While there are MANY valid ways that have been [and should all be] explored to debunk the official fairytale version of what happened on 9-11-01, to me, the key and most obvious [of many] lies is about how the three towers fell. There was simply too much energy involved - many times more than gravitational potential energy and some puny amount of fires could ever hope to produce the effects we all saw, and are indisputable. All but the steel beams were pulverized to dust - something that takes enormous amounts of energy; many of those beams were shot many hundreds of feet laterally; a pyroclastic cloud was formed that expanded to an enormous size and was universally described as HOT; molten metal was formed and remained hot below ground level for months; the symmetry of the collapses of WTC Towers I and II [along with seen and heard and felt explosionS - and the squibs seen] is suspicious enough - as even symmetrically constructed buildings shouldn't fail symmetrically due to fires that were asymmetrically placed. In fact, they shouldn't have collapsed at all UNLESS there were many symmetrically placed explosive devices! The real kicker is WTC 7, which was rather asymmetrical in construction, yet fell into its own footprint neatly and 'politely'* - a magic feat of physics greater than that of the other two towers [also a magic feat according to the official version].

Add to this the near free-fall speeds of the collapses [no to nearly no resistance]; plus the foreknowledge of the collapses - even two different times the collapse of WTC 7 was broadcast on TV, BEFORE it collapsed! Other individuals have come to be known to have had foreknowledge of the collapses, as well. The Laws of Physics didn't take a break on 9-11 under the influence of Osama bin Laden - no matter that the powers that be would like us to believe this is what happened - though they don't explicitly say so...they imply it absolutely!

IMO, there were definitely pre-planted explosives, most likely nanothermite/-ate.

Now that we learn in the last week that the FBI has warned all Police Dept's Nationwide that they believe that those who harbor doubts about the official version of 9-11 should be considered / can be considered as terrorists in plain sight [their wording, not mine!...see my thread on this], they expose their 'hand', methinks. So, those who believe that the Laws of Physics were immutable on 9-11, and were 'violated' in the official version of events are to be seen as 'terrorists'....well we really have become a newspeak police state where up is down and war is peace.

Game. Set. Match. 9-11 Truth has more than proven its case against the 'official fairytale'. Some minor details remain, but the game is over....and they realize it...so are starting to consider putting us in all those empty FEMA/DHS detention camps as Physics/Logical Terrorists. [perhaps for peeking under the petticoats of Secret Empire.]

* 9-11-01 was 11-22-63 on steroids and nanothermite - the same M.O. in both were used: destruction of evidence, planted stories and actors to confuse and promote the official version immediately after the event, non-investigation 'investigations', threats and some deaths of important witnesses and potential or real whistleblowers, outright lies, false 'evidence' planted, changing stories to adapt to unplanned failures and discoveries, an official version that defies the Laws of Physics, a well funded permanent cover-up, magic tricks to confuse and confound, minions of Sunsteinian agents and Mockingbirds to try to control the debate and stop the doubters from gaining traction with the Public, control of the MSM - which the forces that were behind both basically own and control through proxy, ersatz official reports, tampered with evidence and witnesses....and much more...[B].[/B]:hock:: [they both masked a naked grab for more control, money and power through crooked finance, crooked politics, wars and proxy wars, and a diminution of rights and freedoms at 'home'], direct analogy between the single/magic bullet 'theory' and the official NISTian WTC tower collapse 'theory'.
BASTA!

How did you or anyone else determine that there was too much energy involved... whatever that's supposed to mean?

You don't know how much PE was stored in the structure... do you?

Describe and explosive(s) and the mechanism by which these explosive would shoot steel (your claim) almost completely intact... actually assemblies of up to 20 or more facade 3 column panels all remaining attached in a massive sheet?

Or was it the core columns which dislodged and penetrated unscathed through the 80% solid steel facade which were shot off hundreds of feet?

Or do you just make this stuff out out of whole cloth?

Have you studied the steel coming off the collapsing towers? Do they look like they've been exploded off or are falling away?

You were trained poorly, in Physics, logic and/or as a forum provocateur. How do YOU explain molten steel - lots of it from building collapses from fires not hot enough to melt steel? Not to mention nanothermite residues, beams thrown laterally hundreds of yards, timed flashes and squibs....and all the failures that led up to the phony non-interception of the planes [which did not bring down the buildings]? You're using the standard approach of not looking at the full picture of all that happened...and trying to cast doubt on each itty bitty thing with NO logic and against the laws of Physics!

On just the pulverization of the concrete.....alone....

