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From: bruce maccabee <brumac@compuserve.com>
Date: Thu, 13 Nov 1997 21:44:29 -0500
Fwd Date: Fri, 14 Nov 1997 10:23:07 -0500
Subject: Comments on Mexico City Video of 08-06-97 - 2/2

[Part 2]

1b.  The model must be some distance from the camera for the
image to be in focus at full zoom (don't know this minimum focal
distance). This places minimum size requirements on the field of
view of the camera as compared to the location of the camera.
That is, if this were videotaped in a room looking out through a
window, the window must be big enough so that it does not appear
in the video even when unzoomed.

1c. If a 3 dimensonal model it cannot be reflected in glass. One
might imagine a small model, illuminated in some way so as to
make a visible reflection in a glass window.  Looking through the
window the camera would "see" the background objects (buildings,
sky) and a reflection of the model. If videoed with a hand-held
camera the whole picture, background and model reflection, would
jiggle together, as would happen with a real object at a great
distance. The ufo model could be rotating and wobbling. By moving
the model appropriately one could make it appear to move.
However, it would be "difficult" to give it an "instantaneous"
acceleration followed by a constant velocity.  It could not
simply be a small model rotating at the end of a string. It could
be mounted on a rigid rod with appropriate rotation and wobble
dynamics created by a mechanism. However, if the model is bright
enough to have its reflection visible against the bright sky it
would not seem to disappear behind the distant buildings. It's
image would appear to be "in front of" the buildings. And last
but certainly not least, the image of the reflection of a model
in a window cannot be less bright than the background since
background light coming through the window would add to the
reflected light from the model. The fact that the UFO image is
darker than the sky means this is not a simple "reflection on
glass" hoax.

1d.  Similar problems arise if one imagines reflecting the
background on glass with a lighted model farther away than the
glass. In this case one could make the model seem to move behind
the building. Simply place a black paper cutout on the back side
of the glass where the building image appears. Now when the model
moves behind the building image the light from the model will not
get through.  However, when the model is silhouetted against the
sky there will be no portion of the model image that is darker
than the sky.

1e.  A "masked reflection" would also be "difficult".  In this
case a cutout with the shape and size of the reflection of the
model is placed beyond the glass to block background light from
coming through the glass where the image of the model appears.
Motion of the model would have to be accompanied by similar,
perfectly registered, motion of the cutout.

1f.  One big question is how to make a model UFO that is brighter
than the dark building appear to move behind a building? Imagine
being in the room where the video was taken, looking out through
the window. One sees all the nearby and distant buildings. Then
create a flat dark model cutout of the nearby buildings and set
it up some distance, like several feet, from the window. The 2-D
model building is therefore closer to the camera than the window
and the camera is many feet from the window. However, the camera
must be far enough away from the model building so that when
videoed with full zoom the edges are still in good focus. (This
sets size requirements on the room and window. See below.) Now
take a small 3-D UFO model suspended in some way. Have it
illuminated and painted or colored in such a way as to be
somewhat darker than the sky brightness. Naturally this model
must have black spots on its rim and must be rotating and
wobbling in a steady manner. This, and the onset of motion
acceleration) would require a support which is reasonably rigid.
Perhaps a mechanism inside the model would create the rotation
and wobble (wobble about 3 times as fast  as the rotation) and
another mechanism on the floor would drive the horizontal and
vertical components of motion of the support once the "UFO"
starts to move. In this case the model UFO could move behind the
model buildings in a convincing manner. This method would require
some effort at model building, including construction of a
mechanized model UFO and support system, alignment of the model
buildings with the real buildings as seen through the window (I
assume there really are buildings at the locations indicated in
the video!), and, finally,  careful videography with appropriate
lighting (not easy!) using a handheld camera.  It might also be
necessary to shoot the scene from a room with a large window and
to use a special lens on the camera so that the unzoomed view
does not show the edges of the window.

As mentioned above, the distance from the camera to the (flat)
model buildings must be large enough so that the edges are in
good focus. This sets a minimum size requirement on the room that
depends upon the zoom magnification. A reasonable guess is that
to have the distant buildings in good focus and the presumed
nearby model buildings also in good focus would require a
distance from the camera to the models of 20-50 ft. this
requirement, in turn, sets a size requirement on the window. It
must be large enough so that the window edges do not appear in
the picture at the beginning when unzoomed.

1g.  An even more expensive and time consuming way is to "bring
the whole scene into the studio." That is, create  a model of the
whole scene as viewed from the window under hazy conditions. This
would be extremely complicated and sophisticated. A model of the
scene could involve models of the nearby buildings and, as a
background for the distant buildings, a large photograph of the
real scene, like a "diorama." A UFO model would then be supported
in some invisible way at a distance from the camera that is
greater than the distance from the model buildings and then of
course, it would be "easy" to make it move behind the model
buildings.

The UFO model would have to be supported in a manner such as
described in 1f above in order to make it move, rotate and wobble
without introducing a swinging motion characteristic of a model
suspended on a string. If the model were supported by a
transparent rod, for example, a mechanism could be devised to
make the model rotate and wobble as seen. A lightweight model on
a rigid rod would accelerate quickly with little wobble or
vibration. This might also necessitate some special optics
(lenses) for the camera to make the zoom compatible with the
likely short distance (5 - 20 feet from the camera to the
diorama). An actual haze effect could be synthesized by using as
a background a large photo taken on a clear day and then blowing
water vapor or fog into the model scene to create the reduction
of contrast inherent with haze.

