ACCELERATION
Bruce S. Maccabee, Ph.D.
ABSTRACT
Visual and photographic sightings of UFOs carrying out
"impossible" high speed maneuvers are presented for study. For the
first time we are able to quantify the amazing acceleration of these craft.
PROLOGUE
Herbert C., Army private, was stationed at
ACCELERATION
Lillian Sargent, housewife, was standing in the back
yard of her Greenfield, Mass. home in June or July of 1947 (exact date unknown).
She was about half a mile west of a steeply rising small mountain that forms
the eastern border of
ACCELERATION
It was hot in the summer of 1956, but during one night
no place was hotter than the Air Force bases at Bentwaters and Lakenheath in
ACCELERATION
During the night of November 16-17, a 747 jumbo jet
freighter was flying southwestward over
ACCELERATION
It was about 1:15 a.m. on May 1, 1988 and Ed Walters,
standing on the shore of the Santa Rosa Sound with his special stereo
"SRS" camera, was about to take a second stereo picture of a UFO
which he had just photographed hovering over the water. As he sighted through
the viewfinder he was surprised to find that it wasn't there any more. He took
his eye away from the viewfinder to look for it and realized it was over his
head. Suddenly everything went white...an abduction had begun. 5
Subsequent analysis of the stereo pair of photographs
showed that the object was about 450' away when he first saw it. Seconds later
it was stationary over his head.
(need
I say it again...?)
INTRODUCTION
What are these things that come...and go...in the
night....and in the day...so rapidly that we have a hard time seeing them?
The Shadow Knows........but he's not telling, so we'll
have to figure it out by ourselves.
Aside from shape and speed, the most unusual...and
unbelievable...UFO characteristics which have been often reported are the
"right angle" turns and the sudden disappearances of apparently solid
objects in the clear sky. Of course, the witnesses who make these reports are
not perfect observers. Perhaps the turns were not perfectly abrupt, they
only appeared to be. Perhaps the objects did not disappear in the sense of
material objects vanishing without a trace, perhaps they only appeared to
vanish. Physics and technology, as we know it, indicates that it is
physically impossible for substantial objects to make instantaneous turns or
disappear while in plain view. For this reason, conventional scientists have
"solved" the problem posed by these observations by rejecting the UFO
reports altogether. Ufologists have accepted the reports, perhaps reluctantly,
while making excuses for these seemingly impossible feats of the UFOs.
Nevertheless, these reports are made by credible people.
Many years ago (1947) Lillian Sargent, my grandmother, reported to her family
that she saw two round, silvery "flying saucers," each of which made
(what appeared to her to be) a right angle turn. The saucers were at a
reasonably high elevation angle as they moved westward and then abruptly turned
north, so she was in a good position to see the turn. Now, grandma was not an
aerodynamics expert or even a mechanic, but she knew that something was not
right here: "things" do not make right angle turns. Turns are curved.
Nevertheless, she stuck to her story. Hence, we are left with the quandary of
believing a grandmother's report while doubting the "right angle
turn." (If you can't believe your grandmother, who can you believe?
Rhetorical question, only.) (Footnote: this was at a time when many people were
reporting sightings throughout the
Disappearances in the clear sky are equally enigmatic
and have been reported since 1947. The first official reference to the ability
of UFOs to travel at high speed, and even to disappear, is in the draft of an
intelligence collection memorandum written for Brigadier General Schulgen by
Lt. Col. Garrett in October, 1947. (This memorandum, which was released to the
public by the Air Force in 1985, was written in response to General Nathan
Twining's letter of September 23, 1947, which said that flying saucers are
"real and not visionary or fictitious" and outlined reasons for
collecting intelligence information about flying saucers.) Lt. Col. Garrett
based his statements on sightings, not by housewives, but by "many
competent observers including USAF rated officers" and listed a number of
"commonly reported features that are very significant." This list
includes "the ability to suddenly appear without warning as if from an
extremely high altitude" and "the ability to quickly disappear
by high speed or by complete disintegration." (emphasis added) Sudden
appearance and disappearance could be two aspects of the same capability:
extremely high acceleration or deceleration. (Note: the suggestion that a
flying saucer could disappear by "complete disintegration" indicates
just how puzzled the top Air Force officers were by the sighting reports. For
the purposes of this paper, I assume that visual "disintegration,"
suggesting at the very least the termination of the of the light reflecting or
light blocking (opaque) characteristics of a solid, stationary object, does not
occur. Of course, I could be wrong!)
A high quality report of a disappearance event was made
to Dr. James McDonald6 and later to the American Society of
Newspaper Editors 7 in 1967 by William Powell, a general aviation
pilot, and his traveling companion, Muriel McClave. According to Mr. Powell,
they were flying northward at about 4,500' near Willow Grove, Pennsylvania, on
May 21, 1966 at 3:15 p.m. when they saw an unidentifiable object following some
jets that had just taken off to the north from the Naval Air Station at Willow
Grove. Powell at first thought it was an aircraft, and then realized that he
could see no vertical tail fin. "I couldn't determine any tail on this
object. And the more I kept peering at it, I sort of whimsically thought it was
a flying saucer," he told the newspaper editors. "Hey Mick (Muriel),
look at that flying saucer out there," he said and she immediately looked
and saw it. Then they saw it make what appeared to them to be an abrupt, flat
(no banking, no slewing) right turn of about 160° and head toward their plane.
As it approached from the left side of the aircraft, the angular size increased
and Powell tried to "envision some wires or something hanging down from it
that looked like a weather balloon or elongated weather balloon, but it was
exactly what I had heard and read about...so-called UFOs."
The sky was clear except for some cumulus clouds above,
and the visibility range was estimated at 15 miles, so they had a clear view of
this object. Powell estimated that it came to within about a hundred yards of
his aircraft before it passed by to the right. "It was a saucer shape with
a slight raised dome on top. It was all, all very defined, very clear," he
told the newspaper editors. Powell and McClave independently told McDonald that
the disk-like device had a "glistening white rounded dome on top and a red
conical apron below, circular in planform, and moving with its symmetry axis
vertical. It had no wings, tail, propellers or jets. No markings or apertures
were discerned."7 Powell estimated that it closed at an
airspeed of about 200 mph and passed to their right and slightly below their
altitude. He estimated the diameter at 20 feet; McClave thought 40 feet.
"It was just like looking at a Cadillac," Powell told McDonald. It
passed by in a steady motion with no wake, no exhaust and no smoke.
Because of the construction of the cockpit windows in
the Luscombe Silvaire he was flying, Powell could not easily see the object
after it passed to the right. He told the newspaper editors that "Miss
McClave...actually saw it disappear. It never got out of her vision until it
all of a sudden disappeared after the aircraft (i.e., the UFO) was on the right
hand side." According to McDonald, "both had the distinct impression
that after the object passed several tens of degrees aft of the beam it
suddenly vanished from sight. To all of my queries as to whether this seeming instantaneous
disappearance might have been only a matter of extremely high angular
acceleration out of their field of view, both could only reply that they did
not have that impression. They felt that it had instantaneously vanished while
in full view."
A THEORY OF DISAPPEARANCE
So, what happened? Did the object suddenly vanish into
another dimension (whatever that means)? Did it disintegrate (whatever that
means)? Or could it have actually traveled away so fast that the eye couldn't
follow it? In the past I have conjectured that an object traveling at a high
enough angular rate of speed might seem to "disappear." Specifically,
I have guessed that a nominally reflective object without a bright solar glint
which is seen against a brighter background and which travels its own length in
a time much less than the "natural shutter time of the eye" would be
at least very hard to see if not effectively invisible. This is because the
rods and cones, special cells within the retina at the back of the eye (mainly
cones for daytime viewing), take only so many "pictures" per second.
This reasoning would apply also to very faint light
sources or low contrast objects seen against darker backgrounds. However, it
would not apply to bright light sources which leave a "trail" or
retinal image, as, for example, tracer bullets or meteors, which can be
observed even though they move very fast. UFOs seen at night as lights can, of
course, "disappear" by the simple means of turning off the light
sources (or perhaps by shifting the radiation frequency out of the visible
range of the eye.)
The photoreceptors within the retina are spread over the
whole area of the back of the eyeball. The whole area, which corresponds to the
whole field of view of the eye, is made up of thousands of tiny subareas which
can be called "resolution areas" which are described in more detail
below. Each resolution area collects light and "takes a picture" over
a period of about 1/25 sec = 0.04 sec (the "twinkling of an eye"). In
analogy to a camera, this could be called the shutter time (or integration
time) of the resolution area. Because of this shutter time, periodic or
occasional variations in brightness which occur in times shorter than 0.04 sec,
or at frequencies greater than 25 times/second (1/0.04 = 25), are difficult to
see. Hence, to make motions seem continuous, movies are run at 24 - 28
frames/sec and TV and video runs at 30 frames/sec. As another example of the
"shutter time" of the eye, consider watching a fan speed up.
Initially the blades are obvious as they go around, but eventually they become
a blur. As a third example, you can't see a bullet come out of a gun while
looking across the direction of travel.
To pursue this further we must first consider the
obvious: we only see things because of differences. Various objects are
apparent only if there are contrasts between things within our field of view.
If all objects were the same color and brightness and uniformly illuminated we
couldn't distinguish between them. This is obvious to everyone. What is not so
obvious is that the detection of a small object at a distance is crucially
dependent upon not only the contrast between the object and its background, but
also upon the size of the object as compared to the distance and upon how long
it stays at one location or, inversely, how fast the object moves.
To understand the process of seeing a moving object,
first consider the definition of angular size when the size of the object, L,
measured perpendicular to the line of sight, is much smaller than its distance,
D, i.e., L < D/5 or 5L < D. Under this condition the angular size,
measured in radians (rad), is approximately equal to L/D. Hence a 10' object at
100' corresponds to an angle of 10'/100' = 0.1 rad and the same object at 1000'
has an angle of 10'/1000' = 1/100 = 0.01 rad. A more convenient term for small
angles is "milliradian" or mr: 1 rad = 1,000 mr; 1 mr = 1/1,000 rad.
