demolition By Herman Schoenfeld ... Uh, Herman, you're either a troll or a nutjob. Watch the films. See the big shiny things hitting the buildings? Stop shaving your palms with Occam's razor, it ruins the edge. Mitch (and surprise-surprise-surprise...gravity works in a predictable way which is all your "case" shows.) |
WTC Towers: The Case For Controlled Demolition
On Nov 6, 1:13 am, Mitch wrote:
On Nov 5, 7:39 pm, wrote: WTC Towers: The Case For Controlled Demolition By Herman Schoenfeld ... Uh, Herman, you're either a troll or a nutjob. Watch the films. See the big shiny things hitting the buildings? Stop shaving your palms with Occam's razor, it ruins the edge. You can keep Occam's razor sharp if you store in one of those pyramid thingys. |
WTC Towers: The Case For Controlled Demolition
On Nov 5, 10:39 pm, 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 - In other news the Aliens put us here to observe us and to build them Pyramids. |
WTC Towers: The Case For Controlled Demolition
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WTC Towers: The Case For Controlled Demolition
On Tue, 6 Nov 2007 14:08:30 -0500, "JA" wrote:
What's worse? A Conspiracy kook, or someone who TOP POSTS a single line, then quotes a 170 line rambling diatribe GFY! HAPPY? You learn quicker than some... |
WTC Towers: The Case For Controlled Demolition
On Nov 6, 1:00 pm, Gene Kearns
wrote: On Tue, 06 Nov 2007 09:27:46 -0800, Bob Ward penned the following well considered thoughts to the readers of rec.boats: What's worse? A Conspiracy kook, or someone who TOP POSTS a single line, then quotes a 170 line rambling diatribe Uh, somebody that cross posts OT drivel to a gazillion newsgroups? -- Grady-White Gulfstream, out of Oak Island, NC. Homepagehttp://pamandgene.idleplay.net/ Rec.boats at Lee Yeaton's Bayguidehttp://www.thebayguide.com/rec.boats Besides that, Gene, if you look at his calculations, it's quite a piece! It shows that gravity does exist, and does so in a way that can be resisted, but is very predictable! |
WTC Towers: The Case For Controlled Demolition
On Nov 7, 10:23 am, Gene Kearns
wrote: On Wed, 07 Nov 2007 13:50:52 -0000, penned the following well considered thoughts to the readers of rec.boats: On Nov 6, 1:00 pm, Gene Kearns wrote: On Tue, 06 Nov 2007 09:27:46 -0800, Bob Ward penned the following well considered thoughts to the readers of rec.boats: What's worse? A Conspiracy kook, or someone who TOP POSTS a single line, then quotes a 170 line rambling diatribe Uh, somebody that cross posts OT drivel to a gazillion newsgroups? -- Grady-White Gulfstream, out of Oak Island, NC. Homepagehttp://pamandgene.idleplay.net/ Rec.boats at Lee Yeaton's Bayguidehttp://www.thebayguide.com/rec.boats Besides that, Gene, if you look at his calculations, it's quite a piece! It shows that gravity does exist, and does so in a way that can be resisted, but is very predictable! It really wasn't worth my time to verify that figures don't lie, but idiots can figure.... .... been there, done that, in the marathon "catenary" thread with the master of Speedos.... -- Grady-White Gulfstream, out of Oak Island, NC. Homepagehttp://pamandgene.idleplay.net/ Rec.boats at Lee Yeaton's Bayguidehttp://www.thebayguide.com/rec.boats - Hide quoted text - - Show quoted text - Oh, yeah! I surely didn't check all of his math, I do enough of that for myself! But, if you look at the *essence* of his logic and calcs, you'll find that, just like you say, the figures don't lie, they just don't tell a whole lot! |
WTC Towers: The Case For Controlled Demolition
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WTC Towers: The Case For Controlled Demolition
On Nov 7, 11:16 am, Short Wave Sportfishing
wrote: On Wed, 07 Nov 2007 13:50:52 -0000, wrote: On Nov 6, 1:00 pm, Gene Kearns wrote: On Tue, 06 Nov 2007 09:27:46 -0800, Bob Ward penned the following well considered thoughts to the readers of rec.boats: What's worse? A Conspiracy kook, or someone who TOP POSTS a single line, then quotes a 170 line rambling diatribe Uh, somebody that cross posts OT drivel to a gazillion newsgroups? -- Grady-White Gulfstream, out of Oak Island, NC. Homepagehttp://pamandgene.idleplay.net/ Rec.boats at Lee Yeaton's Bayguidehttp://www.thebayguide.com/rec.boats Besides that, Gene, if you look at his calculations, it's quite a piece! It shows that gravity does exist, and does so in a way that can be resisted, but is very predictable! If you can't dazzle 'em with brilliance, baffle 'em with bull****. Gravity works - who 'da thunk it.- Hide quoted text - - Show quoted text - Exactly! |
WTC Towers: The Case For Controlled Demolition
Isn't this easier? (See below)
Bob Ward wrote: On Tue, 6 Nov 2007 07:20:02 -0500, "JA" wrote: sum(k=0)^N (-u_k+(u_k^2+2gh))/g=NUTBAG! wrote in message groups.com... 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 What's worse? A Conspiracy kook, or someone who TOP POSTS a single line, then quotes a 170 line rambling diatribe I'll never understand the complaining about "top posting." If people posted to the top you would not have to scroll down through an article you just read to see the reply. See above. |
WTC Towers: The Case For Controlled Demolition
On Wed, 7 Nov 2007 11:20:34 -0500, "JA" wrote:
"Bob Ward" wrote in message .. . On Tue, 6 Nov 2007 14:08:30 -0500, "JA" wrote: What's worse? A Conspiracy kook, or someone who TOP POSTS a single line, then quotes a 170 line rambling diatribe GFY! HAPPY? You learn quicker than some... Nothing to learn. I have no concern for "top posting" when I'm not trying to continue a discussion. I did not intend for the thread to go on. Your lack of concern proves that you DO have a lot to learn about Internet etiquette - but it's not worth my time to try to educate you when I can solve the problem for myself with my killfile. Others will follow suit, until no one but yourself is seeing your spew. |
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