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Physics911.org WTC Attacks : Calculations on the Possible Use of
Thermite to Melt Sections of the WTC
Posted by webmaster on 2003/11/23 22:41:22 (1079 reads)
Calculations on the Possible Use of Thermite
to Melt Sections of the WTC Core Columns
by D. P. Grimmer
Version 1.0, November 23rd 2003
Abstract
Anomalies involving the collapse of WTC buildings on 9-11 are
discussed from the perspective of possible controlled demolition implosion
rather than of aircraft impact and fuel-fire damage. Considered is the
possible use of thermite to melt sections of the columns of the WTC towers
inner cores, thus aiding in their collapse. This paper will discuss the
structure of the WTC core columns, and estimate the mass of metal to be
melted; calculate the sensible and latent heat energy needed for melting
this mass; discuss the nature and specific energies of the thermite
reaction; estimate the mass and volume of thermite necessary to provide the
energies for melting; and discuss the possible locations where such thermite
could be placed to cause melting, both internal and external to a core
column.
Introduction
Of the events of 11 September '01, perhaps the most dramatic were the
collapses of the WTC towers. Re-played repeatedly on TV, the images of the
collapsing towers and their pyroclastic clouds of debris are seared into our
memories.
What immediately struck some observers, this author included, is how
much these collapses resembled a controlled demolition. Indeed, this was the
first reaction of V. Romero of New Mexico Tech, until he recanted days later
[Ref. (1)]. There has been much discussion on the internet of the observed
anomalies associated with the WTC building collapses (including the delayed
collapse of the unstruck WTC7). Interesting sites can be found at
www.serendipity.li, www.americanfreepress.net, www.misternet.org,
www.911-strike.com, www.plaguepuppy.net, www.whatreallyhappened.com and many
others ( a google search is always useful).
One site deals directly with aircraft impact and fuel-fire physics
[Ref. (2)]. The very anomalous case of the WTC7 building collapse was
archived at Ref. (3); especially interesting are the observations by the
inspection engineer at WTC7 of evidence for vaporized steel. As always,
information about controversial events like 911 must be approached with some
caution, and are not to be taken at face value. Careful analysis and
appraisal is necessary. The internet has gained a reputation as a refuge of
"conspiracy theorists," but recent events (e.g., the falsehoods told by US
officials leading up to the Iraq war) have shown that "reputable" media are
not to be trusted. They may themselves be regarded as purveyors of
"official" conspiracy theories. This present paper hopes to achieve some
level of objectivity about a very controversial subject.
Total objectivity is of course impossible. Subjectively, for this
author, several subevents of the WTC collapses stand out: the reported
seismic spikes associated with the collapses; the observed near free-fall
times of collapse; the pyroclastic clouds of debris; and the pools of molten
steel found in the basement of the WTC tower complex, steel still warm weeks
after 9-11. Analysis of the seismic spikes indicate that the seismic spikes
correlate with the collapses themselves rather than any pre-collapse
explosion [Ref. (4)].
Calculations done by the author correlated the collapse energies with
the seismic signal of explosions at a quarry in the vicinity of the seismic
observatory. These calculations indicate that the seismic spikes of the WTC
events represent energies close to those of the collapses themselves (see
Appendix A for these seismic energy correlation calculations). A sole video
clip purported to show, by video image shaking, evidence of a pre-collapse
WTC2 explosion is not conclusive. A video with shake-free periods for
several minutes before and after collapse is not available. Therefore, wind
flutter has not been disproved as a cause of camera shaking. A second video
from another perspective is not available to show pre-collapse shaking
temporally correlated with the first video. The existence of such a second
video from an independent source would make such video evidence more
credible [Ref. (5)]. From these observations, the author has concluded that
there is no firm evidence of pre-collapse explosions that left seismic
signatures.
[A brief note here about the mathematical notation used in this paper:
subscripts, superscripts and exotic math symbols have not been used. Unlike
most word processor programs, most email formats do not support these fonts.
So, for example, ten to the nth power is denoted here by 10+n; the square
root of N is SQRT(N); a quantity N with the exponent n (i.e., N to the nth
power) is given by N exp(n); an so forth. This was done so individuals can
communicate about this paper in any common email format].
