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 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 diminishing 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 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.
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
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.
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On Mar 7, 1:48 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 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 diminishing 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 support st ructures disabled just prior the collision with the block.
3. The collapsing block merges with the momentarily levita ting 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
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, j , 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 ) SQR T(u_(k-1)^2+74.28) ;/ u_0=0
Tower 2 began collapsing on the 77th floor. Making substitutions Nw, j3 , 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
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.
On Mar 7, 1:48 am, schoenfeld....@gmail.com 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 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 diminishing 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 support st ructures
disabled just prior the collision with the block.
3. The collapsing block merges with the momentarily levita ting 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
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 ) SQR T(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.
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 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 diminishing 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 support st ructures disabled just prior the collision with the block.
3. The collapsing block merges with the momentarily levita ting 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
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, j , 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 ) SQR T(u_(k-1)^2+74.28) ;/ u_0=0
Tower 2 began collapsing on the 77th floor. Making substitutions Nw, j3 , 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
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.
problem is, they're so fixated on it, to give it up would be an admission of their fuckwittery.
They're the new Xtians.
starbuck
oh for fucks sake we dont give a fucking rats arse ok
wrote in message news:
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 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 diminishing 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 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.
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
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, j , 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 Nw, j3 , 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
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
oh for fucks sake we dont give a fucking rats arse ok
<schoenfeld.one@gmail.com> wrote in message
news:8401aa79-5bc9-4c93-8e07-2af4393fb087@s8g2000prg.googlegroups.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
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 diminishing 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 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.
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
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, j , 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 Nw,
j3 , 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.
oh for fucks sake we dont give a fucking rats arse ok
wrote in message news:
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 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 diminishing 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 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.
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
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, j , 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 Nw, j3 , 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
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
SAM
In article <48d4a5cd-f1dd-4253-9519- , says...
Who cares , get over it.
problem is, they're so fixated on it, to give it up would be an admission of their fuckwittery.
They're the new Xtians.
et en frenchie ça fait quoi ?
In article <48d4a5cd-f1dd-4253-9519-
df94db3c0c6b@s19g2000prg.googlegroups.com>, johnvonlaws@hotmail.com
says...
Who cares , get over it.
problem is, they're so fixated on it, to give it up would be an
admission of their fuckwittery.