(For the purist the angle in radians is actually equal to pi/180 times the
inverse tangent, in degrees, of the ratio. However, for angles less than 20°,
the inverse tangent of the ratio multiplied by (pi/180) is very nearly equal to
the ratio itself.) Note: 1 rad corresponds to about 57° 1° = 0.0174 rad = 17.4
mr.
Next, consider that at any time the total angular visual
field of the eye can be divided into many small roughly square angular areas,
the resolution areas mentioned above, which act more or less independently to
provide information to the brain on the brightness and color of whatever scenes
happen to appear within the resolution areas. (This is analogous to the
"pixels" or picture elements in a TV camera system. Each pixel provides
information on brightness and color of a tiny fraction of the scene being
viewed by the TV camera.) The lens on the eye "converts" each
resolution area on the retina to a "resolution angle" within the
field of view of the eye. The resolution angle is the smallest angle over which
the eye can determine that an object being viewed has size and shape and is not
just a "point." If an object subtends an angle less than the
resolution angle then it appears to be a "dot" (unless the object is
much brighter than the background, in which case it will seem to have a greater
size than it actually has because of optical aberrations and light scattering
within the eye).
The size of the resolution angle varies from person to person
and, for any given person it varies and with lighting conditions. At the center
of the field of view (the foveal region) which is about 2° (35 mr) wide, it is
generally in the range 0.2 to 1 mr (0.011° - 0.055°). A person with typical
eyesight might have a resolution angle of about 1 mr, whereas a person with
extraordinarily good eyesight might have resolution as small as 0.2 mr. Moving
outside the central region the resolution angle rapidly increases in size
because the lens of the eye provides proper focus only at the center of the
field of view. To literally see this effect, focus on a word at the center of
this sentence and try to read the words to the left and right of it without
moving your eye. (I can read one or two words to the left or right, but that's
all.)
Now let us work out an example. Consider a 10' square
object, oriented with its edges vertical and horizontal, at 100'. Its angular
size in vertical and horizontal directions is 10'/100' = 0.1 rad = 100 mr.
Hence it covers, or is "seen" by, about 100 to 500 resolution areas
(1 mr to 0.2 mr) in the vertical and 100 to 500 in the horizontal, depending
upon the eye of the observer and the lighting conditions. Such an object, if
stationary or moving slowly, would be very obvious to the observer under normal
lighting conditions. A 10' object at 1000' would cover 10 to 50 resolution
areas vertically and horizontally, still enough for the object to appear to
have size and a square shape. However, at 10,000' the 10' object might appear
just barely larger than a point to people with 1 mr resolution and at 50,000'
(nearly 10 miles) it would have an angular size of 0.2 mr and would appear as a
point, not as a square, to everyone. If the contrast against the background
were not great enough it might not even be visible to most people. Within this
small angle an object which itself is not a bright light, or at least of much
greater brightness than the background, must appear for more than 1/25 sec in
order to be clearly detected.
Now let us consider an object of substantial angular
size that moves transverse to the line of sight at some angular velocity. (The
angular velocity is equal to the actual velocity or speed, perpendicular to the
line of sight, divided by the distance.) At any instant it is being seen by
many resolution areas because it has a large angular size compared to a
resolution area. Over time, it crosses from one resolution area to another and
so on. The amount of time any one resolution area can see the object could be
as great as, but no greater than, the sum of the object's angular size (in the
direction of motion) plus the size of the resolution angle, all divided by the
angular velocity.
To give a specific example, consider the daytime
detectability of a jet airplane moving transversely to the line of sight at a
distance from the observer whose resolution angle is 0.5 mr. Let it be 50? long
in the direction of motion, traveling at the speed of sound (1,100'/sec = 750
mph = "Mach 1") and let it have a good contrast against the sky background.
(Note: a clear atmosphere is assumed. Atmospheric effects reduce contrast
between an object and its background the farther the object is away. This
effect is not considered here.) Assume first that the distance is 100,000' (19
miles). It would subtend an angle of 50'/100,000' = 0.5 mr. The speed of
1,100'/sec would correspond to an angular velocity of (1,100'/sec)/100,000' =
0.011 rad/sec = 11 mr/sec ( = 0.6°/sec). Therefore it would be seen by any
resolution area (0.5 mr) for no more than (0.5 mr + 0.5 mr)/(l l mr/sec) = 0.09
sec. This is more than twice the shutter time of the eye, 1/25 sec = 0.04 sec.
Hence this plane would be detectable. However, a further factor comes into
play: tracking or "panning" by the eyeball. If the observer detects
the presence of the moving plane and then causes his eyeball (or the
combination of eye and head) to rotate with the motion he can cause the plane
to remain continuously within a resolution element and thus increase the
probability of detection. Since the angular speed of the plane is only 11
mr/sec the observer would easily be able to track it with his eye and head.
Now let us consider the same jet plane moving past at a
distance of 1,000' or 1/100th of the previous distance. It ought to be a lot
easier to see at that distance, right? Let's find out. Now its angular length
(apparent size) is 100 times greater because it is "100 times closer"
(50'/1,000' = 0.05 rad = 50 mr) but its angular speed is also 100 times greater
(1,100 mr/sec). If we now add the eye resolution area to the object's angular
size and divide by the angular velocity we find (50 mr +0.5 mr)/1,100 mr/sec =
0.046 sec which is half the previous time. Since this is one "eye
shutter" time it would still be barely detectable. Previously the tracking
rate was only 11 mr/sec or 0.6°/sec. Now it is 100 times greater. Can your turn
your head 60° in one second? Certainly, so once again you could follow the
plane as it moves across your field of view, but your head would be turning
continuously. And you better not blink!
What would happen if the same plane passed by only 100'
away? (I know, that's too close... you'd run away before it got near.) Because
the angular size and speed ratios both depend upon the distance, the time
within a resolution element would again be 0.045 sec, but now you would have to
turn your head at a whopping 600°/sec to follow the plane as it crosses
perpendicular to your field of view. If you don't like headaches, I wouldn't
recommend it.
Of course, in a typical situation with a jet plane the
observer would know it was coming and could prepare to follow it with his eyes,
starting when it first appears far away. At that time it would be traveling at
a relatively slow rate as measured perpendicular to the sighting line
(i.e. the component of speed perpendicular to the sighting line would initially
be small). As it approached, the angular speed would increase, as would the
angular size, and the observer would have to turn his head and eyes faster and
faster to follow it. (Here I am assuming the plane flies along a straight track
past the observer, with the closest approach being 100'.) Then it would be just
a blur as it zoomed by, but as it traveled into the distance the observer could
once again track it as the speed component perpendicular to the line of sight
would decrease.
But, what if the observer weren't prepared? What if he
were watching a stationary jet which "instantaneously" accelerated to
an angular speed of 1,100 mr/sec without any prior warning? In this case it
would be gone out of his central (foveal) field of view (35 mr) in about 1/30
of a second, i.e., before he could react. He would see a streak to the side,
that's all...assuming he didn't happen to blink at the time of acceleration.
Now consider an example that is comparable with an
actual sighting ("Martin Allen") to be described: an observer (0.5 mr
resolution) is watching a stationary, 10' diameter spherical object at a
distance of 1,000'. Its angular size is 10 mr and so it covers a circular area
that is 20 resolution areas in diameter. Suddenly it accelerates at a uniform
rate in a horizontal direction perpendicular to his line of sight and achieves
a speed of l,100'/sec in 1/2 sec. By acceleration at a uniform rate I mean that
the increase in velocity per unit time is constant: it takes 0.5 sec to start
from zero and reach 1,100'/sec, so the velocity increases at a rate of
(1,100'/sec)/0.5 sec = 2,200'/sec every second. We could say that the
acceleration constant, a, is 2,200'/sec2 (which is about 68 times
the acceleration of gravity or 68 "g's"). At any time, t, after
motion begins the velocity is given by v = (a)(t). If we break this into 0.1
sec intervals we can see how the velocity increases: at the end of the first
tenth of a second it is traveling 220'/sec, at the end of the second tenth -
440'/sec, at the end of the third tenth - 880'/sec, and so on to 1,100'/sec at
the end of 1/2 second. Dividing by the distance, the angular acceleration is
l,100'/sec2/1,000' = 1.1 rad/sec2 = 1,100 mr/sec2 and
the angular velocities become 220 mr/sec at the end of the first tenth of a
second, 440 mr/sec at the end of the second tenth, etc., and 1,100 mr/sec at
the end of 1/2 sec.
Now we must ask, what is the maximum time that a
resolution area could "see" this object? The longest time would be
for a resolution area which lies along the (central) horizontal diameter which
is 20 elements (10 mr) wide. (Any resolution elements above or below the
central diameter would "see" the object for less time since
the object is circular.) Let d be the angular distance moved in time t. We
solve the constant acceleration law, d = (1/2)a t2, where a = 2,200
mr/sec2, to find the time: t = SQR(2d/a). (SQR = square root.) The
angular distance moved in completely crossing a resolution area is the sum of
the angular diameter of the sphere, 10 mr (20 resolution areas), plus the size
of the resolution area, 0.5 mr, or 10.5 mr. To cross this angular distance
requires t = SQR([2 x 10.5 mr]/[2,200 mr/sec 2]) = 0.098 sec. The
observer would barely see this but he probably wouldn't be able to react fast
enough to have his eyes start to follow it (typical reaction times to an
unexpected event are 0.1 - 0.3 sec). To cross the next 21 resolution elements
would require only 0.04 sec more because the object velocity increases rapidly
with time. {By this time the sphere has moved a total of 21 mr. To move that
distance required t = SQR([2 x 21 mr]/[2,200 mr/sec2]) = 0.138 sec.
