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Saturday, May 5, 2012

911 - Twin Towers' Dust Clouds

Twin Towers' Dust Clouds

Photographic Evidence of Dust Clouds From the Twin Towers' Destruction

The dust clouds that issued from the Towers' explosive collapses were unlike anything seen in the history of man-made structures. Even conventional explosive demolitions of large buildings produced far less dust. Their appearance and rate of travel resembled the pyroclastic flows of volcanoes.
This page lists photographs which show the dust clouds that continued to expand after the waves of destruction that demolished the towers reached the ground. Photographs listed on the collapses page also show a great deal of dust, whose production started within the first second of each collapse.

Dust Cloud Dominates Lower Manhattan After One of the Towers Disappeared



Views from north of North Tower Dust Seconds After Leveling



Dust Cloud Dominates Lower Manhattan as WTC1 is Leveled


These photographs were taken from a helicopter, and capture the progression of the North Tower's dust cloud.












Vast Volumes of Dust

Dust From Collapses Expanded to Many Times The Towers' Volumes

The dust clouds rapidly invaded the surrounding city, filling the cavernous spaces between nearby skyscrapers in seconds. Eyewitness reports were consistent that it was impossible to outrun the dust clouds. Photographs can be used to calculate the speed at which the dust cloud from the North Tower grew. There is a photograph of the North Tower dust showing the spire and showing dust 700 feet in front of the nearest part of the building's footprint. That distance is calculated using buildings as reference points. Since it is known from real-time movies that the spire fell about 30 seconds after the initiation of the collapse, and that it took about 10 seconds for the bottom of the dust cloud to reach the ground, the average speed of advance on the ground in that direction was approximately 35 feet per second. Both Towers exploded into vast dust clouds, which photographs show to be several times the volumes of the intact buildings by the time the destruction reached the ground. The dust clouds continued to expand rapidly thereafter, growing to easily five times the buildings' original volume by 30 seconds after the initiation of each collapse.
Another feature of the dust clouds was that they upwelled in immense columns, climbing to over the height of Building 7 (over 600 feet) in the seconds immediately after each collapse.
Such behavior clearly indicates the input of huge quantities of heat far in excess of what the friction of a gravity-driven collapse could produce.

Volume of Dust

Volume of Dust Clouds Proves Demolition

Both of the Twin Towers exploded into vast clouds of dust. That the clouds expanded to five times the volume of the towers within 30 seconds of the initiation of their collapses is a conservative estimate.
If the collapses were merely gravity-driven, then any clouds of debris produced in the immediate aftermath should have occupied about the same amount of space as the intact towers before they had time to significantly mix into the surrounding air. The bulk of the clouds could only come from the expulsion of gases in the buildings as they collapsed, and the mixing of ambient air into the clouds. The contribution of mixing increases over time, and is unbounded. However, the dust clouds appear to expand more rapidly than can be accounted for by mixing. This implies that heat energy was being added to the clouds in order to cause the gases to expand, and/or water to vaporize.
Could the known energy sources have accounted for the pre-mixing expansion? This question is treated in some quantitative detail in the paper: The North Tower's Dust Cloud: Analysis of Energy Requirements for the Expansion of the Dust Cloud Following the Collapse of 1 World Trade CenterThis paper estimates the dust cloud volume of the North Tower and shows that, even allowing for expansion due to mixing, the heat sink is many times greater than the tower's gravitational energy. Even without such quantitative analysis, it is clear that the gravitational energy of the towers alone could not have driven the dust clouds' expansion, given limitations on conversion of that energy to heat and the apparent absence of extensive mixing early in the clouds' development.
The expansion of the dust clouds presents problems for the gravity collapse theory that are evident without quantitative analysis. Here we consider the role of the two main factors that could have worked to expand the dust clouds.
  • Heating of the air due to friction of the collapse
  • Mixing of the cloud's gases and suspended solids with ambient air

Did Friction Multiply the Clouds' Volumes?

Suppose that nearly all of the gravitational energy of the towers was converted into friction and therefore heat. Would that have been sufficient to expand the dust clouds? A clue is that in a typical demolition, the volume of the dust cloud grows to only slightly larger than the intact building's volume immediately following the collapse. Even if the gravitational potential energy of the towers was great enough to drive the expansion, it is highly doubtful that much of it would be converted into heat in the dust clouds, for several reasons.
  • Rubble falling through the air would not generate much heat energy until it hit the ground, and then most of the energy would be converted to ground movement and the finer breakup of the rubble rather than heat.
  • Rubble crushing the building would convert much of its kinetic energy to friction in the steel frame in the process of shredding it. The steel frame would not have enough surface area to transfer much heat to the gases during the split second in which the building around any given piece of steel was crushed, so most of the heat would have ended up in the rubble pile.
  • If much of the gravitational energy was converted to heat through friction, it would have necessitated longer collapse times than were observed.
At least one 
academic paper has attempted to explain the rapidity of the collapses by promoting a questionably applicable mathematical model alleged to predict a nearly frictionless total collapse. Since that model has each tower neatly pulling itself down at near the speed of free-fall, there would be very little heat produced to drive the dust cloud expansion.

Did Mixing Expand the Clouds?

Mixing of building air with ambient air could not account for the rapidity of the expansion of the dust clouds, nor their appearance. Mixing of gases can occur through diffusion or convection. Diffusion is not relevant, since it is the space occupied by suspended particles that defines the volume of the cloud. Convection could only expand the cloud if there was a high degree of turbulence on the cloud's boundary, and would have produced a diffuse boundary. That does not appear to have occurred in the early stages of the Twin Towers' dust clouds. The clouds maintained well-defined interfaces as they expanded to many times the buildings' volumes. Moreover, features on the surface of the clouds evolved slowly relative to the movement of large portions of the cloud. The distinct boundaries and persistent shapes mean the clouds were expanding primarily by pushing aside the ambient air, not by assimilating it.
---------------------------

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.
Figure 1. Photograph from Chapter 5 of FEMA's Building Performance Assessment Report.
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.
labelheightdistancedescription
32301011west corner of 45 Park Place
5228729top of south corner of building with stepped roof
6204658east corner of Building 7, 30 stories below top
7600776upwell towering over southeast end of Post Office
8700?upwell slightly higher than the top of Building 7
11190870top of west corner of 22 Cortland St tower
125085888 stories below top of face of WFC 3
134985173 stories below top of upper face of WFC 2
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:
    energy, KWHsource or sink
    + 111,000falling of mass (1.97e11 g falling average of 207 m)
    - 135,000crushing of concrete (9e10 g to 60 micron powder)
         ignoring water vaporization
    - 400,000heating of gasses (2e9 g air from 300 to 1020 K)
    - 11,300,000heating of suspended concrete (9e10 g from 300 to 1020 K)
         assuming water vaporization sink was not supply-limited
    - 1,496,000vaporization of water (2.38e9 g water)
    - 41,000heating of gasses (2e9 g air from 300 to 373 K)
    - 1,145,000heating of suspended concrete (9e10 g from 300 to 373 K)
    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.

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