Hijacker Satam al Suqami's passport, slightly charred, was found in the
World Trade Centre rubble within minutes or hours of the hijackings.  The
contradictory nature of the news reports on its discovery imply an evolving
spin operation.  But the various claimed locations of the passport's
descovery offer a great potential for analysis, and it is fascinating to
consider the passport tale in some detail,  Investigation of factors such as
air resistance and the fireballs' blast wave will enable evaluation of how
thoroughly each 'discovery' claim may be debunked.

The 9-11 commission staff statement reports that "four of the hijackers'
passports have survived in whole or in part".  Two were said to have been
recovered from the UA93 crash site in Pennsylvania, one was from a hijacker
on AA11 (Satam al Suqami) and one (Abdul Aziz al Omari) was found in luggage
that did not make it from the connecting flight Portland to Boston on to
AA11.  ABC News reported the alleged discovery of the Suqami passport on
September 12.  Days later other outlets such as CNN on September 16 and
17 reported that Police Commissioner Bernard Kerik had said on Sunday (the
16th) that a passport belonging to one of the hijackers was discovered a few
days ago by a passer-by, several blocks from the crash site.  The FBI would
not release the name on this mystery passport, leading to speculation that a
second passport had been found at the WTC ruins.  Some reports (e.g. the
Guardian) claimed that it belonged to Mohamed Atta, the infamous ringleader.

Other reports had it that a passport was found "in the vicinity of Vesey
Street", or rescue workers sifting through the tons of rubble found a
passport belonging to one of the suspected hijackers a few blocks from where
the twin towers once stood (BBC).  The 9-11 commission report claims that
Suqami's Saudi passport was picked up by a passer-by and given to a NYPD
detective shortly before the WTC towers collapsed.  This concurs with the
CBS News report of Suqami's passport's discovery on the ground minutes after
his plane Flight 11 hit the North Tower.

So we have "in the vicinity of Vesey Street", "several blocks" from the
crash site, "a few blocks" from the crash site.  The problem is, these are
either in the wrong direction, or are the wrong distance.  The Vesey Street
or front of 7WTC claims have the passport travelling in exactly the wrong
direction, and it seems whoever made this up forgot which flight Suqami was
supposed to be on.  AA Flight 11's impact with the northeast facade was
almost dead centre, and the building's core absorbed much of the aircraft.
Some of the densest parts from AA Flights 11 and 175, such as landing gear
and an engine, passed right through the Towers and were found several blocks
away from the crash site.  The vast majority of the debris remained in the
Towers, and there were no other reports of parts bouncing back.

Let's suppose that the passport became separated from Suqami's clothes or
baggage, managed to avoid incineration in the fireball, managed to avoid the
columns, stairways, elevators and escalators in the core of 1WTC, and
continued in a SSW direction.  1WTC had 110 storeys above ground, its height
was 1368 feet, and the impact area was between floors 94 to 99.  Thus, the
altitude of impact was approximately (96 / 110) * 1368 = 1194 feet.  For an
extremely dense object, the effects of air resistance would be negligible.
There would be very little loss of horizontal momentum, and the time to hit
the ground would be given by t = sqr(2 * height / g) where g is 32.17 feet
per second squared, the gravitational acceleration.  So t = 8.616 seconds,
and if we assume the Government claimed impact speed for Flight 11 of 494
mph, that is 724.5 fps.  (We over-estimate the speed as this helps the case
for finding the passport several blocks away.  The consensus now puts Flight
11's impact speed at 470 mph.  An MIT analysis made it 429 mph.)  So
airborne horizontal distance travelled would be 8.616 * 724.5 = 6242 feet or
1.18 miles.  In fact, the dense engine and landing gear parts did not
continue beyond 1500 feet, but more on that below.

The writer conducted an experiment to determine the drag coefficient of a
passport, or more precisely, the product of drag coefficient and effective
frontal cross-sectional area.  A typical passport weighs some 50 gm, and has
dimensions of 6" x 4" x 1/5".  So a mock "passport" was constructed,
comprised of pages cut from a magazine and sandwiched between two pieces of
cardboard, with the whole taped together.  With the pieces cut to 6" by 4",
a number of pages were inserted to yield the required weight, and the
resulting contraption was found to have a width close to the required 1/5 of
an inch.

This apparatus was then taken to a bridge known to be 250 feet above water
level, dropped over the side and its descent timed.  If air resistance were
negligible, the freefall time to drop 250 feet would be a little under 4
seconds.  The observed descent time was 6 seconds.  A program was then
written to simulate the vertical and horizontal motion of a falling object.

