Analysis of Radar and Air-Visual UFO Observations
on 24 October 1968 at Minot AFB,
North Dakota, USA
Although several photos show more than one echo, in the following calculations I will consider only the most intense echoes. Distance will be in nautical miles (1852 meters), speed is given in nm / hour (knots) and converted into km / h, and all speeds are relative to the speed of the B-52 at ~250 knots (460 km/ h, or 285 mph).
- Photos 771-772. The position of the UFO echo changes respectively from 1.73 nm at 038 degrees, to 1.12 nm at 244 degrees. This corresponds to a displacement of 2.31 nm in 3.77 seconds, which is an average relative speed of 2205 knots or 4085 km /h (2538 mph).
- Photos 772-773. The position of the UFO echo changes respectively from 1.12 nm at 244 degrees, to 1.05 nm at 039 degrees. This corresponds to a displacement of 2.12 nm in 1.29 seconds, which is an average relative speed of 5916 knots or 10957 km / h (6808 mph).
- Photos 773-775. The position of the UFO echo changes respectively for 1.05 nm at 039 degrees, to 1.69 nm at 348 degrees. This corresponds to a displacement of 1.31 nm in 5.58 seconds, which is an average relative speed of 847 knots or 1569 km / h ( 975 mph).
- Photos 775-776. The position of the UFO echo changes respectively from 2.13 nm at 348 degrees, to 1.08 nm at 040 degrees. This corresponds to a displacement of 1.69 nm in 3.43 seconds, which is an average relative speed of 1773 knots or 3285 km / h (2041 mph).
- Photos 776-778. No displacement.
- Photos 778-779. Displacement towards the right of 0.05 nm in 3 seconds, or a relative speed of 60 knots or 110 km / h (68 mph).
- Photos 779-780. Displacement towards the left of 0.05 nm in 3 seconds, or relative speed of 60 knots or 110 km / h (68 mph).
- Photos 780-781. Displacement towards the right of 0.1 nm in 3 seconds, or a relative speed of 120 knots or 220 km / h (136 mph).
- Photos 781-782. Displacement towards the right of 0.04 nm in 3 seconds, or a relative speed of 48 knots or 90 km / h (56 mph).
- Photo 783. The UFO echo disappears in less than 3 seconds.
All radarscope photographs display a central region referred to as the altitude hole, which is related to the altitude of the B-52. A comparison of the altitude hole diameters in successive photos shows that the radius progressively decreases. This verifies that the B-52 was descending in altitude.
While cruising at FL 200 (Flight Level 20,000 feet altitude, or 6100 meters), the B-52’s altimeter would be set to the standard pressure of 29.92 inches of mercury (1013.25 hectopascals). All aircraft at flight level set their altimeters to the same standard pressure, and the ground controllers allocate different flight levels to aircraft in order to avoid collisions due to altimeter-setting errors. According to the Blue Book documents, the B-52 descended from FL 200 down to the altitude of the Minot runway, which is 1723 feet above Mean Sea Level (MSL). On reaching FL 180 (18,000 feet), procedure required the pilot to adjust the altimeter from the standard pressure to the local MSL atmospheric pressure setting, in order to assure accurate altitudes above the ground. In this instance, according to the transcription of communications between RAPCON and the B-52, at 4:09 a.m. (CDT) this corresponded to 30.12 inches of mercury (1019.77 hectopascals).
The change in the altimeter pressure setting of 6.52 hectopascals corresponds to a reduction of the indicated altitude by 190 feet (58 meters). Although the difference is essentially negligible to our calculations, the B-52 actually began its descent at a true altitude of 19810 feet MSL.
For purposes of our study, let us assume that the distance to the edge of the altitude hole in the photos is equal to the B-52 altitude. Table 5 shows that the altitude for photo 771 (at 9:06:14Z) is 2.20 nm, and for photo 782 (at 9:06:51) is 1.82 nm. The time interval between photos is 37 seconds, and the reduction of the altitude hole radius is 0.38 nm (equal to 2307 feet). As a result, the reduction of the altitude hole radius for one minute would be 3742 feet.