Subtract the time required to move 10.5 mr from the time to move 21 mr: 0.138
sec - 0.098 sec = 0.04 sec.} This time is less than the "shutter
time" of the eye so the sphere has effectively disappeared in about 0.138
sec. The speed continues to increase and by the time 1/2 sec has passed the
object has traveled 137 mr (8° or about 137') and is moving at 1,100 mr/sec. At
this speed it moves 21 resolution elements in only (10.5 mr/1,100 mr/sec =)
0.0095 sec which is about 1/4 of the "shutter time". It would
essentially be invisible against the sky background. The observer would have
gotten the split second impression of motion, but by the time he reacted to
that impression it would be "gone." If the observer happened to blink
just as the acceleration began he might think that the object had simply
disappeared or "disintegrated."
STILL PHOTO CONFIRMATION OF
LARGE ACCELERATION
The previous discussion provides a theoretical basis for
believing that high acceleration of an opaque body seen against a lighted
background could account for verbal descriptions of UFOs
"disappearing" or "disintegrating" while in plain view of
the witnesses. I will now present physical (photographic) evidence that also
supports the high acceleration hypothesis for UFO disappearances.
Three previous still photos, all taken by Ed Walters in
Gulf Breeze, Florida, contain evidence of extreme UFO acceleration. The UFOs in
two of these (January 24, 1988 and March 8, 1988) were seen by Ed alone. 5
Each of these photos has the image of an "Ed-type" object which has
linear streaks upward to the top of the picture. The streaks were created as
the object zoomed upward while the camera shutter was open. The linear streaks
decrease in brightness in the upward direction indicating an acceleration of
the craft.
Whereas he took the previous photos when he was alone,
he took a photo of an accelerating bright red UFO on January 8, 1990 while
eight or so other witnesses were present.8 The witnesses reported
that the light was at the center of a much larger circular object which was
seen as a silhouette against a background of dull grey cloud cover. The object
would alternately hover and then dart to a new location not far away and hover
again. Ed's photo shows an overexposed compact image of a red light with a
broad red line extending rightward from the overexposed image to the edge of
the photo. Since the camera was on a tripod the thick line must have been made
as the UFO darted away to the right after remaining stationary for most of the
shutter time (4 sec). The width and brightness of the red line diminish with
distance along its length toward the right. This means that the UFO light was
not simply a point light but rather a light of some size and that it underwent
a large acceleration. The acceleration is estimated to have been greater than
several times that of gravity.8
VIDEO EVIDENCE OF HIGH
SPEED DISAPPEARANCE
Up until 1993 there had been no video evidence to
confirm the conjecture of large acceleration. But in the spring of that year an
astute witness who prefers anonymity obtained a videotape that demonstrates
large acceleration. The full report on this video has been published in the
MUFON UFO Journal.9 An abbreviated version is presented here.
Martin Allen (pseudonym) first saw the UFO at about 1:30
PM on March 24, 1993. It was traveling north to south past his house on
Pensacola Beach. He thought it was a "fat, round-looking cruise
missile" from Eglin Air Force Base10, 11." A few minutes
later he saw another (or the same) one and this time he realized that it wasn't
a cruise missile. It was "crown shaped with a bottom layer". Since he
had now seen it twice coming from the same direction he decided to try to
videotape it if it flew past again. He set up his 8 mm videocamera (Sony CCD
M8; fixed focus; 29° field of view) on his deck and pointed it in the direction
which the "missile" had gone and left the camera running. The camera
ran for two hours, the duration of the videotape, When he reviewed the video he
saw only some helicopters flying along the beach. The next day he set the
camera up again and "I went into the house and went to the bathroom. When
I started to return to work - about 1:30 - I saw the UFO moving fast from the
east. The video camera caught it."10
The video of the object lasts for 29 frames - almost one
second - and shows an object which moved at a steady speed so fast that its
true shape was stretched and distorted by the speed as it passed from left to
right through the field of view of the camera. The actual speed is
indeterminate since the distance was unknown. However, by assuming that the
altitude was constant and using projective geometry I determined that the track
of the object was not straight and that, if it were only 1,000 ft. away when it
was first picked up by the camera, then it probably was traveling several
thousand miles per hour (proportionally faster if at a greater distance).
The witness next saw the crown shaped UFO hovering
southeast (about 160° azimuth, 40° elevation) of his house on March 31, 1993 at
about 2:00 PM. He ran to get his videocamera and three batteries (he didn't
know which one was charged). He placed the camera on the railing of his deck to
steady it and turned it on. The UFO was motionless. In the video one sees the
tops of hazy clouds moving from right to left, whereas the UFO image stays near
the center of the field of view. The first battery ran out after about 40
seconds and he quickly replaced it, but the second battery was dead. He
replaced that with the third battery and videotaped the UFO for another 9
seconds or so at which time it suddenly zipped away so fast that the witness
could barely see it go. He was startled and uttered an expletive (deleted). In
replaying the video frame by frame I found that the disappearance was actually
the result of an extreme acceleration toward the right combined with a loss in
contrast against the background sky. The extreme acceleration made the motion
impossible to follow with the eye (or camera) and the high speed decreased the
time that the image spent at any point on the focal plane. The decreased image
time on the focal plane reduced the contrast with the background sky making the
blurred or streaked image very difficult to see.
About a week later (April 2, 10:15 AM) the witness again
saw the UFO hovering near his house. This time he knew that none of his
videocamera batteries were charged, so he ran for his Polaroid 600 camera. He
was able to take one picture from an outside stairway looking nearly straight
upward at the object before it again accelerated to an extremely high speed and
zipped out of sight. This shows that the crown shaped UFO really is more like a
layer cake with the top cylindrical layer larger in diameter than the lower
layer. There is a "hole" in the bottom which is red. Again the
distance is not known. If it were 1,000' away then its maximum diameter was
about 11'. A black and white copy of the photo is presented in reference 9.
Careful analysis of the March 31 video imagery shows
that there was an extremely high level of acceleration. The images of the UFO
are very easy to see while it is stationary. There is a bright spot at the
upper right, a glint caused by sunlight reflected from the object, and darker
areas near the bottom (darker than the background sky). The image has a compact
nearly circular shape with a width and height of 4 - 5 mm on the 13"
monitor screen. Tests showed that the effective focal length (EFL) of the
camera-video monitor combination is about 535 mm. The size of the image, 4 - 5
mm, therefore corresponds to an angular size of (4 to 5)/535 = 0.0075 - 0.0093
radians. If the distance to the object were known, then simply multiplying the
angular size in radians by the distance would give the actual size as measured
transverse to the line of sight. Unfortunately there was no triangulation
during this sighting, so the actual distance is not known. However, if the
object were at an assumed distance of 1,000', then it was about 7.5' to 9'
wide. If it were 2,000' away it was twice as large, and if it were only 500'
away it was half as large. It was proportionally larger or smaller as the
assumed distance is made larger or smaller.
Once the object starts to move it becomes difficult to
see because the image stretches and fades against the sky background. In spite
of the difficulty in determining the boundaries of the blurred images, I was
able to estimate the distance from the right side of the object in the last
stationary frame to the rightmost end of the image in each succeeding frame
after the acceleration started. These measurements provide estimates of the
angular distance traveled each frame time, 1/30 = 0.033 sec. These distances
increase as time goes on. There are five frames of data before the object
leaves the field of view.
I plotted the estimated distances of the right edge of
each image relative to the right side of the image in the last stationary frame
on log-log paper (see reference 9) in order to determine the nature of the
acceleration. I found that the slope of the log-log plot of distance vs time
seems to be nearly linear with a slope of 2. It can be shown by mathematical
analysis that this means the acceleration was approximately constant and that
the distance as a function of time was, therefore, representable by an equation
of the form x = (l/2)at 2, which is the "constant acceleration
law" that was used above in the discussion of UFO disappearances by
acceleration. In this law a is the "acceleration constant." When a =
"g", the acceleration of gravity, 32 ft/sec2 or 9.8
meters/sec2, this equation describes how objects fall in the
constant gravitational field close to the surface of the earth (excluding the
drag effect of the atmosphere).
As an example of the constant acceleration law, consider Figure 1
which shows several graphs. Two of these at the right side are labelled
"Freely Falling Object." To create the upper falling object graph I
twice videotaped a small ball as it fell. By replaying the tape frame-by-frame
I was able to measure the distance downward on the monitor screen from the
moment of release to within a temporal accuracy of about one tenth of a frame
time or 1/300 sec and a distance accuracy of a couple of millimeters. The
measurements from these two experiments are represented by small squares.
Although small experimental difficulties, which are common in simple
experiments like this, kept the two experimental data sets from agreeing
exactly, it is clear that both experiments produced distances downward on the
monitor screen (measured upward on the graph) which are close to the
predictions of the constant acceleration law which is represented by the solid
line through the data points. (For the expert: the gravitational acceleration
law, (1/2) gt2, where g = 32'/sec2 was appropriately
scaled by the distance from the camera to the falling ball (12.8') and this
scaling yielded an angular acceleration constant of 2.5 rad/sec2.
The equation (1/2) 2.5 t2, after multiplication by the focal length,
535 mm, predicts that actual distance that the image would move after
time t has elapsed.) The lower of the two falling object graphs, which is the
solid line lying closest to the horizontal axis (lower right), shows the
predicted distances on the monitor screen if the ball had been 1,000' away, as
assumed above for the distance to the Martin Allen object, rather than 12.8'.
Clearly at that distance the ball would have hardly appeared to move in the 1/2
sec of elapsed time presented on the graph.
Now contrast this with the graph marked "Martin
Allen." I have drawn a solid line though the data points (triangles). Note
that the solid line has a continuous curvature, just as has the graph for the
freely falling body. This curvature is the signature of an object which is
being accelerated, that is, the speed is steadily increasing. The angular
acceleration constant which fits the Martin Allen data (the leading end points
of the elongated images of the UFO) is about 15.8 rad/sec2. As
pointed out above, the distance to the UFO is not known, so that actual acceleration
constant in ft/sec2 cannot be determined. However, if it were 1,000'
away then the acceleration constant was about 15,800 ft/sec2 or
almost 500 times the acceleration of gravity. (If the distance were more or
less the acceleration would be more or less in proportion to the distance.) For
a "graphic" illustration of what this means, compare the Martin Allen
graph with the lower of the two freely falling body graphs. The image of a
freely falling body 1,000' away would travel about 2 mm on the monitor screen
in 1/2 sec. In the same amount of time the UFO image would move about 500 times
farther, 1,000 mm, a distance which would lie far beyond the boundaries of the
video screen.