The observed near free-fall times of the WTC towers (and WTC7) were a
dramatic signature of a controlled demolition. (The articles at
http://members.fortunecity.com/911 are a valuable resource for presenting
and then challenging the "official" explanation for WTC collapses). Measured
times are all around 10 seconds, which is close to calculated free-fall
time, indicating the tower floors fell without much impediment. They
essentially fell into air [Ref. (6)]. The theory put forth by T. Eagar of
MIT and other "establishment" engineers is that while no steel members
actually melted or failed, the floor assemblies, bolted at their joists to
the outer walls and inner core structures, did fail [Ref. (7)]. The floor
joists attachment bolts were weakened and gave way, twisting sideways and
allowing the initial floor to "unzipper" itself all the way round and
collapse to the floor below. The remaining floors then pancaked all the way
down. Never mind that floor joist cross-members, placed to resist twisting,
and additional support structures were not included in the MIT/FEMA/NOVA
calculations and presentations (nor was the inner core collapse mechanism
explained at all).
Consider the following: if the pancaking effect caused the total
building failure, why is it that no video of either of the WTC collapses
shows any sign of stutter between floor collapses, which should have been
very apparent especially in the first few floors of collapse when the speed
of gravitational collapse was small? Consider also that apologists for the
official conspiracy theory propose that 30% of the gravitational collapse
energy was necessary to create the pyroclastic cloud of debris: that is, in
their own analysis, this energy came out of the gravitational energy. This
means that the time of fall would have been slowed further than what was
observed. When a body of mass m falls from a height h, acted upon by
gravitational acceleration g, it converts its potential energy PE = m x g x
h into kinetic energy KE = (1/2) x m x (v exp2). Here h = (1/2) x g x (t
exp2), t = time of fall, and v =g x t, where v = velocity. Removal of 30% of
the PE to pulverize concrete essentially reduces the amount of energy
available from falling, effectively reducing the gravitational acceleration
to something less than g.
Substituting, in the above equations we have (1.0 - 0.3) x PE = 0.7 x
PE = m x g' x h, where PE, m and h are as before and g' = the effective
gravitational acceleration. Hence, comparing terms for PE, g' = 0.7 g. The
time of collapse under g' will also increase. If we let the effective
collapse time be t', then comparing terms for constant h, (1/2) x g x (t
exp2) = (1/2) x g' x (t' exp2) =
(1/2) x 0.7g x (t' exp2). Hence, (t exp2) = 0.7 x (t' exp2), or (t/t')
= SQRT (0.7) = 0.837. Or, t' = 1.195 t.
Now the observed time t = 10 seconds (a free fall time, the fastest
possible time under g = 9.8 m/sec/sec = 32 ft/sec/sec = 32 ft/s exp2). For
the cloud debris creation to absorb 30% of the gravitational energy, the
observed time of fall would be 10s x 1.195, or almost 12 seconds. This long
a collapse time was observed by no one. Clearly, there are serious flaws in
the official explanation/conspiracy theory.
The implication from the above is that there were major energy sources
other than gravitational involved in the WTC towers collapses. Certainly
that is the conclusion of J. Hoffman in his thorough discussion of the north
WTC tower dust cloud [Ref. (8)]. By calculating the major sources and sinks
observed, particularly the sink of the pyroclastic cloud expansion, Hoffman
establishes that a large amount of energy had to be available to drive that
expansion, in a (minimum) range of 2,706,000 kWh to 11,724,000 kWh (see his
Summary table). Hoffman does not propose an energy source to balance that
sink. In Appendix B, an estimate, for discussion purposes only, of the
amount of thermite-equivalent to provide this energy source is discussed. It
is large, but physically possible.
A discussion of the melted steel found at the base of the WTC complex,
not explained by any official, forms the bulk of the remainder of this
paper. The following discussion explores the possibility of whether it is
possible to get sufficient volume of a relatively slow-reacting chemical
compound, like thermite, either on or inside the inner columns to melt a
section of them or otherwise weaken them to allow for the inner core to
collapse. As Mark Loizeaux of Controlled Demolition, Inc., commenting on the
pools of molten steel he observed at the bases of the towers' elevator
shafts, said: "If I were to bring the towers down, I would put explosives in
the basement to get the weight of the building to help collapse the
structure" [Ref. (9)]. Controlled Demolition, Inc., incidentally was the
company contracted to remove the debris from both the WTC and from the 1995
bombing of the Murrah building in OKC.
