Destruction of the World Trade Center North Tower and Fundamental Physics By David Chandler B.S., physics, Harvey Mudd College, Claremont, CA M.A., education, Claremont Graduate University, Claremont, CA M.S., mathematics, California Polytechnic University, Pomona, CA Running Title: Downward Acceleration of WTC 1 Abstract The roof line of the North Tower of the World Trade Center is shown to have been in constant downward acceleration until it disappeared. A downward acceleration of the falling upper block implies a downward net force, which requires that the upward resistive force was less than the weight of the block. Therefore the downward force exerted by the falling block must also have been less than its weight. Since the lower section of the building was designed to support several times the weight of the upper block, the reduced force exerted by the falling block was insufficient to crush the lower section of the building. Therefore the falling block could not have acted as a "pile driver." The downward acceleration of the upper block can be understood as a consequence of, not the cause of, the disintegration of the lower section of the building. Journal of 9/11 Studies - Feb 2010 1

Introduction The destruction of the World Trade Center on September 11, 2001 was, by any assessment, a momentous turning point in world affairs. More than eight years after the event, the causes of the collapses of the three largest World Trade Center buildings (WTC 1, WTC 2, and WTC 7) remain hotly contested despite official reports by government agencies, first by FEMA then by NIST, attempting to lay the matter to rest. A "9/11 Truth Movement" has arisen, including over 1000 architects and engineers who are calling for a new investigation. The NIST investigators constructed an elaborate computer model of the buildings which they used to model the airplane crashes, but strangely they did not model the actual collapses of the Twin Towers. They took their analysis only up to the point of initiation of collapse, relying, as we shall see, upon a much more simplistic model proposed by Zdenĕk Bazănt[4, 5, 6, 7], which concluded that once the collapse was initiated, total collapse was inevitable. What follows here is an analysis that follows the simplifying assumptions laid out by Bazănt. Using measurements and a level of analysis accessible to an introductory physics class, undergraduate students have it within their power to evaluate the adequacy of the NIST-Bazănt model. Their physics background, even at this stage, equips them for intelligent participation in a significant civic debate. The Pile Driver The twin towers of the World Trade Center were destroyed in a top-down manner. More particularly, the section of the building from about the 98th floor upward to the roofline appeared to decouple and accelerate downward through the lower 98 floors. The mechanism of this process has been debated Journal of 9/11 Studies - Feb 2010 2

both among those limiting their search to a strictly natural explanation of the catastrophe (plane impacts, fire, and gravity) and among those willing to evaluate all possible explanations (including pre- planted explosives). The destruction of a building is a complex process, but simple physics applied to the observed motion of the roofline can constrain the choices among proposed theories. We will focus here on the details of the destruction of the North Tower. It was the first building to be hit by a plane and the second building to fall on September 11, 2001. It can be identified as the tower with the large antenna on its roof. The theory published by Thomas W. Eagar and Christopher Musso in JOM in December 2001,[1] and adopted by the Federal Emergency Management Agency (FEMA) study, postulated that the floor connections broke due to fire, leading to a "pancaking" collapse of the floors. This theory does not provide an explanation for why the core structure also failed, and it was rejected by the National Institute of Standards and Technology (NIST) study. Instead, the NIST report focuses on column failure. On the FAQ page of NIST's website we read: NIST's findings do not support the "pancake theory" of collapse, which is premised on a progressive failure of the floor systems in the WTC towers. (The composite floor system, that connected the core columns and the perimeter columns, consisted of a crossed grid of steel trusses integrated with a concrete slab.) Instead, the NIST investigation concluded that the collapse was caused by sagging floor trusses pulling on the south wall perimeter columns causing them to bow inward and eventually fail. This mechanism requires that the floor trusses remain attached to the perimeter columns, so pancaking is ruled out.[2] In NIST's view, fire caused a critical number of core and perimeter columns to weaken and eventually fail near the impact zone. The following is from p. 151 of their summary document, NIST NCSTAR 1. Journal of 9/11 Studies - Feb 2010 3