The program recalculates vertical and horizontal forces acting upon the
object, and its accelerations and velocities, in 10 uS increments of
simulated time.  (It was found that a move from 100 to 10 uS intervals of
simulated time merely raised the predicted horizontal distance travelled by
a factor of some 1 in 7000.  Computations in simulated time increments of
10 uS will provide an acceptable accuracy for our purposes.)  The drag
forces are calculated from d = Cd * A * r * 0.5 * v ^ 2 where r is the
density of air.  Each iteration recalculates r to allow for variation with
altitude.  Eight variables are inputted: initial altitude, initial object
horizontal speed and bearing, mass of moving object, area of frontal
cross-section, drag coefficient, wind speed and bearing.  (Variables were
processed in metric, but on personal preferences most were inputted as
imperial and converted back to imperial for display or export to
spreadsheet.  Initial vertical velocity is taken to be zero.)

With rotation alternately presenting the 6" x 4" and the 1/5" x 4" sides,
the average frontal cross-sectional area is (2 / pi) * (6 + 1/5) * 4 square
inches (2 / pi being the average absolute value of the sine function).  A
rotation combining the 6" x 4" and 6" x 1/5" sides yields an average
cross-section of (2 / pi) * (4 + 1/5) * 6 square inches.  A rotation
alternating frontal cross-section between the two smallest sides yields
(2 / pi) * (6 + 4) * 1/5 square inches.  Converting to SI units, the average
of these three is some 0.00712 square metres.  If we include another three
possibilities of rotation or non-rotation that maintain a particular side as
front-facing for a significant portion of the travel, the average frontal
area reduces to 0.00636 square metres.  The mass of the object is taken to
be 50 grams.  It was said that Suqami's passport had been "doctored",
presumably with pages removed to cover his tracks, which would tend to lower
the mass and hence distance travelled.

Running the program with an assumed frontal cross-section of 0.007 square
metres, it was found that the drag coefficient had to be set to 0.475 in
order to yield the observed 250 feet descent time of 6 seconds.  A typical
drag coefficient for a flat plate is 4 / pi = 1.273.  For a lightweight
spinning passport, one would expect something less than 4 / pi to allow for
the part of the rotation cycle where the face is presented at an angle such
that most air molecules are deflected sideways.  Anyway, the product of Cd
and A is what matters, and we will use Cd = 0.475 and A = 0.007 m ^ 2, with
the object mass at 0.05 kg.

As above, we assume 1194 feet is the altitude of AA Flight 11 on impact with
1WTC, and we will take the impact velocity to be the Government's claimed
494 mph.  The original program computed in 2-d with no allowance for wind
speed, bearing, and object bearing.  Calculating in 10 uS increments of
simulated time, the total horizontal distance travelled by the passport
before hitting the ground was computed to be 445.9 feet, with a final
horizontal velocity of 2.286 mph, a terminal vertical velocity of 34.73 mph,
and descent time of 24.35 seconds.  Thus, with 1WTC taken as 208 feet
square, the passport would have travelled some 238 feet beyond the southwest
facade of the North Tower, assuming it avoided incineration, furniture,
multiple obstacles in the core, remaining walls and windows, etc.  This
would have placed it on top of, or close to, 3WTC - i.e. short of Liberty
Street and well short of "several blocks" or "a few blocks" away.

The WTC Liberty St - West St - Vesey St - Church St trapezoid block is some
900 feet across, at least.  From Flight 11's initial impact point on the
northeast facade of the former 1WTC to Albany St - two parallel streets
south of Liberty St - is also at least 900 feet.  Rector St is four parallel
streets south of Liberty St at a distance of nearly 1500 feet from the
initial impact point of Flight AA11.  Landing gear was found at the corner
of West St / Rector St, according to Civil Engineering Magazine and the FEMA
report.  An engine and landing gear from Flight 175 was found several blocks
in the opposite direction.

As noted above, a very dense object at 494 mph would have travelled for 1.18
miles horizontally before hitting the ground.  Landing gear from Flight 11
only got as far as Rector Street which is some 1300 feet from the southwest
facade of 1WTC.  Although landing gear would still undergo some deceleration
due to air resistance, it is typically some 5% of the aircraft total mass,
and the effect of air resistance on a passport is very much greater.  At 494
mph the drag force acting on the passport is around 100 newtons, leading to
an initial horizontal deceleration of some 2000 metres per second squared.