To summarize so far: the discussion in the text above and in Appendix
A indicates that the energy of the seismic signal (best viewed as a
semi-logarithmic plot) and the gravitational collapse are very close to
being the same. This coupled with the fact that there is only one short
video clip allegedly showing shaking before collapse of one of the towers
leads an objective observer to conclude that there is no actual proof that
the seismic "spike" signal is nothing more than building collapse. This is
not to say that the seismic signal is 100% guaranteed to be non-explosion
related, just that there is no firm evidence so far for the alleged massive
explosion. That is, this is not an area on which to stake a lot of credence.
The seismic event must be regarded as a "red herring" unless a second,
longer video showing the same behavior appears.
The free-fall times and pools of molten steel are entirely different
matters. They are a matter of public record, observed by many individuals.
So we have evidence of molten steel in the basement; the FEMA report saying
molten steel was not to blame, just weakened floor joist bolts; collapse
times close to free fall; no real record of a massive explosion (although
numerous claims of sounds of smaller explosions and observations of
demolition squibs). The immediate conjecture supported by direct observation
is the following: controlled demolition, characterized by a (relatively)
non-explosive, huge energy release necessary to melt (some) steel. M. Rivero
of whatreallyhappened.com and others have proposed the use of thermite,
familiar to those of us who had the high school chemistry course with an
impressive thermite demonstration. So the question arises: can one get
enough thermite close enough to melt sections of the inner core columns, as
part of a controlled demolition scenario? The following calculations in this
paper indeed do show that it is possible (and I stress possible). Until
simple chemical reactants like thermite can be discarded there is really no
need to invoke the use of highly speculative and sophisticated devices like
thermobaric bombs and scalar EM weapons.
Melting of WTC Inner Core Columns
Evidence of molten steel was found at the very base of the WTC towers,
and is a matter of public record. This present study is by no means
exhaustive. It is intended as a first attempt to test the possibility that
the core columns could have been melted by a known chemical compound.
Thermite was chosen as the reactive chemical compound because it is well
understood, and is used commercially to weld steel parts (e.g. train rail
sections in situ). Other more sophisticated chemical compounds with higher
energy densities, by mass and/or volume, could be used in future
calculations. Broad assumptions will be made, to get rough estimates of
relevant parameters.
Structure of WTC Columns and Their Metal Mass
The best on-line discussion resource found for these calculations was
at Ref. (10). According to this source the inner core consisted of from 44
to 47 box columns (the exact number and layout is not known; the
architectural firm had not released the construction drawings). The
dimensions of the columns reduced in size with increasing height, changing
to I-beams above the 85th floor. The above website article assumes
(generously) that each core box column has the following (average)
X-section: 12"wide x 36"deep x 2' thick. The article goes on to calculate
the X-sectional area of steel as 192 in2. However, this is in error in that
the corners are double-counted, giving a larger x-section than there
actually is. If w = box column width, d = depth, and t = thickness, then the
X-sectional steel area is given by
A = [d x t + (w-2 x t) x t] x 2. For d = 36", t = 2" and w = 12", then
A = [36" x 2" + (12"-2 x 2") x 2] x 2 = 176 in2 = 1.222 ft2.
Floor height was 12ft, so we choose for discussion sake, a 12' high
box column in these calculations. Note that multiple floors could have had
thermite-type compounds placed there. Also, no more than a foot portion,
rather than a full 12 ft of column would be necessary to collapse that
floor. Also, complete melt of a column portion is not necessary to cause
collapse. So, per floor, per column there is a steel volume V = 12' x 1.222
ft2 = 14.67 ft3. Also, note that the internal X-sectional area of a box
column is given by
Aint = [d-(2 x t)] x [w- (2 x t)], and the internal volume by Vint =
12' x [d - (2 x t)] x [w - (2 x t)].
Here, Vint = 12' x [36"-2 x 2"] x [12"- 2 x 2"]/(144 in2/ft2) = 12' x
1.778 ft2 = 21.333 ft3.
The internal volumes will be re-examined later as a possible space to
place the thermite.
The website also mentions that the largest box columns used at the
core bases had the dimensions of 16" wide x 36" deep x 4" thick. It is not
known where exactly the molten steel, that puddled in the WTC basement,
originated in the towers. The melt could have occurred some what higher in
the columns (where "average" box columns would have been), or at the base
where the "largest" box columns were. Molten material would flow down the
various WTC shafts to the lowest point possible, 6 stories (some 72') below
ground level. Applying the same formulae as above, we have for these
"largest" columns, A= [36" x 4" + (16" - 2 x 4") x 4"] x 2 = 352 in2 = 2.444
ft2. Note that this happens to be twice the area as for the "average" box
column assumed above. Again, for a 12' column, V = 12' x 2.444 ft2 = 29.328
ft3. Also, here, the internal volume is Vint = 12' x [36' - 2 x 4"] x
[16' -2 x 4"]/144" = 18.667 ft3.
