Sunday, June 26, 2011

Chemical energy of the combustible office contents

The following is a first draft. I have not yet looked up the numbers in the NIST report, I only googled some numbers, and provide ballpark figures for others.

Each of the office buildings was packed with combustibles: paper, wooden furniture, plastics from computers, cables, carpets, etc. Even the bodies of the humans that died in the towers provided combustible material. There were basically two phases when a portion of all these combustibles burned:

  1. Open flames in office fire, after plane crash and before building collapse
  2. Smoldering underground fires after the collapse

The relevance of the first is to show how much heat was potentially available to heat up and thus damage the steel structure near the impact floors. The relevance of the second is to show why the debris could have burned for so long, created pockets of heat, even melt metals (other than steel, of course), etc. None of this will lead to exact conclusions. My goal is more to give 9/11 truthers a feel for the sheer (potential) magnitude of the fires. Because we again and again find the assertion that fires could not do much damage, and that explosives could do so much more.

First some links:

And some numbers (assumptions), gathered from the links

  • Combustibles per quare meter: 20kg/m2 (4 pounds per square foot, diveded by (0.3m/ft)2, multiplied with 0.45kg/lb. That is a very low value, compared to most office buildings, where a range from 45 to 20 lb/sft is often assumed, due to materials in partition walls and more furniture)
  • Office space total in twin towers (both combined): 400,000m2
  • Average energy density of office combustibles: 10MJ/kg (this is my own, very conservative, estimate; almost all organic materials rate higher; household waste rates around 8MJ/kg, but it contains a great deal of non-combustibles. The number for paper is about 15, plastics range from 20 to 40)

With these numbers as assumptions, we can derive the following through easy calculation:

  • Total mass of combustibles: 8,000,000kg (20kg/m2 * 400,000m2)
  • Mass of combustibles per floor: 37,000kg (8,000,000kg / 214 office floors; maybe there were some less, or slightly more. I rounded to the nearest 1000)
  • Total energy of combustibles: 80,000,000MJ (8,000,000kg * 10MJ/kg)
  • Energy per floor: 370,000MJ

The total energy (80,000GW, or 80TW) is roughly that of

  • 500,000 gallons of fuel, enough for my car to drive around the earth 700 times
  • 20 kilotons of TNT, pretty much equal to the release of the atomic bomb ("Fat Man") that destroyed Nagasaki to end WW2
  • the output of a large (1,000MW) block of a modern nuclear reactor in one day

I recall that the debris on Ground Zero burned for 99 day. That's 8.5 million seconds. So the average power was close to 10MW - 1% of a nuclear power plant, or just under the average for a large on-shore wind turbine. Enough to provide a town of 8,000 with electricity for housholds, industry and public infrastructure (in Germany; other countries may use more or less electricity per inhabitant).

Saturday, June 11, 2011

Controlled Demolition using Explosives: Some references

Under construction!

Post edited June 8th, 2012: References are now numbered; added reference [5]; added "Technical data" and "Observations in video [5]"

In this post, I will try to examine 9/11 truther claims that explosives may have been planted and used to demolish skyscrapers in New York by comparing the events there with what happens in real implosions using high explosives by building demolition experts. I will try to assess the minimum requirements to rig the towers (how much of explosives had to be used, how many charges, how large would those charges have to be, how much and what kind of work must be done beforehand to install these charges, etc.), and then see if the various claims and observations put forward in favour of explosives use can be explained this way at all, or would explain the events of 9/11 better than the commonly accepted theory of structural failure due to fires and plane impacts.

In particular, I want to assess if any truther theory exists, or is even possible, that would explain all their observations.