Motion which obeys the constant acceleration law is also
consistent with the following velocity equation: v = at, where v is the
velocity. Hence after three frames (3/30 = 0.1 sec) the angular velocity was
about 1.59 rad/sec. At 1,000' this would correspond to 1,590'/sec, which is
greater than the speed of sound at sea level (1,090'/sec = "Mach 1").
By the time the object left the screen after 5 frames (5/30 = 1/6 sec) it was
moving at about 2.65 rad/sec. If it were 1,000' away it was traveling at
2,650'/sec or more than Mach 2. As is usual for high speed UFO sightings, the
witness heard no sound associated with either its hovering or departure.
ED WALTERS VIDEOS
Ed Walters had not seen any UFOs for quite a while when
he began to notice some strange objects appearing briefly north of his house, which
is on the south side of the Santa Rosa Sound and looks northward toward the
Gulf Breeze peninsula. On the 15th of November, 1993, he was working in his
office when he noticed a strange object hovering in the sky to the northwest,
possibly over the Santa Rosa Sound or over Gulf Breeze. He grabbed his Sony
camcorder and ran outside and videotaped it as it hovered. The image is very
small, about 1.5 mm in size on a 270 mm wide monitor and appears as a spot that
is slightly darker than the white cloud background. Although the camera
jiggled, as is evident from the motion of the background scenery, the sudden
motion of the object is apparent because it moves in a direction that is nearly
perpendicular to the jiggle motion of the camera. The image is so faint, being
just slightly more apparent than the random electronic TV noise, often called
"snow", that it is difficult to accurately measure its position.
Ed saw another UFO on November 18 but didn't get any
video. He then decided to set up his old video camera on a tripod in his office
to be available when needed. He used his old camera, even though it needs an
external VCR to record the video, because it has a zoom lens. (This videocamera
predates the popular "camcorder" which has the camera and the recorder
together in one "box.") At about 4:35 PM, on November 23, Ed was
working in his office while watching the Sally Jesse Raphael (SJR) show on TV
when he saw a strange object, which he thought was a UFO, appear in the sky. As
quickly as possible he turned on the videocamera. However, the object
disappeared before he could point the camera in its direction. Hence the
beginning of the video shows him pointing it in various directions looking for
the UFO. (Throughout the video one can hear the TV in the background. At the
beginning of the video the TV was transmitting advertisements typical of the
break in a show at the half hour point in time. Then the SJR show resumed.) At
30 seconds into the video he stated that he was going to leave the camera
running in case it should come back. He resumed his work while watching TV (the
sound of the TV can be heard in the background) and was no longer looking out
the window. About 40 seconds later, 70 seconds into the video, the object
appeared again as a small darkish object at the upper right side of the screen.
It traveled in a steady motion downward and to the left, crossing the screen -
about 10° of angular distance - in 57 frames of the video which corresponds to
1.9 seconds (at 30 frames/sec). (If it were at the distance of the far shore,
8,000 ft, it traveled at about 200 mph.) Thirteen seconds later Ed said
"Ooop, oop, oop. There it is! Right out there." Immediately he began
to turn the camera to point it at the UFO. In a few seconds he had it in the
center of view of the videocamera. The scenery below the UFO is the shore and
horizon line on the north side of the Santa Rosa Sound. Unfortunately the image
is too small and poorly defined to show any details of shape. However, Ed gave
the following description of the UFO as he looked through the telephoto lens of
his 35 mm camera (no film in the camera!): "it looks like an egg on the
top and an egg on the bottom and... huh!... a bunch of ball-like things around
the outside." (Note: this description matches the shape of the UFO he
photographed along with an F-15 jet on January 12,1994; see reference 12.) The
UFO remained motionless until about 2 min and 55 seconds into the video, at
which time it disappeared in one frame. During the last 20 seconds of the video
Ed said he was going to the closet to get some film for the camera. To do so he
had to look away from the UFO for several seconds. It was gone when he returned
to the camera. He did not see it disappear. I have not been able to find any
evidence of motion of the UFO. It just simply disappeared. However, I cannot
rule out the possibility that it moved so rapidly in some direction that its
contrast against the sky diminished to a value comparable to that of the
electronic noise. (Note: the disappearance is not a result of the camera being
turned off and back on again after it was gone because the sound track on the
video is continuous.)
Over the next couple of days Ed saw brief flashes of
light in the daylight sky around Gulf Breeze. (Note: other MUFON members, the
'Gulf Breeze Research Team,' also saw brief flashes, although not necessarily
at the same time as Ed.) About noon on November 27 he decided to take his
camcorder and go to the Pensacola beach to see if he could film anything away
from buildings and houses. When he got to the beach he turned on the camera and
left it on continuously as he walked on the beach. He first panned around the
area, showing the tall apartment houses to the east of him, perhaps 2 miles
away, and the white beach running east-west. A motor boat went past heading
east. The glint of the sun off the waters of the Gulf to the south of him was
apparent. As he was walking westward and looking around he suddenly noticed a
UFO approaching from the north, over his right shoulder. He moved quickly toward
the sand dune (north of him) as the UFO moved to a location in the sky east of
him. He knelt down on the sand and pointed the camera eastward, thus capturing
the UFO and also the sky and distant buildings which he had videotaped only a
minute before when there was no UFO. All this time the camera was running and
recording the sounds of the ocean and of Ed describing what was happening. The
UFO image is about 4 mm wide by 2 mm high and has a bright glint on the right
side, toward the sun. (The angular size is about 7.5 mr by 3.7 mr which
corresponds to 7.5' by 3.7' at 1,000' for example.) Because of its relatively
large size and considerable contrast against the blue sky one would think that
it would be visible at least as a streak if it moved. However, after remaining
stationary for a minute or so, in one frame it disappeared. The implication is
an acceleration so great that the UFO moved a considerable distance in 1/30
sec. (Jeffrey Sainio, analyzing the video field by field - there are two fields
per frame - could see only a slight change in the field before it disappeared
indicating a considerable motion in 1/60 sec.)
THE SHADOW KNOWS
Just how great is the acceleration of a UFO? The video
evidence described above provides evidence of large acceleration, but since the
distances to the UFOs are not known the actual accelerations could not be
calculated. However, now, thanks to "the shadow" we can calculate an
actual value.
As of July 13, 1995, Ed had not seen a UFO since April,
1994 (see reference 13). But on July 13 he saw a strange object flash through
the sky northwest of his house. Thinking that maybe the UFO would appear again,
he set up his old videocamera, with its telephoto lens, on a camera tripod in
his office. Since he didn't know when the UFO might return he decided to just
turn the recorder on and tape continuously. He initially thought he would tape
at the 'extra long play' speed, which would give him six hours of video.
However, fortunately, he decided to use the standard play setting on the video
speed because this speed gives better resolution. So he began a daily regimen
of starting a two hour tape in the morning, say at 10:00 AM, and then returning
to review it two hours later. His method was to rewind the tape and then review
it at high speed, hoping to be able to spot a UFO if it appeared briefly. He
would then rewind the tape again and place it back into the VCR to record the
next two hours. He did this two or three times a day for the next several days.
During the afternoon of July 14 he started the tape at
10:00 a.m. and again at 2:00 p.m.. Shortly after 2:00 PM he called me up and
told me that he had briefly seen a UFO again and that he was trying to catch it
on tape. When he reviewed the tape two hours or so later he found that he had
recorded his side of the phone conversation. Furthermore, he found that farther
on in the tape he had recorded a very small image of a very oddly shaped
object... a UFO that he had not seen at the time of its appearance because he
was busy. The next day he showed it to Bland and Carol Pugh but told no one
else. He did not even tell me about this sighting, which occurred after our
conversation.
During the next several days he repeated this procedure
of recording two hour tapes several times each day. Unfortunately he was in the
habit of rewinding and reusing tapes. I say unfortunately because in some way,
not clearly recalled, he managed to record over the July 14 tape. He doesn't
recall exactly when this was, but it might have happened on July 18 when he saw
the UFO appear again and scrambled to insert a videotape and record it.
Whatever the explanation, the fact is that the recording of the July 14 UFO no
longer exists.
He was, by this time, in the habit of just letting the
tripod-mounted camera point in a fixed direction and record while he pursued
his daily activities. Since he was just pointing it in a single direction he
was faced with a decision of whether to use the zoom capability of the lens or
to use the wide angle setting. He knew that the zoom setting narrows the field
of view, thereby reducing the chance that the UFO might enter the field of view
of the camera, while at the same time providing larger, more detailed images of
any UFO that might enter the field of view. On the other hand, he knew that the
unzoomed setting provides a wider field of view, thereby increasing the chance
that the UFO would be within its field of view, but that the UFO image would be
small and indistinct if it were far away. Eventually he decided that there
already were enough videos showing small, indistinct images of UFOs, so he
would take the chance that the UFO would pass through the smaller field of view
of the fully zoomed lens.
On the 18th of July Ed saw the UFO again but did not get
a video since the UFO did not pass into the field of view (he didn't realize
this until after the sighting was over). He kept up his surveillance-by-video
for several more days and then, on July 21 he got lucky! Not only did he see
the UFO, giving him an opportunity to turn the camera on and point it in its
general direction, he also managed to briefly record the UFO itself with the
full zoom.
