PRELIMINARY DISCUSSION - TO BE REVISED AS NECESSARY
This is based on analysis of a video copy originating source unknown
The copy includes the direct video, a 1.6x blowup negative video (sky is dark, UFO appears bright against sky) and a 7x blowup.
The video begins with a "wide angle" shot and immediately zooms in. Once zoomed in it stays that way. The wide angle shot shows numerous nearby buildings. They appear dark against the sky background. What seem to be distant structures are faint in the haze, i.e., they have low contrast with the sky, as expected from atmospheric extinction. The atmospheric extinction coefficient could be estimated from assumed intrinsic brightness of the buildings if the distances were known. This coefficient is probably given in meteorological reports for the time (the "visibility" or "visibility distance"). This could be important in determining the intrinsic brightness of the UFO, assuming it is a real object at some distance. I do not know the distances of buildings in the pictures but something like thousands of feet to a mile or so seems more reasonable than, say, 3 to five miles. There are enough structures in the background so that using parallax one should be able to locate ths position of the videographer.
The UFO is generally well centered. The camera jiggle is obvious and looks as one would expect for a hand held camera. The jiggle is much more noticeable after zoom. Once the UFO starts to move to the right the camera pans with it, jiggling as it goes. The UFO motion seems to be at about a constant rate and so is the pan motion. After the UFO disappears behind the second building the camera sighting direction continues to move to the right as if the videographer expects to see the UFO appear from behind the second building, which would be logical based on the previous continuous motion.
The UFO is initially stationary but obviously tilting back and forth or wobbling at a constantrate. A 7x video blowup shows left-to-right motion of diffuse (edges not sharp) darker areas or dark spots which seem to be on the rim of the UFO. If these are fixed to the surface, then they suggest, but do not prove, rotational motion, counter-clockwise as seen from above. (The dark spots could be "moving" left to right on a non-rotating UFO, thereby giving the impression of motion just as changing light patterns in an electronic sign can give the impression of motion.) I would have to say that the way these appear at the left edge of the UFO and then move to the right is not exactly what I would expect if the spots were fixed with respect to the surface of the UFO. However, the "funny appearance" of the dark spots as they appear and move may be a result of the atmospheric haze (causing low contrast) plus the artifacts of electronic 7x zoom (these features would be very small, almost invisible, in the un-electronic zoomed images). there more be more clarity in the original video. Aside from the "funny appearance," the combination of the motion of the dark spots and the wobble certainly gives a good impression of rotation with wobble or "precession" (see below). An estimate of the rate of the assumed rotation, as based on the motion of the black spots, is 6 to 7 seconds per revolution (about 0.16 rev/sec or 1.0 rad/sec). In other words, it is not spinning rapidly. The wobble requires about 2 sec to complete a cycle (0.5 rev/sec or 3 rad/sec).
After remaining stationary for several seconds the UFO then "instantaneously" accelerates (see below) to a constant velocity which takes it to the right on an upward sloping path. It seems to pass behind the upper left corner of one building and then, because of its upward trajectory it appears above the building. Frame by frame analysis of both the disappearance and the reappearance show consistent "cutting away" of the image, as if it were a real object moving slowly out of view behind the building and then reappearing from behind the building. After reappearance it continues its steady right hand upward motion and wobble. If moves toward a second, higher building. It disappears for good behind the second building.
After the initial camera zoom the UFO image on a 14" diag monitor is about 25 mm wide and about 7 mm high. Since I don't know the effective focal length of the camera lens I can only hazard a guess that the angular size might be on the order of 1/2 to 1 degree. Just before it disappears the second and final time the UFO image length is 20 mm. This suggests that it was about 25% farther from the camera when it went out of sight.
The first nearby building that the UFO goes "behind" - or appears to go behind - has some square windows 5 mm on a side on the monitor. Hence the UFO initially appears to be about 5 times larger than these windows. If, for example, the window were 5 ft wide, then the UFO was more than 25 ft in diameter (assumed round, but there is no proof of this - no "top view" or "bottom view"). assuming it was as it appears, farther away than the building. All further dimensions are scaled according to this assumption, lacking any further information. The UFO was apparently farther away than the building, perhaps as much as twice as far, but not very much farther because it would have been barely visible in the the smog/haze. The UFO image has areas that are darker than the sky background, an important factor discussed below. If the UFO were miles away it would "fade into" the haze and the dark areas would not be as obvious as they are.