Some 9/11 truthers claim, or suggest, that explosives were, or may have been, used to bring down the twin towers, or building 7, or all. They base this claim on assertions like these:

  1. The collapses looked like explosive controlled demolitions
  2. Witnesses heard "explosions" at various times before the collapses, or even during
  3. Lots of concrete was pulverized in mid-air
  4. Large pieces of steel were ejected laterally at significant speeds
  5. There was not enough energy available to turn all of the buildings into fine rubble and dust, so additional energy must have come from explosives or other kinds of weapons
  6. Fires (and plane crashes) alone were not sufficient to cause collapse initiation
  7. The twin towers could not have collapsed all the way to the ground without the help of explosives below the fire/collapse initiation zones
  8. High-speed ejections of dust were observed below the collapse fronts at the twin towers
  9. Freefall acceleration of collapse is characteristic for CD
  10. Symmetry of collapse is characteristic for CD

Some references to real CDs of highrise buildings


Case study A) The Landmark Tower in Fort Worth, Tx, CDed in 2006:


References


[1] D.H. Griffin of Texas, Inc.: A talented team of demolition experts "blow down" Fort Worth's Landmark Tower. (PDF)

[2] D.H. Griffin of Texas, Inc.: Video and photos

[3] A fact sheet

[4] One of many youtube videos, that shows how loud the charges were.

[5] A video shot from 0.4 miles away (2000 feet, 650 meters), from location A in this Google Map


Some technical data from [3]


  • Address: 200 West 7th Street, Fort Worth, TX 76102
  • Roof height: 116 m / 380 ft
  • floors above ground: 30
  • Width: I estimate 90 feet for each face, perhaps slightly less

Observations in video [5]

23 floors plus mechanical penthouse are visible before collapse initiation, that's about 300 feet. First flash is seen at 1:10 minutes. Man comments on it at 1:11. First explosion is heard at 1:12 (as expected about 2 seconds later, as that is the time sound takes to travel 2000 feet). Explosions continue for 6 seconds, to 1:16. First visible movement at 1:12 (possibly already at the end of 1:11 already,but not sure). Building drops out of sight at 1:17 (after roughly 6 seconds). This corresponds to an average acceleration equivalent to 52% of g - but that is rough and dirty, error margin could easily be +/- 15 or 20%! Still, the Landmark Tower fall at significantly less than freefall!

What one can't fail to notice is that, at a distance of over 600 meters, or 5-6 city blocks, and amid the loud noise of 2 helicopters overhead, the many loud explosions are very clearly heard!

The building leans to the left (west) as it falls. I estimate that the roof has moved laterally as much as half the width of the building (ca. 45 feet / 15 meters) by the time it drops behind the overpass. This was by design - reference [1]: "The implosion was designed so that the building would fall into the two- level basement and into trenches dug on the north and west sides of the structure.". The Landmark Tower collapse was far from symmetric!



Some crude calculations


Potential energy (gravity)


I consider all estimates that follow to be conservative, that is, if I am wrong, the results would shift in a direction that is unfavourable to many truther standard arguments.

The Landmark, at about 115m high and 30m by 30m wide, had a volume of about 100,000m3. Elsewhere, I have argued with good reason that an office highrise would have 1/6 the average density of water, which would make it swim like a large steel ship, or 170kg/m3. So I estimate the total mass of the Landmark to be about m=17,000,000kg.

The height of the building was 115m, but its center of mass would be at most at 50% that height, more probably around 41% of 115m, or h=47m

Potential energy of the building, that was mostly released during the collapse, therefore is
E = m*h*g = 17,000,000kg * 47m * 9.8m/s2 = 7,830,200,000J, or rounded 7,830MJ


Chemical energy (explosives)


To bring down the Landmark, they used "only 364 pounds, consisting of 198 pounds of 60-percent nitroglycerine-based gel in 1-1/4 inch sticks, and 166 pounds of RDX (a C-4 derivative)" [1]. That's 53.9kg of pure nitroglycerine and 75kg of a C-4-like explosive.

According to Wikipedia, nitroglycerin has a molar mass of 227g/mol and a standard enthalpy of combustion of -1.529 MJ/mol. This translates into a chemical energy density of 1.529/0.227 MJ/kg = 6.7MJ/kg. 53.9kg of pure nitroglycerine thus have a chemical energy of 53.9kg * 6.7MJ/kg = 363MJ.
I have no direct reference on the enthalpy/energy density of C-4 or RDX at this moment, but read that it is about 1.125 to 1.25 times as "brisant" as nitroglycerine. An estimate of 7,6MJ/kg is thus not unreasonable (though probably too high; that's a conservative estimate with regard to truther claims). 75kg of this stuff would bring 75kg * 7,6MJ/kg = 570MJ to the demolition.

