Various sites give slightly different results but the following figures seem to be generally accepted.
I will tend to use numbers on the high side since those make the best case for conspiracy theories.
The gravitational potential energy of an object is the energy it takes to raise it to a certain height, or the energy obtained by letting it fall. The formula is U = mgh. U is the standard symbol for potential energy, m is mass in kilograms, g is the gravitational acceleration of the earth and h is the height in meters. Energy is in joules. One watt is one joule per second, and a joule is roughly the energy needed to raise one pound one foot.
For the World Trade Centers, the towers were 400 meters high and their mass was 600,000 tons or 600 million kilograms. So the total gravitational potential energy in one tower was 6 x 108 kg x 9.8 m/sec2 x 400 m x 1/2. The factor of 1/2 comes from the fact that some mass fell 400 meters and some fell only a short distance, and the overall result is as if it all fell the average distance. So we have U = 1.2 x 1012 joules. A kiloton is 4.2 x 1012 joules, so the gravitational potential energy is about a quarter of a kiloton or 280 tons of high explosive, per tower.
The planes that hit the towers were Boeing 767-200's, with a loaded mass of about 140,000 kg. They impacted at about 600 km/hour or 167 m/sec. So their kinetic energy was K = 1/2 mv2 = 1/2 x 140,000 x 1672 = 2 x 109 joules.
The basic 767-200 has a fuel capacity of 63,000 liters, and accounting for fuel burned before impact, call it 50,000 liters. Jet fuel has an energy content of about 35 million joules per liter. So the energy content of the fuel on each plane was 1.75 x 1012 joules or about 0.4 kiloton. An appreciable amount of that energy would have been released explosively, the rest during the fires following impact.
The energy from the collapse of one tower would have been roughly equivalent to a magnitude 3.5+ earthquake and the energy from the plane impacts somewhat less, depending on how much fuel exploded on impact. The impacts of the planes themselves would have been only a small part of the total energy released. The actual observed magnitudes were less because not all the energy was converted into seismic waves.
Some conspiracy theorists claim that large amounts of the buildings were unaccounted for by the size of the rubble pile. Since only 12% of the building volume was solid, the towers should collapse into a pile 12% of the original height of the building, or just about 50 meters high. Since 18 meters of that pile would be filling the basement, the above-ground portion would be 32 meters high.
The actual rubble pile reached the fifth story of adjacent buildings, so well outside the footprint of the tower the pile was five stories, or about 15 meters high. The pile would have been roughly conical, and would have included a lot of void space, increasing its height and offsetting the larger diameter of the pile. Overall the rubble pile is what you'd expect.
So it simply isn't true that the rubble pile is only a small percentage of what would be expected. Some conspiracy sites allege that the rubble pile is only 5% of what would be expected. Others use a figure of 33% as the height of a rubble pile relative to the original building and then argue that the pile should have been 140 or so meters high. But when Controlled Demolition Inc. (http://www.controlled-demolition.com) dropped a 23-story, 439-foot (134 m) building in Detroit in 1997, they ended up with a pile averaging 35 feet high (11 m) and a maximum of 60 feet (18 m) high. The rubble pile was an average of 8% of the height of the original building and a maximum of 14%. Scaling that up to the World Trade Center, we get heights of 33 to 58 meters. In other words, the rubble pile at the World Trade Center is totally in line with other large building collapses. 33% may work for a small building a few stories high, but a large building will compress the debris pile a lot more and also fill void spaces more effectively with pulverized debris.
|I could be wrong, but that looks like a mighty substantial pile of debris behind the firemen.|
A couple of revealing studies have been done on the dust from the World Trade Center. One was by the U.S. Geological Survey (http://pubs.usgs.gov/of/2001/ofr-01-0429/). They measured the composition of the dust and found
|Carbon, organic %||0.98||4.02||2.48|
|Carbon, Carbonate %||1.24||1.89||1.55|
|Loss on Ignition %||7.96||22.8||16.35|
Those figures are about what would be expected for a mix of concrete, drywall, and insulation. The loss on ignition indicates how much of the dust was combustible, mostly cellulose from drywall binder and paper. Titanium is partly from minerals in the concrete aggregate, and partly from paint. Titanium dioxide refracts light extremely strongly and is used in paints to make the paints opaque. The sulfur reflects gypsum, which is hydrous calcium sulfate and the principal ingredient in drywall..
Gypsum, paper, asbestos and paint were insignificant in amount compared to the concrete and steel in the towers. The mere fact that they show up at all in chemical and physical analyses completely demolishes the idea that large portions of the towers were turned to dust.