So what horizontal velocity would propel a dense object for 1300 feet given
an initial altitude of 1194 feet?  From t = sqr(2 * h / g) we have t = 8.616
seconds of descent time.  1300 feet / 8.616 seconds = 150.89 fps = 102.88
mph.  So this suggests that the resistance of passing through 1WTC slowed
the densest debris to some 103 mph before exiting the southwest facade.
Admittedly, the landing gear would undergo some deceleration due to drag and
so the exit speed would have been a little greater than 103 mph.  The
lighter passport should have decelerated more than the heavier pieces after
fragmentation and separation; however, let's be generous and assume that the
passport exited the southwest facade at a horizontal velocity of 150 mph,
and did not lose any altitude whilst passing through 1WTC.  Computations
indicate that its horizontal travel before hitting the ground would be 347.5
feet.  So 208 plus 347.5 equals 555.5 feet beyond the impact point on the
northeast facade.  This is 109.6 feet further than the 445.9 feet if the
passport is assumed to detach itself from everything else at the initial
impact, starting at 494 mph at the northeast facade.  So far, it has not
quite cleared the Marriott Hotel roof and is still short of Liberty Street,
so is clearly not "blocks away".

According to most accounts, the wind at the time of the Flight 11 impact was
northwesterly, with a speed of some 10 to 20 mph.  This speed may be an
overestimate; the mean September windspeed for New York is 8 mph averaged
over 18 years.  Most images of the burning Towers are taken from the
northeast showing the plume drifting leftwards, i.e. blowing to the
southeast.  Southeast was the direction quoted on a Newsday report based on
high resolution satellite photos that it had obtained.  Essentially this
crosswind would have blown debris across the WTC site rather than add or
subtract greatly to the horizontal travel along the original trajectory.
Let's assume the wind blows debris southeast along a bearing of 135 degrees,
and the speed is 15 mph or 22 fps.  With the time for the passport to hit
the ground at 24.35 seconds, the maximum correction needed for a very light
object with the wind exactly in line would be 24.35 secs * 22 fps = 535.7
feet.

(A weather station at Central Park, New York, reported 9.2 mph and WNW at
8:51 a.m. on 9/11, which is less favourable to the "found a few blocks away"
story than the above NW 15 mph.  However, at higher altitudes, windspeed
was probably higher and may have veered a few degrees to the north.)

The WTC site maps are orientated with north offset some 30 degrees from the
vertical.  (One paper on the Internet suggests 40, but a check on a number
of street maps indicated that this is too high and Liberty Street and the
Liberty St-facing facades of the former Twin Towers are 30 degrees off an
east-west line.  An assumption of 40 degrees would hinder the case for the
passport travelling several blocks, since the wind is then blowing along a
bearing of 135 - 40 = 95 on the site maps, i.e, almost sideways.
Consequently, the force would do very little to extend the passport's travel
beyond Liberty St but would greatly increase the chance of a collision with
the South Tower.)

If we imagine the Flight 11 debris going straight through the middle of
1WTC and straight down on the site plans, this is a bearing of about 210
degrees.  In fact, landing gear found at the West St / Rector St junction
suggests we should take about 10 degrees off this bearing.  Let's suppose
the debris is initially on a bearing of 200 degrees which is close to SSW,
and the wind blows the smoke plume on a bearing SE or 135 degrees.
Along the debris trajectory the strength of the wind becomes
cos (200 - 135 degrees) * 22 fps = 0.4226 * 22 fps = 9.298 fps.  The
maximum 535.7 feet of extra travel in 24.35 seconds if the wind direction
were perfectly behind the original trajectory becomes 226.4 feet.  Add this
to the 555.5 feet beyond the NE facade of 1WTC travelled by a passport
exiting the SW facade at 150 mph and we have 781.9 feet.  This would almost
take us to Cedar St one block away, provided the passport misses St Nicholas
Greek Orthodox Church.  But the wind is mainly blowing the passport across
the WTC site towards Church St.  There is a much bigger obstacle in its
path...

An object exiting the centre of the 1WTC SW facade along a line straight
down on the WTC site plan would travel for some 340 feet before it is level
with the far side - the SW facade - of 2WTC.  At this point the corner is
about 115 feet away.  Thus, in order to avoid hitting 2WTC, the object's
total motion along a bearing of 120 degrees - or to the right on the site
maps - cannot exceed 115 feet until its bearing 210 or "vertical" motion
exceeds 340 feet.  We initially presume that the original bearing of the
debris is not straight down at 210 degrees but is 200 degrees (from location
of landing gear assuming the wind had little effect on this; we shall also
examine the results for other trajectories.)