If the UFO were twice as far as the building, then it would be about 50 ft in diameter, assuming as before that the square windows are 5 ft wide.
I have studied the UFO acceleration by plotting the position of the right end of the UFO image relative to the building it (seems to ) disappear behind. For several seconds the spacing is constant with fluctuations (83-85 mm on the monitor). Fluctuations in the spacing are a result of the continual wobble of the UFO combined with the frame-by-frame fluctuations in the image shape and "edge fuzziness", a phenomenon caused most likely by electronic noise in the video camera. Then, suddenly, there is motion to the right (toward the building). The abrupt change from stationary to moving is noticeable to the naked eye when running the video forward (in time). The UFO image is seen to suddenly start moving to the right, what seems to be an "inertia-less" (instantaneous) onset of motion, with what appears to be a constant velocity.
When viewed in reverse, the UFO is moving constantly to the left and appears to suddenly stop, as if hitting an invisible brick wall. (Crash dummies inside?)
The left edge of the building is sufficiently sharply focused in the 1.6X blowup video negative (sky dark) to allow reasonably accurate (to within 1 mm on the monitor) measurements of the spacing between the left end of the UFO image and the image of the edge of the building. This method allows for measurement of the UFO motion irrespective of the camera jiggle, i.e., by using the building as a reference the camera jiggle is essentially removed. (It still has the effect of smearing the edges of the images slightly.) A graph of spacing vs frame number shows the following odd result: in one (or less than 1) or at most 2 frames the UFO achieves its full foward speed. There appears to be no swinging as one would expect for a model hanging on a string. Also, the rotation and wobble (precession) do not appear to be affected by the onset of motion. (More precise analysis using the original video may turn up some slight changes in the rotation and wobble.) Using the estimate of the UFO being 25 ft in diameter, the steady speed to the right corresponds to about 16.9 ft/sec or about 11.5 mph. This would be doubled if the UFO were twice as far away (and changed in proportion to the assumed UFO size and distance scale). If it achieved this 16.9 ft/sec speed in 1 frame, 1/30 sec, then it achieved an acceleration of about 16 "g's" (16 times the 32 ft/sec^2 acceleration of gravity). If in two frames, then 8 g's. This sort of acceleration would be enough to cause wobble in any model hanging on a string. This acceleration, since it seems to cause no effect to the "normal" wobble and rotation of the UFO must be acting through its "center of mass" (else, there would a torque or twisting motion that would change the wobble in some way). If the UFO weighed 1 pound and accelerated in 1/30 sec, then the force applied would be 16 pounds. If it weighed 1 ton (2,000 lbs) the accelerating force would be the equivalent of the weight of 16 tons.
NOTE: THESE SPECIFIC NUMBERS ARE ONLY ROUGH ESTIMATES TO GET "IN THE BALLPARK". THE ACTUAL VALUES DEPEND UPON DIMENSIONS WHICH ARE PRESENTLY ONLY GUESSED AT.
CONSIDERING THE HOAX HYPOTHESIS:
In general there are three possibilities: a hoax, a misidentification or the "real thing" (a True UFO - unexplainable as conventional a phenomenon). The possibility of a misidentification seems unlikely because of the shape. Even if one could prove that there was a 25 - 50 foot blimp with a gondola on top that was hovering and rocking so that the front and rear ends alternately went up and down (but not rotating) and having dark areas moving long the side near toward the camera, this would not explain the "instantaneous" acceleration. That leaves only the hoax or the real thing.
Factors to be considered and their relevance to the hoax hypothesis are: 1. The presumed hoax must either use a model of some sort or it is an electronic construction
1a. If a model, then it is not likely a full sized model at a great distance (thousands of feet, beyond the buildings) from the camera (rotating, wobbling, accelerating), but more likely a small model within a room where the video was shot. Therefore reject the full sized model hypothesis. (However, it is to be noted that this is the only method that could potentially create witnesses to the "UFO" who were not associated with the hoax.)