In summary, we have for a 12 ft. high core box-column, for a
1.. 12" wide x 36"deep x 2" wall thickness (hereafter referred to as
an "average" box column), that it has 14.67 ft3 = 0.415 m3 volume of steel,
and 21.33 ft3 = 0.604 m3 of internal volume; and
2.. 16" wide x 36" deep x 4" wall thickness (hereafter referred to
as a "largest" box column), that it has 29.328 ft3 = 0.832 m3 of steel and
18.667 ft3 = 0.529 m3 of internal volume.
Sensible and Latent Heat Energies Needed for Melting a Core Column
Section
Knowing the volume of steel involved, we next turn our attention to
calculating the energy needed to melt a core column section. We decided to
use values for the element iron rather than steel for the following
pragmatic reasons:
1.. steel is mostly iron (Fe);
2.. whatever steel is chosen, may be the wrong kind and would be
contested: Fe is a given and known quantity, whereas there are many steels;
3.. Fe values found were readily available and reasonably
self-consistent;
4.. except for stainless steels, the thermal properties of steel are
relatively close to Fe, although the mechanical properties may certainly
differ more.
For Fe we will use the following values:
Density = 7874 kg/m3
Melting point = 1811 K = 1538 C
Specific heat = 25.1J/mol K = 449 J/kg K = 0.449 kJ/kg K
Latent heart of fusion = 13,800 J/mol = 2.47 x 10+5 J/kg
Latent heat of evaporation = 347,000 J/mol = 6.21 x 10+3 kJ/kg
mol = gm mole equivalent = 0.0558 kg for Fe
For a 12 ft high core Fe column, we have
1.. for the "average" box column, 0.415 m3 x 7874 kg/m3 = 3267.71 kg
Fe; and
2.. for the "largest" box column, 0.832 m3 x 7874 kg/m3 = 6551.17 kg
Fe.
Taking 300 K as "ambient" temperature on 9-11, then the temperature
difference up to the melting point of Fe is given by
1811 K - 300 K = 1511 K (give or take a few degrees K).
Hence, the energy needed to raise a 12 ft high Fe column to its
melting point temperature is given by
1.. for an "average" column, 3267.71 kg x 1511 K x 0.449 kJ/kg K =
2.22 x 10+6 kJ; and
2.. for a "largest" column, 6551.17 kg x 1511 K x 0.449 kJ/kg K =
4.44 x 10+6 kJ.
To actually melt the Fe at 1511 K, we need to provide the latent heat
of fusion:
1.. for "average" column, 3267.71 kg x 2.47 x 10+2 kJ/kg = 8.07 x
10+5 kJ; and
2.. for "largest" column, 6551.17 kg x 2.47 x 10+2 kJ/kg = 1.62 x
10+6 kJ.
Thus we see that the sensible heat energies involved are almost a
factor of 3 times larger than the latent heats.
Hence, for the total amount of energy needed to melt a 12 ft high Fe
column, we need:
1.. for "average" box column, (2.22 + 0.81) x 10+6 kJ = 3.03 x 10+6
kJ; and
2.. for "largest" box column, (4.44 + 1.62) x 10+6 kJ = 6.06 x
10+6kJ
Energies of the Thermite Reaction
An iron oxide/aluminum "thermite" mixture consists of 23.7% Al, 74.7%
Fe2O3 by weight, in the reaction
Fe2O3 + 2 Al => Al2O3 + 2 Fe + 849 kJ/mol.
Thus, 849 kJ of energy are released for every g-mole-equivalent (mol)
of Fe2O3 that reacts with 2 mol of Al.
For Al, with a density of 2.699 g/cm3, there are 26.98 g/mol.
For Fe2O3, with a density of 5.24 g/cm3, there are 159.70 g/mol.
So then, 159.70 g of Fe2O3 + 53.96 g of Al (213.66 g total) produces
849 kJ of energy, or 3.974 kJ/g = 3.974 x 10+3 kJ/kg (Note that this gives
the proper % component mixtures by weight).