The later revision of the falling object simulator computes in 3-d with
object and wind horizontal vectors resolved into two axes.  For ease of
determining whether an object can avoid hitting 2WTC, it is useful to align
the inputted object and wind bearings with the WTC site plans,  Thus, the
direction "straight down" on the site plans is really a bearing of 210
degrees but is inputted as 180; and the wind bearing of 135 SE is inputted
as 105.  We take the WTC site plan vertical axis as the z-axis and the
horizontal axis as the x-axis.

The computations showed that after 340 feet of travel along the z-axis, the
travel along the perpendicular x-axis - partly as a result of the wind and
partly on account of its original bearing being offset 10 degrees from the
z-axis - would have been 326 feet.  It cannot get this far, because 2WTC is
in the way.  After only travelling 207 feet along the z-axis the passport
has moved 115 feet along the x-axis, and so at this point it has hit the NW
facade of 2WTC, at an altitude of 1076 feet.  Hence, for an initial object
bearing of 200 degrees and a 15 mph wind, the passport does not escape the
WTC block, and is in the vicinity of Liberty St not Vesey St.

Let's suppose the initial bearing was 210 degrees, straight down on the site
plans, and the landing gear deviated from this by 10 degrees because it was
blown by the wind.  (It is rather implausible, but this gives the passport a
better chance of avoiding 2WTC.)  Now the object just hits the corner of
2WTC.  Its x-coordinate hits 115 feet at z = -337 feet, just short of 340
feet, at an altitude of 708 feet.  Let's give it the benefit of the doubt
and pretend it just misses; it's only a matter of 3 feet which is well
beyond the accuracy of our maps and estimates.  The final position at
y = 0 (zero altitude) is x = 353 feet, z = -484 feet.  The opposite side of
Liberty St corresponds to around z = -485, and x = +353 places the passport
in front of the Bankers Trust Building.  So the passport has made more
progress in this case but is still not "blocks away" or nearest to Vesey St.

Let's suppose the passport exited 1WTC on a bearing of 220 degrees, and the
windspeed was 20 mph.  Now the passport eludes 2WTC by about 25 feet,
passing through the coordinates x = +90, z = -340.  The final z-coordinate,
if no obstacles were in the path, is computed as -528 which is some 43 feet
beyond the far side of Liberty St.  However, the 565 feet tall Bankers Trust
Building is in the way (even if it were only 1 inch tall the final
x-coordinate is +439 feet which still corresponds to the BTB "roof").  The
passport hits the front of the BTB at x = +343, y (altitude) = +196, z =
-485, and so ends up about 10 feet short of its position in the previous
paragraph.

We find that there is no realistic prospect of the passport being able to
clear the next block's buildings and flutter down into the streets beyond to
be discovered by a lucky passer-by.  With a light wind, it cannot clear
Liberty St.  With a strong wind, the passport is liable to hit 2WTC unless
it exits 1WTC at a bearing 20 degrees or more off the landing gear direction
of travel.  If the wind suddenly veered to a bearing of 200 or so at the
time of Flight 11's impact - and there is no evidence of this - one might
expect that its strength would be curtailed on the leeward side of 1WTC even
with a few holes in the wall.  At best, the passport might avoid hitting a
building facade, and might travel a few feet down a side street if the
conditions were right.  But these unlikely conditions presuppose a number of
further unlikely conditions.

Then there is the possibility of the passport hitching a ride during flight
along with other debris.  Ideally, it would have to become separated from
Suqami's clothes, or the cargo hold and Suqami's suitcase breaks up; then
the passport flies out and then firmly attaches itself to the landing gear,
and a bystander happens to spot it in Rector St.  But this is untenable.  A
more plausible scenario would have the cargo hold containing Suqami's
suitcases breaking apart on initial impact, but the suitcase containing the
passport remaining intact, and managing to avoid columns, etc, and exiting
1WTC at 150 mph.  Let's suppose the suitcase plus contents weighs in at 30
pounds (we assume Suqami was not told he was on a suicide mission), and is a
"flight bag" style, not too large at 8" x 12" x 18".  For average frontal
cross-section, we take the average of (8 + 12) * 18, (8 + 18) * 12, and
(12 + 18) * 8, and multiply by 2 / pi; this obtains some 194 square inches
or 0.125 square metres.

