We
See Conspiracies That Don't Exist
The Physics of 9/11
by
Manuel Garcia, Jr. (CounterPunch)
Wednesday
Nov 29th, 2006 10:50 PM
Activist,
physicist and frequent CounterPunch essayist Manuel Garcia, Jr. intensifies debate
by professing his objections to theories promulgated by the 9/11 Truth Movement
about the destruction of Buildings 1, 2, and 7 at the N.Y. World Trade Center
on September 11, 2001.
Five years
after the events of September 11, 2001, conspiracy theories abound as an anxious
public seeks to find a comprehensible story for that day and more broadly for
their socio-political world. People need reliable foundations upon which to base
the many assumptions and conventions they use to carry on their lives.
Half
a century ago, public anxiety about the danger of atomic energy and the terror
of thermonuclear war exhibited itself in sightings of flying saucers, and a fad
of monster movies. C. G. Jung wrote about flying saucer sightings as an instance
of "mass psychosis": a "psychological infection" that spreads
among people who lack sufficient understanding to rationalize fearsome political
forces and unstable social conditions (Flying Saucers: A Modern Myth, 1958). Jung
was sensitive to any indication that another "psychological epidemic"
might erupt, as Nazism did, among a population whose government possessed awesome
military power. Mass psychosis is a myth held in common, which releases the population
from the "normal" restraints of rationality and international social
conventions, so they can pursue their mythical vision. The ignorance -- and the
fears that spring from it as prejudices -- of the entranced population is "projected"
onto "enemies" whose destruction is sought in the irrational effort
to eliminate the actual problem of psychological tensions, (1)
A
more entertaining expression of popular anxiety is the monster movie. "Godzilla,"
"Rodan," "Them," "The Thing" and many others safely
frightened viewers with stories of monsters whose introductions into human society
were caused by atomic bomb testing, or were accompanied by radioactivity. For
most Americansthe major source of any knowledge of physics is probably this type
of motion picture.
The myths we construct
to express our understanding of the realities we are immersed in are limited by
the range of our knowledge. When the myths are meant to cover over fears about
forces beyond our control, they can be conspiracy theories. Consider these pairings
of fears and rationalizations:
fear
of political power --> conspiracy theories;
metaphysical
fear (fear of death) --> religion, a theological conspiracy ;
fear
of personal inadequacy-->racism,
fear
of strange cultures--> ultra-nationalism
Certainly,
so long as there are more than two people on Earth, conspiracies will occur. But
too often we invoke a conspiracy in constructing our story of the world because
we lack specific information about the sciences, economics, history and other
relevant fields of specialized knowledge. Experience has shown that if the evidence
allows for several explanations to a given problem then the hypothesis with the
fewest assumptions is most probably correct. This principle is called Occam's
Razor and is attributed to the 14th-century English logician and Franciscan friar
William of Occam (c. 12951349) (2).
The
events of September 11, 2001, were unsettling for many Americans because their
existing myths were shattered; these myths had provided comfort and lain undisturbed
in consciousness since indoctrination had lodged them there. The increasing power
of communications technology --global telephone networks, the Internet --and the
accelerating disregard of subtlety by the elite in its management of public perceptions
about government policies has eroded the myths --or illusions --of many Americans.
So, trust in government has been broken, fear of its power is vivid, and understanding
of the physical mechanisms of Nature is limited. This psychology will naturally
sprout conspiracy theories about 9/11.
The
aim of this article is to supply some understanding of physics as it relates to
several of the features of the 9/11 events, so that readers can expand their range
of rationality and hence their political maturity.
The
reports on the investigations of the collapse of the World Trade Center buildings
conducted by the National Institute of Standards and Technology (originally the
National Bureau of Standards) are to be found at a special NIST website ("NIST
& The World Trade Center, Final Report (Sept. 2005),"
This
multi-volume Final Report, issued in September 2005, is the "official word."