Total chemical energy of the explosives is about 363MJ + 570MJ = 933MJ.
(I assumed that a preparation with 60% nitroglycerine would have only 60% the energy of pure stuff; if I assume 100%, then the total chemical energy raises to about 1175MJ).

Comparison Potential vs. chemical energy (explosives)

The total energy available to cause all the destruction at the Landmark Tower demolition site was 7,830MJ (from gravity) + 933MJ(from explosives) = 8,763MJ.

Explosives provided 933/8763 = 11% (rounded) of the total energy, gravity 89%.

Monday, April 25, 2011

License Lookup for Professional Engineers in US states

Others:

Friday, September 10, 2010

Chemical energy of the jet fuel

Accoring to Wikipedia, which claims to quote NIST, either plane hitting the two WTC towers contained about 10,000 gallons of jet fuel, or 30,400kg:

According to the estimation in NIST's NCSTAR 1.5, page 58, AA11 carried 30,000kg of jet fuel, and UA175 carried 28,100 kg at the time of impact

http://en.wikipedia.org/wiki/American_Airlines_Flight_11
http://en.wikipedia.org/wiki/United_Airlines_Flight_175

Wikipedia further says about jet fuel:

Specific energy: >42.80 MJ/kg

So, AA11 carried with it fuel which, upon combustion, would this much energy as heat:
Efuel = 30,000kg * 42.8MJ/kg = 1.284 * 1012J

UA175 carried with it fuel which, upon combustion, would this much energy as heat:
Efuel = 28,100kg * 42.8MJ/kg = 1.203 * 1012J

At this time, I haven't found data about how much of that fuel burned outside of the towers and was not availabe to do damage inside.

In addition, each plane carried about 12,000kg of other combustibles (cargo, tires, mail, luggage, cabin materials). Humans are not included. "Other combustibles" generally having somewhere between 10 and 30 MJ/kg energy. For example: Paper about 15, many plastics 25-30. An assumption of 15MJ/kg seems not entirely unreasonable. So each plane put about 180GJ of chemical energy into the towers.

Kinetic energy of flight 175

The kinetic energy (KE) of a moving object is given by the formula

E = 1/2 m * v2

Where, in the case of flight UA 175:

  • m is the mass of the plane: That is, empty mass plus fuel load plus passengers, their baggage, and additional cargo. AA 11 was a Boeing 767-222, which has an operating emtpy weight of 80,130kg and a maximum take-off weight of 142,880kg. Maxium fuel capacity is 63.216l (see Specs at ZAP16.com). Maximum range is 7,300 km. Flight UA171 had 168 passenger seats, but only 56 passengers (33% capacity), plus 9 crew members. 65 people, weighing on average 70kg, have a mass of 4,550kg. For each, luggage, food, drinks and other supplies of 20kg may be added, or 1,300kg. It was scheduled to fly from Boston to Los Angeles, a distance of about 46% of its maximum range. Wikipedia, quoting NIST, states that it carried about 38,000l of fuel - about 60% of maximum fuel capacity, by the time of impact. Jet fuel has a specific weight of about 0.8 kg/l, so 38,000l fuel is about 30,000kg. The total mass of the plabe was thus at least:
    m = 80,130kg + (4,550+1,300)kg + 30,000kg = 115,980kg
    (empty weight + passengers + fuel)
  • v is the velocity of the plane at impact, which was estimated by NIST as 545mph or 243m/s

Using these estimates, the kinetic energy of flight AA11 works out as

Ekin = 1/2 * 115,980kg * (243m/s)2 = 3.42 * 109J

Kinetic energy of Flight 11

The kinetic energy (KE) of a moving object is given by the formula

E = 1/2 m * v2

Where, in the case of flight AA 11:

