The first draft of this work posted online (July 2005) can be found here and here.   Back-up Page for A Refutation of the Official Collapse Theory Original at http://janedoe0911.tripod.com/BilliardBalls.html

Experimental Evidence is the Truth Theory must Mimic.

Introduction Very shortly after the events of September 11, 2001, the U.S. government proclaimed its certitude concerning who the attackers were -- 19 Arabs suicide bombers under the guidance of one Osama bin Laden. What followed in quick succession were ‘authoritative’ pronouncements, through NOVA and a few academicians, about what brought the WTC towers down. This early public authoritative consensus was that the buildings could not withstand the horrific onslaught of the plane crashes and subsequent fires.  Since that time questions have arisen about the veracity of the Official Government Theory of the events of 9/11. One area of particular interest has been the issue of the WTC tower “collapses”.  The purpose of this site is to look at that question from a single, simple perspective -- that of the timing of those “collapses”. Absent other forces, gravity alone must have generated them. We will examine whether that was possible, from the perspective of the law of gravity and the visual record.

According to the "Official Story," how long did it take the WTC towers to collapse? Page 305 of the 9/11 Commission Report states, "At 9:58:59, the South Tower collapsed in ten seconds, .... The building collapsed into itself, causing a ferocious windstorm and creating a massive debris cloud."  (Chapter 9. html, pdf) The August Fact Sheet (Answers to Frequently Asked Questions) by NIST states, "NIST estimated the elapsed times for the first exterior panels to strike the ground after the collapse initiated in each of the towers to be approximately 11 seconds for WTC 1 and approximately 9 seconds for WTC 2." (Question #6.) The height of the South Tower (WTC2) is 1362 feet, and the height of the North Tower (WTC1) is 1368 feet, which are nearly the same. Do these values seem reasonable?     Let's calculate a few values we can use as a reference.

Other values of interest: (Note, these are only for reference and are not used as the "collapse" time.) Columbia University's Seismology Group recorded seismic events of 10 seconds and 8 seconds in duration, which correspond to the collapses of WTC2 and WTC1, respectively.

Information Based on Seismic Waves recorded at Palisades New York  Seismology Group,  Lamont-Doherty Earth Observatory, Columbia University Event origin time (EDT)  (hours:minutes:seconds) Magnitude (equivalent seismic) Duration Impact 1 at North Tower 08:46:26±1 0.9 12 seconds Impact 2 at South Tower 09:02:54±2 0.7 6 seconds Collapse 1, South Tower 09:59:04±1 2.1 10 seconds Collapse 2, North Tower 10:28:31±1 2.3 8 seconds

For the following, I used the height of WTC1 as 1368 feet and considered each floor to be a height of 12.44 feet.  (1368/110 =12.44 ft/floor). I assumed gravity = 32.2 ft/sec2  or  9.81 m/sec2.

Simplicity What can you prove with simple models of an enormously complex situation?  Let's say I tell you that I ran, by foot, to a store (10 miles away), then to the bank (5 more miles), then to the dog track (7 more miles), then to my friend's house (21 more miles), then home ...all in 2 minutes. To disprove your story, you could present to you a simple case. I would present to you that the world's record for running just one mile is 3:43.13, or just under four minutes.  So, it does not seem possible that I could have run over 40 miles in 2 minutes.  i.e. It does not seem possible for me to have run 43 miles in half the time it would take the holder of the world's record to run just one mile.  Even if you gave me the benefit of having run all 43 miles at world-record pace, it would not have been possible for me to have covered that distance in two minutes. Remember, the proof need not be complicated.   You don't need to prove exactly how long it should have taken me to run that distance.  Nor do you need to prove how much longer it would have taken if I stopped to place a bet at the dog track.  To disprove my story, you only need to show that the story I gave you is not physically possible.  Now, let us consider if any of those collapse times provided to us seem possible with the story we were given.

Case 1:  Free-fall time of a billiard ball dropped from the roof of WTC1, in a vacuum

Let's consider the minimum time it would take the blue billiard ball to hit the pavement, more than 1/4 mile below (see below).  Start the timer when the ball is dropped from the roof of WTC1.  We'll assume this is in a vacuum, with no air resistance.  (Note, large chunks of the building will have a very low surface area-to-mass ratio, so air resistance can be neglected.) From the rooftop of WTC1, drop one (dark-blue) billiard ball over the edge. As it falls, it accelerates. If it were in a vacuum, it would hit the pavement, 1368 feet below, in 9.22 seconds, shown by the blue curve in the figure, below.  It will take longer if air resistance is considered, but for simplicity, we'll neglect air resistance.  This means that the calculated collapse times are more generous to the official story than they need to be.