The North Tower's Dust Cloud

Analysis of Energy Requirements for the Expansion of the Dust Cloud Following the Collapse of 1 World Trade Center

by Jim Hoffman
October 16, 2003
[Version 3.1]

On September 11th, Both of the Twin Towers disintegrated into vast clouds of concrete and other materials, which blanketed Lower Manhattan. This paper shows that the energy required to produce the expansion of the dust cloud observed immediately following the collapse of 1 World Trade Center (the North Tower) was much greater than the gravitational energy available from its elevated mass. It uses only basic physics.

Introduction

Vast amounts of energy were released during the collapse of each of the Twin Towers in Lower Manhattan on September 11th, 2001. The accepted source of this energy was the gravitational potential energy of the towers, which was far greater than the energy released by the fires that preceded the collapses. The magnitude of that source cannot be determined with much precision thanks to the secrecy surrounding details of the towers' construction. However, FEMA's Building Performance Assessment Report gives an estimate: "Construction of WTC 1 resulted in the storage of more than 4 x 10^11 joules of potential energy over the 1,368-foot height of the structure." That is equal to about 111,000 KWH (kilowatt hours) per tower.
Of the many identifiable energy sinks in the collapses, one of the only ones that has been subjected to quantitative analysis is the thorough pulverization of the concrete in the towers. It is well documented that nearly all of the non-metallic constituents of the towers were pulverized into fine powder. The largest of these constituents by weight was the concrete that constituted the floor slabs of the towers. Jerry Russell estimated that the amount of energy required to crush concrete to 60 micron powder is about 1.5 KWH/ton. (See http://www.911-strike.com/powder.htm.) That paper incorrectly assumes there were 600,000 tons of concrete in each tower, but Russell later provided a more accurate estimate of 90,000 tons of concrete per tower, based on FEMA's description of the towers' construction. That estimate implies the energy sink of concrete pulverization was on the order of 135,000 KWH per tower, which is already larger than the energy source of gravitational energy. However, the size of this sink is critically dependent on the fineness of the concrete powder, and on mechanical characteristics of the lightweight concrete thought to have been used in the towers. Available statistics about particle sizes of the dust, such as the study by Paul J. Lioy, et al., characterize particle sizes of aggregate dust samples, not of its constituents, such as concrete, fiberglass, hydrocarbon soot, etc. Based on diverse evidence, 60 microns would appear to be a high estimate for average concrete particle size, suggesting 135,000 KWH is a conservative estimate for the magnitude of the sink.
A second energy sink, that has apparently been overlooked, was many times the magnitude of the gravitational energy: the energy needed to expand the dust clouds to several times the volume of each tower within 30 seconds of the onset of their collapses. Note that the contents of the dust clouds had to come from building constituents -- gases and materials inside of or intrinsic to the building -- modulo any mixing with outside air. Given that the Twin Towers' dust clouds behaved like pyroclastic flows, with distinct boundaries and rapidly expanding frontiers (averaging perhaps 35 feet/second on the ground for the first 30 seconds), it is doubtful that mixing with ambient air accounted for a significant fraction of their volume. Therefore the dust clouds' expansion must have been primarily due to an expansion of building constituents. Possible sources of expansion include:

• thermodynamic expansion of gases
  
• vaporization of liquids and solids
  
• chemical reactions resulting in a net increase in the number of gaseous phase molecules
  

Any chemical reactions induced by the collapse of a tower would have been insignificant sources of gas production, given the very short window of time of 30 seconds. Only the detonation of large quantities of explosives could have driven the third source of expansion. A commentary of version 3 of this paper by an anonymous author calculates that it would take 14 tons of the high explosive amatol to produce the expansion. Any role of explosives in leveling either tower is incompatible with the official explanation of the collapses. I assume explosives were not used, and consider only some combination of the first two sources of expansion: increases in gas temperatures and vaporization of water (ignoring vaporization of other substances). These are both energy sinks, so estimates of total energy can be plotted as a function of their relative share.How much energy was involved in expanding the dust cloud from either tower? To calculate an estimate we need to answer four questions:

1. What was the volume of the dust cloud from a collapse at some time soon after it started, and before it began to diffuse?
   
2. How did the mixing of the dust cloud with ambient air contribute to its size, and how can this be factored out to obtain the volume occupied by gases and suspended materials originally inside the building?
   
3. What is the ratio of that volume to the volume of the intact building?
   
4. How much heat energy was required to produce that ratio of expansion, based on different assumptions about the relative dominance the thermodynamic and vaporization energy sinks?
   