1b. The model must be some distance from the camera for the image to be in focus at full zoom (don't know this minimum focal distance). This places minimum size requirements on the field of view of the camera as compared to the location of the camera. That is, if this were videotaped in a room looking out through a window, the window must be big enough so that it does not appear in the video even when unzoomed.
1c. If a 3 dimensonal model it cannot be reflected in glass. One might imagine a small model, illuminated in some way so as to make a visible reflection in a glass window. Looking through the window the camera would "see" the background objects (buildings, sky) and a reflection of the model. If videoed with a hand-held camera the whole picture, background and model reflection, would jiggle together, as would happen with a real object at a great distance. The ufo model could be rotating and wobbling. By moving the model appropriately one could make it appear to move. However, it would be "difficult" to give it an "instantaneous" acceleration followed by a constant velocity. It could not simply be a small model rotating at the end of a string. It could be mounted on a rigid rod with appropriate rotation and wobble dynamics created by a mechanism. However, if the model is bright enough to have its reflection visible against the bright sky it would not seem to disappear behind the distant buildings. It's image would appear to be "in front of" the buildings. And last but certainly not least, the image of the reflection of a model in a window cannot be less bright than the background since background light coming through the window would add to the reflected light from the model. The fact that the UFO image is darker than the sky means this is not a simple "reflection on glass" hoax.
1d. Similar problems arise if one imagines reflecting the background on glass with a lighted model farther away than the glass. In this case one could make the model seem to move behind the building. Simply place a black paper cutout on the back side of the glass where the building image appears. Now when the model moves behind the building image the light from the model will not get through. However, when the model is silhouetted against the sky there will be no portion of the model image that is darker than the sky.
1e. A "masked reflection" would also be "difficult". In this case a cutout with the shape and size of the reflection of the model is placed beyond the glass to block background light from coming through the glass where the image of the model appears. Motion of the model would have to be accompanied by similar, perfectly registered, motion of the cutout.
1f. One big question is how to make a model UFO that is brighter than the dark building appear to move behind a building? Imagine being in the room where the video was taken, looking out through the window. One sees all the nearby and distant buildings. Then create a flat dark model cutout of the nearby buildings and set it up some distance, like several feet, from the window. The 2-D model building is therefore closer to the camera than the window and the camera is many feet from the window. However, the camera must be far enough away from the model building so that when videoed with full zoom the edges are still in good focus. (This sets size requirements on the room and window. See below.) Now take a small 3-D UFO model suspended in some way. Have it illuminated and painted or colored in such a way as to be somewhat darker than the sky brightness. Naturally this model must have black spots on its rim and must be rotating and wobbling in a steady manner. This, and the onset of motion acceleration) would require a support which is reasonably rigid. Perhaps a mechanism inside the model would create the rotation and wobble (wobble about 3 times as fast as the rotation) and another mechanism on the floor would drive the horizontal and vertical components of motion of the support once the "UFO" starts to move. In this case the model UFO could move behind the model buildings in a convincing manner. This method would require some effort at model building, including construction of a mechanized model UFO and support system, alignment of the model buildings with the real buildings as seen through the window (I assume there really are buildings at the locations indicated in the video!), and, finally, careful videography with appropriate lighting (not easy!) using a handheld camera. It might also be necessary to shoot the scene from a room with a large window and to use a special lens on the camera so that the unzoomed view does not show the edges of the window.
As mentioned above, the distance from the camera to the (flat) model buildings must be large enough so that the edges are in good focus. This sets a minimum size requirement on the room that depends upon the zoom magnification. A reasonable guess is that to have the distant buildings in good focus and the presumed nearby model buildings also in good focus would require a distance from the camera to the models of 20-50 ft. this requirement, in turn, sets a size requirement on the window. It must be large enough so that the window edges do not appear in the picture at the beginning when unzoomed.