For an infinitesimally compacted powder mixture, this would occupy a
volume of 159.70g x (cm3/5.24 g) + 53.96 g x (cm3/2.699 g) = (30.48 + 20.0)
cm3 = 50.48 cm3.
A separate analysis of a CuO/Al thermite mixture (used to weld copper
parts) indicates a powder packing fraction of 0.82 (82%) can be achieved.
Let's assume a powder packing fraction of 0.82. Hence, our Fe2O3/Al thermite
mixture would occupy not 50.48 cm3, but 61.5 cm3.
Thus the physical density of our densely-packed Fe2O3/Al thermite
mixture is
213.66 g/61.5 cm3 = 3.474 g/cm3 = 3.474 x 10+6 g/m3 = 3.474 x 10+3
kg/m3,
and our energy density (per volume) is given by
849 kJ/61.5 cm3 = 13.805 kJ/cm3 = 1.3805 x 10+7 kJ/m3.
Thus to melt a 12 ft high Fe column, we need
1.. for an "average" column, (3.03 x 10+6 kJ)/(3.974 x 10+3 kJ/kg) =
0.7625 x 10+3 kg = 762.5 kg of thermite. This would occupy a volume of 762.5
kg/(3.474 x 10+3 kg/m3) = 0.219 m3. Note that this volume of thermite is
less than the internal volume Vint calculated earlier, 0.604 m3. Actually,
the internal volume of the "average" box column could be filled with 0.604
m3/0.219 m3 = 2.76 times more than needed to do the job. Alternatively, the
column does not require as high a packing density ( i.e. <0.82) and yet be
able to load a sufficient charge of thermite mixture to cause melting
2.. for a "largest" column, (6.06 x10+6 kJ)/(3.974 x 10+3 kJ/kg) =
1524.9 kg thermite. This would occupy a volume of 1524.9 kg/(3.974 x 10+3
kg/m3) = 0.439 m3. Note that this volume of thermFite also is less than the
earlier calculated Vint = 0.529, but would require a moderately high packing
density, approximately > 0.82 x 0.439/0.529 = 0.68.
Other Locations Where Thermite Could Be Placed to Cause Core Box
Column Melting
In the preceding section, the amount of thermite needed to cause
melting was calculated, and compared to the internal volume available. Just
as insulation in building walls is introduced by means of relatively small
holes drilled through walls, so could thermite have been placed into the
interiors of the core box columns. For the "average" columns this would
certainly work, since there is ample volume to overcharge with a low packing
density (>0.5). The "largest" columns could be filled in the same way,
although some way to "settle" the compound powders might be necessary to
achieve a packing density from a pour to be > 0.68.
Rather than fill the interior of a column with chemical compound, what
if the thermite compound was applied to the outside of the column, under a
layer of "fire-proofing" protective cladding/thermal insulation? How thick
would an exterior layer need to be applied?
(a) For an "average" box column, if T is the thickness of the applied
outside layer of thermite compound, it would have a X-sectional area given
by
Acoat = [T x (d + 2 x T) + T x w] x 2, where d = 36" and w = 12" as
before.
This can be rewritten as Acoat = 2 x [2 x Texp2 + T x (d + w)]
For a 12 ft = 3.658 m column, the volume of the coating of thickness
T is given by
Vcoat = 2 x 3.658 x [2 x Texp2 + (d + w) x T] = 0.219 m3, or
2 x Texp2 + (d + w) x T = 0.219 m3/ (2 x 3.658 m) = 0.0299 m2, or
2 x Texp2 + (d + w) x T -0.0299 m2 = 0. This is in the form of a
quadratic equation, where the solution is given by
T (in meters)= {-b + SQRT(bexp2 - 4 x a x c)}/2 x a, where here
a = 2, b = (d + w) = 12" + 36" = 48" = 1.219 m, and c = -0.0299 m2.
Substituting,
T = {-1.219 + SQRT[(1.219)exp2 - 4 x 2 x (-0.0299)]}/(2 x 2).
Simplifying,
T = {-1.219 + SQRT[1.486 + 0.2395]}/4 = {-1.219 + SQRT[1.725]}/4 =
= {-1.219 + 1.313}/4, or
T = 0.0236 m = 0.93", which is less than 1" of coating for the
"average" column.
(This solution can be verified by substitution in the original
equation for Vcoat).
(b) For a "largest" box column, here Vcoat = 0.439 m3 and (d + w) =
16"+36" = 1.321m.