Another study (http://www.ehponline.org/members/2002/110p703-714lioy/lioy-full.html) found that half or less of the dust in their samples was concrete, and the other half was fibers of various kinds. Most of the fiber was glass fiber, but 10-20% was cellulose. Neither study measured the bulk density of the dust because it wasn't meaningful for either study, and would depend on the length of time the dust had settled and whether or not it had rained. But all the photographs in both studies show very fluffy dust.
So how much dust was actually created? One conspiracy site (http://janedoe0911.tripod.com/StarWarsBeam3.html#Dust) argues as follows (my addenda are in blue):
If a WTC tower were completely turned to dust, how much dust might we expect?
Suppose the building's materials were reduced to 10% of its original volume.
Volume of one WTC tower = (207 ft)x(207 ft)x(1368 ft) = 58,617,432 cubic feet
Dust Volume (from one WTC tower) = (1/10)xVolumetower (approx.) = 5,861,743 cubic feet
One square mile = (5280 ft)x(5280 ft)
Dust Volume for one WTC tower (approx.) = (1/10)x(207/5280)2x(1368x12 inches) = 2.52 inches deep over 1 square mile, (The terms are regrouped to put all the squared terms together)
or equivalent to 1-inch deep over 2.52 square miles.
An area of 2.52 square miles would be a radius of 0.896 miles. Note that the area would include both land and water.
Suppose the building's materials were reduced to only 5% of the original volume.
Dust Volume for one WTC tower (approx.) = (1/20)x(207/5280)2x(1368x12 inches) = 1-inch deep over 1.26 square miles,
An area of 1.26 square miles would be a radius of 0.634 miles.
These calculations suggest that the towers had enough material to yield dust about an inch deep and cover approximately a square mile in lower Manhattan, plus the dust carried over the Hudson River, the East River, Brooklyn, the Upper Bay, and into the upper atmosphere. So where did all the dust come from? It looks like it all came from the towers.
|The assumption that the volume of building materials is about 10% of
the total volume of the towers is in line with the figures at the top of
this page, and the math is basically OK. This is pretty typical of the
pages that assert that the towers were mostly turned to dust.
Incidentally, several figures on that page will show fist sized chunks
of the concrete that supposedly all disappeared.
So, want photographic proof that the concrete wasn't all pulverized to microscopic fragments? Here it is. Not only are there chunks, but the rest looks more like sand than fine dust. Note the absence of suspended dust in the air.
The first problem here is that dust is not equivalent to solid material. More than half of the volume of any powdered solid is empty space, especially immediately after it settles. But the analyses above show that about half of the dust was actually fibers of various sorts and fully 10% was organic fibers derived mostly from paper. And the photos of the dust samples show very fluffy dust. So the density is probably not the 2.4 grams per cubic centimeter of bulk concrete but much less.
Second, the dust wasn't an inch thick over a square mile. Photos show dust an inch or so deep in the immediate vicinity of the towers, although higher accumulations occurred. If we model the dust as a broad cone rather than a disk, its volume is only one third that of the disk. Between the low density of the dust, the fact that most of the dust landed close to the towers, and the fact that half of the dust was materials other than concrete, the volume of concrete represented in the airborne dust is maybe 10% of the volume of the settled dust itself. This is the dust off site. Of course, the dust on the collapse site itself is from the building collapse.
So, in place of estimating that the towers could make a disk an inch thick and a mile in diameter, we have to reduce the volume of the dust by a factor of 3 to model the dust pile as a cone. We reduce that by a factor of at least 2 and probably a lot more to account for the porous nature of dust, and by another factor of 2 to account for the fact that half the dust is not concrete. So we have to reduce the estimates of the concrete dust volume by at least a factor of 12. So instead of a million tons of concrete dust we have 80,000 or less.
If the dust is a cone 5 cm thick (.05 meters) at the towers and a radius of one kilometer, the volume of the dust pile is .05 x pi x 1000 x 1000/3 = 52,000 cubic meters. That's only a sixth of the volume of the concrete in the towers. If half of that volume is empty space (I'm being generous), and half of what's left is other stuff, we have 13,000 cubic meters of concrete or 4% of the concrete in the towers. This is so poorly constrained it won't convince any conspiracy buff, but it shows that we don't need to pulverize the whole building to get the observed dust.
There's a potentially valuable source of data on dust. Following 9/11, large vacuum trucks sucked up dust from the area and disposed of it. Somewhere there are dispatch records that can be used to get a more accurate estimate of the dust. But the trucks could haul 15 tons, and there were up to 16 of them working for several weeks. If they could make five runs a day (I'd bet on more like one or two) for 30 days, that's 15 x 16 x 5 x 30 = 36,000 tons. Again, this is too loose to convince any conspiracy buff, but it's only 11% of the total concrete in the towers, and a large portion of the dust wasn't concrete.