Collapse Initiation •The bowed south wall columns buckled and were unable to carry the gravity loads. Those loads shifted to the adjacent columns via the spandrels, but those columns quickly became overloaded as well. In rapid sequence, this instability spread all the way to the east and west walls. •The section of the building above the impact zone (near the 98th floor), acting as a rigid block, tilted at least 8 degrees to the south. •The downward movement of this structural block was more than the damaged structure could resist, and global collapse began. [3] A series of papers by Zdenĕk Bazănt,[4, 5, 6, 7] with various co-authors, describe what has become known as the "pile-driver" hypothesis, which appears to have been relied upon by the NIST investigation. Bazănt describes a scenario in which the top assembly of the building remains rigid as it crushes the lower sections of the building into rubble. Only when the lower section has been crushed into a compact debris pile does the top assembly crush itself. This proposed process has become known as "Crush-Down" followed by "Crush-Up." His claim is that once collapse is initiated, it becomes inevitable. Using Bazănt's analysis as a rationale, the NIST report limits its own investigation to the events leading up to the "initiation" of collapse, claiming that everything thereafter was inevitable and required no further investigation. NIST thereby sidesteps any consideration of what actually happened during the collapse itself, including evidence that might bring the correctness of Bazănt's analysis into doubt. Journal of 9/11 Studies - Feb 2010 4

The Accelerating Destruction The roofline of the North Tower appears to drop suddenly in what some observers loosely describe as "free fall" or "near free fall." To measure the actual motion of the roof line, a high quality copy of a video by Etienne Sauret (similar to a version available on YouTube[8]) was used. The Sauret video shows the North Tower's north face, which is identifiable by the presence of the aircraft impact hole. It is a particularly good video for our purposes because it shows a nearly level, nearly perpendicular view of the face of the tower taken from a distant stationary camera. A number of software packages allow the placement of markers frame-by-frame on a video clip for kinematic analysis. One such program is Tracker,[9] which is part of the Open Source Physics project.[10] The frame rate of the Sauret video clip, which is the standard NTSC rate of 30,000 frames per 1001 s, or approximately 29.97 fps, serves as the time base. The vertical scale was calibrated by the floor spacings which, apart from the sky lobby and the mechanical floors, are known to be 12 ft 0 in apart.[11] The vertical position of the roof line was marked every six frames (0.2 s intervals) and the data was exported to a spreadsheet for analysis. (See Table 1.) Frame # T (sec) y (m) vy (m/s) 216 0.00 82.397 222 0.20 82.399 0.010 228 0.40 82.401 0.010 234 0.60 82.403 -0.562 240 0.80 82.176 -1.708 246 1.00 81.720 -2.665 252 1.20 81.110 -3.400 258 1.40 80.360 -4.520 264 1.60 79.302 -5.860 270 1.80 78.016 -7.165 276 2.00 76.436 -8.485 282 2.20 74.622 -10.005 288 2.40 72.434 -11.505 294 2.60 70.020 -12.648 Journal of 9/11 Studies - Feb 2010 5

300 2.80 67.375 -13.968 306 3.00 64.433 -15.285 312 3.20 61.261 -16.240 318 3.40 57.937 -17.358 324 3.60 54.318 -18.300 330 3.80 50.617 -19.443 336 4.00 46.541 Table 1: Video Measurement Data--Frame numbers indicate every 6th frame relative to the start of the video clip. The frame rate of the video is NTSC standard, 29.97 fps, yielding a measurement interval of 0.20 s. The y-values are the height of the roof line relative to an arbitrary origin. Velocities are computed by the symmetric difference differentiation algorithm. A graph of the height of the roof line vs. time (Figure 1) displays the characteristic shape of a parabola indicating a downward acceleration. The vertical component of velocity was computed using a symmetric difference numerical differentiation algorithm, v = yn +1 yn 1 . (1) n 2 t A graph of velocity vs. time (Figure 2) shows near uniformity of the downward acceleration from the 6th computed velocity point onward. When the roof line begins to fall, it quickly transitions to nearly uniform downward acceleration. Journal of 9/11 Studies - Feb 2010 6

Figure 1: Graph of the height of the roof line (measured from an arbitrary origin) vs. time at 0.2 second intervals. Note that once it begins to fall the path appears approximately parabolic. Journal of 9/11 Studies - Feb 2010 7

