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WTC Towers: The Case For Controlled Demolition
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,
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.
> wtc2 :: Double
> wtc2 = cascadeTime 417 110 77
By Herman Schoenfeld
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,
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.
> wtc2 :: Double
> wtc2 = cascadeTime 417 110 77
By Herman Schoenfeld
On Apr 15, 2:10 am, schoenfeld....@gmail.com wrote:
[snip]
*raises hand*
So where do the planes that CRASHED INTO THE BUILDINGS fit into your
conspiracy theory?
[snip]
*raises hand*
So where do the planes that CRASHED INTO THE BUILDINGS fit into your
conspiracy theory?
On Apr 15, 4:16 am, Eric Gisse <jowr...@gmail.com> wrote:
> On Apr 15, 2:10 am, schoenfeld....@gmail.com wrote:
> [snip]
>
> *raises hand*
>
> So where do the planes that CRASHED INTO THE BUILDINGS fit into your
> conspiracy theory?
To say nothing of the fact that there is zero evidence that thousands
of pounds of explosives could have been packed into the building with
nobody noticing.
Someone far smarter than me did the math on that and figured it would
have taken something crazy like 37 pallets of explosives per day over
the course of a year to bring the buildings down. Naturally there's no
evidence that this was going on.
- Jordan
> On Apr 15, 2:10 am, schoenfeld....@gmail.com wrote:
> [snip]
>
> *raises hand*
>
> So where do the planes that CRASHED INTO THE BUILDINGS fit into your
> conspiracy theory?
To say nothing of the fact that there is zero evidence that thousands
of pounds of explosives could have been packed into the building with
nobody noticing.
Someone far smarter than me did the math on that and figured it would
have taken something crazy like 37 pallets of explosives per day over
the course of a year to bring the buildings down. Naturally there's no
evidence that this was going on.
- Jordan
<schoenfeld.one@gmail.com> wrote in message
news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
Sad strange little man. Do you still believe in Santa Claus and the Easter
Bunny as well? Pathetic.
On 15 Apr, 13:29, "boodybandit" <allaboutga...@comcast.net> wrote:
> <schoenfeld....@gmail.com> wrote in message
>
> news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
>
> Sad strange little man. Do you still believe in Santa Claus and the Easter
> Bunny as well? Pathetic.
Remember that this spam has been posted to hundreds of groups see
http://groups.google.co.uk/groups/profile?enc_user=isqvSBgAAACr5FANHdiGO5mpK2pQ9cxMtiDKbEn1fjJfYkQTWXi1Vg
and the poster will not be reading any of the replies.
> <schoenfeld....@gmail.com> wrote in message
>
> news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
>
> Sad strange little man. Do you still believe in Santa Claus and the Easter
> Bunny as well? Pathetic.
Remember that this spam has been posted to hundreds of groups see
http://groups.google.co.uk/groups/profile?enc_user=isqvSBgAAACr5FANHdiGO5mpK2pQ9cxMtiDKbEn1fjJfYkQTWXi1Vg
and the poster will not be reading any of the replies.
On Apr 16, 12:35 am, Captain Paralytic <paul_laut...@yahoo.com> wrote:
> On 15 Apr, 13:29, "boodybandit" <allaboutga...@comcast.net> wrote:
>
> > <schoenfeld....@gmail.com> wrote in message
>
> >news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
>
> > Sad strange little man. Do you still believe in Santa Claus and the Easter
> > Bunny as well? Pathetic.
>
> Remember that this spam has been posted to hundreds of groups seehttp://groups.google.co.uk/groups/profile?enc_user=isqvSBgAAACr5FANHd...
> and the poster will not be reading any of the replies.
I read all the replies.
> On 15 Apr, 13:29, "boodybandit" <allaboutga...@comcast.net> wrote:
>
> > <schoenfeld....@gmail.com> wrote in message
>
> >news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
>
> > Sad strange little man. Do you still believe in Santa Claus and the Easter
> > Bunny as well? Pathetic.
>
> Remember that this spam has been posted to hundreds of groups seehttp://groups.google.co.uk/groups/profile?enc_user=isqvSBgAAACr5FANHd...
> and the poster will not be reading any of the replies.
I read all the replies.
schoenfeld.one@gmail.com wrote:
> On Apr 16, 12:35 am, Captain Paralytic <paul_laut...@yahoo.com> wrote:
>> On 15 Apr, 13:29, "boodybandit" <allaboutga...@comcast.net> wrote:
>>
>>> <schoenfeld....@gmail.com> wrote in message
>>> news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
>>> Sad strange little man. Do you still believe in Santa Claus and the Easter
>>> Bunny as well? Pathetic.
>> Remember that this spam has been posted to hundreds of groups seehttp://groups.google.co.uk/groups/profile?enc_user=isqvSBgAAACr5FANHd...
>> and the poster will not be reading any of the replies.
>
> I read all the replies.
So why post your conspiracy theories to groups about radio dramas,
cigars, crusies and video games? Who are you trying to impress?
--
neil h
google brights
> On Apr 16, 12:35 am, Captain Paralytic <paul_laut...@yahoo.com> wrote:
>> On 15 Apr, 13:29, "boodybandit" <allaboutga...@comcast.net> wrote:
>>
>>> <schoenfeld....@gmail.com> wrote in message
>>> news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
>>> Sad strange little man. Do you still believe in Santa Claus and the Easter
>>> Bunny as well? Pathetic.
>> Remember that this spam has been posted to hundreds of groups seehttp://groups.google.co.uk/groups/profile?enc_user=isqvSBgAAACr5FANHd...
>> and the poster will not be reading any of the replies.
>
> I read all the replies.
So why post your conspiracy theories to groups about radio dramas,
cigars, crusies and video games? Who are you trying to impress?
--
neil h
google brights
Retards. The fucking buildings were designed to fail this way.
These crack pots really belive this shit.
<schoenfeld.one@gmail.com> wrote in message
news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
> 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
These crack pots really belive this shit.
<schoenfeld.one@gmail.com> wrote in message
news:1a7a218d-078f-4b9d-99d9-ada8d0cc2cda@q24g2000prf.googlegroups.com...
> 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
[Default] Thus spake "Tom" <Nospam@eatme.com>:
>Retards. The fucking buildings were designed to fail this way.
>These crack pots really belive this shit.
And you had to repost the entire thing.
>Retards. The fucking buildings were designed to fail this way.
>These crack pots really belive this shit.
And you had to repost the entire thing.
Dillon Pyron wrote:
> [Default] Thus spake "Tom" <Nospam@eatme.com>:
>
>> Retards. The fucking buildings were designed to fail this way.
>> These crack pots really belive this shit.
>
> And you had to repost the entire thing.
.... and top post it again at that.
---
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> [Default] Thus spake "Tom" <Nospam@eatme.com>:
>
>> Retards. The fucking buildings were designed to fail this way.
>> These crack pots really belive this shit.
>
> And you had to repost the entire thing.
.... and top post it again at that.
---
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Tested on: 4/20/2008 20:55:55
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