There is a vast amount of dry text, much data, descriptive summaries of detailed
calculations of the impact ruptures, fires and heating, subsequent deformation,
load-shifting, buckling and ultimate failure of the buildings. NIST addressed
the sequence of events and shifting of loads leading up to the failure that allowed
the upper blocks to drop; it did not proceed to a detailed simulation of the collapses
to the ground. NIST justified this on the grounds that there was sufficient energy
in the descending blocks to crush the lower structures, once failures had occurred.
The controlled demolition hypothesis
for the collapse of the World Trade Center buildings is described at length in
a Wikipedia article ("Controlled demolition hypothesis for the collapse of
the World Trade Center,"
The popularity
of 9/11 conspiracy theories (also outlined in a useful Wikipedia entry) has prompted
NIST to present a very nice webpage addressing the usual questions of the conspiracy
viewpoint, and providing clear descriptions in non-technical English of the physics
and engineering explanations embodied in the NIST WTC Towers Final Report .
Summary
of NIST Findings
The World Trade Center
Towers (WTC 1, WTC 2) were tall square buildings with supporting columns grouped
along the vertical axis (center) and closely spaced along the perimeter (building
faces). A "hat truss," at the top of each building, tied the outer walls
to the central columns; and this truss had a height equal to that of five stories.
A hijacked airliner was crashed into
each building about 10 or 20 stories down from the top. The columns along one
face of the building were sheared for a height of several floors, as were many
of the columns at the core. The exploding fuel from the airliner ignited fires
throughout the levels within the impact zone, as well as dropping fire down the
stairwells and elevator shafts at the building's core, and billowing up to higher
levels. The shocks of impact and detonation loosened the "fire protection"
thermal insulation on steel beams in the impact zone.
The
damaged core columns in the impact zone could no longer hold up all the weight
they were meant to carry. The core columns in the upper block now found it necessary
to partially hang from the hat truss. The hat truss pressed down much more forcefully
on the perimeter columns, transferring the load of the hanging weight. The added
compression of the perimeter columns could only be distributed to the three undamaged
faces, and because of the irregularity of the damage one face assumed a much higher
load than the other two.
The fuel fire
burned up to 1,100 degrees C (2,000 degrees F) for perhaps 10 minutes. It ignited
the many plastic furnishing (carpets, curtains, furniture, equipment cases, clothing,
fixtures, office ceilings and partitions), paper items (paper supplies, books,
pressed wood), and some structural elements (gypsum wall boards, plastic plumbing),
which then continued the fire. The exposed steel beams in the impact zone heated
to between 700 C to 1,000 C. Steel at 700 C has 50 per cent to 70 per cent of
its strength at habitable temperatures; and steel at 1,000 C has between 10 per
cent to 30 per cent.
The floors in the
impact zone sagged because of broken joints to central columns, heat causing their
metal framing to soften, weaken and expand; also because of the weight of debris
fallen from above . The sagging floors twisted their joints to the perimeter columns
(on the three intact faces); the length of column above a floor joint being twisted
inward. For one face of the building, the combined stress of the original weight
above it, the added compression from the hat truss, and the torque from the sagging
floors were too much. Its perimeter beams were bent inward to the point of failure,
and they buckled.
The NIST investigation
was an extremely detailed analysis by 200 engineers and building professionals,
describing the conditions of the buildings from the instant an airplane collided
to the moment a collapse began. The next section of this CounterPunch report carries
the story downward from the point where NIST leaves off. NIST concentrated its
resources on the greatest uncertainty: what initiated the collapse? It was understood
that once an upper block of the building was in motion the structure below would
be unable to counter the dynamic forces, and collapse would proceed to the ground.
Physics Problem Number 1 -- Free Fall
of the WTC Towers
"How could the
WTC towers collapse in only 11 seconds (WTC 1) and 9 seconds (WTC 2), speeds that
approximate that of a ball dropped from a similar height in vacuum (with no air
resistance)?" (NIST FAQ #6)
The
suspicion behind this question is that the Towers were weakened by surreptitious,
controlled demolitions. In this view, the structure below the impact zone (where
airplanes collided, exploded, and fires burned) "should have" provided
resistance to the descent of the block above the impact zone, slowing or even
stopping the collapse.