He was working at his desk listening to tape recorded
rock music at about 9:30 AM to 9:40 AM (he wasn't sure of the exact time) when
he first noticed a flash in the sky and he saw a strange object travel quickly
from west to east, passing north of him over the Santa Rosa sound or over Gulf
Breeze. It was gone too quickly for him to turn on the camera. Suddenly it
appeared again, once more passing through the sky to the west, although this
time not in a continuous motion (it temporarily reversed direction once). He
turned on the camera and immediately described what he had seen just moments
before. The audio channel of the videotape recorded Ed's description while the
video channel recorded the scenery, including the waves moving roughly westward
on the water of the Santa Rosa Sound, the trees on the distant shore about
7,600 ft away and the sky above.
TRANSCRIPT OF THE AUDIO
CHANNEL
|
TIME |
|
|
(0:00) |
"The camera is set
up here. I've got it on full zoom." (The camera shows the south shore of
Gulf Breeze west of Shoreline Park. There is rock music in background from
Ed's tape player.) |
|
(0:10) |
"Full zoom, full infinity....
The UFO has been coming back and forth from left to right, uh" |
|
(0:20) |
"from west to east
and, uh, I've got the camera set up so that I can maybe get that bad baby if
it should again cross over Gulf Breeze.... This camera's got a positive"
|
|
(0:40) |
"negative. I'm going
to try to turn it on. There we go... That's a negative picture." (Here
he reversed the "polarity" so that bright areas of the scene became
dark and vice-versa). "That's pretty neat, but I probably should leave it
on regular." (At this point he returned the polarity to normal.) |
|
(0:50) |
"There we go.."
|
|
(1:00) |
(At this time there is a
pause in commentary. There is no break in the background music. Ed was still
looking out the window.) |
|
(1:18) |
"Oop, Oop, Oop,
there it is off to the left." |
|
(1:20) |
"coming this
way..coming this way.. just a .. it's stopped." |
|
(1 :25) |
"coming back. .doin'
a loop..doin' a loop" |
|
(1:30) |
(At this time the UFO appears
at the left of screen, moves rapidly toward center, reverses direction and
leaves at the left of the screen) |
|
(1:31) |
"comin', uh, went
back to the left" |
|
(1:35) |
"back to the left...
gone .. gone into the haze." |
|
(1:40) |
"OK! All right! My
God, I don't know if I got it or not." |
|
(1:50) |
"I'll wait just a
moment to see.." (Ed waited to see if it would come back; it didn't.) |
|
(2:06) |
END TAPE. |
Ed didn't tell me about this video until a week and a half
later, on August 2. He told me that he hadn't mentioned it because he didn't
think the video was very important since the UFO only appeared briefly and
since it had an overall shape similar to what he photographed numerous times in
1987 and 1988. In other words, it appeared roughly like an inverted layer cake,
with a short bottom section that had a diameter smaller than the main upper
section (similar to the UFO photographed by Martin Allen). The bottom of the
lower section was what he had called the power ring during the 1987 and 1988
sightings because it was very bright underneath. However, there were no lights
visible in this case on either the top or the bottom. He said the color was not
bluish-metallic like the 1987-88 UFO, but, instead, it was brownish. He said
that the appearance of the UFO in the video was very brief as it moved into the
field of view and back out again within a second. What impressed him the most
was the ability of the UFO to reverse its motion in such a short time.
As we talked Ed got more interested in the video and
wanted me to estimate the size of the UFO. Therefore I asked him to do an
experiment. (Ed, unlike any other UFO witness I have worked with, has done many
experiments over the years, including experiments that would have exposed his
photos as hoaxes if they had been hoaxes.) I needed to calibrate his
camera-video screen combination to determine its effective focal length. Ed
placed a yardstick at a distance of about 30 feet from the camera (outdoors on
the patio overlooking the Santa Rosa Sound) and determined that it's image was
a little bit wider than the 11" wide video screen. That meant that the
field of view of the camera-screen combination was about 3'/30' = 0.1 rad or
about 5.7°. Then, by stopping the videotape and looking at the UFO in one frame
he was able to determine that the UFO image was about 1/2" wide. Hence its
angular size was about [(0.5")/(11")] x 0.1 rad = 0.0045 rad, which
corresponds to about 4.5' at 1,000', 9' at 2,000', etc. He had the impression
that the UFO was about as far away as the tree line on the opposite shore of
the Santa Rosa sound, a distance of about 8,000'. At that distance the UFO
would have been about 34' wide. (This initial estimate is only 7' larger than
the value determined after the careful analysis described below.)
In order to observe the shape and color and to measure
the size of the UFO, Ed had to run the video backwards and forwards several
times. He commented to me about the fast reversal of motion which seemed to
occur in only two or three frames. And then he said something which came as
great surprise, even a shock, to me: "I think I see a shadow." When
he said this my alertness level increased several fold because the existence of
a shadow could mean that there was a possibility for the three-dimensional
location of the UFO! But the UFO appeared to be in the sky above the distant
shore. Where, I wondered, could there be a shadow? "What?" I asked.
"You mean a shadow on the water?" "Nope. A shadow on the
trees." This caught me by surprise. How could that be? I asked Ed to
measure the height, on the TV screen, of the UFO image above the shoreline and
above the trees. Ed did so. It was about 5" above the distant shoreline
and several inches above the tree line on his monitor screen. That meant that
the UFO must have been just at the right height above the water to cast the
shadow on the trees! Furthermore, the sun must have been in the direction of a
line drawn from the shadow to the UFO. I quickly turned on my computer and called
up an astronomy program (Expert Astronomer, distributed by Expert Software,
Coral Gables, Florida, 33134) which indicated that at 9:30 AM the sun was at an
azimuth of about 90 degrees and at 9:40 it was at about 91 deg. Ed then used a
compass to determine that the camera was pointing at an angle of about 310
degrees magnetic (which turned out to be within a degree or so of the
geographically determined azimuth). I knew that with these data and an accurate
measurement of the horizontal spacing between the UFO and the darkened area I
could determine the actual location of the UFO in 3-D space.... if the darkened
area actually were the shadow.
A few days later I received a copy of the video. I
studied it carefully and determined that there is, indeed, a roundish, rapidly
moving area that slightly darkens the tree images as it moves first to the
right and then to the left, just as the UFO moves to the right and then to the
left. This darkened area first appears at the left of the screen a fraction of
a second after the UFO has entered the field of view. The darkened area moves
to the right, decelerates and stops moving at the same time that the UFO
decelerates and stops. Immediately after stopping the darkened area then
accelerates and moves to the left, again in synchronism with the motion of the
UFO. In other words, the dynamics of the darkened area generally match the UFO
dynamics. The similarity in motion of the darkened area and the UFO is strong
evidence that the dark area is, in fact, a very weak shadow of an opaque body,
the UFO. But is it in the right place as determined by the sun? To answer that
question I carried out more careful calculations based on careful measurements
of the video images. Figure 2
shows the video frame with the UFO at its rightmost position. Figure 3
is a computer enhanced image by Jeff Sainio which shows the location of the
shadow area along with the UFO image.
ANALYSIS OF THE VIDEO
Ed's video of the yardstick at 30' provided the needed angular calibration: a distance of 10" at 30', with an angular size of 0.0278 rad or 1.60°, created an image 7.5 cm long on my 13" (diagonal) monitor screen. This corresponds to an angle calibration factor of .021 deg/cm or 0.021 deg/mm. At my request Ed made and videotaped a square grid several feet in size. This experiment showed that the horizontal and vertical magnification factors of the optical-electronic system are same, so there is very little lateral distortion of the image. I measured several important distances within the frame when the UFO and the (assumed) shadow were at the farthest to the right and not moving. These distances were measured on a computer-enhanced video frame provided by Jeff Sainio and are illustrated in Figure 4
the vertical distance from the water line to the center of the UFO image - 12.8 cm; the vertical distance from the water line to the center of the shadow image - 1.1 cm; the horizontal distance from the center of the shadow image to the center of the UFO image - 7.6 cm. Because of the problems of fuzziness of the images it is difficult to determine the exact center points so these measurements could be off by (+/-)0.1 cm. These measurements were then combined with the measured sighting direction (310° +/- 1°) and the solar azimuth (90° at 9:30 AM or 91° 9:40 AM) to determine the location of the UFO, assuming that the darkened area is, indeed, the shadow. Figure 5
illustrates the geometry of the situation. To be perfectly exact one would set
up a three dimensional model since the UFO was above the water. However, the
angular elevation of the UFO image is only 12.8 cm x 0.21°/cm = 2.69° above the
distant shoreline, so it is allowable to use a planar triangle approximation,
i.e., as if the UFO were on the water surface. The illustration shows the
locations of the camera, the shadow on the trees and the UFO. Two sighting
lines emanate from the camera location and travel toward the UFO and the
shadow, respectively. The third line emanates from the shadow and points in the
direction of the sun. This line, of course, passes through the location of the
UFO. The angle between the sighting lines from the camera is determined by the
7.6 cm horizontal distance between the shadow and a point at shadow level that
is directly below the image of the UFO: 7.6 x 0.21 = 1.6°. The size of the
acute angle between the sighting line to the assumed shadow and the direction
to the sun at 9:30 AM when the solar azimuth was about 90° is 310° - 270° =
40°. At 9:40 AM the solar azimuth was about 91° and therefore the acute angle
would be 1° less, or 39°. All three angles of the triangle can be calculated
from trigonometric relationships using the angle values 40° or 39° along with
1.6°. The distance from the camera to the assumed shadow on the trees was
estimated from a map to be about 7,600 ft. Finally, using the law of sines the
other sides of the triangle can be calculated. For 9:30 AM the result is based
on solving these equations:
|
7,600' |
|
H |
|
D |
|
------- |
= |
------- |
= |
------- |
|
sin[l80-(40+1.6)] |
|
sin(l.6) |
|
sin(40)
|
where H is the horizontal component of the distance from
the shadow to the UFO (i.e., the distance as seen from far above the ground level)
and D is the horizontal distance from the camera to the UFO. The above
equations yield H = 320? and D = 7,360'.