Since I have better photographs for North Tower dust, I did the calculation for it.

1. Quantifying Dust Cloud Volume

To answer question 1, I made estimates based on photographs taken at approximately 30 seconds after the onset of the collapse. The photo in Figure 1 appears to have been taken around 30 seconds after the initiation of the collapse of the North Tower. The fact that the spire is visible directly behind Building 7 indicates the photo was not taken later than the 30 seconds, since video records show that the spire started to collapse at the around 29 seconds. In this photograph, as in other ones taken around that time, the dust clouds still have distinct boundaries.
[TABLE]
[TR]
[TD][/TD]
[/TR]
[TR]
[TD]Figure 1. Photograph from Chapter 5 of FEMA's Building Performance Assessment Report.[/TD]
[/TR]
[/TABLE]
I used landmarks in this photo to make several approximate measurements of the frontier of the dust cloud. The following table lists some of them. Measurements are in feet. The first column lists heights above the street, and the second lists distances from the vertical axis of the North Tower.
[TABLE]
[TR]
[TH]label[/TH]
[TH]height[/TH]
[TH]distance[/TH]
[TH]description[/TH]
[/TR]
[TR]
[TD]3[/TD]
[TD="align: right"]230[/TD]
[TD="align: right"]1011[/TD]
[TD]west corner of 45 Park Place[/TD]
[/TR]
[TR]
[TD]5[/TD]
[TD="align: right"]228[/TD]
[TD="align: right"]729[/TD]
[TD]top of south corner of building with stepped roof[/TD]
[/TR]
[TR]
[TD]6[/TD]
[TD="align: right"]204[/TD]
[TD="align: right"]658[/TD]
[TD]east corner of Building 7, 30 stories below top[/TD]
[/TR]
[TR]
[TD]7[/TD]
[TD="align: right"]600[/TD]
[TD="align: right"]776[/TD]
[TD]upwell towering over southeast end of Post Office[/TD]
[/TR]
[TR]
[TD]8[/TD]
[TD="align: right"]700[/TD]
[TD="align: right"]?[/TD]
[TD]upwell slightly higher than the top of Building 7[/TD]
[/TR]
[TR]
[TD]11[/TD]
[TD="align: right"]190[/TD]
[TD="align: right"]870[/TD]
[TD]top of west corner of 22 Cortland St tower[/TD]
[/TR]
[TR]
[TD]12[/TD]
[TD="align: right"]508[/TD]
[TD="align: right"]588[/TD]
[TD]8 stories below top of face of WFC 3[/TD]
[/TR]
[TR]
[TD]13[/TD]
[TD="align: right"]498[/TD]
[TD="align: right"]517[/TD]
[TD]3 stories below top of upper face of WFC 2[/TD]
[/TR]
[/TABLE]
To approximate the volume I used a cylinder, coaxial with the vertical axis of the North Tower, with a radius of 800 feet, and a height of 200 feet. All the above reference points lie outside of this volume. Although the cylinder does not lie entirely within the dust cloud, there are large parts of the cloud outside of it, such as the 700 foot high upwelling column south of Building 7. The cylinder has a volume of:
pi * (800 feet)^2 * 200 feet = 402,000,000 feet^3.
I subtract about a quarter for volume occupied by other buildings, giving 300,000,000 feet^3.

2. Factoring out Mixing and Diffusion

To accurately answer question 2 would require detailed knowledge of the fluid dynamics involved. However it does appear that for at least a minute, the dust cloud behaved as a separate fluid from the ambient air, maintaining a distinct boundary. There are several pieces of evidence that support this:

• The WTC dust clouds inexorably advanced down streets at around 25 MPH. This is far faster than can be explained by mixing and diffusion.
  
• As the dust clouds advanced outward, features on their frontiers evolved relatively slowly compared to the clouds' rates of advance. This indicates that that clouds were expanding from within and that if surface turbulence was incorporating ambient air, it's contribution to expansion was minor.
  
• The top surface of the clouds looked like the surface of a boiling viscous liquid - churning but not mixing with the air above. Sinking portions of the clouds were replaced by clear air, not a mixture of the cloud and air.
  
• The dust clouds maintained distinct interfaces for well over a minute. Mixing and diffusion would have produced diffuse interfaces.
  