So, 2 x Texp2 + 1.321 x T = 0.439m3/(2 x 3.658 m) = 0.0600, or
2 x Texp2 + 1.321 x T - 0.0600 = 0. So, using the quadratic solution
again,
T = {-1.321 + SQRT[(1.321)exp2 - 4 x 2 x (-0.600)]}/(2 x 2).
Simplifying,
T = {-1.321 + SQRT[1.745 + 0.48]}/4 = {-1.321 + SQRT[2.225]}/4 =
{-1.321 + 1.492}/4, or
T = 0.04275 m = 1.683", which is less than 1-3/4" of coating for the
largest column.
In short, if a coating slightly less than 2" thick of a thermite
coating were applied to the outer surface of any box column, that is
sufficient chemical compound to melt that column section. A protective,
insulating and cosmetic/disguising layer (e.g. fiberglass/foam) 1" or less
would also be helpful.
Conclusions
In this paper we have attempted to establish the amount of thermite
that would be necessary to melt a box column at or near the base of the WTC
towers' cores, to see if the amount necessary was physically feasible, or
would require an unrealistic amount sure to attract detection before its
use. We have used thermal parameters for iron, and assumed thermite as the
chemical compound. The analysis is thus imperfect, since the structural
steel used may have slightly different properties, requiring more (or less)
of the chemical compound. A different, more sophisticated compound may have
required even less volume than has been calculated here.
Still the implications are clear: such a melting of a section of all
the inner core box pillars is possible, using relatively simple technology.
Such compounds could have been applied to the interior or the exterior of
even the largest of these columns in a surreptitious manner, to accomplish
the task of melting and collapse. The amount necessary for complete melting
of a segment of even the largest box column was calculated, and found
possible. Of course complete melting was not necessary to cause total
failure: a lesser amount of a thermite-like compound could have been used to
raise the temperature of the steel to a point where the columns would fail
before melting, although some melting must have occurred to account for the
steel pools.
It is pure speculation if, how, and when this was done. The columns
would have been most easily filled during the initial construction phase,
but this requires belief in a foresight and 30-40 year "master plan" that
may be difficult for many to think possible. (Many buildings are constructed
with ultimate demolition in the design, to make way for future construction
in urban areas. Usually, the building design includes cavities for
controlled demolition explosive placement. The non-availability of WTC tower
blueprints makes it difficult to access this possibility).
However, there have been undoubtedly a number of opportunities under
the guise of maintenance: many stories exist about problems with the
"insulation" adhering to the steel support structures of the WTC towers.
Also, the first attack on the WTC towers in 1993, in the basement of the
complex, offered an opportunity for access and "repair" to demolition
experts and construction personnel. Thermite is a relatively safe compound,
requiring high temperature to initiate reaction - a magnesium fuse is
commonly used. We will probably never know exactly what sequence of events
unfolded to culminate in the WTC collapses of 11 September 2001.
Acknowledgments
The author wishes to acknowledge discussions with A.K. Dewdney, J.
King, J. Longspaugh, B. Mayeux, J. Russell, R. Stanley, S. Walker and other
friends and associates of SPINE. Of course, the author takes full
responsibility for the content of this work; any errors are his alone.
Appendix A: WTC Seismic Energy Correlation Calculations
F. Moscatelli of Swarthmore College has provided figures on the energy
releases involved in the WTC tower collapses in an article by the BBC [Ref
(11)]. The article reports the gravitational energy for both towers plus
sundry other collapses as 6.8 x 10+11 J, +-25%. Hence, for one WTC tower,
the gravitational energy involved can be approximated by ½ x 6.8 x 10+11 J =
3.4 x 10+11 J = 94,400 kWh +- 25%. (Here, using an energy unit conversion
site is handy [Ref. (12)]). This figure for single tower collapse seems
about right, and agrees with the figure of 100,000 kWh used at various other
sites; an estimate of 160,000 tons of steel, concrete, etc., per tower
yields a value of 85,000 kWh (J. Russell, personal communication); FEMA's
Building Performance Assessment Report indicates about 111,000 kWh per tower
(see J. Hoffman's dust cloud analysis at Ref.(13)); see also various
websites listed in the Introduction). Hence, a first order calculation
suggests that the amount of gravitational energy involved in the collapse of
a WTC tower is on the order of 94,400+-23,600 kWh.