As I have pointed out previously, I calculated these
distances assuming that the dark image area on the trees is the shadow.
Fortunately there is a way to check this assumption. If it were the shadow,
then, not only would the line from the shadow to the UFO point toward the sun's
azimuth (the basic assumption used in the above calculation), but also the
shadow-UFO line would point upward toward the sun's angular elevation. To
calculate the angular elevation it is first necessary to calculate the actual
altitude of the center of the UFO, Au, above the altitude of the center of the
assumed shadow, As; i.e. to calculate (Au-As). Then it is necessary to
calculate the ratio (Au-As)/H and finally to find the inverse tangent of (the
angle whose tangent is) that ratio. The center of the UFO image is about 12.8
cm above the water line image. This corresponds to an angle of 2.69 deg. and at
distance D = 7360' its altitude is Au = 7360 tan(2.69) = 346'. The center of
the shadow is 1.1 cm or 0.23 deg. above the water line which corresponds to As
= 7,600 tan(0.23) = 31' above the water line. The difference in these heights,
Au - As = 346-31 = 315', is the altitude of the UFO above the assumed shadow.
The angular elevation of the shadow-UFO line is therefore the inverse tangent
of [(Au-As)/H]= (315/320) = 0.984 which is almost exactly 44.5° (inverse
tan(1.000) = 45° exactly).
If the complete calculation is repeated for the time
9:40 AM, with 40° replaced by 39°, corresponding to the solar azimuth of 91°,
we find H = 326', D = 7,349', Au = 345', As = 31', and the angular elevation
being the inverse tangent of (345-31)/326 = 0.963 which is 43.9°. Notice that the
calculated elevation angle shrinks from about 44.5° to about 44° as the assumed
time of the video increases from 9:30 to 9:40 AM.
So, how does this compare with the actual solar
elevations at these times? The astronomy program says that at 9:30 AM the
elevation was about 43° and at 9:40 AM it had increased to about 45°. Since the
elevation calculated from Ed's video is greater than the solar elevation at
9:30 AM (44.5°vs 43°) but is less than the solar elevation at 9:40 AM (44° vs
45°) it is clear that at some time between these times the elevation calculated
from the video would equal the actual solar elevation. Of course, calculations
such as these are not expected to be perfectly accurate, either in the case of
the astronomy program which contains approximations and rounding off errors, or
in the calculation based upon Ed's video, which contains measurement errors.
Therefore these calculations do establish a good degree of consistency between
Ed's video and the independent solar elevation data and provide strong evidence
that the darkened area on the trees is, in fact, the shadow of the UFO.
SIZE AND SPEED OF THE UFO
Using the above results the size and speed of the UFO
are easily determined. The slant range from the camera up to the UFO was
approximately 7,360'/cos(2.69) = 7,370'. Because the edges of the UFO image are
not perfectly distinct precise estimates of the size cannot be made. To within
an accuracy of about 10% the UFO image is about 1 cm (0.21°)wide by 1/2 cm
(0.105°) high on the monitor screen. Therefore its actual size was about (7,370
tan(0.21)=) 27' by 13.5'. These estimates could be off by a foot or two.
The motion of the image of the shadow on the trees
proves that the UFO, as indicated on Figure 5, moved parallel to the beach. The
reason for concluding that the UFO moved parallel to the beach is based on
three facts: (1) as nearly as can be determined from the very faint image, the
shadow stays at the same elevation on the tree line as it moves back and forth,
(2) the UFO image travels at a constant elevation, to within the accuracy of
these measurements, and (3) the sun was not on the horizon but at an
appreciable elevation angle (about 44°). If the UFO had moved at a slight angle
to the beach, its distance from the vertical "wall" of the tree line
would have changed and its shadow would have moved up and down on the tree line
as it traveled to the right and then to the left along a horizontal path. In
fact, if the UFO had moved at a sufficiently steep angle to the beach its
shadow would have moved either closer to the water or farther from the water
than the distance of the tree line, and in either case the shadow would have
disappeared from the tree line. Since the image of the shadow is not observed
to move up and down I conclude that the UFO maintained a fixed distance from
the beach. Since the beach at that point along the shore runs essentially
perpendicular to the line of sight from the camera, the UFO motion was also
essentially perpendicular to the line of sight.
The horizontal position of the center of the UFO image as a function of frame number is illustrated in
with the position when it first appears taken as zero distance at frame 0 or
time 0. The graph shows both the positions moving to the right (squares) and
also to the left (triangles). The positions were measured in mm on the screen.
A mm of motion (0.021°), projected to the distance of the UFO, 7,370',
corresponds to about 7,370 tan (0.021) = 2.7' (perpendicular to the line of
sight to the camera). The slope of the graph of position vs time is the speed.
Changes in slope correspond to changes in speed, i.e., to acceleration or
deceleration (which is acceleration in the opposite direction to the motion).
The slope of the graph as the UFO moved to the right shows that the speed was
essentially constant at 9.1 mm per frame time for 11 frames, after which the
speed decreased rapidly to zero. Since a frame time is 1/30 sec (at 30
frames/sec, the standard video rate), the UFO traveled to the right at a rate
of [(9.1 mm/(1/30 sec) x 2.7'/mm] - 737'/sec or about 500 mph before
decelerating.
The deceleration to zero speed at a position 121 mm from
the left edge of the field of view required about 4 1/2 frames. Then the UFO
reversed its direction and moved to the left. The acceleration to full
"exit" velocity required about 6 1/2 frame times. The slope of the
graph as the UFO traveled to the left is about 10 mm per frame time indicating
that it departed at a slightly higher speed than it entered. Using the
calibration of 2.7'/mm and the frame duration, 1/30 sec, one finds that the
speed to the left was about 810'/sec or 552 mph.
Since the UFO stopped its forward motion in about 4 1/2
frames, the average deceleration was 737'/sec divided by 4.5 frame times (0.15
sec) or about 4,900'/sec2, or about 150 "g's". The average
acceleration (to the left) was about 810'/sec divided by 6.5 frame times (0.217
sec) or about 3,740'/sec2 or about 117 g's. (Note to the physics
purist: the deceleration can be interpreted as an acceleration to the left
caused by a force directed toward the left. The force began 4 1/2 frame times
before the motion stopped and continued as the UFO slowed, reversed direction
and subsequently accelerated to its final leftward speed. The reversing force
did not drop to zero until the UFO reached its final leftward velocity about 6
1/2 frames after it stopped moving to the right.)
The reversal of direction on a dime (with 9 cents
change!) is an anomaly that we can't explain.
THE SHADOW KNOWS
I have made use of the presence of the shadow on the
tree surface to calculate the location of the UFO in three dimensional space,
so the existence of the shadow is an important feature of this video. However,
the shadow itself seems a bit unusual in that it is so faint and it seems to be
almost twice as large as the size of the UFO itself. The question then arises
as to whether or not this is consistent with what might be expected from a real
object (UFO) a few hundred feet from the far shore. The following discussion
shows that it is consistent.
The shadow of an object blocking light from a source
such as the sun consists of two regions: the umbra and the surrounding penumbra.
Within the umbra there is no direct illumination from the sun. Within the
penumbra, which surrounds the umbra, there is illumination by only part of the
sun's disc. Outside the penumbra there is total illumination by the sun. If the
sun were infinitely distant or if it were a point source of light rather than a
"disc" the penumbral region would not exist, that is, the edge of the
shadow would be sharp and the transition from fully illuminated to completely
shaded would occur over zero distance. Thus the existence of the penumbral
region, which is a region of gradual darkening, is a consequence of the angular
size of the light source. If you imagine a spherical object blocking the light
source, then the perfect shadow of the sphere, which would be created if the
source were a far distant point of light, would be a circular area with the
same radius as the object itself. As the effective angular size of the light
source grows the shadow becomes less sharp, more diffuse or "less
perfect." The penumbral region is an annulus with an outer radius and an
inner radius. (The inner radius of the penumbra equals the radius of the
umbra.) For a circular object of radius R at distance D from a surface that is
perpendicular to the light rays, the outer radius, Ro, of the annular penumbra
is given by the following equation: Ro = R + D tan (A/2), where A is the
angular size of the light source in degrees. Under the same conditions the
inner radius, Ri, is given by the equation Ri = R - D tan(A/2). Thus the width
of the penumbral region, Ro - Ri, is 2D tan(A/2) ( = D tan A for small angles).
Within this annular region the brightness of the surface varies continually
from the brightest outside the penumbra to the darkest within the umbra. The
brightness gradient, or the slope of the curve of brightness vs distance
(radius), is greatest halfway through the penumbral region at radius R. Because
Ro is larger than R the shadow can appear to be larger than the object itself.
Just how much bigger the shadow appears would depend upon the angular size of
the light source and the amount of brightness contrast between the umbral
region and the unshaded surface.
If there were no atmosphere on the earth, shadows would
be (almost) completely dark. However, the gasses and particulate matter within
the atmosphere scatter the sunlight in all directions. Areas shaded from direct
sunlight still receive light from the sky and from surrounding objects. Hence,
even on a clear day the umbral region will not be totally dark. As the cloud
cover obscures more and more of the sun the contrast in brightness between the
umbral region and the areas outside the penumbra is reduced, ultimately to
(almost) zero when the sun is completely obscured. As the umbral region gets
brighter (less dark) with increasing cloud cover another phenomenon occurs: the
shadow appears to grow in size. This is because the effective angular size of
the sun, angle A above, actually increases somewhat with cloud obscuration (an
effect I discovered many years ago (in the middle 1970's) while working on the Trent/McMinnville
photos). There is a monotonic relationship between the effective angular size
and the contrast between the unshaded and umbral areas on a surface. For a
clear sky the brightness ratio or contrast (outside brightness divided by umbral
brightness) is a maximum value (more than 20 to 1) and the effective angular
size is about 0.5°, which is what would be expected from geometric
considerations alone. However as the obscuration increases the effective
angular size increases, reaching almost 3° when the sun is almost totally
obscured. In this particular UFO case the shadow is weak enough so that the
effective angular size of the sun could be as large as 2°. To an observer at a
distance from the surface the radius of the shadow will appear larger than
radius the object itself, but it will not appear as great as Ro calculated
above because the outer edge of the penumbra has too little contrast with
respect to the brightness of the surrounding sky to be
detected.