A lot of people confuse optical density with amount of dust. The fact that the dust cloud was opaque means only that light didn't penetrate it. The clouds that hung above the site weren't much denser than air so the total volume of dust in them was not large. Typical clouds in the sky contain a few grams of material per cubic meter. If we assume the 9-11 cloud had 50 grams per cubic meter - ten times more than even thick water droplet clouds, and the dust cloud occupied a cubic kilometer, far more than its actual volume, we have a billion cubic meters times 50 grams per cubic meters, or 50 billion grams, 50 million kilograms, or 50,000 tons of dust, paltry compared to the million ton mass of the towers.
So while the four lines of evidence above are pretty loosely constrained, it's interesting that they all independently converge on a few tens of thousands of tons of dust. Any way you slice it, there was just not that much dust.
One of the more scientifically respectable arguments against the conventional view of 9-11 is that it would take more energy to crush the concrete than was available. One site uses a figure 0f 1.5 kilowatt hour per ton to crush concrete to 60-micron (.06 mm) powder. One kilowatt hour is 3,600,000 joules, so it takes 5,400,000 joules to crush a ton of concrete to 60 micron powder. Crush the 390,000 tons of concrete in a tower to powder and it takes 2.1 x 1012 joules to do the job. That's twice the gravitational potential energy of a tower. In other words, crushing the concrete should have absorbed so much energy that the collapse would have been halted.
The rule of thumb is that energy to crush a brittle solid is proportional to the total area of the fractures. If we have a cubic meter of rock and crush it into cubic pieces of dimension x, their volume will be x3 and there will be 1/x3 pieces. Their surface area will be 6x2. So the total surface area is 6x2*1/x3 pieces = 6/x. The energy to produce those particles will be inversely proportional to the size of the particles. If you assume the particles are spheres of diameter x, you have particles of volume πx3/6 and surface area πx2 (The radius is x/2). So you have 6/πx3 particles, each with surface area πx2 and the total surface area is - wow - 6/x again. When doing a lot of these types of calculations, the exact shape of the particles doesn't matter.
Some 9-11 sites erroneously claim the energy is proportional to the square root of size, evidently because they realize that area of a particle decreases as the square of size, but they don't take into account that the number of particles goes up as the inverse cube of size.
Except there just wasn't that much dust. If we assume 50,000 tons of fine dust per tower (generous compared to the estimates above) that's only 270 million joules or a quarter of the gravitational potential energy. As we can see from the photo above, most of the material was not fine powder. If we assume the stuff under the fireman's boots is 600 microns (0.6 mm or sand sized) then the energy needed is only a tenth of what is needed to make 60 micron powder. At that rate it would take 2.1 x 1011 joules to crush all the concrete to sand, or about a sixth of the available gravitational potential energy.
The problems with the crushed concrete argument are:
Serious overestimation of the amount of dust
Serious underestimation of the amount of coarse debris
Failing to account for much of the dust being derived from easily fragmented internal materials like paper and drywall.
Supposedly, videos of the collapse of a remnant of one tower show it vanishing into dust. In addition, many conspiracy theorists claim that much of the steel from the World Trade Center has vanished.
The USGS data above show iron contents in the dust ranging from half a per cent to 4 per cent, with an average of 1.6%. Since iron makes up 5% of the crust, we'd expect a few per cent iron in concrete. Add to that some iron oxide from corrosion by the concrete in contact with steel and mechanical abrasion during the collapse, and the numbers are consistent with the iron content we find. We do not find the iron concentrations we'd expect if large amounts of iron were powdered.
So, powdering the steel? The chemistry tells the story. It simply didn't happen. Collapsing and leaving a trail of dust behind is not the same thing as turning into dust.
One of the favorite theories for bringing the towers down, apart from thermite or demolition charges, is directed energy weapons. These are especially favored by folks who argue that large parts of the towers were turned to dust or vapor.
Real directed energy weapons fall into very limited categories.
So directed energy weapons have been considered mainly for three purposes:
So directed energy weapons can deliver a lot of punch to a small, visible and unobstructed target, and even air is an obstruction for these purposes. And they can deliver enough energy to frazzle human nerve endings and damage the retina. Evidence for weapons systems capable of punching into the interior of a building or powdering concrete and steel over a large area? Zero, zip, nada, bupkis.
One architect has criticized me for using too large a figure for concrete. He insists that the concrete was much lower in density.
Bring it on. I'm all for it. The less the mass of the concrete, the easier it is to account for a lot of things. For example, if the floors were very porous light weight concrete, the energy needed to pulverize them would have been far less than that needed to break up standard concrete. And there would be a larger dust to solid ratio, and maybe even less dust overall, and the concrete would pulverize into smaller pieces. As I noted, I used large figures because those make the best case for conspiracy theories.
Created 30 January, 2006; Last Update 02 June, 2010
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