Figure 2: Velocity is here plotted as a function of time for the roof line of WTC1. The regression line is computed for the 6th computed velocity onward. The slope, in this context, is the acceleration: -6.31 m/s2 with an R2 value of 0.997. Observations For the current analysis we follow Bazănt's simplifying assumptions [4, 5, 6, 7] by treating the upper section of the building as a solid block with mass m. The only two relevant forces acting on the falling block are gravity (mg) and an upward normal force (N) due to its interaction with the lower section of the building. Applying Newton's Second Law and solving for N, we get mg N = ma (2) Journal of 9/11 Studies - Feb 2010 8

so N = mg ma (3) Our data shows that from the sixth computed velocity data point onward, the upper block is accelerating uniformly (with an R2 value of 0.997) at a = -6.31 m/s2, or in other words, 64% of the acceleration of gravity. For this value of a, N = mg 0.64mg = 0.36mg (4) Therefore the upward-acting normal force is 36% of the weight of the upper block, as illustrated in Figure 3. Journal of 9/11 Studies - Feb 2010 9

Figure 3: Consider the upper section of the building to be a block of weight mg. Since the acceleration of the block is measured to be downward at 0.64g, the net force acting on it must be 0.64mg. The gravitational force is mg, so the upward normal force must be 0.36mg. The upper and lower sections of the building exert equal but opposite forces on each other, so the load on the lower section of the building is 36% of the weight of the upper block. Explicitly invoking Newton's Third Law puts this result in another light. Since the forces in the interaction are equal and opposite, the falling block exerts a force of only 36% of its weight on the lower section of the building. In other words, as long as the falling block is accelerating downward we have the counter-intuitive result that the force it exerts on the lower section of the building is significantly less than its static weight. It is difficult to imagine how an upper block exerting a force of only 36% of its static weight could crush the larger, stronger, undamaged lower section of the building to the ground, when the building, at any level, was designed to support several times the weight above it. Assuming a safety factor of between 3 and 5 [12], the observed acceleration implies that close to 90% of the strength of the lower section of the building must have been eliminated by forces other than the supposed "pile driver," suggesting that some sort of controlled demolition was at work. One might argue, in terms of the strength of the various elements, that the impact of the falling block might crush the lower section of the building (although this assertion has been challenged [13]), but it cannot crush the lower block while it maintains its downward acceleration. Prof. Graeme MacQueen and Tony Szamboti have made a parallel observation, based on a similar measurement, in their paper, "The Missing Jolt: A Simple Refutation of the NIST--Bazănt Collapse Hypothesis."[14] They point out that any increased force on the lower section of the building must be accompanied by a decrease in the momentum of the falling block. The transfer of momentum (which implies a loss of momentum for the Journal of 9/11 Studies - Feb 2010 10

upper block) is what gives rise to the impulse. The falling block can lose momentum only to the extent that it decelerates. It should therefore experience a "jolt" which we should be able to see in the video analysis. But from the fact that the upper block continues to move downward without deceleration, it is clear that there was no jolt despite the significant deformation of the building in the first three seconds. The fact that a downward accelerating block would exert a force less than its own weight on the target block may be difficult to accept intuitively, but that is because our experience suggests the target block would resist the crushing blow. A rapidly moving hammer head driving a nail into a solid block of wood typically exerts a force on the nail many times the weight of the hammer head. But that is true only if the nail resists the blow. The large force that drives the nail into the wood is matched by a force that simultaneously decelerates the hammer head, which is why multiple blows are typically required. If, however, the nail is placed on a block of Styrofoam it will not significantly resist the blow. It will be driven into the block with very little force. The falling hammer head will meet so little resistance that it will be able to accelerate the whole time. In the case of WTC1, the falling block acts like the hammer head driving the nail into Styrofoam, but, changing the picture a little, it is the interface between the two blocks that is "soft." Something other than the falling block (explosives?) must be destroying the structural integrity of the interface zone so that it offers only a small fraction of the resistance it was designed to provide. Some might object to oversimplifying the model quite this much. It has been argued that the crushed material at the interface of destruction is accreted to the upper section so the mass of the falling block grows as it falls, producing an avalanche effect.[15] I would argue, from the fact that a major fraction of the mass landed outside the footprint of the building, that accretion was at most partial, but let us consider the effect of any such accretion. Newton's Second Law applied to a system of variable mass can be stated Journal of 9/11 Studies - Feb 2010 11

dp dp Fext + = , (5) dt accreted dt system where p is momentum and Fext represents the net external force acting on the system. The accreted mass is initially at rest, so it brings no new momentum into the system: dp = 0 . (6) dt accreted Since p = mv we can write, dp d ( mv ) dv dm Fext = = = m + v . (7) dt system dt dt dt In our situation (letting the downward direction be positive), Fext = mg N (8) where N is the normal force, as in our earlier analysis. Recognizing dv as simply the acceleration, a, dt we can write (mg N ) = ma + v dm . (9) dt Journal of 9/11 Studies - Feb 2010 12