The above discussion shows how the weather conditions
(haze, thin cloud) could have caused the shadow to be very faint (very low
contrast with the surrounding brightness). It also provides an explanation of
one way in which the shadow of the UFO can appear larger than the UFO itself.
There is also another, more important effect, specific to this particular
video, which causes the shadow to be larger than the UFO: if the shadow of an
object appears on a surface which it not perpendicular to the light rays, i.e.,
not perpendicular to the line from the center of the shadow to the light source
(and passing through the center of the object), then the shadow will be larger
than the object (everyone knows this... simply look at your own shadow when the
sun is near the horizon!). Assume for simplicity that a sphere makes a shadow
on some vertical surface that is perpendicular to horizontally traveling light
rays. The perfect shadow of this sphere (distant point source of light, no
atmosphere) is a circular area with a diameter equal to the diameter of the
sphere (and the center of the sphere lies along the line from the light source
to the center of the shadow). Imagine rotating this surface about a vertical
axis through the center of the shadow. Now the vertical height of the shadow is
the same as before, but the horizontal width is now larger by a factor (l/cos
B), where B is the rotation angle (of the normal, or perpendicular, to the
surface away from the direction of the light rays). The shadow now has an
elliptical shape. For B = 90°- 50° = 40°, as in this case (see Figure 5) the
shadow expansion factor is 1.3. Now imagine raising the elevation of the light
source an angle E above horizontal while leaving the sphere fixed in place. The
elliptical shadow of the sphere will move downward on the vertical surface and
it will tilt (the major axis will not be horizontal, as before). It will also
grow some more because the angle between the normal to the surface and the
direction of the light rays increases. This angle is now equal to the inverse
cosine of [(cos B)(cos E)]. If E = 44°, as in this UFO case, the angle between
the surface normal and the light rays is 56° and so the expansion factor is now
1.3/cos(56) = 1.8. Thus the major axis of the elliptical shadow would be 1.8
times greater than the diameter of the sphere and the minor axis would be the
same width as the diameter of the sphere. The major axis is tilted with respect
to the horizontal axis by an angle equal to the inverse tangent of [(tan
E)/(sin B)] which, in this case, would be about 56°.
The above discussion shows how the projection of the
shadow on a tilted surface changes the shape of the shadow of a very simple
surface (sphere). However, this UFO was not a sphere and so its shadow was not
an ellipse. The UFO can be crudely modelled as a vertical cylinder about 27' in
diameter and 10' high (ignoring the smaller diameter protrusion from the
bottom). The center of the UFO was at a horizontal angle (B) of about 40° and a
vertical angle (E) of about 44° with respect to the normal (perpendicular) to
the "surface" provided by the tree line. By simple shadow projection
of a 2.7 to 1 cylinder on a tilted surface using the above angles one can show
that the shadow is approximately a fat oval shape which is longest along a
direction tilted at 60 - 70° with respect to horizontal. Unfortunately the
actual shadow image was so faint that variations in the reflectivity of the
trees have distorted its shape. It appears nearly circular. However, the
darkest part of the upper portion lies above and to the right of the darkest
part of the lower portion, thus producing a slight "tilt" in the
expected direction. Thus, although the shape of the shadow does not seem to be
exactly as expected, it does appear to be about twice as large as the UFO and
so is consistent with what would be expected from the combination of the effect
of the increased effective angular size of the sun (making the penumbra larger
than normal) and the effect of projecting the shadow onto the tree
"surface."
ANOMALY SQUARED
(or is it cubed?)
The existence of a UFO is, by itself, an anomaly. Then there are the anomalously large deceleration and acceleration which have, for the first time, been quantified. These are "first order" anomalies which are apparent upon visual inspection of the video. However, there is also a second order anomaly which only became apparent after careful analysis of the motion of the shadow of the UFO. This anomaly was discovered by Jeff Sainio when he was trying to add frames of the video together to make a better image of the shadow. He and I had assumed that if he shifted each frame appropriately so as to keep the UFO image in one position as he added frames together (electronically laying one on top of another), that all of the shadow images would lie on top of one another. That is, we had assumed that the horizontal spacing between the UFO image and the shadow image would be constant. If this were so, then the images in all these frames would add together coherently, whereas the random noise (electronic video noise and variations in the reflectivity of the tree "surface") would add incoherently, thus providing an improvement in "signal to noise ratio" by a factor of approximately the square root of the number of frames added. We assumed that the spacing would be constant because the horizontal angle between the UFO and the shadow is, or should be, determined by the location (elevation and azimuth) of the sun. As I have already demonstrated, at its rightmost position the shadow of the UFO is exactly where we would expect it to be with the sun as the illuminating source. However, Jeff discovered that when the UFO image is moving, whether to the right or left, the shadow image is a small amount to the right of the position that would be expected with the sun as the illuminating source. Moreover, the magnitude of the shift in the shadow position changes with position. Figure 7 illustrates this anomaly.
The vertical axis shows the distance of the shadow
image from the left edge of the frame (in degrees) and the horizontal axis is
frame number. The solid line which passes through the circles indicates the
location of the geometrical shadow, that is, where the shadow would be if it
were aligned properly with the sun and the UFO. (Essentially, the solid line
shows the motion of the UFO but shifted several degrees to the left.) The
squares are the positions of what appear to be the darkest parts of the
shadows. These positions can only be estimated because the shadow is so faint
and "modulated" in a random manner by the reflectivity of the tree
"surface." The vertical lines through the squares indicate the
apparent widths of the shadows and thus are a measure of uncertainty in the
shadow position. Note that at the top (center) of the graph, where the UFO and
shadow stopped moving, the agreement between the geometrical shadow position
and the actual shadow position is perfect, to within the accuracy of
determining the shadow position. However the shadow positions deviate from the
geometrical positions at the left (entering the frame) and at the right
(leaving the frame) of the center of the graph.
Jeff and I thought that "pincushion"
distortion in the lens might explain this anomaly, even though for a good
quality lens and the narrow field of view one would not expect much field
distortion. To aid in our analysis Ed did yet another experiment. He videotaped
a grid of horizontal and vertical lines at a distance of 30'. Analysis of the
video proved that there is very little optical distortion, and certainly not
enough to explain this anomaly. I also studied the nature of the
tree"wall" on which the shadow appears. I could find nothing related
to the trees that could explain this effect. Hence, we are left with the video
evidence which seems to imply that the light rays were somehow bent around the
UFO!
(Note: this video is discussed further in the Appendix
where it is compared with hoax hypothesis. The conclusion is that it would be
too difficult for Ed to fake a video such as this.)
CONCLUSION
Recent videos show UFOs accelerating and even
"disappearing." These videos provide, for the first time,
quantitative evidence that UFOs are capable of extreme acceleration and speed.
Such extreme acceleration immediately raises several questions. How was the
acceleration achieved in the absence of any apparent means of propulsion (no
rocket blasts, no explosions, no obvious electric or magnetic phenomena)? Why
was there no noise associated with the departure? What happened to the
occupants, if any? These are questions which have been asked repeatedly over
the last (nearly) fifty years. Because these questions have been based on
visual observations of possibly questionable accuracy, such as the
Powell/McClave report cited above, they have generally been treated lightly (if
at all!) by scientists. But now, with some "hard" data to go on, it
appears that we must confront the ridiculous (by our standards) evidence that
phenomenal acceleration, apparently without the usual action-reaction, is
possible.
So far as we know, acceleration is a result of the
application of a force to an object. However, a force does not "act
alone:" a force on one object requires an "equal and opposite"
force on some other object. This goes back to the long-ago discovery, quantified
several hundred years ago by Isaac Newton, that a change in momentum (the
product of velocity times mass) of one object is accompanied by an opposite
change by some other object (conservation of momentum). This is the famous
"action-reaction" principle. Rockets work because the hot gas
molecules, rapidly expanding out through the rear of the rocket, push hard -
exert a force - on the rocket body before they are ejected. Firing a bullet out
of a gun is another example of action-reaction, as anyone who has fired a high
power rifle, a shotgun or a handgun is aware. Over a short distance (inches)
the force of expanding hot gases (the exploding gunpowder) accelerates the
bullet to velocities so great that the bullet cannot be seen. If the barrel of
a gun were transparent so you could watch what happens, you would see the
bullet "disappear" from the barrel.
The examples of the action-reaction principle at work in
our flying machines should be contrasted with the video image of the UFO
acceleration: there is no evidence of action-reaction occurring...no
propellers, no jet exhaust...nothing. Yet, the fact that the UFO accelerated
somewhat uniformly, rather than just instantaneously achieving a high travel
velocity, suggests that a force was applied. Newton's first law relates the force
to the mass and acceleration: F = ma, where F is the force on a massive body
and m is the amount of inertial mass. To get a "feeling" for this
equation, imagine holding in your hand a 1 lb weight which, by definition, has
a mass m = 1/32 of a "slug". The downward force on your hand is F =
ma = mg = (1/32 slug)(32 ft./sec2) = 1 lb. (Note that the
acceleration of gravity, g, is used in place of a, even though the mass is not
moving! Gravity acts like acceleration. This is the basis for "general
relativity.") Now suppose you want to accelerate this 1 lb weight to the
speed 1,590'/sec in 0.1 sec, corresponding to the speed achieved by the UFO in
the Allen video if it were 1,000' away (see above), using a force that produces
a constant acceleration. How much force would you have to apply? Use the
velocity equation to find the acceleration: a = v/t = (1,590'/sec)/0.1 sec =
15,900'/sec2. Now use the force equation, F = ma, to find F: (1/32)
x 15,900'/sec2 = 497 lb! In other words, you would have to push on
the mass so hard for 0.1 sec that it would be like supporting a 497 lb weight.
