Reijo Yli-Karjanmaa
Physics teacher, retired

Version 3.1, June 18, 2005

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.


I have calculated (and partly estimated) above that the energy needed to cause the observed phenomena is at least 200 000 kWh (pulverization + expansion work of the dust cloud). In addition to this, energy is needed to break the supporting steel structures and to increase the internal energy of the dust cloud. These unknown energy needs may be many times the calculated one.

But we have potential energy less than 50 000 kWh available for the destruction.

According to the calculations and considerations we can conclude that the potential energy was by far insufficient to account for the totality of phenomena observed and its quality was unsuitable for some of them.

I have examined the North Tower above because Hoffman’s findings of the dust cloud were about the North Tower’s collapsing. But the same conclusions are valid cocerning the South Tower.

Collapses are not paranormal incidents. We can infer that the towers were pulled down using some form of controlled demolition.

About the Investigations

The conclusion of the FEMA report is vague: "With the information and time available, the sequence of the events leading to the collapse of each tower could not be definitively determined."

NIST (National Institute of Standard and Technology) is working on its study which was planned to be reported in December 2004. NIST promised then to report in January, then in the spring of 2005. In the latest briefing on April 5th 2005, they told us the report will come out in September (the drafts in June).

NIST emphasizes more than FEMA the office fires and the dislodging of the fireproofing as the causes of the collapses but in any case it is crucial that the following oddities irreconcilable with a gravitational collapse are explained:

Exactly these features are typical of or at least possible features in a controlled demolition. The report also ought to include the relevant energy calculations.


Hoffman, Jim:The North Tower's Dust Cloud

Federal Emergency Management Agency's (FEMA) The WTC Building Performance Report:

German engineers' article:

Lioy, Paul J. et al.:


Steel in the News: 

US Geological Survey:

NIST's WTC project:

(1) The FEMA report estimates that the maximum power of the fires was 1 - 1.5 GW. When the collapse began the fires were going down. When the floors where the fire was shattered in a very short time, perhaps in one second, the energy released by the fires during that time was very small, surely less than 1 GW x 1s = 1000 MJ = 280 kWh. That could have no significance. If the mean power of the fires is assumed to have been 600 MW and the burning time 1 h 43 min, we get the whole energy released: about 1 000 000 kWh. The structures absorbed 2/3 of it, less than 700 000 kWh. Back to the Influence of the Fires    Back to the section on the ruins

(2) According to the FEMA report the walls of the columns were four inches thick at the ground level and only 1/4 inches in the top floors. So the whole mass of the columns at the base was over tenfold compared with the mass at the top. Back

(3) We can calculate that the mean specific heat capasity is about 0.7 kJ/(kg · ºC) using 0.46 kJ/(kg · ºC) for steel and 0.92 kJ/(kg · ºC) for concrete assuming their masses are the equal. When the potential energy is 4 x 10 11 J and the mass of the tower is 250 000 tons, we can calculate that the mean temperature raise is 2.3 degrees (ºC).  Back to the section on potential energy   Back to the section on the ruins

(4) The height of the 110-story building was 417 m. The floor height was 3.8 m. When the time of collapsing was 15 seconds, floor slabs shattered at 0.14-second intervals, seven slabs per second. We can calculate that if the body’s initial velocity is zero, it needs 0.87 s to fall onto the next floor slab. However, with the collapse speed observed the lower floorslab shattered at the time 0.14 s, when the body had only fallen 0.10 m.  Back