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November
28, 2006
We See Conspiracies That Don't Exist
The
Physics of 9/11
By MANUEL GARCIA, Jr.
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
Americans the 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. 1295-1349)
(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@idiom.com
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."
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.
Part Two (published here for
the first time) is his report on the Thermodynamics
of 9/11.
Part Three, "Dark
Fire", is his report on the collapse of the World Trade
Center's Building 7.
JoAnn Wypijewski wrote her essay "Conversations
at Ground Zero" after a day spent with people at the
site on 9/11/2006.
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This characterization of the populace' ignorance can cut both ways.
Ignorance of physics can help to explain why people so readily accept
the official story that they Towers "collapsed" in spite of the
obvious reality that they exploded.
EXERCISE: Find Garcia's "hammer"
Figure 1 from Bazant's report shows essentially the same scenario
that NIST ultimately adopted.