posted 02-02-2004 10:54 PM
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
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
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:
steel is mostly iron (Fe);
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;
Fe values found were readily available and reasonably self-consistent;
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
for the "average" box column, 0.415 m3 x 7874 kg/m3 = 3267.71 kg Fe; and
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
for an "average" column, 3267.71 kg x 1511 K x 0.449 kJ/kg K = 2.22 x 10+6 kJ; and
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:
for "average" column, 3267.71 kg x 2.47 x 10+2 kJ/kg = 8.07 x 10+5 kJ; and
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:
for "average" box column, (2.22 + 0.81) x 10+6 kJ = 3.03 x 10+6 kJ; and
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
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
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 ˝ 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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