This is also the amount of energy that can be roughly back-calculated
from a Palisades observatory WTC collapse seismic event of 2.2 (average)
magnitude, and compared to a Palisades recorded quarry explosion seismic
event "calibration" of 1.5 (average) magnitude. The quarry explosions were
caused by the detonation of 80,000 lbs = 40 tons of ammonium nitrate/fuel
oil (ANFO), equivalent to approximately 0.30 x 40 = 12 tons of TNT = 13,946
kWh, where 1 ton ANFO = 30% of 1 ton of TNT energy equivalent, and 1 ton TNT
= 4.186 x 10+9 J = 1,163 kWh. If we take the ratio of the magnitudes of the
seismic energies for the WTC collapse and for a quarry explosion, we have
the ratio of (10+2.2)/(10+1.5) = 158.5/31.6 = 5.02. Hence, the seismic
energy of the WTC event compared to a quarry explosion can be given roughly
by 5.02 x 13,946 kWh = 70,009 kWh. This is just at the lower limit of the
calculated gravitational collapse energy calculated above, 70,800 kWh. Also,
consider that some portion of the towers' concrete mass that was pulverized
into suspended fine dust would not appear in a seismic spike signal. Some
estimated 90,000 tons of the estimated 160,000 tons of material per tower
was concrete (i.e. 56% of tower mass was concrete, while 44% was steel,
etc.). Assume, for discussion's sake, that half the concrete per tower was
converted into fine dust that did not contribute to the immediate seismic
signal (i.e. 28% of tower mass). Subtracting this 28% of tower mass would
decrease the "average" figure of 100,000 kWh of total gravitational energy
per tower to 68,000 kWh. Again this is close to the crudely calibrated value
of 70,009 kWh. Although these calculations involve arguable assumptions, the
author only wishes to demonstrate that claims the observed seismic spike
indicated a massive pre-collapse explosion are not supported by the
mathematical analysis. The conclusion the author arrived at is that the
seismic spikes observed were certainly of the same magnitude as, and not
separate from, the WTC towers' gravitational energies.
It has been the main thrust of this paper that explosions leaving a
seismic spike would not have been necessary to bring down a structure like a
WTC tower. A slower reaction would still cause core failure. Whether a
chemical reaction takes place over a period of say, 1 second, or 1
millisecond, the energy released is the same. Since power =
energy/unit-time, then a reaction taking 1 millsecond would have 1000 times
the power as a reaction taking 1 second, but still release the same amount
of energy. This is the difference between a blast and a melt. The melt would
not (necessarily) leave a seismic signature.
Appendix B: Calculation of the Amount of Thermite-Equivalent Needed to
Provide the Energy Source for the Energy Sinks Calculated by J. Hoffman in
His Analysis of the WTC North Tower Pyroclastic Cloud
As an exercise, calculations are presented here of the amount of
thermite needed to fill the energy sinks calculated by J. Hoffman in his
analysis of the WTC north tower pyroclastic cloud [Ref.(13)]. It should be
stated at the outset that thermite is not definitely proposed as the
mechanism for this cloud expansion. Just as for the collapse of the inner
core, the calculations are done to see if it is possible to contain enough
thermite-equivalent within the WTC tower structures to create the effect of
the pyroclastic cloud.
Ignoring water vaporization, Hoffman calculates a total energy sink to
be filled by a source of 11,724,000 kWh; see his Summary table at Ref (13).
This allows for thermodynamic gas expansion only (no water vapor expansion).
For water vapor expansion only (no water supply limit for vaporization), the
energy source required is 2,706,000 kWh. This is regarded by Hoffman as a
lower-limit range for the sink, 2,706,000 to 11,724,000 kWh.
In this present paper, we calculated that the energy density per
volume for densely packed thermite is given by 1.3805 x 10+7 kJ/m3. Since, 1
kWh = 3600 kJ, then the thermite energy density is given by 3,835 kWh/m3.
Hence, to reach the lower limit of Hoffman's range, a volume of 705.6 m3 of
densely-packed thermite would be needed, and to reach the upper limit of the
range, 3057.1 m3 would be required.
Let us do a rough estimate of the volume inside of the core columns of
a WTC tower, as a first place chosen to put the above calculated m3 of
thermite. Let us assume the following for a WTC tower: the 6 floors of the
basement and the first 6 floors above ground are "largest" box columns; the
remaining 79 floors from the 7th to the 85th are "average" box columns;
above the 85th floor the supports are I-beam , not box columns, without
internal volume. Let us further assume 47 core columns per floor. (These
assumptions, while reasonable, are somewhat arbitrary, in this
"boundary-value" calculation).
