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Re: DATA on collapsing WTC



At 22:25 9/21/01 -0700, Glenn wrote:
Ludwik Kowalski and I have discussed through private emails our approaches
to calculating the acceleration of the North Tower of the World Trade
Center (WTC) and determining whether the tower was in free-fall during its
collapse. Ludwik concludes that the tower was not in free-fall with an
acceleration of magnitude of approximately 0.3g - 0.7g. I conclude that the
tower was in free-fall with an acceleration of 0.95g - 1.05g. We are
unable to resolve this discrepancy, but we have agreed to present this
matter to the Phys-L members for discussion and possible resolution.

Ludwik found a large variation in the
calculated acceleration, depending on the number of datapoints in a set and
the location of that set of datapoints among all the data.
/snip/ These results are consistent with other
attempts, and he concludes that the tower was not in free-fall.

Carlson's approach --

Taking the data during the collapse I calculated the time since the
beginning of the collapse and the magnitude of the tower's
displacement. Using all of the approximately 120 datapoints I calculated a
best power law of the form y=at^n, where y is the magnitude of the
displacement and t is the time since the beginning of the collapse.
/snip/
I look forward to comments from the group.

Thanks.

Glenn

------------
Glenn A. Carlson, P.E.

If the structure were articulated and not space-filling, we would
have reason to expect that it would follow the usual form of free
displacement with time. We are however, not attempting to
demonstrate a Newtonian free fall law, we have enough confidence
to assume it.

The structure was triumphantly not articulated, and was able
to withstand a design side force of a magnitude that the designers
predicted, and the ensuing gravity force.

Nevertheless, we were faced with a live demonstration of the
effects of a localized articulation of fire weakened columns.
Elsewhere, they retained a larger measure of their strength in
compression.

We have every reason to suppose that the gravity force was
opposed by the force required to crush the remaining columns,
so a model that reflects this opposition of forces would be reasonable.
It may be that an m*t -m*t^2 model looked too convenient, or too
reminiscent of a non physical model for Glenn's taste.
For my part, I evaluated the piece part fit, and returned to
Glenn's original form.

As to Ludwik's approach: you will recall that he faced just the same
difficulty with an unopposed trajectory in the lab setting some
years ago.
Certainly dissecting a motion is feasible, it is the basis of
flight simulator models and moon shot trajectory computation.
The crux of the method is to consider the largest possible
difference of time that leads to acceptable error,
which time and distance interval is always small.

I find that Ludwik's conclusion that the WTS was not in free fall
is self evidently correct, though his evidentiary support is mistaken.
I conclude that Glenn's second model (a pure power law) is faulty,
in that it is unphysical.

I mention in passing, that an appropriate model may well show a
lower match with the data, than an unphysical model - and in this
case, I believe Glenn was uncomfortable with the exceptionally good
fit of the two term model he first mentioned.
When accounting for the instrumental artifacts I find an
elevated R squared value of 99.95% for the two term
plus residuals model for example.
Nevertheless, it seems more appropriate to me. I have not been
conditioned by the physics educator's need to verify Newton.


brian whatcott <inet@intellisys.net> Altus OK
Eureka!