• There are reports of people being picked up and carried distances by the South Tower dust cloud, which felt solid. New York Daily News photographer David Handschuh recalled:
  Instinctively I lifted the camera up, and something took over that probably saved my life. And that was [an urge] to run rather than take pictures. I got down to the end of the block and turned the corner when a wave-- a hot, solid, black wave of heat threw me down the block. It literally picked me up off my feet and I wound up about a block away.

Initially the dust clouds must have been much heavier than air, given the mass of the concrete they carried and the distances they transported it. As time went on the cloud became more diffuse, but all of the photographs that can be verified as being within the first minute show opaque clouds with distinct boundaries, indicating the dominant mode of growth was expansion, not mixing or diffusion. It seems reasonable to assume that mixing with ambient air did not account for a significant fraction of the expansion in the volume of the dust cloud by 30 seconds of the start of the North Tower collapse. Nevertheless, I reduce the estimate of the dust cloud volume of building origin to 200,000,000 feet^3, imagining that a third of the growth may have been due to assimilation of ambient air.

3. Computing the Expansion Ratio

The answer to question 3 is easy. The volume of a tower, with it's 207 foot width and 1368 foot height, is:
1368 feet * 207 feet * 207 feet = 58,617,432 feet^3.
So the ratio of the expanded gasses and suspended materials from the tower to the original volume of the tower is:
200,000,000 feet^3 / 58,617,432 feet^3 = 3.41.

4. Computing the Required Heat Input

Above I identified two energy sinks that could have driven expansion of the dust cloud: thermodynamic expansion of gases, and vaporization of liquids and solids. Since most constituents and contents of the building other than water would require very high temperatures to vaporize, I consider only the vaporization of water in evaluating the second sink.
It is clearly not possible to determine with any precision the relative contributions of these two sinks to the expansion of the dust cloud. If the cloud remained uniform in temperature and density for the first 30 seconds, then the expansion would consist of three distinct phases:

• The temperature would increase to 100 C, accompanied by thermodynamic expansion.
  
• The temperature would remain at 100 C until all of the water was vaporized.
  
• The temperature would increase above 100 C, again accompanied by thermodynamic expansion.
  

Since such uniform conditions were not present, I will first treat the two energy sinks separately, and will compute the energy requirements for each if it alone were responsible for the expansion.

4.1. The Thermodynamic Expansion Sink

The ideal gas law can be used to compute a lower bound for the amount of heat energy required to induce the observed expansion of the dust cloud, assuming that the expansion was entirely due to thermodynamic expansion. That law states that the product of the volume and pressure of a parcel of a gas is proportional to absolute temperature. It is written PV = nRT, where:
P = pressure
V = volume
T = absolute temperature
n = molar quantity
R = constant
Absolute temperature is expressed in Kelvin (K), which is Celsius + 273. Applied to the tower collapse, the equation holds that the ratio of volumes of gasses from the building before and after expansion is roughly equal to the ratio of temperatures of the gasses before and after heating. That allows us to compute the minimum energy needed to achieve a given expansion ratio knowing only the thermal mass of the gasses and their average temperature before the collapse.I say that the ideal gas law allows the computation of only the lower bound of the required energy input due to the following four factors.
The finite size of molecules leads to a slight departure from the ideal gas law wherein the expansion of a parcel of gas leads to a decrease in its temperature. This means that slightly more heat energy is needed to achieve a given expansion ratio than is predicted by the ideal gas law.
The dust cloud at the time of the photograph used to estimate its volume had not finished expanding. Videos show that it continued to expand well after the 1 minute mark.
The suspended dust in the cloud had many times the mass of the gasses. This increased the energy needed to expand the dust cloud since it takes energy to lift and accelerate mass.
The suspended dust in the cloud had many times the thermal mass of the gasses. Increasing in temperature of the dust cloud to a level needed to induce the observed expansion entailed raising the temperature of the gasses and suspended solids by similar amounts. Since the solids had many times the thermal capacity of the gasses, this multiplied the energy requirements.
In this paper I examine only the fourth factor. Before considering its effect on energy requirements, I first consider the energy requirements of heating only the gasses in the clouds to the level needed to achieve the observed expansion.
According to the ideal gas law, expanding the gasses 3.4-fold requires raising their absolute temperature by the same ratio. If we assume the tower was at 300 degrees K before the collapse, then the target temperature would be 1020 degrees K, an increase of 720 degrees. Given a density of 36 g/foot^3 for air, the tower held about 2,000,000,000 g of air. Air has a specific heat of 0.24 (relative to 1 for water), so one calorie will raise one g of air 1 / 0.24 = 4.16 degrees. To raise 2,000,000,000 g by 720 degrees requires:
2,000,000,000 g * 720 degrees * 0.24 = 345,600,000,000 calories
= 399,500 KWH
To evaluate the energy requirements of the fourth factor, it is necessary to consider the composition of the dust cloud. The cloud was a suspension of fine particles of concrete and other solids in gasses consisting mostly of air. Since concrete was the dominant solid, I will ignore the others, which included glass, gypsum, asbestos, and various hydrocarbons. The small size of the particles, being in the 10-60 micron range, would assure rapid equalization between their temperature and that of the embedding air. Therefore any heat source acting to raise the temperature of the air would have to raise the temperature of the suspended concrete by the same amount. Assuming all 90,000,000,000 g of concrete was raised 720 degrees (300 K to 1020 K), the necessary heat, given a specific heat of concrete of 0.15 is:90,000,000,000 g * 720 degrees * 0.15 = 9,720,000,000,000 calories
= 11,300,000 KWH.
If we assume that the water vaporization sink absorbed all available energy once temperatures reached water's boiling point, we can compute the size of the heat sink of thermodynamic expansion that was in play as temperatures rose from room temperature to 100 C, or from 300 K to 373 K:
2,000,000,000 g * 73 degrees * 0.24 = 35,040,000,000 calories
= 40,744 KWH
The associated sink of heating the suspended solids to this temperature would be:90,000,000,000 g * 73 degrees * 0.15 = 985,500,000,000 calories
= 1,145,000 KWH.