Earlier we calculated for a "largest" box columns, 0.529 m3 of
internal volume, while for an "average" column we arrived at 0.604 m3 of
internal volume. Hence, per floor of "largest" core columns we have an
internal core volume of 47 x 0.529 m3 = 24.86 m3; and per floor of "average"
columns, an internal core volume of 47 x 0.604 m3 = 28.39 m3. Twelve floors
of "largest" core columns provides 12 x 24.86 m3 = 298.3 m3 of volume, while
79 floors of "average" columns provides 79 x 28.39 m3 = 2242.8 m3 of volume.
Thus we have a grand total of 2541.1 m3 of core column inner volume
available for controlled demolition charges. Note that this available volume
of 2541.1 m3 is within the range of volumes needed above for densely-packed
thermite, 705.6 m3 to 3057.1 m3.
It is not likely that all the core volumes could be filled in this way
with high-density thermite. Recall that a less-than 2" thick thermite
coating applied to a column exterior as "insulation" was sufficient to melt
it. The surfaces of columns and floors are more likely places to apply
chemical compounds disguised as "insulation" (Recall reports about the WTC's
"shoddy" construction, rumored influenced by organized crime; recall also
reports about problems getting the "insulation" to adhere).
Let us do one more calculation for illustration. For simplicity, this
time consider the case of a WTC tower with 91 floors of all "average" box
columns, including the basement and first 6 floors above ground. Let each
floor have 47 such columns, for 47 x 91 = 4277 columns total. These 12' tall
column surfaces are to be coated with 3057.1 m3 of a thermite like compound.
This works out to 0.71 m3 per column. How thick would this coating need to
be? As before when we considered a core column's surface coating for an
"average" column, let the volume of the coating be Vcoat ( = 0.71 m3,
instead of 0.219 m3 as before). Then,
Vcoat = 2 x 3.658 x [2 x Texp2 + (d + w) x T] = 0.71 m3 , or
2 x Texp2 + (d + w) x T = 0.71 m3/(2 x 3.658 m) = 0.097 m2.
Simplifying,
2 x Texp2 + (d + w) x T - 0.097 = 0.
This is again in the form of a quadratic equation, where a =2; b = (d
+ w) = 12" + 36" = 48" = 1.219 m; and c = -0.097 m2. Then, as before,
T = {-1.219 + SQRT[(1.219)exp2 - 4 x 2 x (-0.097)]}/(2 x 2), or
T = {-1.219 + SQRT[1.486 + 0.776]}/4 = {-1.219 + SQRT[2.262]}/4 or
T = {-1.219 + 1.504}/4 = 0.071 m = 2.81".
In short, if a coating slightly less than 3" thick of a thermite like
coating were applied to the outer surfaces of the box columns, that volume
would contain sufficient energy to account for the pyroclastic cloud, under
the conditions of the largest energy sink calculated by Hoffman.
This paper will not consider the much greater surface areas and
coating volumes provided (and thinner coatings allowed) by the WTC floors
themselves -- what better places to heat and pulverize concrete? That is
left for the reader to ponder.
References
(1)
http://www.maebrussell.com/Articles%20and%20Notes/WTC%20Explosives.html and
http://emperors-clothes.com/news/albu.htm
(2) http://emperors-clothes.com/news/albu.htm
(3) http://www.geocities.com/streakingobject/07NYTimes7WTCwhy.html
(4) http://www.ldeo.columbia.edu/LCSN/Eq/20010911_WTC/WTC_LDEO_KIM.pdf
and
http://victoria.indymedia.org/news/2003/04/13974.php
(5) See for example http://www.whatreallyhappened.com/shake2.html as
one site of the video clip.
(6) http://members.fortunecity.com/911/wtc/proof.htm
(7) http://members.fortunecity.com/911/wtc/nova.htm
(8) http://physics911.org/net/modules/news/article.php?storyid=12
(9)
http://www.americanfreepress.net/09_03_02/NEW_SEISMIC_/new_seismic_.html
(10) http://www.misternet.org/nerdcities/WTC/wtc-demolition.htm
(11) http://news.bbc.co.uk/1/hi/sci/tech/1550326.stm
(12) http://www.convert-me.com/en/convert/energy/
(13) http://physics911.org/net/modules/news/article.php?storyid=12
© Derrick P. Grimmer, Ph.D., 16th November 2003
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