During that 0.1 sec it would travel (l/2)(15,900'/sec2) (0.12) =
79.5 ft. You would have to maintain the constant force over this distance, not
an easy task unless you have very long arms. Of course, the greater the
acceleration and the greater the mass, the greater the required force. But, in
any case, you have to supply the "reaction force."
(Note: A UFOnaut inside a UFO accelerating at 500 g's
would be pushed by the walls of the craft with a force that would make him seem
to weigh almost 500 times his "normal" weight on earth. A human body
might be crushed at that acceleration, and the skin might be pulled off the
bones, unless the human were suspended in a liquid and the lungs and other body
cavities were filled with liquid.)
Where, then, did the UFO get the force to accelerate?
What did it push against? Was there something invisible in the sky pulling or
pushing it? Did it have an invisible jet-like exhaust? Trying to answer questions
such as these have led theorists to speculate that the UFO uses magnetic fields
to push against the earth's magnetic field. However, even if one were to assume
that extremely high fields could be created by the UFO, this mode of propulsion
is questionable because of the dipole or multipole nature of magnetic fields
(one tends to get rotation about an axis rather than linear motion of the
magnetic body). Other suggestions are even more bizarre. If the inertial mass
were reduced a smaller force could produce the same acceleration. Reduction of
inertial mass by some factor would, presumably, reduce the required force by
the same factor. If it were possible to reduce the inertial mass to near zero,
then a small amount of ejected matter or even photons of light could propel an
object. Some people have proposed warping space or travel into another
dimension or time travel. Unfortunately, "reduction of inertial
mass," "space warp," "travel into another dimension,"
"time travel," travel to a "higher plane of existence," and
other similar terms have no operational meaning, so far as we know at present.
That is, no one knows how to do these things, or even if they can be done.
Another related question is, how did the UFO manage to
maintain itself at an altitude above earth with no visible means of support?
Magnetic levitation has been proposed, but again the magnetic field just
doesn't work as simply as that and huge fields around the UFO would be needed
to support any reasonable mass. Alternatively, one might conjecture that, if a
UFO could reduce its inertial mass, as suggested above, then perhaps it could
also reduce its gravitational mass (since these are equal according to numerous
experiments). If the gravitational mass could be reduced then the force against
gravity needed to support the UFO could be small, just as the accelerating
force could be small.
Returning to the "right angle turns" mentioned
at the beginning of this paper, the discovery that UFOs have the capability of
extreme acceleration provides a possible explanation for the abrupt changes in
direction that have been reported. To change direction the UFO would apply to
itself, in some way, a decelerating force to arrest its motion in one direction
while applying to itself an accelerating force for a sufficient time to achieve
the desired speed in the new direction. These forces would be of such extreme
magnitude that to the human observer it would appear that the UFO
"instantaneously" stopped its initial motion and commenced its new motion.
The bottom line is that UFO dynamics is still a mystery.
However, we now have some evidence to establish the measure of that mystery.
ACKNOWLEDGMENTS
I thank the witnesses mentioned herein for their
reports. I thank Bland Pugh and Gary Watson for investigating the Allen
sighting, for providing needed information and video copies and for carrying
out important experiments with the witness' camera. I thank Ed Walters for
taking the time to perform experiments which were necessary for proper
evaluation of his videos, and I thank Jeff Sainio for helpful discussions and
for providing computer enhanced versions of the videos.
REFERENCES
1. MUFON
report by witness, E. Douglas & D. McKay, investigators (1996)
2. Witness
testimony as recalled by Lillian Sargent and by Bernice, her daughter, in the
late 1960's (Lillian was my grandmother)
3. The
Scientific Study of Unidentified Flying Objects,D. S. Gilmor, Editor; E. U.
Condon, Project Director, published by the Air Force in 1969; Bantam Edition,
1969
4. Maccabee,B.,"Fantastic
Flight of JALl628."International UFO Reporter, March/April,1987(Center for
UFO Studies, Chicago)
5. Walters,
Ed and Frances, The Gulf Breeze Sightings, Morrow Pub. Co., NY (1990)
6. McDonald,
James, "Science, Technology and UFOs," a lecture presented in January
8, 1968 to the United Aircraft Research Laboratories, and "Some
Pennsylvania Cases and their Bearing on the Condon Report," a lecture
presented at Mansfield State College, May 15, 1969. Although McDonald first
mentioned the case in his January, 1968 lecture, according to the second listed
paper he interviewed Powell before Powell's speech to the newspaper editors in
April, 1967. McDonald's lectures are available from the Fund for UFO Research,
Box 277, Mt. Rainier, MD 20712
7. Testimony
of William Powell, April 22, 1967. I thank Philip J. Klass for sending me, in
September, 1975, a copy of his verbatim transcript of Mr. Powell's speech
before the American Society of Newspaper Editors.
8. Maccabee,
Bruce, "Not Just Another Evening Stroll" available from the Fund for
UFO Research, Box 277, Mt. Rainier, MD 20712; this sighting is also presented
in "Gulf Breeze Without Ed." MUFON UFO Symposium Proceedings, 1991,
pg. 209-211
9. Maccabee,
B. and J. Sainio, "Cruise-missile UFO Disappears",MUFON UFO Journal
#308, December 1993
10.
Martin Allen (pseudonym), private
correspondence
11.
Information from the investigation by Bland
Pugh and Gary Watson.
12.
Maccabee, B., "Gulf Breeze UFO Photo
Analyzed," MUFON UFO Journal #314, June 1994
13.
Maccabee, B., "Waterspout UFO
Photographed," MUFON UFO Journal #319, November, 1994
APPENDIX
Ed's July 21 video has been studied to determine whether
or not it could be a hoax. The following discussion asks and answers these
questions: if it were a hoax how would it be done, and is the hoax hypothesis consistent
with Ed's technical ability and equipment?
Very sophisticated computer-aided image creation
programs should be able to create a video such as this which shows a
"UFO" and "shadow" moving with respect to the background.
For example, in a Hollywood-level production the hoaxer could begin by
videotaping the background scenery from Ed's office along with a prepared
speech to form the audio track. Then the hoaxer would use sophisticated
computer aided image generation to superimpose the UFO image and the shadow
image appropriately in each frame. True, it would take more than the average
special effects (SFX) person to think of including a computer program to create
a shadow image on the trees (it would be much simpler to leave the shadow out;
no one would miss it) and an even more creative SFX person to make sure that
the shadow is in its correct position relative to the UFO (i.e., to make the
hoax shadow agree with the solar shadow position) but there might be such a
person. Of course, to find the correct shadow position the hoaxer would use an
astronomy program that would calculate the correct shadow position relative to
the UFO in each frame; there would be no loss of tracking of the type
illustrated in Figure 7. It would take an exceptionally clever SFX person to
think of making the shadow NOT track the UFO perfectly. And, of course, the SFX
person would have to be sure that the UFO image was appropriately blurred for
motion on a frame by frame basis (computer based model programs typically
create images with sharp, rather than motion blurred edges) and the shadow
image would have to be appropriately sized (bigger than the UFO image, as
discussed above), appropriately faint and appropriately "modulated"
by the random reflectivities of the distant trees. In other words, this SFX
person would have to be a major genius, use high powered technology and spend a
lot of time to get it right and all for.... nothing (no money, no credit). So
forget that.
A method more appropriate to Ed's "low tech"
capabilities would be to have a model UFO on a string or perhaps painted on a
piece of glass. With the camera stationary he would move the model, silhouetted
against the sky, into and out of the field of view. Sounds easy so far. Why not
just leave it at that? But there is the shadow. Could he move a model shadow
along a string at the same time as the model UFO in such a way that at the
brief instant that the UFO was stationary the model shadow and the model UFO
would appear to align with the sun? If the UFO and shadow models were on
separately operated strings, there would be a low probability of making their
motions match at all, to say nothing of having them seem to align with the sun.
However, if he painted (or pasted) a model UFO on a piece of plate glass and made
a smudge on the glass at the location of the shadow he could get them to move
together as he slid the plate glass to the right and then to the left in front
of the camera. Of course he would have to take a course in astronomy and
another in optics and yet another in plane geometry in order to know how to
place the model shadow at the right place relative to the model UFO in such a
way that the images of these models would appear to align with the sun. Ed is a
clever fellow, so say the skeptics. But, he's not that clever! There would
still be several problems: the plate glass would have to be large and outside
his office. The camera lens was operated at full zoom and was focused at
infinity. Therefore, to have the model images appear to be in focus as well as
the distant trees the models would have to be perhaps twenty or more feet away.
The piece of glass would have to be larger than the field of view of the camera
at all times since no edges of plate glass are seen in the video. At twenty
feet the piece of glass would have to be at least two feet high and more than
three feet wide since it would have to slide back and forth at least a foot.
This glass would have to be supported in such a way, perhaps on some sort of
track, such that it wouldn't tilt or wobble as it is moved back and forth, and
all supports and mechanical devices would have to be outside the field of view
of the camera. All of these mechanical technicalities would make the moving
glass with painted (pasted) on model hoax method very difficult.
There are two other "minor" problems: (1) any
plate glass would cause reflections of nearby objects or the sky (there are
none), and (2) the shadow model would track perfectly with the UFO model since
they are both on the same piece of glass. Now, relative to problem (2), one
could hypothesize TWO pieces of glass side by side, one with the UFO model and
one with the shadow model and both moving at the same time and at the correct
speeds so that when they stop moving during the period of motion reversal the
shadow and UFO appear to align with the sun. This would compound the problem
tremendously. (But Ed is a very, very clever fellow...we are told.) However,
problem (1) above can't be solved (large sheets of glass that are
antireflectance coated on both sides at all visible wavelengths aren't
available).
The bottom line is that any hoax hypothesis which fairly
accounts for the dynamics and positions of the UFO image and the shadow...
fails! I conclude that the July 21 video is not a hoax.