Minot AFB, Operations Division chief Colonel Arthur Werlich, who was also a B-52 pilot and responsible for the UFO investigation, provided the speed of the B-52 during its descent in the Basic Reporting Data:
C. MANNER OF OBSERVATION: (1) GROUND-VISUAL, AND AIR ELECTRONICS (ASQ-38 IN STATION KEEPING MODE). (2) NO OPTICAL AIDS USED. (3) B-52H, JAG31. ELECTRONIC SIGHTING DATA: FL200 TO APPROXIMATELY 9,000 FEET, 116 DEGREES MH, 280-230 IAS, MINOT AFB: VISUAL SIGHTING DATA: 3200 FEET MSL, 335 DEGREES MH, APPROXIMATELY 180 IAS.
The B-52’s indicated air speed during descent ranged from 280 to 230 nm / h (knots; kt), or an average speed of 250 kt, which would require 14.4 seconds for the B-52 to travel a distance of one nautical mile. During the 37 seconds that were captured by the photographs, the B-52 traveled a distance that ranged from 2.36 to 2.88 nm, or an average distance of about 2.57 nm.
If the radius of the altitude hole were equal to the altitude of the B-52 above the ground, then the aircraft would have traveled between 2.36 and 2.88 nm while descending 0.38 nm. This corresponds to a descent slope of:
- Arctg (0.38 / 2.36 or 2.88) = 9.1° and 7.5° respectively.
Let us examine the transcription of communications between Radar Approach Control (RAPCON) and the B-52 aircraft at the moment when communications resumed following the VHF radio transmission failure.
According to the documents, the B-52 was at an altitude of 19810 feet MSL, at a distance of 35 nm from the Deering TACAN transmitter (situated adjacent to the runway at 37% of the length from the northwest end). If the B-52 descended 2307 feet each time and moved forward 2.36 or 2.88 nm at an altitude equal to the MSL altitude of the runway at 1723 feet, the distance traveled would have been:
- 2.36 or 2.88 (19810 — 1723) / 2307 = 18.50 and 22.58 nm.
If the beginning of the descent of the B-52 had been 35 nm from the TACAN, it would have touched the ground at either 16.5 or 12.42 nm ahead of the runway (30.6 or 23 km). Because this is not possible, the actual rate of descent had to be much less than that, which also means that the radius of the altitude hole is not equal to the B-52 altitude. As a result, a constant corrective factor must be applied, which takes into account that the radar antenna had to be tilted upwards from its horizontal axis in keeping with information in the technical manual for Station Keep mode. We can determine the order of magnitude of the corrective factor, which is the cosine of the angle of incline (Tilt) of the antenna radar. In order to do that, let us write equations for photos 771 and 783. Our variables are as follows:
- Tilt = tilt-up angle of the radar antenna. Tilt is also the half of the top angle of the blind cone of the radar centered on the nadir of the B-52.
- K = Cos (Tilt)
- Alt771 = ground altitude of the B-52 during photo 771 in nautical miles.
- Alt783 = ground altitude of the B-52 during photo 783 in nautical miles (1 nm = 1852 m or 6072 feet).
Alt771 = 2.20 K (1)
Alt783 = 1.82 K (2)
Next, let us examine the descent slope of the B-52 within strict limits while keeping in mind that certain parameters are still not accurately known. The speed of the B-52 must be between 280 and 230 knots, which corresponds to a traveled distance between 2.364 and 2.878 nm over the course of 37 seconds. The beginning of descent must be located 35 nm from the position of the TACAN adjacent to the runway. The end of descent must be at the distance prescribed by the Instrument Approach Procedures in the 2003 Terminal Procedures (approach plates) for Minot AFB. Which is either at the Outer Marker located at 14 nm from the Deering TACAN at an altitude of 3500 feet MSL, or at the Final Approach Fix (Middle Marker) located at 6.3 nm from the TACAN at 3200 feet MSL. As a result, the slope of the smallest descent rate corresponds to a traveled distance of:
- 35 - 6.3 = 28.7 nm.