Suppose this suitcase exits 1WTC at 1194 feet altitude on a bearing of 170
with a 15 mph wind bearing 135.  The program predicts a landing point of x =
+373, z = -1300 feet in the vicinity of Rector St which is a few blocks
away.  But over a range of weights and sizes, the chance of the suitcase
landing in a street rather than on a building roof is little better than
10%.  If the weight was only 15 pounds and the cross-section doubled to
0.25 m^2, the final coordinates disregarding buildings of (+477, -820) point
to a landing in Albany Street (a couple of blocks from WTC).  But the
Bankers Trust Building is in the way and the suitcase lands on the roof.
Although at a stretch we can place the passport where it was allegedly
found, this scenario can be discounted.  If Suqami the suicide hijacker was
not a fictional concoction and his suitcase complete with contents had been
found at the site of the passport find, news reports would have been
plastered with tales of Suqami's Koran, Arabic flight manuals, will,
terrorist training manuals, credit card links to flight bookings and car
rentals, etc, and the FBI would be carrying photos of the items on its
website.  The reports only mention discovery of a passport and nothing else.

Let us consider the possibility of the passport being blasted backwards by
the expanding jet fuel fireball, so as to be found in the vicinity of Vesey
St.  As above, this still retains the bizarre scenario that Suqami's
passport, the whole passport, and nothing but the passport landed in Vesey
St.  Taking the operational empty weight of a Boeing 767-200ER at a little
over 80,000 kg (we don't count the fuel), and assuming 81 passengers and
their baggage are 100 kg apiece, the Flight 11 debris is around 90,000 kg.
Let's suppose its mean density is just a little less than the density of
aluminium, then 90,000 / 2400 = 37.5 m^3 = 2,288,377 ins^3.  Any of five
hijacker passports could have been found per aircraft.  The five passports
are 24 cubic inches, so 24 / 2,288,377 = 1 / 95,349.  This is greater than
the probability of a hijacker's passport being found neatly preselected and
unaccompanied by any other Flight 11 debris, after allowing for other
values of the preselected proportion.

But that presupposes that the passport-containing suitcase was in the stern
cargo compartment, the cargo compartment and suitcase broke up on impact
with the NE facade perimeter columns, the hydrocarbon explosion as the jet
fuel spilled across 1WTC reversed the passport's direction of travel
(without doing likewise to another 90,000 kg of debris,  The hijackers were
reportedly either in the cockpit or controlling the first or business class
area; they were not particularly concerned with the passengers and crew who
had been moved to the rear of the plane and were free to make cell phone
calls.  The forward cargo compartment or Suqami's pockets or carry on
baggage would have been the wrong side of the wing and centre fuel tanks for
the passport to be propelled towards Vesey St.

High order explosives such as TNT produce a supersonic shock wave on
detonation, with very high overpressures at short range.  The pressure load
from a typical hydrocarbon deflagration is of longer duration but still only
around 50mS.  According to the FEMA report (Chapter Two) and Civil
Engineering Magazine, May 2002, the fireballs of Flights 11 and 175 expanded
to their maximum diameters in about two seconds, and the resulting
overpressures were less than one pound per square inch.  The blast would
result in extensive local window breakage, but no significant structural
damage.  If we take the maximum diameter for each of the three fireballs to
be 300 feet, then a radius of 150 feet in 2 seconds is only 75 fps and well
in the subsonic region.

Let's consider the effect on Suqami's passport, should it manage to separate
from its surroundings to be hit by the jet fuel explosion.  Suppose the
overpressure is 1 psi for a duration of 100 mS.  We previously calculated
the average frontal cross-section of the passport at some 0.007 m^2 which is
10.85 square inches.  Thus, the force acting on the passport is 10.85 lbf or
48.26 newtons.  We'll suppose the plane initially impacts at 350 mph,
decelerates to 300 mph after entering the perimeter columns, then debris
decelerates to 200 mph after passing through the core, then decelerates to
150 mph on exiting the far perimeter columns.  If the explosion blast occurs
after the stern cargo hold and contents has already broken up, and the
passport had separated and just slowed to 300 mph, then a force of 48.26 N
on 50 gms produces 48.26 / 0.05 = 965.2 m/s^2 acceleration.  After 0.1
seconds the change in velocity is 0.1 * 965.2 m/s = 96.52 m/s = 216 mph.  So
velocity = 300 - 216 mph = 84 mph in the original forward direction,
provided the blast vector is 180 degrees off the original velocity vector.
And following the positive phase, the negative phase tends to suck debris
back towards the centre of the explosion.  Hence, the claim of Vesey St for
the passport find is unacceptable, unless we propose a conspiracy theory
which holds that Flight 11 was pre-fitted with high explosives.
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