We have
seen the collapse of the Twin Towers in Manhattan (NY) on Sept. 11,
2001. The collapses of the Towers looked unreal, nightmarish. It is
worth considering whether they were only gravity driven incidents
initated by fires as alleged. The impacts of the jets did not damage
the supporting structures of the buildings so badly as to cause them
to collapse immediately.
In
the following, I will examine the phenomena connected with the
collapse of the North Tower by comparing the energy available with
that needed. I am indebted to Jim Hoffman for his ground-breaking
article
"The North Tower’s Dust Cloud" version 3.0
which inspired me to make these calculations. Contrary to Hoffman,
however, I am not trying to calculate the total energy needed to cause
these phenomena. I think that is not possible with the data we have.
But I will try to show that the gravitational potential energy of the
tower is insufficient in quantity and poor in quality for explaining
the phenomena seen. The physics used is of high-school level.
The
Phenomena Seen
Preceding
the collapse there was a fire triggered by the impact of the jet.
First, the jet fuel burned up in a short time and the fires then
continued as office fires on some floors until the collapse of the
tower.
Then we
saw how the skyscraper turned into powder and pieces of steel from top
to bottom in a very short time. The powder, which consisted of
concrete and other non-metallic materials, formed, with the gases
apparently from inside the building, a cloud with clear boundaries, a
phase of its own. The volume of this cloud expanded in a short time to
a volume many times that of the tower.
The ruins
mainly consisted of dust and pieces of steel. They cooled slowly and
the smoldering of the debris lasted months.
According
to the official explanation the energy source for all those phenomena
was the gravitational potential energy of the skyscraper and the heat
energy of the fires.
The
Formation of the Dust and the Expansion of the Dust Cloud
When a
body is crushed, the smaller the pieces it breaks into the greater the
need of energy. During the collapse, about 90 000 tons of concrete
were pulverized into an aerosol whose mean particle diameter was 100
µm. According to Russell, whom Hoffman cites, we need energy 1.5 kWh/t
to pulverize concrete. The total energy need is 90 000 t × 1.5 kWh/t =
135 000 kWh.
The rapid
expansion of the dust cloud may only be caused by a sudden increase in
pressure (lasting perhaps only microseconds) of the gases inside the
building during the collapse. Expansion results from the natural
leveling off of the pressure difference between the outside air and
the the cloud. The reason for the increase in pressure could be a
sudden increase in temperature while liquid materials, chiefly water,
produces gaseous substances. Another possibility is a very fast
chemical reaction generating plenty of gases from liquid and/or solid
substances that could be hot too.
Pulverization, breaking up the steel structures and the phenomenon
that caused the expansion of the dust cloud need energy to happen. The
causative phenomenon makes energy to become stored into the material
which then increases its internal energy. The gas of the dust cloud
can perform work (i.e. expand) using its internal energy;
simultaneously it becomes cooler. We are able to calculate only those
energies that the pulverization and expansion required.
According
to Hoffman the volume of the dust cloud expanded 3.4-fold in 30
seconds. He has already taken into consideration turbulence, i.e. the
mixing of the ambient air with the cloud, by decreasing the volume one
third. The dust cloud continued its expansion after the first 30
seconds but the influence of the turbulence increased rapidly becoming
soon the ruling phenomenon.
Paul J. Lioy et al.
examined the dust. According to the examination in the beginning the
dust really expanded to all directions, also against the wind. This
makes it clear that the dust cloud really expanded. Later the dust
floated with the wind until it settled. There was a 10-cm-thick layer
of powder 700 m away from the tower. According to the report the
degree of pulverization of the building materials was the previously
unseen.
The base
of the both towers was a square whose side was 63.1 m, and the height
of the towers was 417 m. The volume of the each tower was then (63.1m)
2 × 417 m = 1.66 × 106 m 3 .
I assume
the air pressure to be normal, 1.01 × 105 Pa. The dust
cloud pushes the surrounding air from its way while expanding. The
work equals pressure × the increase of volume = 1.01 × 10 5
Pa × (2.4 × 1.66 × 106 m 3 ) = 4.0 × 1011
J = 110 000 kWh.
We do not
know the proportions in which the sudden increase in pressure was
contributed to by the increase in temperature on one hand and the
generation of gaseous substances (through the vaporization of liquids
and chemical reactions) on the other. Therefore, that increase in the
internal energy that remained within the system cannot, as far as I
understand, be calculated.
As seen
above we need 245 000 kWh energy to the pulverization of the concrete
and to expanding the dust cloud. When the mechanism of the
pulverization is unknown, we can say that the energy needed is at
least 200 000 kWh. In addition, the energy that remained within the
system as the increase of its internal energy may be many times as
high as the calculated energy. Breaking the steel structures increases
the energy needed but I cannot even estimate this energy need.