The slope of the largest descent rate corresponds to a traveled distance of:
- 35 - 14 = 21 nm.
The loss of altitude of the slope of the smallest possible descent rate corresponds to:
- 19810 - 3200 = 16610 feet or 2.736 nm.
The loss of altitude of the slope of the largest possible descent rate corresponds to:
- 19810 - 3500 = 16310 feet or 2.686 nm.
Thus, the slope of the smallest possible descent rate is:
- 2.736 nm / 28.7 nm = 0.095331 (or an angle of 5.44°).
The slope of the largest possible descent rate is:
- 2.686 nm / 21 nm = 0.1279048 (or an angle of 7.3°).
Naturally, the smaller slope corresponds to a lesser speed, whereas the larger slope corresponds to a higher speed.
Let us call:
- Dis771 = the distance traveled since the beginning of descent at the time of photo 771 expressed in nm.
- Dis783 = the distance traveled since the beginning of descent at the time of photo 783 expressed in nm.
If the MSL altitude of Minot AFB is 1723 feet or 0.284 nm, and if 19810 feet corresponds to 3.2625 nm, then the slope of the smallest possible descent rate (departure at 35 nm from the Deering TACAN) is:
Dis783 - Dis771 = 2.364 nm (3)
Alt771 + 0.284 = 3.2625 - 0.1028571 Dis771 (4)
Alt783 + 0.284 = 3.2625 - 0.095331 (Dis771 + 2.364) (5)
Alt783 + 0.284 = Alt771 + 0.284 - 0.2431542 nm = Alt 771 + 0.284 - 1476 feet. (6)
The slope of the largest possible descent rate (departure at 35 nm from TACAN) is:
Dis783 - Dis771 = 2.878 nm (7)
Alt771 + 0.284 = 3.2625 - 0.1279048 Dis771 (8)
Alt783 + 0.284 = 3.2625 - 0.1279048 (Dis771 + 2.878) (9)
Alt783 + 0.284 = Alt771 + 0.284 - 0.36811 nm = Alt 771 + 0.284 - 2235 feet. (10)
In any case, according to (1) and (2) we have:
Alt783 / Alt771 = 1.82 / 2.20 = 0.8272727 (11)
Alt783 = 0.8272727 Alt771. (12)
Regarding the slope of the smallest possible descent rate (departure at 35 nm from the TACAN) we have the following:
Alt783 = Alt771 - 0.2431542 nm = 0.8272727 Alt771 (13)
Alt771 = 1.4077346 nm = 8548 feet (14)
Alt783 = 7071 feet. (15)
And, according to (4):
Alt771 + 0.284 = 3.2625 - 0.095331 Dis771. (4)
Dis771 = 15.27 nm (16)
Dis783 = 15.27 nm + 2.364 = 17.64 nm. (16 bis)
For this hypothesis the distance of photo 783 from the TACAN would be:
Distance 783 from TACAN = 35 - 17.64 = 17.36 nm. (16 ter)
As a result, the smallest descent slope is compatible with the radarscope photographs.
If we consider the slope with the largest possible descent (departure at 35 nm from the TACAN), we have the following:
Alt783 = Alt771 - 0.36811 nm = 0.8272727 Alt771 (17)
Alt771 = 2.13116 nm = 12940 feet (18)
Alt783 = 17631 nm = 10705 feet. (19)
According to (8):
Alt771 + 0.284 = 3.2625 - 0.1279048 Dis771. (8)
Dis771 = 9.50 nm (20)
Dis783 = 9.50nm + 2.878 = 12.38 nm. (20 bis)
For this hypothesis the distance of photo 783 from the TACAN would be:
Distance 783 from TACAN = 35 - 12.38 = 22.62 nm. (20 ter)
As a result, the largest descent slope is also compatible with the radarscope photographs.