Solving for N, we have N = (mg ma ) v dm . (10) dt Note that this is the same as our previous result (Eq. [3]) except the normal force is reduced even further, since both v and dm are positive. dt Therefore, perhaps counter-intuitively, any accreted material reduces the effectiveness of an assumed pile driver. This result may become reasonably intuitive once one recognizes that the falling block must transfer some of its momentum to the accreted mass to bring it up to speed. Summary The fact that the roof line of the upper section of the North Tower continued to accelerate downward through the collision with the lower section of the building indicates that the upper section could not have been acting as a pile driver. As long as the roof line was accelerating downward, the upper block, exerted a force less than its own static weight on the lower section of the building. Any accretion of material into the upper block would have acted as an inertial brake, reducing the force of interaction even further. The undamaged lower section of the building was built to support several times the weight of the material above it, but whether or not we take the safety factor into account, the reduced force exerted by the falling mass could not have been what caused the violent destruction of the building seen in numerous videos. The persistent acceleration of the top section of the building is strong confirmation that some other source of energy was used to remove the structure below it, Journal of 9/11 Studies - Feb 2010 13

allowing the upper block to fall with little resistance. Having assumed the existence of an indestructible falling block, with or without accretion, we have demonstrated that, given the observed acceleration, such a block could not possibly have destroyed the lower section of the building. When we turn to the video evidence we see that even the hypothesized existence of a persistent upper block is a fiction. Videos show that the section of the building above the plane impact point was the first section to disintegrate. It was significantly reduced in size prior to the onset of destruction of the lower section of the building. Once the roof line descends into the debris cloud there is no further evidence even of its continued existence. Whether or not it was completely destroyed early in the collapse is a moot point. We have shown that even if it continued to exist intact, it could not have played a significant role in the destruction of the building. A small section of a structure, consisting of a few floors, cannot one-way crush-down a significantly larger lower section of same structure by gravity alone. Acknowledgments I would like to express appreciation to the volunteer staff of Architects & Engineers for 9/11 Truth and others in the broader 9/11 Truth community who provided encouragement and critical discussion for this paper. Also I appreciate the correspondence with Charles M. Beck, who led me to think through the implications of accretion for this analysis. Journal of 9/11 Studies - Feb 2010 14

References [1]T. W. Eagar and C. Musso, “Why did the World Trade Center collapse? science, engineering, and speculation,” JOM, vol. 53, no. 12, pp. 8-11, 2001. [Online]. Available: http://www.tms.org/pubs/journals/JOM/0112/Eagar/Eagar-0112.html [Accessed Mar 1, 2009] [2](2006) NIST’s investigation of the Sept. 11 World Trade Center disaster—Frequently Asked Questions. [Online]. Available: http://wtc.nist.gov/pubs/factsheets/faqs_8_2006.htm [Accessed Mar 1, 2009] [3]NIST NCSTAR 1. [Online]. Available: http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201.pdf [Accessed Mar 1, 2009] [4]Z. P. Baznt, “Why did the World Trade Center collapse?” SIAM News, vol. 34, no. 8, pp. 2-6, 2001, (It is noteworthy that this paper was submitted on Sept. 13, 2 days after 9/11). [Online]. Available: http://www-math.mit.edu/~bazant/WTC/ [Accessed Mar 1, 2009] [5]Z. P. Baznt and Y. Zhou, “Why did the World Trade Center collapse—Simple analysis,” J. Eng. Mech., vol. 128, no. 1, pp. 2-6, 2002.[Online]. Available: http://www-math.mit.edu/~bazant/WTC/WTC-asce.pdf [Accessed Mar1, 2009] [6]Z. P. Baznt and M. Verdure, “Mechanics of progressive collapse: Learning from World Trade Center and building demolitions,” J. Eng. Mech., vol. 133, no. 3, pp. 308-319, 2007. [Online]. Available: http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/466.pdf [Accessed Mar 1, Journal of 9/11 Studies - Feb 2010 15