The
Influence of the Fires
There was plenty of heat produced by the fires. My estimate is that
400 000 kWh heat energy was released while 10 000 gallons fuel burned.
However, some of the fuel did not burn and some of it burned
incompletely. According to the Federal Emergency Management Agency's (FEMA)
The WTC Building Performance Report
(May 2002), the burning of the jet fuel lasted only about five
minutes. Fires were continuing as office fires which produced also
plenty of heat energy. But the energy released during the collapse was
very small
(1) .
According
to the FEMA report one third or even one half of the heat energy fires
produced went out of the building. The influence of the fires is
indirect. In addition to having been the main reason for the collapse
(so FEMA says), they may also have made concrete more brittle so that
the energy needed for pulverization became smaller for some floors.
About the
Nature and Utilizability of the Potential Energy
The
potential energy of the tower was "more than 4 × 1011 J =
110 000 kWh" in relation to the ground level, says FEMA. I think that
"more" may only mean a little more, not much more.
Because the sources mentioned above (and e.g.
this one ) give
very inconsistent data concerning the mass of the towers, it seems
best to calculate the mass from the potential energy. As the masses of
the support columns were manifold in the lower floors compared with
the top floors, I deduced that the point of gravity was possibly at
the height 160 - 170 m from the ground. The mass of the tower above
the groud level is then 250 000 tons
(2) . I think I
can reduce the building to consist of equal masses of steel and
concrete.
A
body will begin to fall when its support is eliminated. Its potential
energy changes into kinetic energy. When it hits another body, both
are probably broken, and the kinetic energy is converted into heat;
the conversion is full once both stop. The associated increase of
temperature is very small
(3) . As such,
potential energy is capable of breaking steel supports and in part of
pulverizing concrete, but it according to
one article
seems not to be suitable for the complete pulverization of concrete.
Gravity-driven collapse of a building takes place in accordance with
the principle of minimun resistance and breaks the building into large
chunks. In this case one would expect that the top of the tower above
the impact area would topple over as a whole and break when hitting
the ground.
The
tower shattered from top to ground floor in fifteen (or fewer)
seconds, which is amazing. In this kind of quick shattering the
potential energy of the building is mainly left unused: The dust,
one-third of the mass, does not press the structures under it while
floating in the air! The steel bodies which start from rest after a
collision with the falling structures do not have time to get to the
next floor to break it because the collapse is so fast
(4) . Because
of the dust cloud we did not see how the central core was broken.
Perhaps it started from the ground level; if so, its potential energy
was fully used. As parts of the building did not collapse, the
concrete powder remained afloat and steel components and portions of
the outer walls fell to the sides, the estimated amount of potential
energy that was available for the destruction of the building must
have been clearly less than 50% of the total, ie. less than 50 000
kWh.
Potential
energy is fully incapable of bringing about the causative phenomenon,
the sudden increasing of the preassure, of the expansion of the dust
cloud.
The Ruins
The
ruins mainly consisted of steel and dust. There were fires and
smoldering, and water was used to cool the ruins and extinguish the
fires. But according to the
US Geological Survey
, on September 16th there were still hot spots, temperatures ranging
from 500 to 600 ºC on the surface. On September 23th, no hot spots
were found. Steel that had literally been in a molten state was found
in the basement five to seven weeks later, says
an article.
According to a construction company called
LiRo involved
in clearing up Ground Zero after 9/11, "[s]ome [steel] beams pulled
from the wreckage [we]re still red hot more than 7 weeks after the
attack." The ruins were smoldering a long time, and according to Paul
J. Lioy et al. it wasn’t until on December 14th that the FDNY could
announce that they had extinguished the fires.
Let’s imagine a potential energy driven collapse of the North Tower.
Its potential energy changes into heat energy. But the resulting
increase in temperature is only two to three degrees Centigrade
(3) . When the
heat energy produced by the fires - which raised the temperature of
the structures and therefore, of the debris - is taken into account
(it was seven times the potential energy), the increase of temperature
is still below 20 ºC
(1) . It is
clear that in the beginning there were to be differencies in
temperatures, but they should have leveled off soon. According to the
laws of thermodynamics it is not possible that hot spots become hotter
while cool points become cooler. It seems to me that the mean
temperature in the ruins should not have exceeded 40 ºC as the
temperature that morning was about 20 ºC outside. Taking into account
the hot spots measured and the red hot steel found it seems to me
quite certain that the post-collapse mean temperature was far above 50
degrees C. That is impossible to explain without an extra source of
energy. The smoldering fires are, I think, not the answer. The
seismic findings
also point to extra source of energy.
Conclusions