22+ Witnesses Observe a UFO Larger than a Football Stadium
Yukon Territory, Canada

Investigated by Martin Jasek, M.Sc., P. Eng.


Calculation of UFO Size

Human beings can perceive the size of "unfamiliar objects"* at short distance reasonably accurately. However, this accuracy drops off dramatically after a distance of about 10 metres (33 ft). This is the limit of our binocular vision. To be able to estimate distance and size further away, our eyes would have to be further apart. If we have more than one person, each standing in different locations, we effectively have eyes that are "further apart". This is the basis for the size calculations below. (*For familiar objects (such as a car, building or an animal) for which the size of the object is know to begin with, their distance can be estimated fairly accurately well beyond the 10 metre range. The difficulty comes with unfamiliar objects when both the size and distance are not known).

A reasonably accurate estimate of the size of the UFO (or UFOs) was accomplished through a method based on geometry called "triangulation". Triangulation relies on the observation of an object (in this case a UFO) from at least two different vantage points at the same time. In addition to this, it also relies on an estimate of the angular size from at least one of the witnesses. One way to describe angular size is by comparing the size of the UFO to something being held out at arms length distance. An example would be "the UFO was the size of a fist at arm's length". Another way to describe angular size is to compare the UFO’s size to something else in the scene. An example would be "the UFO was about twice the size of that mountaintop".

Given the large number of witnesses and vantage points associated with this case, six separate calculations of UFO size could be made.

A trip to the Fox Lake sighting location was made with FOX3. The witness showed the locations along the highway where he and FOX2 pulled over to watch the UFO. This distance was measured to be 570 metres apart. We know from FOX2’s testimony that he was directly underneath the edge of the UFO at one point in time (See 3rd drawing by FOX2, Figure 8). 

The next task at hand was for FOX3 to provide an estimate of the angular size of the UFO when it appeared to be directly over FOX2. He was asked to use local land marks to point to the location where the extreme left of the UFO was when the UFO was over his cousin. Then he was asked to point to a location on the extreme right side of where the UFO was when it was over his cousin.   Finally, FOX3 was asked to point with both arms at the two directions (Figure 32). This distance was measured to be about 1.2 metres (4 feet) apart. The perpendicular distance from his eyes to the tip of his hands was measured to be 0.4 metres (1.3 ft). Using trigonometry, this calculates out to be about a 113 degrees of angular distance. Projecting this angle forward the 570 metres distance to the UFO one obtains a UFO size of 1710 metres or about 1.7 kilometres (1.1 miles) in length (See Figure 2). Note that the angle in Figure 2 is only about 80 degrees and not 113. However, the size of the UFO is presented as the calculated 1.7 km. The reason for this distortion of the angle is the fact that the precise shape of the UFO is not known and the shape of the UFO is important in determining its size for close observers (less than about 3 UFO lengths). Nevertheless, this smaller angle is conservative. For a more detailed discussion about this click here (under construction).

It was also of interest to obtain the elevation of the UFO in this observation. Especially since it was almost directly overhead of FOX2. While on location with FOX3, the investigator asked him to take a photograph of the scene and hold his finger at the spot where the bottom of the UFO was when it was over his cousin (FOX2), (See Figure 33). An angular height of 6.5 degrees above the ground was determined from the photograph. Using trigonometry one obtains a height of the UFO of only 65 metres (213 ft) above FOX2! This is consistent with FOX3’s estimate of 4 or 5 lamppost heights.

Calculation #2 and #3
FOX4 was presented with a panoramic set of photographs taken of the scene from his vantage point. He was asked to mark on the photo the length of the UFO. He was also instructed to hold the photograph 8 to 9 inches away from him in order that the angular size of the landmarks and actual scene was about the same. He gave two estimates (Figure 12). The two angles worked out to be 12.8 and 8.44 degrees angular size for the UFO. Since it was established that FOX2 and FOX3 were observing the UFO at the same time further up the lake, we know the distance to the UFO to be about 8 km (5 miles). Again, projecting those angles out to that distance, the UFO size for the two estimates worked out to be 1.8 km (1.1 miles) and 1.2 km (0.75 miles) in length respectively. (Figure 2). Note: the photographs were taken with a standard 50 mm lens (35mm camera) as not to distort the size of the objects in the seen such as a wide angle lens does or magnify them like a telephoto.

Calculation #4
Similarly to above, FOX5 was presented with the same panoramic set of photographs taken of the scene. She gave her estimate of angular UFO size in Figure 12. The angle worked out to be 3.95 degrees. Projecting this angle out towards the UFO 8 km (5 miles) away, one obtains a UFO size of 0.88 km (0.55 miles) in length.

Calculation#5 and #6
These two calculations were based on observations by witnesses near the Village of Pelly Crossing. To her credit, PEL2 compared the size of the UFO she observed to something in the scene at the time of observation. She compared the UFO to the size of the star constellation, "The Big Dipper". This is more accurate than estimating after the fact or from a photograph. Since she perceived the angular length of the UFO to be the same length as the Big Dipper, from the position of the stars we can deduce that the angle was about 25 degrees. (See drawing by PEL2 (Figure 23) and angle projected in map shown in Figure 22). Since PEL4, 5, 6, and 7 were observing the UFO at about the same time from a different vantage point, we could triangulate a location of the UFO shown in Figure 22. The estimated trajectory of PEL2 was also used for a second calculation. The second calculation would not normally be considered a triangulation since it involves observations from only one vantage point. However, some weight has to be given to the estimated UFO trajectory of witness PEL1 that is even further away from PEL2. By projecting the angle of the Big Dipper out to these two trajectory locations, one obtains two more calculations of UFO size. The first trajectory is 2.6 km (1.6 miles) away and yields a UFO size of 1.2 km (0.75 miles) in length. The second trajectory is 4.4 km (2.8 miles) away and yields a UFO size of 2.0 km (1.3 miles) in length.

To summarize we have obtained the following sizes of the UFO by means of triangulation:

FOX3 with FOX2:    1.7 km (1.1 miles)
FOX4 with FOX2:    1.8 km (1.1 miles)
FOX4 with FOX2:    1.2 km (0.75 miles)
FOX5 with FOX2:    0.88 km (0.55 miles)
PEL2 with PEL4,5,6,7:    1.2 km (0.75 miles)
PEL2 with PEL1:    2.0 km (1.3 miles)

This is consistent with witness testimony of the object appearing to be "huge" in the sky. Several witnesses gave size estimates of their own and these were generally smaller than those obtained through the more accurate triangulation:

FOX2:     0.5 km (0.3 miles) based on relative size to lake width (Figure 7)
FOX3:     0.21 km (0.13 miles)- comparable to a football stadium
FOX4:     0.5 to 0.7 km (0.3 to 0.4 miles) – direct estimate
PEL1:     1.2 km (0.75 miles) – direct estimate
PEL3:     0.5 km (0.3 miles) – direct estimate

By any stretch of the imagination or calculation, this thing was BIG!

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