4.2. The Water Vaporization Sink

At 100 C at sea-level, water expands by a factor of 1680 when converted to steam. Hence it is reasonable to expect that water in the building accounted for a significant part of the expansion. How much energy would be required to expand the volume of the cloud by the 3.41 ratio if water vaporization were entirely responsible for the expansion? Since water vaporization involves the introduction of volumes steam from comparatively negligible volumes of water, I assume that all the incremental volume was occupied by steam. The estimated 3.41 expansion ratio means that the incremental volume was:
200,000,000 feet^3 - 58,617,000 feet^3 = 141,383,000 feet^3
= 4,003,542,000 liters
Given the 1680 to 1 ratio between the volume steam and liquid water, 2,383,000 liters of water would have been required. The heat of vaporization of water is 540 calories/gram at 100 C. Therefore the heat energy required to produce the expansion is:2,383,000,000 g * 540 = 1,286,820,000,000 calories
= 1,496,000 KWH
Was there enough water in the building for this sink to be anywhere near this large? That is a matter of great uncertainty. Even well-cured concrete has a significant moisture content. Assuming that the estimated 90,000 tons of concrete in the tower was 1 percent water by weight, that would have provided 900 tons of water or about 900,000 liters -- well short of the 2,383,000 liter estimate above. However, there is a large amount of uncertainty in the water content of the concrete, which, like the rest of the remains of the disaster, was apparently disposed of with little or no examination. Moreover there were other sources of water in the building, such as the plumbing system, which could have accounted for tens of thousands of liters, and, gruesomely, people. The thousand victims never identified could have accounted for about 30,000 liters of water.

4.3. Which Energy Sink Was Dominant?

Both thermodynamic expansion and water vaporization have the capacity to produce vast expansion in gas volume given sufficient heat. Two major difference in the features of these sinks may help in understanding the relative contributions of each. First, thermodynamic expansion to the observed ratio requires very high temperatures, whereas vaporization-driven expansion occurs at a constant temperature of 100 C. Second, vaporization-driven expansion would be limited by the available supply of water.
If all the expansion was due to thermodynamic expansion, it would require that the dust cloud was heated to an average temperature of about 1020 K. Certainly the temperatures of the cloud near the ground were no-where near that high. Eyewitness reports show that the cloud's ground-level temperatures more than a few hundred feet away from its center were humanly survivable. Most of these reports are from the South Tower collapse, and it is unclear how similar the dust cloud temperatures following the two collapses were. Although serious fires raged in Buildings 4, 5, and 6, other nearby buildings that suffered extensive window breakage from the tower collapses, such as the Banker's Trust Building, and Word Financial Center Buildings 1, 2, and 3, did not experience fires. Digital photographs and videos show a bright afterglow with a locus near the center of the cloud, commencing around 17 seconds after the onset of the North Tower's collapse. Once the afterglow started, the cloud developed large upwelling columns towering to over 600 feet, and the previously gray cloud appeared to glow with a reddish hue. This suggests that at lest the upper and central regions of the North Tower cloud reached very high temperatures, but the evidence is insufficient to draw even general quantitative conclusions about the ranges and distributions of temperatures.
If enough water was present for vaporization to drive most of the expansion, temperatures in much of the cloud would have remained around 100 C until most of the water had vaporized. Thermodynamic expansion would occur in regions with liquid phase water until 100 C was reached, and again after the water was vaporized.
To the extent that thermodynamic expansion was the dominant factor driving the expansion, the distribution of concrete dust in the cloud, and its relationship to the temperature distribution in the cloud, would greatly affect the total energy requirements. Less energy would be required if the hotter portions of the cloud had a lower density of dust. The density was probably greater toward the central portions of the cloud, which also seem to have experienced the most heating. On the other hand, much of the dust may have settled out by the 30 second mark. The violent churning of the cloud, and the opaque appearance of its frontier, suggest that most of the dust had not settled that early.

