Report On Phoenix Light Arrays
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CALIBRATION OF SIGHTING DIRECTIONS
The angles, distances and altitudes presented below are the result of a long
series of calibrations of the nighttime videos using daytime and evening
videos and film to determine accurate sighting directions and angular elevations.
The angles are true azimuth (relative to map north) as determined by using
a contour map to provide reference directions. The contour map (Arizona Atlas
and Gazetteer, by DeLorme Mapping) shows the location of a particular peak
in the Estrella range which is 4512 ft high and which appears near the center
of the field of view of K's video. K's daytime comparison video shows where
this peak appears relative to the scenery that appears in the nighttme video
scene, FIGURE 1 (a single frame from th video). This peak also appears in
photographs taken by L that show the evening sky, the lights of the city
and neaby house lights. These photographs were anglecalibrated and used
to determine the angle between the sighting line to the 4512' peak and the
angle to a nearby house light which appears in the nighttime video (see
FIGURE
2). There is a similar situation, although not as precise, for the R video
(see FIGURE 4). The P video is different in that an evening comparison video
was not made before a wall was built (by a neighbor) which blocks the view
of distant ground lights of known direction. Hence, in this case the sighting
direction was estimated from onsite inspection with the witness pointing
in the direction of the sighted lights, a direction that is within a few
degrees of south (i.e., azimuth 180 +/ 5 degrees).
The cameras used by L, K and P were calibrated to determine the number of
degrees per unit length on the film in unzoomed and maximum zomed conditions.
(Alternatively, one could say that the effective focal length was measured).
This is done by a standard technique: place a yardstick at a known distance
to create a known angle and measure the size of the image on film or on a
video display. (The angular size of the yardstick image is twice the inverse
tangent of 3/2 feet divided by the distance.) Dividing the angle by the length
of the image on the film or screen provides a calibration in terms of degrees
per unit length (i.e., per inch, per millimeter or, in a computer "grabbed"
frame, degrees per pixel). (This method is satisfactory for angles up to
20 degrees or so. A more accurate method for angles greater than 10 degrees
makes use of the effective focal length determined by the ratio of the distance
to the yardstick divided by 3 (feet) and multiplied by the measured size
of the image.) The calibrated photos and videos are used to determined angular
spacings between the lights of interest.
The azimuth (the angle measured clockwise from true north) of the 4512' peak
from the location of the K house on the topographical map is 204.75 (+/
0.5) degrees. A line from the L house to the 4512' peak gives azimuth 221.3
(+/ 0.5) degrees. Also needed for the trigonometric calculation are the
azimuth and distance from the K house to the L house. These are 134.75 (+/
0.5) degrees and 7.5 miles. (Note: a large scale city map suggests the spacing
is more like 7.8 miles. However, 7.5 is used here to be consistent with the
topographical map.) The topographical map also indicates that the altitudes
of the K and L houses are about 1,600 ft (that of Phoenix itself is about
1,000  1,100 ft). The estimated heights of the lights are based on L's video
data.
The sighting lines and light locations for the slanted linear array illustrated
above are given below. First are the data for K and L which are quite precise,
thanks to the availability of an unambiguous common reference point (the
4512' peak). These are followed by the data from the R and P videos.
TABLE 1: JANUARY 14, 1998 LINEAR ARRAY OF LIGHTS FROM THE K AND L VIDEOS



CALCULATED 

CALCULATED 
LIGHT 
AZIMUTH 

DISTANCE 

ALTITUDE ft 
(order of 
(+/ 1 deg ) 

(+/ 5 miles) 

(+/ 1000 ft) 
appearance ) 
FROM K 
FROM L 
FROM K 
FROM L 
(AMSL*) 
1)left end light 
199.0 
204.1 
79 
76 
15,000 
2)next to right 
202.3 
207.8 
75 
72 
16,000 
3)next one 
207.3 
213.5 
68 
66 
17,000 
4)right end 
209.0 
215.5 
65 
64 
17,500 
SPACINGS between lights: 1 to 2  6 miles; 2 to 3  9 miles; 3 to 4  3.4 miles
*AMSL = above mean sea level
FIGURE 9 is a graph or map created using the above azimuth directions and
the locations of the K and L houses. It shows that the linear array was actually
a slight curve as seen from above.
Figure 9

