David Chandler responds to Frank Greening
June 17, 2009
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:
This is my response to his letter.
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?
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.
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.
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.
The main problem with Chandler’s analysis is that he is ignoring what actually happens to a
building during collapse.
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.
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.
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.
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 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.
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
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.
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.
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
that the upper block remains intact. The significant thing, as I’ve shown, is that the force of
resistance is significantly less than the weight of the falling block. If you assume the upper
block is accreting mass, as you have challenged me to consider, even the statement that the
resisting force is constant is no longer true.
FG, in a lengthy paragraph, shortened here:
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). Etc. …. Thus we see that E1/M is indeed approximately constant for the floors of
You are using circular reasoning. You are not dealing with the reality. You are dealing with
consequences of your simplifying assumptions. More to the point, none of this is relevant to
the issue at hand. I have laid out a clear, coherent argument that the falling block could not
deliver the force needed to crush the bottom section of the building while it continued to
accelerate downward. None of what you say in the previous paragraph or the remainder of
your letter even addresses this issue.
On the question of energy transfer, deceleration and all that, I would say…etc.
What on earth do you mean by “energy transfer, deceleration, and all that…”? Many of the
fragments in this paragraph are true enough, but they don’t go anywhere. They don’t advance
your argument. They don’t challenge mine. They are not illuminating. There’s nothing here
to respond to.
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.
You are engaging in pseudo academic obfuscation. In my video I have made the argument
that the constant acceleration of the top section of the building implies that the resistive force
is much less than the weight of the falling block. If I’m wrong, show me how. You seem to
be hoping non-technical readers will assume what you have said is profound. It is not
profound. It is incoherent.
Unsuspecting readers may not understand the significance of your last line. They should be
informed that the reason you view the application of Newton’s 3rd Law of motion as naïve, is
because, as you have clearly and repeatedly stated in both private correspondence and public
forums, that you believe Newton’s 3rd Law does not apply to falling buildings. That, of
course, is utter nonsense. Your entire letter needs to be read and understood in the light of
this concluding statement. Your argument is not with me; it is with Isaac Newton.