The NIST response
is that the lower structure was only designed to hold up the weight above any
given floor statically, not dynamically. The force imparted by the collision of
the upper block was beyond the limits of the lower structure to resist. The lower
structure was essentially crumbled by a "hammer" of descending material,
and the mass of this hammer increased during the course of the collapse.
Let's
explore further.
¦ Problem 1,
Force Balance
Once the framing in the
impact zone has failed, the upper block is accelerated by gravity until it crashes
into the lower structure below the impact zone. Labeling the mass of the upper
block m, and its speed v, the block would have a momentum m*v and an energy of
(1/2)*m*v^2. Its weight would be m*g, where g is the constant of gravitational
acceleration (9.81 meters/second^2).
The
balance of forces on the upper block as it impacts the lower structure is presented
here as the impulse momentum form of Newton's 2nd Law:
The
time rate of change of momentum = The sum of the forces,
[m*v(final)
- m*v(initial)]/dt = F - m*g.
Here,
positive direction, velocity and force are taken to be vertically upward; dt is
a label for "delta t", a very brief time interval during which the impact
occurs and the momentum changes from m*v(initial) to m*v(final); and F is the
force of resistance by the lower structure. If A is the net horizontal cross-sectional
area of the load-bearing columns of the lower structure, then F/A is the average
compressive stress across that area.
This
type of force balance is applied to the impact at each floor, sequentially, by
redefining m as the mass above it, v(initial) as the outcome of the alternating
floor impacts and free falls during prior compaction, and v(final) as the outcome
of the latest impact.
We can regroup
the terms of the force balance as follows:
F
= m*g + m*[v(final) - v(initial)]/dt,
F
= m*g*[1 + {v(final) - v(initial)}/(g*dt)],
F/(m*g)
= 1 + {v(final) - v(initial)}/(g*dt).
Before
each building was perturbed, the upper block did not have any motion, v(initial)
= v(final) = 0, and the magnitude of the upward-directed, resisting force of any
part of the structure was equal to the weight of material above it; F/(m*g) =
1.
When an upper block drops through
an impact zone that has lost structural strength, and crashes into the rigid lower
structure, it imparts a dynamic force in addition to its weight. The dynamic force
is the second term in the last expression for F. The total force, F, acts during
the time interval dt during which the momentum of the upper block is reduced (in
magnitude) from m*v(initial) to m*v(final). Clearly, the lower structure will
crumble when F is greater than the maximum force it can support, or when F/A is
greater than the maximum stress it can withstand.
¦
Problem 1, Numerical Example of Progressive Collapse
Free
fall without air resistance from a height H takes time T, given by
T
= square root [(2*H)/g].
At any time
0 < t < T during the free fall, the velocity is given by
v(t)
= -g*t, (negative sign for downward direction),
and
position is given by
h(t) = H - (1/2)*g*t^2.
So, for H = 440 m (=1443 feet) the free
fall time is T = 9.5 s, and the velocity slamming into the ground is -92.9 m/s
= -208 mph.
What actually happened in
the buildings? We consider a suggestive numerical example.
With
the onset of failure, the upper block drops through a space of L = 3 meters, taken
to be the distance between floors. Starting from rest at time t = 0, the block
reaches a velocity of v = -7.7 m/s at t = 0.78 s. The descending block makes contact
with the topmost stationary floor of the lower structure.
We
will assume these floor structures to be dL = 1 meter thick (1 meter = 3.28 feet).
Each floor structure is a framework of steel below and within a layer of concrete.
The floors spanned a distance of between 10 m and 20 m between the outer square
perimeter (63.4 m a side) and the core support along the axis of the building,
which housed elevator shafts, stairwells and support columns, within a rectangular
area of [42 m x 27 m].