  • m is the mass of the plane: That is, empty mass plus fuel load plus passengers, their baggage, and additional cargo. AA 11 was a Boeing 767-223ER, which has an operating emtpy weight of 82,380kg and a maximum take-off weight of 179,170kg. Maxium fuel capacity is 90,770l (see Boeing technical specs). Maximum range is 12,195 km. Flight AA11 had 158 passenger seats, but only 81 passengers (51% capacity), plus 11 crew members. 92 passengers, weighing on average 70kg, have a mass of 6,440kg. For each, luggage, food, drinks and other supplies of 20kg may be added, or 1,840kg. It was scheduled to fly from Boston to Los Angeles, a distance of about 30% of its maximum range. Wikipedia, quoting NIST, states that it carried about 38,000l of fuel - about 42% of maximum fuel capacity, by the time of impact. Jet fuel has a specific weight of about 0.8 kg/l, so 38,000l fuel is about 30,000kg. The total mass of the plabe was thus at least:
    m = 82,380kg + (6,440+1,840)kg + 30,000kg = 120,660kg
    (empty weight + passengers + fuel)
  • v is the velocity of the plane at impact, which was estimated by NIST as 750km/h or 208m/s

Using these estimates, the kinetic energy of flight AA11 works out as

Ekin = 1/2 * 120,660kg * (208m/s)2 = 2.61 * 109J

There are, however, other numbers available for mass an velocity: NIST: 443mph = 198m/s, which would lower my estimate to 2.365 * 109J

GPE of building WTC7

The mass of of building WTC7 had potential energy in the gravitational field (GPE) given by the formula

E = m * g * h

The values of m, g, and h are not all known, but can be estimated as follows, using measurements taken from Wikipedia and NIST's revised technical briefing of November 19, 2008:
  • g: That value is known. It is about 9.805 m/s2 in New York
  • h: Is the height of the center of mass of the building above ground level, minus the hight of the center of mass of the rubble after the collapse. The latter may have been up to 5m. The former would be somewhat lower than half the hight of the roof of the building, considering these factors: a) floors would have about equal masses from ground to top b) load-bearing structure (columns, mainly) would be much heavier in the lower part than the upper part. In my blog post "Potential energy of the mass of each twin tower" I showed that Gregory H. Urich, in his paper "Analysis of the Mass and Potential Energy of World Trade Center Tower 1", assumes that the center of mass would be about at 41% percent of the height of the building. Since WTC7 had a height of 186m, the center of mass might have been near a height of 76m. Deduct from this up to 5m to account for the height of the rubble pile, the total mass descended by a height of h= 71m.
  • m: Is the total mass of WTC7. As I write this (september 9, 2010), I know no good source that gives that mass. In my post on the GPE of the twin towers, however, I found that a good estimate would be one sixth of the displacement of water. The volume of WTC7 can be computed by its height (186m), width of the south front (247ft = 75m), north front (329ft = 100m), and depth (140ft = 42.7m): V = 186m * (75+100)m/2 * 42.7m = 694942.5m3. Total mass would therefore be 694942.5/6 tons or about m = 1.16 * 10E8 kg
Therefore, I estimate the total GPE of WTC7 that was converted into other forms of energy to be about

E = 1.16*10E8kg * 9.805m/s2 * 71m = 80,753,980,000J
I will round that down to

GPE = 8 * 10E10J

Potential energy of the mass of each twin tower in the gravitational field (GPE)

When mass is lifted against the force of gravity, it acquires potential energy in the gravitational field (GPE) according to the formula

E = m * g * h

Where

  • m is the mass, measured in g or kg.
  • g is the (nearly) constant acceleration of earth's gravity - in New York, that value is about 9.805 m/s2
  • h is the difference in hight, in meters, measured between the "ground" level from which the mass was lifted to where it was lifted. In the case of an object like a building, one would have to consider the height of its center of mass

What was the total mass m of a twin tower?

If you google this, you may find various quoted figures. One often given is 500,000 metric tons. This appears too round a number to be accurate.