2009] [7] Baznt, Le, Greening and Benson, Journal of Engineering Mechanics, ASCE, Vol. 134 (2008), “What Did and Did not Cause Collapse of WTC Twin Towers in New York” Available: http://wtc7lies.googlepages.com/Bazant_WTC_Collapse_What_Did__Did_No.pdf 8] E. Sauret. 9/11: North Tower collapse (Sauret). [Online]. Available: http://www.youtube.com/watch?v=xGAofwkAOlo [Accessed Mar 1,2009] [9]D. Brown. Tracker ver 2.53. [Online]. Available: http://www.cabrillo.edu/~dbrown/tracker/ [Accessed Mar 1, 2009] [10]Open Source Physics project, NSF DUE-0442581. [Online]. Available: http://www.compadre.org/osp/ [Accessed Mar 1, 2009] [11] NIST NCSTAR 1, Figure 2-2. [Online]. Available: http://wtc.nist.gov/NCSTAR1/PDF/NCSTAR%201.pdf [Accessed Mar8, 2009] [12]T. Szamboti. (2007, May) The sustainability of the controlled demolition hypothesis for the destruction of the Twin Towers. [Online]. Available: http://www.journalof911studies.com/ [Accessed Mar 1, 2009] [13]G. Ross. (2006, Jun.) Momentum transfer analysis of the collapse of the upper storeys of WTC 1. [Online]. Available: http://www.journalof911studies.com/articles/Journal_5_PTransferRoss.pdf [Accessed Mar 1, 2009] Journal of 9/11 Studies - Feb 2010 16

[14]G. MacQueen and T. Szamboti. (2009, Jan.) The missing jolt: A simple refutation of the NIST- Baznt collapse hypothesis. [Online]. Available: http://www.journalof911studies.com/volume/2008/TheMissingJolt7.pdf [Accessed Mar 1, 2009] [15]C. M. Beck. (2007, Nov.) Mathematical models of progressive collapse and the question of how did the World Trade Centers perish. [Online]. Available: http://arxiv.org/PS_cache/physics/pdf/0609/0609105v8.pdf [Accessed Mar 1, 2009] Journal of 9/11 Studies - Feb 2010 17

Frank Greening’s Challenge to David Chandler F. R. Greening Hamilton, Canada I note with amusement that someone who calls himself Reprehensor has posted the recent e- mail exchange between myself and Steven Jones on 9/11 Blogger. From the 40-plus comments Reprehensor’s post has generated, I see that many researchers view my opinions on Chandler’s “proof” that the collapse of WTC 1 must have been a CD, as evidence that I misunderstand the basic rudiments of Newtonian physics. Well, I beg to differ and will now go through Chandler’s arguments to clarify my position on this issue. Chandler’s argument appears to be as follows: During the collapse of WTC 1, an upper portion of the building, (let’s say the top 13 floors), started moving downward relative to the lower fixed portion of the building, causing the lower portion to be crushed. Let’s call the (initial) mass of the upper block M(upper). For WTC 1, M(upper) was about 30,000 tonnes and the initiating drop distance was 3.7 meters or one story height. Measurements of the motion of the upper block, (while it was still visible), show it dropped about ten story heights during the first 3 seconds with an approximately constant acceleration of 6.31 m/s^2 or 64 % of g. From this observation Chandler concludes that the block was subject to a net force of 0.64M(upper)g. Prior to the collapse of WTC 1, the lower portion of the building was perfectly capable of holding up the upper block which we know exerted a downward force equal to M(upper)g. So why, once the collapse started, was the lower section of WTC 1 not able to support a load of 0.64M(upper)g? Chandler’s answer to this question: During the collapse of WTC 1, the only way the upper block could have accelerated at 64 % of g was for the lower section of the building to have continuously lost its load-carrying capacity, presumably through the occurrence of column failures ahead of the collapse front. The fact that the downward acceleration was not far below g shows that columns failed without significant resistance. This, concludes Chandler, proves that the destruction of WTC 1 was a controlled demolition. This all sounds like a very nice exercise in Newtonian mechanics, …. so how could it possibly be incorrect? Well, the main problem with Chandler’s analysis is that he is ignoring what actually happens to a building during collapse. In the collapse of WTC 1, the upper section is not the only part of the building that is set into motion. Evidently, the top of the lower section also started to move downwards, floor-by-floor. This means that some of the potential energy of the upper block was converted into kinetic energy of some portion of the lower block. Thus columns and beams at lower levels of the collapse front were set in motion as they were pushed downwards or sideways by a growing avalanche of debris. This means that we no longer have two distinct masses, M(upper) and M(lower). We have M(upper) = M(Initial upper) + dM/dt, and we have M(lower) = M(Initial lower) – dM/dt. And this is strictly true only in the absence of mass shedding. Obviously this situation greatly complicates momentum transfer calculations because you have to include a dM/dt term as well as a dv/dt (acceleration) term. I challenge David Chandler to re-do his WTC 1 collapse analysis with inclusion of a dM/dt term. I note too that Chandler gives no consideration to energy transfer in the collapse of WTC 1 & 2.Energy balance requires that: a = g – E1/3.7M(upper), ……….. where E1 is the energy needed to collapse one floor

