Thoughts on the Chandler / Greening Dialog on WTC1’s Collapse by Dr. John Wyndham
Thoughts on the Chandler/ Greening Dialog on WTC1’s Collapse
Regarding the dialog between David Chandler and Frank Greening on applying Newton’s Third Law of Motion to the “pile driver” theory of WTC1’s collapse, kudos to Chandler for his clear analysis. Greening’s arguments, for the most part, miss the point. Chandler’s rebuttal of Greening stands on its own, but the arguments are worth repeating both to affirm Chandler and to help create a scientific consensus on his analysis.
From an old copy of a widely used textbook, the 929 page University Physics by Sears, Zemansky, and Young (sixth edition), on page 4 we read “An equation must always be dimensionally consistent; this means that two terms may be added or equated only if they have the same units.” Greening’s equations that add or subtract M (units = mass) and dM/dt (time rate of change of mass, units = mass/time) are in basic error. Perhaps Greening can restate his equations correctly for all those interested.
Further, on page 24 of the above text, in the section titled “Idealized models” we find these words: “the analysis is hopelessly complicated if we try to include all these effects; we need to make a simplified model” and “an approximate description is a lot better than no description at all, which may be the alternative if the problem is so complex as to defy analysis.” So, far from being naïve, Chandler’s analysis of Bazant and Greening’s “pile driver” theory is in the best tradition of physical science. Rather than conceding any truth to this theory, Chandler uses the ancient and powerful method of reductio ad absurdum in which one starts with an assumption and then shows that the inferred results are absurd, thus invalidating the original premise.
To Chandler’s forthright responses to Greening’s arguments, one might add that the WTC1 and WTC2 collapses have nothing in common with a rock slide, as Greening suggests, unless of course the rocks are connected by steel girders. Greening does not really begin, as he implies, to “quantify the complexities of the WTC1 collapse.” Instead, he presents a hodgepodge of statements that miss the point of Chandler’s simple argument and may befuddle the average, non-scientific reader.
Some may wonder how Greening’s E1 (energy) is related to Chandler’s F (force). Greening rephrases Chandler’s equation in terms of the energy, E1, needed to collapse one floor. His train of thought appears to be as follows: Using the equation W (work) = F (force) x Distance (d), the work or energy needed to collapse one floor is W = E1 = 3.7F where F is the downward force exerted by the upper block on the lower and 3.7 meters is the height of one story. From Chandler we have Mg - F = Ma, where F is the equal and opposite upward force of resistance. So, Mg - E1/3.7 = Ma. Dividing each side of this equation by M, we arrive at g - E1/3.7M = a, which is what Greening puts forward as a new insight. However, as Chandler notes, this is not a new insight. Greening is implicitly acknowledging Newton’s third law of motion and supporting Chandler at the same time.
The collapse time (11 - 12 seconds) for WTC1 indicates an average acceleration of 0.64g for the entire collapse. Even if the falling block accretes all the mass (without shedding), the resistive force at each stage will still be only 0.36Mg, where M is the mass above the crush front. As Chandler has pointed out, this resistive force is much less than the upward normal force of Mg when the building was standing intact. The observed collapse, if solely due to gravity, is therefore absurd. No matter how much damage occurred at the floors where the plane hit and the fires burned, the “pile driver” theory does not explain the progressive accelerated collapse through the undamaged floors of the building. This conclusion, by itself, indicates that explosives were used to take out the columns. Taken with all the other evidence, the case for controlled demolition is overwhelming.
Greening’s arguments do nothing to invalidate Chandler’s reasoning and conclusion. If mass is shed, or if some energy is converted into other forms, this results in a less effective “pile driver.” The only fault I can find with Chandler’s responses is that, in his first response, he omits mass (M) from the forces he specifies as 0.64g and 0.36g. But these omissions appear to be scientific typos.
Chandler’s straightforward analysis avoids the complexity that often obscures a simple solution to a problem. This application of the laws of physics would make an excellent problem for physics students. Also, let’s hope other scientists will weigh in on Chandler’s analysis. Unless someone produces a major flaw in the argument, Chandler may well have unearthed the Rosetta Stone for disproving the official story of the towers’ collapses.
John D. Wyndham PhD (Physics)