Figure 10

The sighting directions of the lights videotaped by R and P are not as well
determined. In the case of R the sighting directions are determined in reference
to notwelldefined geographical features: Santan Mountains at about 194
(+/ 3) degrees azimuth and a small, flattopped butte about 3 miles away
at about 243 (+/2) degrees azimuth. The sighting line to the left end light
of the array could be at an azimuth as low as 218 deg or as large as 223
deg. Hence I have chosen to make that sighting line 221 deg in order to make
it agree with the location of the left end light as determined by the K and
L triangulations. The angular spacing between the left end and right end
lights is also not well determined since the camera was neither fully zoomed
nor fully unzoomed. Reference to a rather indistinct feature, the length
of the ridgeline of the roof a nearby house that appears silhouetted against
the horizon (FIGURE 4), provides an approximate angle calibration (degrees
per unit length along the video screen) which leads to the estimate that
the right end light is about 11 deg to the right of the left end. Hence the
sighting line to the right end light is set at 232 deg azimuth. Upon plotting
this azimuth from R one sees it crosses the sighting lines from K and L a
few miles southwest of the point where the K and L sighting lines cross (FIGURE
10), suggesting that the lights may have been farther away from K and L than
is given in Table 1 above.
A similar problem occurs with the P video. In this case it is known that
the general direction was due south based on the layout of the house and
the street. The sighting line was basically parallel to a porch wall that
runs almost exactly northsouth (perpendicular to the eastwest road in front
of the house). However, varations from this due south direction could well
have been 5 degrees or so. (Unfortunately the only ground reference light
is now blocked from calibration by a wall some distance away. It might still
be possible to get an exact direction to the ground light with further onsite
investigation, however.) The P camera was calibrated using the method outlined
above. The angular length of the array was determined to be about 17 degrees.
In order to compare with the positions of the end lights as determined by
K and L, the direction to the left end light was arbitarily set to agree
with the left end light of K and L, just as was done with the left end sighting
line in the R video (FIGURE 10). It turns out that the sighting line from
P to the left hand light (#1) as defined by the K  L triangulation is due
south (azimuth 180). Hence the azimuth the right hand light is 180 + 17 =
197. Upon plotting this azimuth one finds that the direction to the right
end light is too far to the right to agree with the position of the right
end light as determined by K and L (FIGURE 10) and, in fact, intersects the
K sighting line at a location about 10 miles farther away than indicated
in Table 1. In fact the P and R sighting lines to the right end light intersect
at a location about 14 miles farther from K and L than the intersection of
the K and L sighting lines. If one uses only the P and R sighting lines and
rotates the R sighting lines to 218 deg (left end) and 229 deg (right end)
one gets intersection points with the P sighting lines which are even farther
away from the observers than is shown in FIGURE 10.
TABLE 2: JANUARY 14, 1998 LINEAR ARRAY DATA FROM THE R AND P VIDEOS

AZIMUTH 

DISTANCE 




(+/ 5 miles) 


FROM R 
FROM P 
FROM R 
FROM P 
left end 
221(+/ 1) 
180(+/ 5) 
85 
61 
(not determined) 




(not determined) 




right end 
232(+/ 1) 
197(+/ 5) 
>76 
>42 
The conclusion from these triangulations
is that the lights of the linear array were more than 60 miles from K and
L and may have been more than 80 miles away.
Other information about the lights not related to sighting directions is
also of interest. It is obvious from the videos that all the lights are very
bright, confirming the observations of the witnesses. The exact colors are
not obvious from the videos, which show basically white lights. However,
one type of data from the videos is reasonably unambiguous, namely, the durations
of the individual lights. Unfortunately the various witnesses either did
not have their cameras running before the lights appeared or made short "camera
stops" during the sighting. Nevertheless, the time durations are typically
found to be in the 4 to 5 minute range, as illustrated below. (Note: the
R video is not included since all the lights were already on when R started
videotaping.)
TABLE 3: DURATIONS OF THE LIGHTS minutes:seconds

From K video

From L video

From P
video 
left end light 
4:26 
4:20 
4:30(?) 
next one to right 
4:35 
over 4 min 
4:37 
next one 
4:42 
over 3:38 
4:23 
right end light 
4:40 
over 4 min 
4:45 




(note: K stopped his camera; estimated stop
time is 15 seconds incorporated into these duration estimates. L stopped
for an unknown time duration.)
By comparing the positions of the lights with nearby fixed lights one can
determine that these lights drifted slightly to the left and
downward.
LIGHTS SEEN AT THE FAR RIGHT BY K AND L
Shortly after the linear array lights disappeared K and L (but not R and
P) noticed first one, then two, then three lights close together and far
to the right of the direction to the linear array. They videotaped these
lights. The sighting directions to the approximate center of these lights
is given below.
TABLE 4: JANUARY 14, 1998 LIGHTS AT THE FAR RIGHT seen by K and L only
AZIMUTH 

DISTANCE 
ALTITUDE 

FROM K 
FROM L 
FROM K 
FROM L 

219.75 
224.7 
87 
86 1/2 
8,000 ft 
The location of these lights is illustrated
in FIGURE 11 along with illustration of the locations of the linear array
and the triangle discussed below.
THE JANUARY 14, 1998 TRIANGULAR ARRAY OF LIGHTS
A few minutes after the linear array lights disappeared other lights appeared
(including the "far right lights" discussed above) and then a triangle was
formed as illustrated in FIGURES 5 
6 
7 and
8. The positions of the triangle
lights as determined from the K and L videos is illustrated in
FIGURE 12
in relation to the other formations .
TABLE 5: JANUARY 14, 1998 TRIANGLE OF LIGHTS as determined from the K and L videos.

AZIMUTH 

DISTANCE 

ALTITUDE 

FROM K 
FROM L 
FROM K 
FROM L 
(Based on L) 
leftmost light 
199.0 
203.9 
82 
79 
13,000 
middle (upper) 
200.1 
205.1 
81 
78 
20,000 
rightmost light 
202.2 
207.1 
84 
81 
15,500 
It is interesting to note that in the K,
L and R videos the upper (middle) light appears between the left and right
side lights, with the upper light a bit more to the right in the R video
because of his sighting direction. However, in the P video the upper light
appears over the left hand light. This can only occur if the upper light
is closer than the lower lights, as is, in fact, determined by the K an L
sighting directions.
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© copyright B. Maccabee, 2000. All rights reserved.