The fact that a is observed to be approximately constant means E1/M is also ~ constant. That E1/M should be more or less constant is consistent with the design of WTC 1 & 2, or indeed any tall building. When I say that E1 is “the energy to collapse one floor” please note that E1 includes all the energy consumed during the descent of the upper block through one floor height (~ 3.7 meters). The E1 term therefore includes the energy to “fail” the columns, the energy to crush the floor trusses and office furniture, the energy to fracture and crush the concrete, etc. Because the value of a/g is 0.64 and (at the start of the collapse) M ~ 33,000 tonnes, we see that E1 ~ 0.5 GJ. Now I fully realize that the core columns are “stronger” on the lower floors of the Towers, however, because the acceleration, a, is observed to be constant for the first 3 seconds of collapse, E1/M must also be constant over this time, namely for the first ten floors to collapse in WTC 1 – floors from approximately level 96 to level 86. The core column areas for these floors were approximately 2 m^2 for floor 96 and 3 m^2 for floor 86. The extra mass picked up over ten floors (ignoring any mass shedding) would be about 20,000 tonnes, so we have M increasing by a factor of 53,000/33,000 = 1.6; and E1, assumed to be directly proportional to the column areas, increasing by 1.5. Thus we see that E1/M is indeed approximately constant for the floors of interest. On the question of energy transfer, deceleration and all that, I would say there is obviously a lot of energy transfer going on during the collapse of WTC 1 because the upper block is performing work on the lower section of the building by accelerating material such as steel columns and beams, concrete, etc, located at the collapse crush front. Thus some of the potential energy released by the downward motion of the upper block was converted into the “internal” kinetic energy of a layer of debris/rubble at the crush front. And some of the K.E. so created was “lost” through sideways ejections of material; nevertheless, calculations show that the overall velocity of the falling mass tends to increase. Furthermore, I believe it is quite realistic to consider the collapse not as a drop-bump-drop-bump, … motion, but as a s-m-o-o- t-h process of destruction leading to a continuous buildup of momentum. In this way the collapse of WTC 1 (and WTC 2) had a lot in common with a rockslide. The collapse of WTC 1 is best studied by considering how potential energy was converted to kinetic energy and dissipated at the crush front and subsequently within the steadily growing debris/rubble layer. This debris layer was not only a sink for potential energy, but a source of random fluctuations in the motions of the individual debris particles. These fluctuations cannot exert a net resultant force against the downward motion of the upper block but rather serve to control the gravitational work rate. In fact, if this type of collapse should attain a state of dynamic equilibrium, there will be a balance between the production of fluctuation energy at the crush front and the conversion of this energy to heat within the debris layer through the dissipating effects of many random collisions of debris particles. It is considerations such as these that help to quantify the complexities of the WTC 1 collapse, not naïve applications of Newton’s 3rd Law of motion. F. R. Greening Hamilton, Canada