(Click on image to enlarge.) Figure 1.  Minimum Time for a Billiard Ball dropped from the roof of WTC1 to hit the pavement below, assuming no air resistance.

Notice that the billiard ball begins to drop very slowly, then accelerates with the pull of gravity. If in a vacuum, the blue ball will hit the pavement, 1368 ft. below, 9.22 seconds after it is dropped. That is, unless it is propelled by explosives, it will take at least 9.22 seconds to reach the ground (assuming no air resistance).

Let's consider the "Pancake Theory"

According to the pancake theory, one floor fails and falls onto the floor below, causing it to fail and fall on the floor below that one, and so forth. The "pancake theory" implies that this continues all the way to the ground floor.  In the case of both WTC towers, we didn't see the floors piled up when the event was all over, but rather a pulverization of the floors throughout the event.  (see pictures below)  So, clearly we cannot assume that the floors stacked up like pancakes.  Looking at the data, we take the conservative approach that a falling floor initiates the fall of the one below, while itself becoming pulverized.  In other words, when one floor impacts another, the small amount of kinetic energy from the falling floor is consumed (a) by pulverizing the floor and (b) by breaking free the next floor.  In reality, there isn't enough kinetic energy to do either.[Trumpman][Hoffman]   But, for the sake of evaluating the "collapse" time, we'll assume there was.  After all, millions of people believe they saw the buildings "collapse."   Model  A Model B (a): The floors remain intact and pile up like a stack of pancakes, from the top down.   (b): The floors blow up like an erupting volcano from the top down (c): Note that the top "block" begins to disintegrate before the damaged zone starts to move downward. Video clip courtesy of 911review.org Figure 2:  Possibilities to consider for modeling the collapse.   Which of the two models, above, best matches the images below?   (a) WTC2, demonstrating there is little to no free-fall debris ahead of the "collapse wave," (b) layer of uniform dust left by the "collapse." Figure 3:  Images from the "collapse."     If there was enough kinetic energy for pulverization, there will be pancaking or pulverization, but not both.  For one thing, that energy can only be spent once.  If the potential energy is used to pulverize a floor upward and outward, it can't also be used to accelerate the building downward.   In order to have pancaking, a force is required to trigger the failure of the next floor.  If the building above that floor has been pulverized, there can be no force pushing down.  As observed in the pictures below, much of the material has been ejected upward and outward.  Any pulverized material remaining over the footprint of the building will be suspended in the air and can't contribute to a downward force slamming onto the next floor.  With pulverization, the small particles have a much larger surface-area-to-mass ratio and air resistance becomes significant.  As we can recall, the dust took many days to settle out of the air, not hours or minutes.   So, even though the mechanism to trigger the "pancaking" of each floor seems to elude us,  let's consider the time we would expect for such a collapse.  (a) (b) (c) (d) Figure 4.  Images illustrating what really happened that day. To illustrate the timing for this domino effect, we will use a sequence of falling billiard balls, where each billiard ball triggers the release of the next billiard ball in the sequence.  This is analogous to assuming pulverization is instantaneous and does not slow down the process.  In reality, this pulverization would slow down the "pancake" progression, so longer times would be expected.   Thus, if anything, this means the calculated collapse times are more generous to the official story than they need to be.

Case 2: ‘Progressive Collapse’ in ten-floor intervals

To account for the damaged zone, let’s simulate the floor beams collapsing every 10th floor, as if something has destroyed 9 out of every 10 floors for the entire height of the building.  This assumes there is no resistance within each 10-floor interval.  i.e. We use the conservative approach that there is no resistance  between floor impacts.  In reality there is, which would slow the collapse time further.  Also, there was only damage in one 10-floor interval, not the entire height of the building.  Thus, if anything, this means the calculated  collapse times are more generous to the official story than they need to be.  Refer to the figure below. The clock starts when the blue ball is dropped from the roof (110th floor).   Just as the blue ball passes the 100th floor, the red ball drops from the 100th floor.   When the red ball passes the 90th floor, the orange ball drops from the 90th floor, ... etc.   Notice that the red ball (at floor 100) cannot begin moving until the blue ball reaches that level, which is  2.8 seconds after the blue ball begins to drop.  This approximates the "pancaking" theory, assuming that each floor within the "pancaking" (collapsing) interval provides no resistance at all.    With this theory, no floor below the "pancake" can  begin to move until the progressive collapse has reached that level. For example, there is no reason for the 20th floor to suddenly collapse before it is damaged.  With this model, a minimum of 30.6 seconds is required for the roof to hit the ground. Of course it would take longer if accounting for air resistance.   It would take longer if accounting for the  structure's resistance that allows pulverization.  The columns at each level would be expected to absorb a great deal of the energy of the falling floors. Thus, if anything, this means the calculated  collapse times are more generous to the official story than they need to be.