However, to make this convincing several model buildings at
different distances would be created within the diorama.  But
this would require sophisticated model building, a mechanical
operating system for the model and its motion, considerable time
and considerable expense.

So far, the bottom line on the hoax possibility using a model is
that it probably could be done, but would require a considerable
effort and expense.

2a.  How about the possibility of an electronic construction?  In
this case one imagines a video of the background scene with the
UFO image added in electronically.  Because the image jiggles
right along with the images of the buildings, this hand-held
jiggle must be somehow deduced by the software frame by frame and
then added to the frame-by-frame location of the UFO image.

2b  Alternatively one might imagine that the scene was shot with
a tripod mounted camera showing the more of the scene than
actually appears in the video. This sampling of the scene was at
high resolution (many pixels). The scene was a single, stationary
frame. This single large frame was copied many times (about 700).
Then the UFO image was added frame-by-frame. About 700 frames
were created which show the UFO image first stationary and then
moving frame by frame to the right and upward at a constant
speed.  On a frame by frame basis the UFO image was partially
"erased" in a ste-by-step manner as it "moved behind" the image
of the first building, and then it was "created" as it seemed to
appear from behind the building.  After the series of frames with
the UFO had been created, then the dynamics of the camera
vibration and panning were simulated. One can imagine this was
done by making a frame-by-frame mapping of the first (700) frames
onto a second series of about 700 frames.  Each of the second
series of frames was a subset of the first, i.e., a smaller frame
size (fewer pixels). Initially in the unzoomed section the new
frames were about the same size as the orignal frames.  However,
the zoom was creased by using "pixel magnification" and this
justifies using high pixel resolution in the first set of frames.
The center of each new frame is a "semi-random"  location
relative to the center of the original frame in such a way that
the centers of the new frames wander about the original frame
center to synthesize camera vibration. Once the UFO image starts
to move in the original frames, the mean center point of the
second series of frames also begins to move in a "random walk"
manner characteristic of a hand-held panning camera. One can
imagine that by using a method such as just outlined the video
wwas constructed. Naturally this would require very sophisticated
computer based image construction...Hollywood level, probably.

COMMENT ON HOAX HYPOTHESIS:  there may be other techniques not
mentioned above. However, it would seem that if this was a hoax
then it was extremely well done. Of course, no method except the
full scale UFO hoax with a real object thousands of feet from the
camera would create bonafide witnesses. Hence if there are
witnesses and it can be proven that they have no relationship to
the video, then this can be labelled a real event! The video
might be able to stand on its own even in the absence of
witnesses. However, it is difficult to imagine something as
obvious as a 25-50 ft UFO flying close to  city buildings would
be noticed by only the videographer.

RELATION BETWEEN ROTATION AND WOBBLE:

The continuous dynamic motion of the UFO is intriguing. If a hoax
the constancy of the motion implies some motor driven mechanism
that keeps the rotation and wobbling steady.

However, if not a hoax....

Assume the UFO can be modelled as a rotating solid disc of some mass m. The average or mean axis of rotation is assumed to be (nearly) vertical. However the instantaneous axis (the spin axis at any particular instant) does not appear to be vertical. If you imagine the spin axis as a line, this line appears to make an angle with the (assumed) vertical mean axis. This angle may be (seems to be) constant. As time goes on this line sweeps out - or lies "on" - a cone shaped surface in space, with the apex of the cone at the center of the disc. (Note: The earth has a "wobble" or precession such that the instantaneous spin axis of the earth rotates about the average spin axis every 26,000 years (about).)

If the wobble is actually a uniform precession of the spin axis,
as with a gyroscope or any spinning body, then there must be a
torque (twisting force) acting on the disc in a direction always
perpendicular to the spin axis (if not perpendicular, the torque
would change the spin rate as well as the precession rate). There
is a "simple" (nothing is simple!) approximate relation between
the torque, the precession rate and the spin angular momentum: T
= PM, where P is the angular rate of precession (in radians per
second; 2 pi radians = 360 degrees), T is the applied torque and
M is the angular memomentum about the spin axis. For a uniformly
thick disc of mass m, M = (1/2)msr^2  where s is the spin rate
(in radians per second) and r is the radius. In this case s is
about 1 rad/sec and P is approximately 3 rad/sec. Unfortunately
there is no way of knowing what the effective mass of the UFO
might be. Nor is there any indication of what the torque might
be. If we knew either or these we could calculate the other and,
perhaps, learn something interesting. This torque might be a
result of a huge magnetic field associated with the UFO being
acted upon by the magnetic field of the earth, although
considering that the spin axis is nearly vertical it would seem
that only the vertical component of the earth's field would be
involved. It might also be a torque applied by the UFO to itself
in some way to maintain the orientation of the UFO relative to
the local earth surface as the earth spins.


TO BE REVISED AS INFORMATION BECOMES AVAILABLE