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The Five Sided Fantasy Island -- an analysis of the Pentagon explosion

Rebutting "Pentagon 9/11 Getting the Facts Straight"

Eyewitnesses and the Plane-Bomb Theory

(This was written regarding Eric Hufschmid's "concrete physics problem" challenge, early in March.)

Gravitational potential energy is the energy released in a structural collapse, which may typically be dissipated by concrete crushing in a "pile driver" effect. 

This energy is calculated by the equation U=mgh, with mass in kg, gravitational force constant g=9.8m/s/s, and h in meters. The energy units in this equation are joules (watt-seconds) but large energies are more commonly expressed in kilowatt hours (1kwh=3.6e6 joules). 

Because the WTC towers are both massive and tall, the gravitational potential energy of each tower is enormous.

Assuming a mass of 750,000 tons (6.8e8 kg) falling from an average height of 207 meters (half of the overall height of 1365 feet), the gravitational potential energy is about 1.4e12 joules or 400,000 kwh.

The energy required to crush rock is roughly proportional to 1/sqrt(powder diameter), so the exact amount of energy required is critically dependent on the fineness of the powder. The energy required to reduce solid rock to 60 micron powder is about 20 kwh/ton:
http://www.elorantaassoc.com/eob97.htm

However, concrete is softer than rock, and a round number for the energy required to crush concrete is around 1.5 kwh/ton:
http://www.b-i-m.de/public/ibac/mueller.htm

With roughly 600,000 tons of concrete in each WTC tower, the available energy from gravitational potential energy was only about 0.7 kwh per ton of concrete. However, given the uncertainty in the size of powder, the available energy is "in the ballpark". 

Compared to other buildings, the WTC (being so much taller) would have much greater gravitational energy per ton of concrete, so we would expect to find an unusually fine powder compared to most building collapse events.

How much difference would explosives have made? As a particularly massive example of controlled demolition, the Kingdome weighed 110,000 tons:
http://abcnews.go.com/sections/tech/Geek/geek000316.html

and required 5000 lbs of dynamite to destroy:
http://seattlepi.nwsource.com/local/stack05.shtml

So we might guess the amount of powder required to demolish a WTC tower might be as much as 30,000 pounds (or perhaps less, given the much taller and more lightly built structure). The energy content of dynamite is given as only 0.47 kwh per pound:
http://www.elorantaassoc.com/eob97.htm

Thus, if explosives were used, they would only have contributed about 15,000 kwh, which is largely negligible compared to the gravitational energy. In a controlled demolition, gravity does the lion's share of the work, while the explosives serve only to destroy the physical integrity of the structure.

This doesn't prove (one way or another) what brought down the structures, but the powder production doesn't seem inconsistent with the physics of the situation. 

Furthermore, it's important to remember that the structure of the towers would have been gravely damaged by the airplane impacts. In this situation, the loads in the structure would re-distribute themselves among the intact members, causing some elastic deformation and possibly very high local stresses.

In this situation, even a very moderate amount of further weakening by fire might have been sufficient to set off a chain reaction of events that would progressively destroy the towers.
See the articles by G. Charles Clifton at  http://www.hera.org.nz

If this was the mechanism, then it's not impossible that there might have been some explosive sounds, or some extra puffs of concrete at some distance from the primary initiating point of the collapse.

Nevertheless, in a truly open society there would be serious questions about the causes of the WTC tower collapse events. The initial speculations in the press about high temperatures and melting steel in the WTC towers were purely bogus. Collapse of any modern steel structure is highly unusual, and collapses caused primarily by fire simply do not occur. The design of the WTC towers was intended to be survivable even in the event of an airliner impact.

Finally (and this is a very important point) the collapse of WTC building 7 is very difficult to explain.

Even for those with no interest in conspiracy theories, there would be important lessons to be learned from a thorough forensic investigation of the ruins, in terms of the effectiveness of fireproofing and the strength of the trusses and other components of the tube structure. There is absolutely no excuse for the rapid disposal of the debris of this event -- every piece should have been photographed and checked for clues.

-Jerry Russell

[Note added 7/11/03: this analysis assumes that the concrete was mostly smashed when it hit the ground, which is most likely incorrect.  Also, the mass of concrete in the towers is seriously overestimated.]