(Click on image to enlarge.) Figure 5.  Minimum time for the collapse, if nine of every ten floors have been demolished prior to the "collapse."

Case 3: ‘Progressive Collapse’ in one-floor intervals

Similar to Case 2, above, let's consider a floor-by-floor progressive collapse. Refer to the figure below:

(Click on image to enlarge.) Figure 6.  Minimum time for the collapse, if every floor collapsed like dominos.

Case 4: ‘Progressive Collapse’ at near free-fall speed

Now, consider the chart below.

(Click on image to enlarge.) Figure 7.  Minimum Time for a Billiard Ball dropped from the roof of WTC1 to hit the pavement below, assuming no air resistance.

Let's say that we want to bring down the entire building in the time it takes for free-fall of the top floor of WTC1. (Use 9.22 seconds as the time it would take the blue ball to drop from the roof to the street below, in a vacuum.) So, If the entire building is to be on the ground in 9.22 seconds, the floors below the "pancaking" must start moving before the "progressive collapse” reaches that floor, below. To illustrate this, use the concept of the billiard balls. If the red ball (dropped from the 100th floor) is to reach the ground at the same time as the blue ball (dropped from the 110th floor), the red ball must be dropped 0.429 seconds after the blue ball is dropped. But, the blue ball will take 2.8 seconds after it is dropped, just to reach the 100th floor in free fall. So, the red ball needs to begin moving 2.4 seconds before the blue ball arrives to "trigger" the red ball's motion.  I.e.,  each of these floors will need a 2.4 second head start.  But this creates yet another problem.  How can the upper floor be destroyed by slamming into a lower floor if the lower floor has already moved out of the way? Case 2, above, shows the red ball being dropped just as the blue ball passes that point.  Remember, I'm assuming the building was turning to dust as the collapse progressed, which is essentially what happened.  So, for the building to be collapsed in about 10 seconds, the lower floors would have to start moving before the upper floors could reach them by gravity alone. Did we see this? I believe it's pretty clear in some of the videos. The "wave" of collapse, progressing down the building, is moving faster than free-fall speed. This would require something like a detonation sequence. Realizing that, for example, the 40th floor needs to start moving before any of the upper floors have "free-fallen" to that point, why would it start moving? There was no fire there. And, if anything, there is less load on that floor as the upper floors turn to dust.  In the picture (at right), notice that WTC2 is less than half of its original height, yet has no debris that has fallen ahead of the demolition wave.  Figure 8.  WTC2, demonstrating there is little to no  free-fall debris ahead of the "collapse wave."    So, how could the ground rumble for only 8 seconds while WTC1 "disappeared?" I don't think this part of the building made a thud when it hit the ground. Figure 9.  Dust from "collapse."   This part of the building surely took a lot longer to hit the ground as dust than it would have if it came down as larger pieces of material. We know that sheets of paper have a very high surface-area-to-mass ratio and will stay aloft for long periods of time, which is why paper is an excellent material for making toy airplanes.  The alert observer will notice that much of the paper is covered with dust, indicating that this dust reached the ground after the paper did.  In the above picture, there are a few tire tracks through the dust, but not many, so it was probably taken shortly after one (or both) of the towers were down.  Also, the people in the picture look like they've just come out of hiding, curious to see what just happened and to take pictures.   If there had been a strong wind blowing the dust around, it would blow the paper away before it would have blown the dust onto the paper.  So, the fact that much of the randomly-oriented paper is covered with dust indicates the relative aerodynamic properties of this dust.  Also, notice the dark sky as well as the haze in the distance.  This was a clear day with no clouds in the sky... except for the dust clouds.  This overcast appearance as well as the distant haze can only be explained by dust from the "collapse" that is still suspended in the air.  In a conventional controlled-demolition, a building's supports are knocked out and the building is broken up as it slams to the ground.  In a conventional controlled-demolition, gravity is used to break up the building.  Here, it seems that the only use of gravity was to get the dust out of the air. Conclusion: In conclusion, the explanations of the collapse that have been given by the 9/11 Commission Report and NIST are not physically possible.  A new investigation is needed to determine the true cause of what happened to these buildings on September 11, 2001.  The destruction of all seven WTC buildings and especially WTC1 and WTC2 may be considered the greatest engineering disaster in the history of the world and deserves a thorough investigation.