Impact is a very
brief process whose duration is dt = 1/100 s. During the impact, energy ripples
through the floor structure as elastic waves in the steel and concrete; the velocity
of these stress waves is V(steel) = 1900 m/s and V(concrete) = 930 m/s; the wave
speed is a property of the material (P-waves). The waves traverse the thickness
of the floor structure in a time dL/V = 5/10,000 s for steel and 1/1000 s for
concrete, so they can bounce between 10 to 20 times across the 1 m thickness;
and they can run along the span of the floor within 0.005 to 0.01 s.
The
waves alert the volume of the floor structure to the imposition of a new load,
and infuse that volume with much higher stress. The floor structure is deflected
downward a distance d = -0.077 meters (3 inches) during impact. In becoming stressed,
the floor structure absorbs some of the energy of the descending block, slowing
it by dv = 0.5 m/s (in this example). Within dt = 1/100 s, the floor structure
has transmitted the force of the new load to its joints with the building's core
and periphery.
Recalling the last form
of the force balance, and inserting the numbers from this example, we find the
magnitude of the total reaction force to be
F/(m*g)
= 1 + dv/(g*dt) = 1 + 0.5/(9.81*0.01) = 6.1,
a
load of six times the weight of the upper block.
I
continued this particular calculation, floor by floor, as a sequence starting
from rest: free fall for 3 m, impact delays transit for 0.01 s and decreases descent
velocity by 0.5 m/s, free fall for 3 m, transit delay and velocity decrement as
before, and so on. The block reaches the ground in 10 s with a total of 87 floor
impacts. The collapse of 344 m (1128 feet) accelerates from -7.2 m/s (-16 mph)
after the initial impact, to -46 m/s (-104 mph) at the ground.
Now,
a little bit more about waves.
¦
Problem 1, Wave Trains and Stress Concentration
Elastic
waves are launched from the collapse front (the leading edge of descending material,
like "weather front") at the moment of first impact. Within 0.01 s,
a stress wave has traveled through the metal framework to five levels below the
collapse front, a distance of 20 m. These lower levels experience a rapid --dare
I say explosive? --increase in the stress within their frames. Bolts and rivets
may be sheared, and joints ruptured by the resulting impulsive forces.
For
example, assume a carbon steel (HR 0.45C) bolt or rivet of 1 inch diameter is
used to support a force of 8,000 kilograms, equivalent to a stress of 22,500 pounds-per-square-inch
(psi). This stress is only one quarter of that material's tensile strength of
90,000 psi; an apparently conservative design. However, an unexpected increase
in load by a factor of five, to a total of 48,000 kg, or 135,000 psi, would probably
rupture the joint.
The stress wave from
the initial impact races down the lower structure, arriving at ground level in
0.18 s (we continue with the numerical example). During that time, the collapse
front has descended another 1.3 m. The stress wave is like a messenger telling
the material it passes to "move down and compress" in response to the
advancing collapse front. On reaching the ground, the wave could transmit some
of its energy past the building's foundation to radiate as a seismic wave through
the earth, and another portion of its energy would reflect back up (the major
effect, especially if the foundation is more rigid than the building it supports).
The message of the upward running wave is "compress even more, dead-end down
below."
Elastic waves launched
by an impulsive load on a structure that remains intact --like a bell being struck
--will ripple back and forth, spreading out the initially concentrated stress
of the strike. If the load is suddenly imposed and then remains constant, as with
a book being dropped on a sturdy table, then the elastic waves die out into a
fairly uniform distribution of stress throughout the volume. If the load is a
short pulse, like striking a bell, then the waves will eventually die out as a
fairly uniform heating of the material.
Just
as there are ripples on wavelets, and wavelets on big rollers across the surface
of the ocean, so will each elastic wave launched by the collapse be a jumble of
waves of different size grouped together. The many individual collisions of material
that make up the global impact of the upper block into a floor structure will
each send off their own ripples, which all build up into a composite for the elastic
wave.