Summary

The dominant energy source assumed to be in play during the leveling of each of the Twin Towers was the gravitational energy due to their elevated mass. The energy sinks included the thorough pulverization of each tower's concrete, the vaporization of water, and the heating of air and suspended concrete dust in the ensuing dust cloud. Estimates for these energies are:
[TABLE]
[TR]
[TH]energy, KWH[/TH]
[TH]source or sink[/TH]
[/TR]
[TR]
[TD="align: right"]+ 111,000[/TD]
[TD]falling of mass (1.97e11 g falling average of 207 m)[/TD]
[/TR]
[TR]
[TD="align: right"]- 135,000[/TD]
[TD]crushing of concrete (9e10 g to 60 micron powder)[/TD]
[/TR]
[TR]
[TD="colspan: 2"] ignoring water vaporization[/TD]
[/TR]
[TR]
[TD="align: right"]- 400,000[/TD]
[TD]heating of gasses (2e9 g air from 300 to 1020 K)[/TD]
[/TR]
[TR]
[TD="align: right"]- 11,300,000[/TD]
[TD]heating of suspended concrete (9e10 g from 300 to 1020 K)[/TD]
[/TR]
[TR]
[TD="colspan: 2"] assuming water vaporization sink was not supply-limited[/TD]
[/TR]
[TR]
[TD="align: right"]- 1,496,000[/TD]
[TD]vaporization of water (2.38e9 g water)[/TD]
[/TR]
[TR]
[TD="align: right"]- 41,000[/TD]
[TD]heating of gasses (2e9 g air from 300 to 373 K)[/TD]
[/TR]
[TR]
[TD="align: right"]- 1,145,000[/TD]
[TD]heating of suspended concrete (9e10 g from 300 to 373 K)[/TD]
[/TR]
[/TABLE]
The imbalance between sources and sinks is striking, no matter the relative shares of the thermodynamic and water vaporization sinks in accounting for the expansion. Moreover, it is very difficult to imagine how the gravitational energy released by falling mass could have contributed much to any of the sinks, since the vast majority of the tower's mass landed outside its footprint. The quantity for the crushing of concrete appears to be conservative since some reports indicate the average particle size was closer to 10 microns than 60 microns. The quantity for the heating of suspended concrete has a large amount of uncertainty, but the energy imbalances remain huge even when it is ignored entirely. All of these energy sink estimates are conservative in several respects.

• They are based on an estimate of dust cloud volume at a time long before the cloud stopped growing.
  
• They use a liberal estimate of the contribution of mixing to the volume.
  
• They ignore thermal losses due to radiation.
  
• They ignore the resistance to expansion due to the inertia of the suspended materials, and energy requirements to overcome it.
  

Conclusion

The amount of energy required to expand the North Tower's dust cloud was many times the entire potential energy of the tower's elevated mass due to gravity. The over 10-fold disparity between the most conservative estimate and the gravitational energy is not easily dismissed as reflecting uncertainties in quantitative assessments.
The official explanation that the Twin Tower collapses were gravity-driven events appears insufficient to account for the documented energy flows.