1g. An even more expensive and time consuming way is to "bring the whole scene into the studio." That is, create a model of the whole scene as viewed from the window under hazy conditions. This would be extremely complicated and sophisticated. A model of the scene could involve models of the nearby buildings and, as a background for the distant buildings, a large photograph of the real scene, like a "diorama." A UFO model would then be supported in some invisible way at a distance from the camera that is greater than the distance from the model buildings and then of course, it would be "easy" to make it move behind the model buildings.
The UFO model would have to be supported in a manner such as described in 1f above in order to make it move, rotate and wobble without introducing a swinging motion characteristic of a model suspended on a string. If the model were supported by a transparent rod, for example, a mechanism could be devised to make the model rotate and wobble as seen. A lightweight model on a rigid rod would accelerate quickly with little wobble or vibration. This might also necessitate some special optics (lenses) for the camera to make the zoom compatible with the likely short distance (5 - 20 feet from the camera to the diorama). An actual haze effect could be synthesized by using as a background a large photo taken on a clear day and then blowing water vapor or fog into the model scene to create the reduction of contrast inherent with haze.
However, to make this convincing several model buildings at different distances would be created within the diorama. But this would require sophisticated model building, a mechanical operating system for the model and its motion, considerable time and considerable expense.
So far, the bottom line on the hoax possibility using a model is that it probably could be done, but would require a considerable effort and expense.
2a How about the possibility of an electronic construction? In this case one imagines a video of the background scene with the UFO image added in electronically. Because the image jiggles right along with the images of the buildings, this hand-held jiggle must be somehow deduced by the software frame by frame and then added to the frame-by-frame location of the UFO image.
2b Alternatively one might imagine that the scene was shot with a tripod mounted camera showing the more of the scene than actually appears in the video. This sampling of the scene was at high resolution (many pixels). The scene was a single, stationary frame. This single large frame was copied many times (about 700). Then the UFO image was added frame-by-frame. About 700 frames were created which show the UFO image first stationary and then moving frame by frame to the right and upward at a constant speed. On a frame by frame basis the UFO image was partially "erased" in a ste-by-step manner as it "moved behind" the image of the first building, and then it was "created" as it seemed to appear from behind the building. After the series of frames with the UFO had been created, then the dynamics of the camera vibration and panning were simulated. One can imagine this was done by making a frame-by-frame mapping of the first (700) frames onto a second series of about 700 frames. Each of the second series of frames was a subset of the first, i.e., a smaller frame size (fewer pixels). Initially in the unzoomed section the new frames were about the same size as the orignal frames. However, the zoom was creased by using "pixel magnification" and this justifies using high pixel resolution in the first set of frames. The center of each new frame is a "semi-random" location relative to the center of the original frame in such a way that the centers of the new frames wander about the original frame center to synthesize camera vibration. Once the UFO image starts to move in the original frames, the mean center point of the second series of frames also begins to move in a "random walk" manner characteristic of a hand-held panning camera. One can imagine that by using a method such as just outlined the video wwas constructed. Naturally this would require very sophisticated computer based image construction...Hollywood level, probably.
COMMENT ON HOAX HYPOTHESIS: there may be other techniques not mentioned above. However, it would seem that if this was a hoax then it was extremely well done. Of course, no method except the full scale UFO hoax with a real object thousands of feet from the camera would create bonafide witnesses. Hence if there are witnesses and it can be proven that they have no relationship to the video, then this can be labelled a real event! The video might be able to stand on its own even in the absence of witnesses. However, it is difficult to imagine something as obvious as a 25-50 ft UFO flying close to city buildings would be noticed by only the videographer.
RELATION BETWEEN ROTATION AND WOBBLE:
The continuous dynamic motion of the UFO is intriguing. If a hoax the constancy of the motion implies some motor driven mechanism that keeps the rotation and wobbling steady.
However, if not a hoax....
Assume the UFO can be modelled as a rotating solid disc of some mass m. The average or mean axis of rotation is assumed to be (nearly) vertical. However the instantaneous axis (the spin axis at any particular instant) does not appear to be vertical. If you imagine the spin axis as a line, this line appears to make an angle with the (assumed) vertical mean axis. This angle may be (seems to be) constant. As time goes on this line sweeps out - or lies "on" - a cone shaped surface in space, with the apex of the cone at the center of the disc. (Note: The earth has a "wobble" or precession such that the instantaneous spin axis of the earth rotates about the average spin axis every 26,000 years (about).)