Greening vs. Chandler and Newton’s Laws: The occasion for Frank Greening’s letter is correspondence with several physicists, chemists, and engineers discussing arguments I made in a video posted on the Architects and Engineers for 9/11 Truth YouTube page: http://www.youtube.com/watch?v=xG2y50Wyys4. This is my response to his letter. ------------------------------ FG: Chandler concludes that the block was subject to a net force of 0.64M(upper)g. Prior to the collapse of WTC 1, the lower portion of the building was perfectly capable of holding up the upper block which we know exerted a downward force equal to M(upper)g. So why, once the collapse started, was the lower section of WTC 1 not able to support a load of 0.64M(upper)g? Response: You are confused on this point. It was the net force on the upper block which was 0.64g downward. The net force consists of the downward force due to gravity combined with the upwardly directed normal force. For the net force to come out 0.64g, the normal force had to have been 0.36g. By Newton’s third law, the load on the lower section was also 0.36g. FG: Chandler’s answer to this question: During the collapse of WTC 1, the only way the upper block could have accelerated at 64 % of g was for the lower section of the building to have continuously lost its load-carrying capacity, presumably through the occurrence of column failures ahead of the collapse front. The fact that the downward acceleration was not far below g shows that columns failed without significant resistance. This, concludes Chandler, proves that the destruction of WTC 1 was a controlled demolition. Response: Close, but you have turned my quantitative assessment based on evidence into a hand-waving general statement. In particular, the resistance force is measurably only 36% of the weight of the falling block. Since the lower section of the building was designed to carry 3-5 times the weight of the upper section, the lower section appears to have lost about 90% of its load carrying capacity. Some mechanism apart from the falling mass must have operated to account for this failure. FG: The main problem with Chandler’s analysis is that he is ignoring what actually happens to a building during collapse. Response: My analysis here follows the general model laid out by Bazant and Greening, which is indeed far removed from what actually happened. The Bazant-Greening model postulates a coherent falling block which observations show did not exist. At most there was a falling mass of disassociated rubble from a top section of the building that largely disintegrated before the lower section of the building even started to descend. I adopt the Bazant-Greening model to show its internal contradictions. What I show is that EVEN IF the top block were an indestructible pile driver, it would deliver less force to the undamaged lower section of the building than it would if it merely remained motionless. FG: We no longer have two distinct masses, M(upper) and M(lower). We have M(upper) = M(Initial upper) + dM/dt, and we have M(lower) = M(Initial lower) – dM/dt. And this is strictly true only in the absence of mass shedding.

Response: The equations you have written are clearly in error since the units of the terms do not even agree. It appears that you are trying to say, in pseudo-calculus terms, that the falling mass can be considered to grow as it sweeps up material that is crushed at the interface. I comment on the sloppiness of your equations because what I see you doing repeatedly is using mathematics to muddle the issue rather than clarify it. The reader shouldn’t have to come to the rescue and infer what you probably mean by your equations. It is interesting that you do acknowledge that there is a neglected term for mass shedding which you do not attempt to quantify. Given that a majority of the mass of the building lands outside its footprint, this seems like a major oversight. FG: Obviously this situation greatly complicates momentum transfer calculations because you have to include a dM/dt term as well as a dv/dt (acceleration) term. I challenge David Chandler to re-do his WTC 1 collapse analysis with inclusion of a dM/dt term. Response: I have already done these calculations and they are included in my paper on the downward acceleration of WTC1 which is undergoing peer review for another journal, so cannot yet be published here. I assume the reason you throw this down as a challenge to me is you assume, wrongly, that turning this into a variable mass problem will “greatly complicate” the issue. Actually, it does not greatly complicate the issue. It takes only a few extra lines to modify the analysis. Briefly, the accreted mass is initially at rest, so it adds inertia but no momentum to the upper block. The net result is that the accretion of mass results in a DECREASE in the force of interaction with the lower section of the building. I might also note that the fact that you would challenge me to demonstrate something that actually strengthens my argument is pretty clear evidence that you have not done, and perhaps you are not able to do, the analysis yourself. Nevertheless you “up the ante.” You brush aside adverse conclusions based on a simple model and seek refuge in a more complex model, even though you have not followed through and investigated the implications of the more complex model yourself. I must emphasize again that I am using YOUR model, which requires a rigid falling block. I adopt it to show its flaws, but it is your model nonetheless. FG: I note too that Chandler gives no consideration to energy transfer in the collapse of WTC 1 & 2. Energy balance requires that: a = g – E1/3.7M(upper), ……….. where E1 is the energy needed to collapse one floor Response: Multiply this equation through by M and you get Ma = Mg – F, where F is the average force of resistance. This is exactly the equation I use in my analysis. Contorting it around to express the force in terms of energy adds nothing to the analysis. It is certainly not any kind of “energy balance” and it does not represent something I have left out of my analysis. FG: The fact that a is observed to be approximately constant means E1/M is also ~ constant. That E1/M should be more or less constant is consistent with the design of WTC 1 & 2, or indeed any tall building. Response: All you are doing is agreeing with me that the acceleration is approximately constant for the period under observation, which proves that the resistive force is approximately constant. There is nothing profound in this. In fact it is an artifact of the Bazant/Greening assumption 2