[TABLE="class: contentpaneopen, width: 548"]
[TR]
[TD="class: contentheading"]High Temperatures, Persistent Heat & 'Molten Steel' at WTC Site Contradict Official Story[/TD]
[TD="class: buttonheading, width: 100%, align: right"][/TD]
[TD="class: buttonheading, width: 100%, align: right"][/TD]
[/TR]
[/TABLE]
[TABLE="class: contentpaneopen, width: 548"]
[TR]
[TD]Written by Richard Gage, AIA, Andrea Dreger & Gregg Roberts [/TD]
[/TR]
[TR]
[TD="class: createdate"]Tuesday, 24 August 2010 15:31[/TD]
[/TR]
[TR]
[TD]

Extremely high temperatures were evident before and during the destruction of the World Trade Center Twin Towers and at Ground Zero. Seven minutes before the destruction of the South Tower, a flow of molten metal appeared, accompanied by several smaller flows, as documented by the National Institute of Standards and Technology (NIST). The material's glowing color showed that its temperature was close to "white hot" at the very beginning of the flow and "yellow-orange" further down. Iron-rich spheres in the WTC dust are additional proof of temperatures above the melting point of iron. Pyroclastic-like, rapidlyexpanding dust clouds after the destruction of the Towers can also be explained only by the expansion of hot gases.
[TABLE="width: 210, align: right"]
[TR]
[TD="align: left"]An excavating machine at Ground Zero lifts debris dripping with molten metal[/TD]
[/TR]
[/TABLE]
The high-temperature phenomena at Ground Zero are documented by various sources:
Bechtel engineers, responsible for safety at Ground Zero, wrote in theJournal of the American Society of Safety Engineers: "The debris pile at Ground Zero was always tremendously hot. Thermal measurements taken by helicopter each day showed underground temperatures ranging from 400ºF to more than 2,800ºF."
The fact that high-temperature phenomena were an important issue at Ground Zero is underscored by the large number of thermal images acquired: images by SPOT, MTI, AVIRIS/NASA,"Twin Otter"/U.S. Army, and at least 25 images by EarthData, taken between Sept. 16 and Oct. 25. In addition, temperature measurements by helicopter were taken each day, and the firefighters used onsite sensors too.
Many witnesses, including rescue personnel and firefighters working on the piles, described the phenomenon of "molten steel." Terms used in witness statements are, for example, "molten steel," beams "dripping from molten steel," "molten steel … like you're in a foundry. Like lava, from a volcano." Aphotograph taken on September 27 by a Ground Zero worker shows an excavating machine lifting debris from the WTC wreckage dripping yellow/orange molten metal.
WTC clean-up workers and 9/11 artifacts architect Bart Voorsanger, in the PBS video "Relics from the Rubble," described what must have been several tons of "fused element[s] of steel ... molten steel and concrete and all of these things …all fused by the heat," weighing several tons each. These foreign objects came to be known as "meteorites."

The heat at Ground Zero was not only extreme, it was also persistent, as proven not only by witness statements and a photograph by LiRo Group / Engineering of orange-red glowing steel as late as October 21, but also by thermal images taken by NASA and EarthDatasatellites. The EarthData thermal images also show that the "hot spots" remained at the same locations. The phenomenon did not "move" across the site, like one would expect from fire as it consumes the fuel available in any one location.
University of California professor Abolhassan Astaneh-Asl, the first structural engineer given access to the WTC steel at Fresh Kills Landfill notes, "I saw melting of girders at the World Trade Center." Astaneh also "describes the connections [between supporting columns] as being smoothly warped: If you remember the Salvador Dalí paintings with the clocks that are kind of melted it's kind of like that. That could only happen if you get steel yellow hot or white hot perhaps around 2,000 degrees.'".
Iron workers at the site pointed out that huge columns that werebent into horseshoe shapes - without the flanges showing any cracks or buckling. They cited, "It takes thousands of degrees to bend steel like this".
FEMA documents in their Appendix C of its May 2002 WTC Building Performance Assessment Team study, for sample 1, "evidence of a severe high temperature corrosion attack on the steel, including oxidation and sulfidation with subsequent intergranular melting." A "sulfur-rich liquid" containing "primarily iron, oxygen, and sulfur" "penetrated" into the steel.
The extremely high temperatures contradict the official story. Office and hydrocarbon fires burning in open air (~500° to 1,500° F) cannot reach temperatures in the range that iron or structural steel melts (2,700° F). This was even acknowledged by NIST's Co-Project Leader, John Gross, in the same public talk where he stated regarding the phenomena of molten steel, "I know of absolutely nobody, no eyewitnesses that said so, nobody that's produced it." Yet there is abundant proof of the molten metal, which subsequent tests reveal to be iron, in the debris piles. Furthermore, NIST itself performed extensive fire tests to establish the temperatures reached by the WTC office and jet fuel fires. The temperatures established are far below the temperatures required to produce all of the above phenomena which occurred both before and during the destruction and at Ground Zero.
The steel problem was "solved" by NIST by excluding most of the steel from being systematically examined for failure modes and heat excursions. The steel collected by the Port Authority, which has been stored in Hangar 17 at JFK Airport, was not included in the investigation except for 12 pieces. Of the 236 pieces that NIST possessed, many were excluded based on the circular argument that only columns from impact and fire floors were of interest in the investigation. Thus, NIST avoided having to discuss 51 of its 55 core columns. Sample 1 from FEMA's Appendix C was also excluded.
In addition, NIST developed a new method of "visual examination" that it then substituted in place of the systematically used tool. NIST's "paint cracking" method has the following "advantages": paint cracks can be produced not only by high temperature excursions, but also by "corrosion"/ "environmental degradation" and by plastic deformation; many columns had no paint left for examination, Moreover, by relying on a method that requires microscopic examination, NIST was able to ignore pieces that were obviously heat-affected but had come from non-fire floors. A contractor's report that employed common visual examination was "reviewed": NIST contrasted the contractor's results with their newly developed method and their fire exposure observations, and by employing again a circular argument. NIST's steel "examination" shows that its "working hypothesis" was in fact its premise, and that NIST gone to great lengths to maintain this premise.