A new elastic wave is launched
with each impact between the collapse front and a stationary floor structure.
As the collapse front accelerates, the time interval between wave launchings decreases.
The building below the collapse front experiences an increasing level of stress
and becomes filled with intersecting wave trains moving up and down by the time
of the second impact at 1.13 s. Elastic waves that pass through each other will
produce a heightened stress where they coincide, just like crossing water waves
that mound noticeably.
This agitated
lacework of stresses ahead of the collapse front will probably cause many fractures
and break many joints prior to the arrival of the front. The sudden shifts in
the volume of rooms and office spaces being compressed and twisted by the elastic
wave trains can easily expel jets of air and dust out of windows, perhaps giving
the impression of smoke from a gun barrel. The collapse front will push a blast
of air down before it and also produce lateral jets of air from the building below
it. These air streams are analogous to the water expelled sideways and into vortexes
alongside a paddle pushing a canoe through still water.
All
these wave effects occur in the upper block as well, from the moment of first
impact. The upper block will quickly fill with elastic waves, which will rupture
internal joints; the block shatters, as is vividly seen in the video recordings
of the WTC collapses. The shorter length of the upper block, and its lack of firm
connection (like a foundation), will contribute to the speed of its disintegration.
In a very real sense the upper block was "blown up," but naturally by
elastic waves rippling a destructive compression through it rather than artificially
by intentional controlled demolition.
Pancaking,
Buckling and Hyping (Red Herring #1)
Two
days after the collapse of the World Trade Center Towers, Zdenek P. Bazant, a
civil engineering professor at Northwestern University, publicized his theory
of the collapse initiation. His conjectures about loosened fire insulation and
heated steel losing strength survived the subsequent scrutiny by NIST. However,
NIST rejected Bazant's proposed mechanism for the initiation of the collapse,
referred to subsequently as the "pancake model" or "pancaking."
Because of its early appearance on the scene, Bazant's model was widely circulated.
Critics of NIST and the "official" story will point to the divergence
of NIST's conclusions from Bazant's, four years earlier, as an indication of ignorance,
confusion --or worse --complicity and cover-up on the part of the "government"
people.
Bazant's pancake model is shown
in Figure 1 of his report . Bazant assumed that interior columns within the impact
zone would weaken from heating, buckle, and then the upper block would fall through
the impact zone onto the lower structure. This impact would cause the columns
in the immediate levels below ("3 to 10 seems likely") to bow, or in
Bazant's words:
"This causes failure
of an underlying multi-floor segment of the tower, in which the failure of the
connections of the floor-carrying trusses to the columns is either accompanied
or quickly followed by buckling of the core columns and overall buckling of the
framed tube, with the buckles probably spanning the height of many floors, and
the upper part possibly getting wedged inside an emptied lower part of the framed
tube."
In other words, the upper
block falls within the perimeter columns onto a lower floor, and that shock pops
the floor joints around the perimeter and at the core for 3 to 10 floors below.
Once in motion, this process would crush all beneath it.
NIST
concludes:
"NIST's findings do
not support the pancake theory of collapse[The] investigation showed conclusively
that the failure of the inwardly bowed perimeter columns initiated collapse and
that the occurrence of this inward bowing required the sagging floors to remain
connected to the columns to pull the columns inwards. Thus, the floors did not
fail progressively to cause a pancaking phenomenon."
For
a shot from the hip two days after the collapse, Bazant did pretty well. But,
after the NIST legion did all the necessary homework, we now have an accurate
result. NIST shows pictures of the inward buckle of the perimeter wall, taken
from a police helicopter. Pancaking versus NIST is a nonexistent technical argument
only to be found in the imagination of some conspiracy-minded people. The technical
community migrated from early hypotheses of the initiation, like pancaking, to
the NIST conclusions as a consequence of doing the hard work required. And, there
was always unanimity on what drove the collapse once it was initiated: excess
dynamic force produced from the gravitational potential energy contained within
even one level spacing. Once the top began to fall, it was going to crush the
building below it, regardless.
