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 angle-calibrated 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 on-site 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.

*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 not-well-defined geographical features: Santan Mountains at about 194 (+/- 3) degrees azimuth and a small, flat-topped 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 north-south (perpendicular to the east-west 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 on-site 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.

	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

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.)

	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

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.

AZIMUTH		DISTANCE	ALTITUDE
FROM K	FROM L	FROM K	FROM L
219.75	224.7	87	86 1/2	8,000 ft

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 .

	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