Using two extreme speeds of the B-52 at 280 and 230 knots, we have concluded that the smallest and largest descent slopes are compatible with radar photographs. But what would happen if we consider an averaged speed of 250 knots, while keeping the largest slope? For this hypothesis the 37-second distance traveled during the radar photographs would have been 2.57 nm. We then calculate:
Dis783 - Dis771 = 2.57 nm (21)
Alt771 + 0,284 = 3.2625 - 0.1279048 Dis771 (22)
Alt783 + 0.284 = 3.2625 - 0.1279048 (Dis771 + 2.57) (23)
Alt783 = Alt771 - 0.3287 nm = Alt 771 - 1996 feet (24)
Alt783 = 0.8272727 Alt771 (12)
Alt783 = Alt771 - 0.3287 nm = 0.8272727 Alt771 (25)
Alt771 = 1.903 nm = 11555 feet (26)
Alt783 = 1.5743 nm = 9559 feet. (27)
According to (22):
Dis771 = 8.409 nm (28)
Dis783 = 8.409 nm + 2.57 nm = 10.98 nm. (29)
For this hypothesis the distance of photo 783 from TACAN would be:
Distance 783 from TACAN = 35 - 10.98 = 24.02 nm. (30)
As can be seen, the largest descent slope and an average speed of 250 knots are compatible with the radarscope photographs. Note that the reduction of the speed of the B-52 by 30 knots moves photo 783 away from the TACAN by 1.40 nm. Could we refine the speed and the position of the B-52 during the photographs by drawing on other physical evidence?
Photo 783 is the only photo in the series that shows the apparent details of a large ground feature. The lack of terrain features in the other photos is normal because the region is relatively flat, and mostly farm fields with few topographical details. This feature is located near the 5 nm (9.26 km) range limit of the radar mode and is quite large, since the distance between the heading markers (7 and 8) is one nautical mile (1852 m). It appears to be a body of water, which returns less of the radar signal than the surrounding terrain.
Here is what we can see in the upper left corner of photo 783:
In order to properly orient the feature to a map of the region, we can rotate the photo to the true course of the B-52 at 122 degrees. The resulting image is a 50% transparency with a change of scale in order to superimpose the photo on the map in Figure 6.
The apparent watercourse seems to correspond to a section of Lake Darling, ND, located just west of the missile Launch Facility N-7, and the small rural town of Grano, ND. The B-52 radar seems to paint the west bank of the lake. Let us consult a more detailed topographical map.
On this topographical map the narrowing contour lines reveal that elevations adjacent to the shoreline of the lake are comparatively abrupt. Considering that photo 783 was acquired at a distance of ~ 4.3 nm and a ground altitude of ~1.3 nm, the viewing angle would be 16.6 degrees. It is conceivable that at this limited perspective the west shore would be somewhat concealed from the radar, though the characteristic peninsulas within the hooked-bays in the center of the map is rather clear. To understand more clearly what the radar has captured, let us consult a satellite photograph of this section of Lake Darling, ND.
On the satellite photograph we clearly see the shoreline and roads, as well as drainage flows along the elevated terrain adjacent to the lake. At the time of the radarscope photos, the B-52 would have been situated in the west-northwest to west direction at roughly 7-4 nm. If we convert the scale and orientation of photo 783 and superimpose it on the satellite photograph we get the following:
Properly scaled and oriented to the true heading of the B-52, when we place the B-52 on the flight track we see that the curves of the shoreline of Lake Darling correspond to those of the dark terrain features on the periphery of radarscope photo 783. In fact, several details of the radar image of the lake correspond extremely well to those of the satellite photograph as indicated in Figure 35.