Some want to cite "natural thermite reactions" for the high-temperature phenomena: airplane aluminum must have reacted with rust. This possibility can be ruled out based on the findings of a study that was conducted in 2002 at the Colorado School of Mines for the Minerals Management Service. Officially, the study, whose lead author is a close research associate of T. W. Siewert of NIST, is about thermite-sparking in offshore environments. But due to a very odd study design the question about the feasibility of natural thermite reactions in the WTC is answered too. The authors established the ignition temperatures for rust, dehydrated rust and iron-oxide-based thermite reactions. The necessary temperatures are so high that one can conclude that thermite reactions between airplane aluminum and rust (some rust was on beams according to documents), dehydrated rust (rust dehydrates in fire) or iron oxide (iron oxide was part of the primary paint) were not feasible in the WTC. Also tested was what happens when aluminum impacts rust at very high velocity, so, interestingly, even the possibility that the impacting airplanes caused natural thermite reactions can be ruled out.
The overwhelming evidence of these extremely high temperatures, which normal office fires and jet fuel cannot produce, cries out for a new investigation. The hypothesis of explosive controlled demolition must be examined and, if confirmed, followed wherever it leads, so that Americans can know for sure what was the real cause of the catastrophic loss of life at the WTC on 9/11 and the identities of everyone who was responsible for it.
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Peter

In addition to the failure of the official lie to explain the "collapse" we have the behaviors of the principals of the national security state

presented in Ryan, Another Nineteen:

A Vonnegut Cat's Cradle:

nice, nice,
very nice:
so many traitors in the same device

FBI Director Freeh, Director of Central Intelligence Tenet
"I see nothing, nothing!"

And they suppressed those who were not so willfully blind.

A few still insist the non-existent heat weakened the steel

much as non-existent single bullet caused seven wounds

An official explanation which explains nothing

followed by an enforcement through suppression of critical thinking

Your information is very compelling; just one example in the following paragraph:

The steel problem was "solved" by NIST by excluding most of the steel from being systematically examined for failure modes and heat excursions. The steel collected by the Port Authority, which has been stored in Hangar 17 at JFK Airport, was not included in the investigation except for 12 pieces. Of the 236 pieces that NIST possessed, many were excluded based on the circular argument that only columns from impact and fire floors were of interest in the investigation. Thus, NIST avoided having to discuss 51 of its 55 core columns. Sample 1 from FEMA's Appendix C was also excluded.
In addition, NIST developed a new method of "visual examination" that it then substituted in place of the systematically used tool. NIST's "paint cracking" method has the following "advantages": paint cracks can be produced not only by high temperature excursions, but also by "corrosion"/ "environmental degradation" and by plastic deformation; many columns had no paint left for examination, Moreover, by relying on a method that requires microscopic examination, NIST was able to ignore pieces that were obviously heat-affected but had come from non-fire floors. A contractor's report that employed common visual examination was "reviewed": NIST contrasted the contractor's results with their newly developed method and their fire exposure observations, and by employing again a circular argument. NIST's steel "examination" shows that its "working hypothesis" was in fact its premise, and that NIST gone to great lengths to maintain this premise.


So, we see a very Red Queen Meets White Knight for Tea with White Rabbit, "We only looked where we wanted to look, and only saw what we wanted to see, and all it means is what we want it to mean."


Now Alice will be given the Acquilla Clemmons warning.