The
Absurdity of "Controlled Demolition" (Red Herring #2), by Pierre Sprey
Pierre Sprey is CounterPunch's technical
reviewer of this report. His comments about the controlled demolition hypothesis
are so cogent that I include them here.
Sprey:
There is not the slightest need to postulate
pre-placed explosive charges to explain why the towers collapsed at near free
fall speeds. Let me note a few practical aspects of explosive demolitions that
make the explosive charge hypothesis improbable to the point of absurdity:
1.
Any demolitions expert concocting a plan to hit a tall building with an airplane
and then use pre-placed explosives to UNDETECTABLY ensure the collapse of the
building would never place the explosives 20, 30 and 60 floors below the impact
point. Obviously, he would put the explosives on one or more floors as close as
possible to the planned impact level.
2.
It is inconceivable that our demolitions expert would time his surreptitious explosions
to occur HOURS after the aircraft impact. He couldn't possibly be absolutely certain
that the impact fires would even last an hour. Quite the opposite: to mask the
booster explosions, he'd time them to follow right on the heels of the impact.
3. To ensure collapse of a major building
requires very sizable demolition charges, charges that are large enough to do
a lot more than emit the "puffs of smoke" cited as evidence for the
explosives hypothesis. I've seen both live and filmed explosive building demolitions.
Each explosion is accompanied by a very visible shower of heavy rubble and a dense
cloud of smoke and dust. Just that fact alone makes the explosives hypothesis
untenable; no demolitions expert in the world would be willing to promise his
client that he could bring down a tall building with explosions guaranteed to
be indistinguishable from the effects of an aircraft impact.
My
Conclusions
The WTC towers collapsed
at speeds approaching that of free fall because:
1.
The dynamic force created out of the gravitational potential energy within the
space of just one level spacing was far in excess of the static force the framing
was designed to support, and
2. Elastic
waves launched from the collapse front quickly filled the building --both lower
structure and upper block --with large dynamic stresses, which weakened and ruptured
joints well in advance of that material entering the collapse front.
The
towers shattered, and the pieces fell to the ground.
In
part 2 of this report I address the topic of heat, a prominent feature of many
conspiracy theories about the collapse of the WTC buildings. In part 3 I address
the collapse of WTC 7
Manuel Garcia
a native New Yorker who works as a physicist at the Lawrence Livermore National
Laboratory in California with a PhD Aerospace & Mechanical Engineering, from
Princeton His technical interests are generally in fluid flow and energy, specifically
in gas dynamics and plasma physics; and his working experience includes measurements
on nuclear bomb tests, devising mathematical models of energetic physical effects,
and trying to enlarge a union of weapons scientists. He can be reached at mango
[at] idiom.com
http://www.counterpunch.org/physic11282006.html
CounterPunch Special Report: Debunking
the Myths of 9/11
Alexander Cockburn
here assembles his two prime commentaries in a final, expanded essay, "The
9/11 Conspiracists and the Decline of the Left."
http://www.counterpunch.org/cockburn11282006.html
Manuel Garcia Jr, physicist and engineer,
presents his three separate reports, undertaken for CounterPunch.
Part
One is his report on the Physics of 9/11.
http://www.counterpunch.org/physic11282006.html
Part Two (published here for the first
time) is his report on the Thermodynamics of 9/11.
http://www.counterpunch.org/thermo11282006.html
Part Three, "Dark Fire", is
his report on the collapse of the World Trade Center's Building 7.
http://www.counterpunch.org/darkfire11282006.html
JoAnn Wypijewski wrote her essay "Conversations
at Ground Zero" after a day spent with people at the site on 9/11/2006.
http://www.counterpunch.org/jw11282006.html
http://www.counterpunch.org/physic11282006...