One back-of-the-envelope estimate occurred to me the other day: Compare a Twin Tower to ship, and estimate its displacement. Looking at steel ships. I'd think that they displace about one sixth of their total volume. Surely, the WTC would float on water like a ship, if you assumed the windows would not break. The volume of the tower is 415m x 63m x 63m = 1647135m3. Displacement might be 1647135m3/6 = 274522.5m3, or 274,522.5 tons.

A very thorough estimate was given by Gregory H. Urich, B.S. Electrical and Computer Engineering, in his whitepaper "Analysis of the Mass and Potential Energy of World Trade Center Tower 1":

His result: WTC1 had a mass of 288,100 metric tons (in the Abstract, page 1). That's only about 5% off of my back-of-the-envelope, confirming my method wasn't so bad.

Urich also gives us an estimate of GPE in 5.1 Summary of Results (p. 23): 480,600 MJ, or 4.806 * 1011J

With E = m * g * h <=> h = E / (m*g), this corresponds to an estimated hight of the Center of mass of
h = 4.806 * 1011J / (288,100,000kg * 9.805m/s2) = 170m
(rounded to full meters), or 41% of the height of WTC1. This seems to be reasonable, considering that...

  • Most of the 110 floors are evenly spaced and nearly identical to each other, making the mass of them evenly spread
  • The perimeter columns likewise are of the same dimensions from about 3rd floor to roof, making their mass evenly distributed along the total height
  • The massive core columns, on the other hand, are much more massive in the lower floors and become lighter and lighter towards the top. Their center of mass, in isolation, would likely to be much lower than half the hight of the tower; maybe 25% or 30% of its height, or 104-125m

I note in passing that Urich, on page 4 (3.1 Popular numbers) quotes FEMA (Hamburger ed.al.) with an estimated GPE of "> 4 E+11 J" and NIST (Sunder ed.al.) with an estimated total mass of "> 250,000 tons", confirming that both operated with conservative, realistic numbers.

When that mass collapsed, a good portion of it formed a debris heap above ground level. Thus, not all the potential energy was realeased in the fall. It is difficult to estimate the height of the center of mass of the rubble after the fall. It certainly wasn't very much: Much of the rubble actually fell below ground level (into the basement. and very much more assembled  below 1m than beteween, say, 10 and 11 meters above ground. So I have reason to assume that the new center of mass was at most 5m above ground level, or under 3% of the original height of 170m. I will therefore go with Urich's original number, bearing in mind that a 3% deviation is easily possible, given the uncertainties we have about mass and mass distribution.

Conclusion:
I agree with G. Urich that each of the Twin Towers had a

  • mass of about 2.88* 108 kg
  • GPE of about 4.8 * 1011J

Energy considerations

The variously proposed mechanisms by which the WTC highrises have been turned from erect buildings to piles of smoldering rubble all seek to explain the forces necessary to initiate and propagate these destructions. Viewed with the eyes of a phycist, "force" was applied over a certian "time" along certain "distances", creating "heat" and doing "work". In short: "energy" was transformed.

Many Conspiracy Theorists (CTers) claim that plane impacts and fires would not be sufficient to explain collapse initiation. Some go even further and claim that obervations like "pulverisation of concrete and steel" or "molten steel" would require more energy, heat or force than was available in the common storyline.

So we need to look at the energy available, and the energy (supposedly) needed for various CT claims:

If a CTer claims that the energy available as GPE, combustibles, and kinetic energy was insufficient, and proposes a different mechanism such as high explosives, thermitic incendiaries, or Directed Energy Weapons (DEW; for example lasers),  then it is clear that this method should add a substantial amount of energy in relation to the available energy. Certainly, adding 10% would not suffice, since that is within the margin of error of many of the considerations listed above. We don't know the mass of each building precisely, and we don't know precisely how much concrete was turned into pieces of what sizes to compute the fracture energy. We have no precise idea about how much metal was heated to what temperatures at what time. I suggest that any CTer claim that rests on the assumption that the energy contained in the buildings and planes alone was insufficient to explain the destrcution, must propose a method that adds, at least, 50% of that energy.

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