If the wobble is actually a uniform precession of the spin axis, as with a gyroscope or any spinning body, then there must be a torque (twisting force) acting on the disc in a direction always perpendicular to the spin axis (if not perpendicular, the torque would change the spin rate as well as the precession rate). There is a "simple" (nothing is simple!) approximate relation between the torque, the precession rate and the spin angular momentum: T = PM, where P is the angular rate of precession (in radians per second; 2 pi radians = 360 degrees), T is the applied torque and M is the angular memomentum about the spin axis. For a uniformly thick disc of mass m, M = (1/2)msr^2 where s is the spin rate (in radians per second) and r is the radius. In this case s is about 1 rad/sec and P is approximately 3 rad/sec. Unfortunately there is no way of knowing what the effective mass of the UFO might be. Nor is there any indication of what the torque might be. If we knew either or these we could calculate the other and, perhaps, learn something interesting. This torque might be a result of a huge magnetic field associated with the UFO being acted upon by the magnetic field of the earth, although considering that the spin axis is nearly vertical it would seem that only the vertical component of the earth's field would be involved. It might also be a torque applied by the UFO to itself in some way to maintain the orientation of the UFO relative to the local earth surface as the earth spins.
TO BE REVISED AS INFORMATION BECOMES AVAILABLE
MEXICO CITY VIDEO ANALYSIS PRELIMINARY DISCUSSION PART TWO
I have discovered new and significant information from my continued study of the video. Before I present it I would like to point out that I am working from a video copy made from a tape that was received over the "airwaves" by a person in Mexico City. Therefore it is not as clear as the original. In fact, the pictures in the just-published November issue of the MUFON Journal are clearer. Hence I many hope for yet further information when I get a "perfect" copy of the video.
Those of you who subscribe to the MUFON Journal will see printed therein information that was circulated in the network over a month ago (Bill Hamilton's initial report of Oct 1 on UFO Updates and a report from UFO Roundup of Oct. 12).
Further analysis of the video shows that the zoom factor is about 4. This is low for the typical videocamera. Probably the camera was partly zoomed before the first video images. I assume it was zoomed to maximum. This has bearing on the focal length and on the field of view and on the hoax hypotheses discussed in the first part of this analysis.
The UFO appears on video for 23 seconds. The video continues for another 11 seconds after it disappears behind the second building. At the beginning of the video the UFO is stationary for about 8 seconds before moving to the right.
Further checks of the wobble rate confirm that the wobble cycle is approximately 2.2 (+/- 0.2) sec/wobble, or about (1/2) wobble per second. A further check of the rotation rate confirms the roughly 0.16 cycles/sec. or about 6 sec per revolution cited previously.
Bill Hamilton wrote that the rotation rate was once per second, but I don't think this is correct. The moving dark spots are what give the impression of rotation.
I measured the number of frames it takes for a spot to move 0.2 times the length (diameter) of the (assumed circular) disc image.
This motion was measured at the center of the disc image and so corresponds to an angle (relative to the center of the disc) of 0.2 radians (almost exactly). This measurement was difficult to make because the dark spots were so diffuse (could do better with a better copy of the video blowup). However, I found that it requires 5 to 7 frames for a spot to move 0.2 rad. Picking 6 frames as an average number, this means 0.2 rad per (6/30 sec) or 0.2 rad / (1/5 sec) = 1.0 rad/sec. But there are 2 pi = 6.28 (approximately) radians in a revolution, so it requires 6.28 second per revolution. The inverse of this is 0.16 revolutions per second, which is the value given in the first part of this analysis (but without justification).
The UFO's horizontal motion relative to the left hand edge of the first building was discussed in the first part of this analysis. The velocity was found to be constant to a good degree of accuracy as long as the UFO was visible. After the UFO reappeared above the first building and traveled in a level trajectory toward the second it slowed down. Just before it disappeared it was going about 0.6 times as fast as the initial horizontal speed. The measurements suggest some slight oscillation in the speed, but higher resolution will be necessary to prove this.
Careful measurements of the image size using the negative image format (sky dark) and adjusting the brightness so that the UFO is just "above" visible, I find that the initial length on this 1.6x blowup is 38 mm. While above the center of the first building it's length is about 40 mm, suggesting that it got closer. Then, just before disappearing its length is 33 mm long indicating that it moved away.
A study of the image brightness has revealed significant information which is consistent with the above image size measurements. By setting brightness levels appropriately I determined that the image brightness is lowest (greatest contrast against the bright sky) when the UFO is over the first building. The image brightness is slightly higher (slightly less contrast) before the UFO moves behind the first building. Then, of particular significance, is the fact that as it moves toward the second building the contrast decreases (image brightens) continually until it disappears.
The significance of the image brightness changing (image contrast changing) is based on the haze effect or atmospheric "extinction." The farther an object moves away into a bright sky background with haze, the brighter it appears, eventually at some distance reaching the brightness of the sky background, at which distance it "disappears" because there is no longer any contrast between it and the background. For example, a black sphere that moves away from the observer will grow smaller but it will also increase in brightness. The increase in brightness is a result of light scattered by haze particles or dust or air molecules into the path of the light from the sphere to the observer. In this case we have an object, the UFO, which is not as bright as the sky background. When first seen it has some brightness level and contrast to the sky and a size measurement of about 38 mm. Then a few seconds later it's brightness is lower (and contrast is greater) and the image size is greater, both of which are consistent with the UFO moving closer to the camera (about 5% closer). Then as it moves to the right the brightness increases as the size decreases (by about 18%) indicating the object started moving away from the camera before it disappeared behind the building. In fact, it appears to have initiated a curved path away from the camera just before it disappeared behind the building. One may imagine that, if this not a VERY clever hoax, the UFO never appeared on the right side of the second building because it had made a "left turn" (but not at East Gate) and disappeared in the distance.
THIS IS A PRELIMINARY ANALYSIS. SOME NUMBERS (maybe all numbers) QUOTED HERE MAY CHANGE AS A RESULT OF INFORMATION OBTAINED IN THE FUTURE.
The only conclusion possible so far is that if this is a hoax...... then we should all turn left and disappear into the haze..... (where is that East Gate when we need it?)
MORE MEXICO VIDEO ANALYSIS - PART 3
Thanks to a respondent who made his own measurements of the motion of the UFO I have discovered that my estimates of velocity,acceleration and rotation speed are wrong.
I used a blowup version of the video to make the velocity and acceleration measurements. By comparing the time it takes (number of frames) for the UFO to disappear behind the first building I determined that the blowups had also been slowed down. The correct calculations and comparisons with the original calculations are shown below.
From Direct Video From Blowup
frames to go behind building 20 frames
time is #frames times 1/30
sec times scale factor
20 x (1/30)=0.67 sec 47 x (1/30) x 0.425=0.67 sec
Velocity based on previous calculation using 1.6x and assuming 25 ft wide UFO : 16.9 ft/sec
Corrected velocity (use scale factor) 16.9/.425 = 39.7 ft/sec
The velocity change (zero to 39.7 ft.sec) appears to take place in 1 frame of the direct video. Hence the acceleration is 39.7/(1.30) = 1191 ft/sec^2 which corresponds to 37 g's ( g = 32 ft/sec^2).
If the acceleration took place in 2 frames the magnitude of the acceleration was 1/2 of this.
THIS NUMBER SUBJECT TO FURTHER MODIFICATION.
Because of the time scale factor change the wobble rate is about twice what was given before and the apparent rotation rate is about twice what was given before.
NEW INFORMATION : I have been informed that the videographer is known, the original video exists, and there are 9 other witnesses. I cannot verify this information, it is what have been told. I was also told that one of the witnesses was at street level on the opposite side of the building where the UFO finally disappeared andthis witness claims that she saw the UFO "disappear."
If so, this could explain why it was not seen in the video reappearing from behind the building.
Note: if there really is a "Klingon Cloaking Device" it could explain visual reports of objects seeming to fade out without apparent motion.