Based on these maps, we can accurately determine the location of the B-52 at the precise time of photo 783, by measuring the pixel distance and the direction of the southern end of the peninsula within the hooked-bays. The distance of the B-52 in the photo is 4.658 nm at 078 degrees, although this result is an inclined distance measured from an altitude of 1.763 nm above the ground. Consequently, it is necessary to use Pythagoras’ theorem to calculate the distance measured on the ground:
(Ground Distance)2 = (4.658) 2 - (1.763)2 (31)
Ground Distance #783 = 4.31 nm (31 bis)
Accordingly, the ground distance from the B-52 to the south hooked-bay within the elbow of the lake is 4.31 nm at azimuth 258 degrees. When we draw this direction and distance on the USGS map we find that the coordinates are located precisely on the straight B-52 TACAN approach trajectory extending from the WT fix to the runway at Minot AFB. We now have an independent verification that the B-52 was on the correct descent trajectory to Minot AFB. In addition, we now know the precise location of the B-52 at 09:06:51Z, in relation to the Deering TACAN located adjacent to the runway at Minot AFB:
- TACAN distance = 18.8 nm ( 34.8 km) at 306° true.
The B-52 was in fact 16.2 nm (30.0 km) away from the WT fix, where it began the descent following a standard 180° turnaround. This position is drawn on the map of Figure 36.
Unfortunately, none of the other photos reveal easily identifiable details of the terrain. However, since the B-52 heading is toward the top of the photos and the ground is moving downwards, we can attempt to discern the lake in photo 782. By significantly forcing the contrast and brightness of the positive image, it is possible to differentiate what appear to be details of the lake near the same heading markers (7 and 8). These blurred stains are definitely present, though only slightly above the radar noise of the ground.
To determine whether photos 782 and 783 are correlated, we shall make use of specialized software in order to examine the photos at the level of pixels. We find that both photos contain a blurred peak, which indicates a vertical displacement of 0.211 nm between the two photos. However, since photo 782 is very noisy this maximum is not very accurate.
It would appear that the B-52 moved 0.211 nm during 2.98 seconds (rather than 3 seconds, since the rotation of the antenna is 2 degrees less in azimuth), and the speed of B-52 was 254 knots (470 km / h). For a B-52 in descent this speed is quite reasonable, even though the measurement might not be very reliable due to the poor resolution of the lake feature in photo 782.
The radarscope photos were taken over a total period of 37.5 seconds (photo 771 at 1.5 seconds, and 12 photos at 3 seconds each), and the extreme indications of the clock are also equal to a period of 37.5 seconds (09:06:14—09:06:51.5Z = 37.5 seconds). Therefore, the B-52 traveled 2.65 nm at the previously measured speed. The two extreme positions in relation to the Deering TACAN are:
- Photo 783: 306° at 18.8 nm
- Photo 771: 306° at 18.8 + 2.65 = 21.45 nm.
We observe that the first radarscope photo (771) was exposed directly west of the missile Launch Facility November-7, at a distance of 7.65 nm (14.2 km). In relation to the WT fix, the B-52 was therefore:
- Photo 783: 126° at 16.2 nm
- Photo 771: 126° at 13.55 nm.
Assuming a constant speed of 254 knots, at the beginning of the photos (771), the B-52 was in flight for 3.2 minutes after having passed directly over the WT fix, and had a remaining 5.07 minutes of flight before passing over the Deering TACAN transmitter.
What is readily apparent is that the position indicated by Col. Werlich is entirely incompatible with the direction and distance to the shorelines of Lake Darling, as well as the altitude of the B-52 at the time of the photos.
It is possible to illustrate to scale the successive positions of the echo in relation to the B-52 along its trajectory. Because the radar measures only distance and azimuth, we cannot determine the true altitude of the UFO. Consequently, in Figure 41 we assume that the UFO and B-52 were at co-altitudes. In the more probable hypothesis that the UFO was beneath the B-52, the following figure depicts a UFO trajectory that is too extensive by a factor we will be calculating later. Whereas the azimuths between the UFO and the B-52 would remain consistent, the distance would vary depending on the altitude angle (slant range) of the UFO below the altitude of the B-52. Consequently, it would be necessary to generate a slight anamorphous effect in order to illustrate the trajectory from this perspective.
The radar will paint the actual size of a target if the target is not moving relative to the radar antenna, though, as with all optical photography, a small rapidly moving target could appear enlarged on the radarscope if it is moving in the same direction as the radar beam sweep. Therefore, we can assume that the dimensions of the UFO radar echo could have increased artificially due to the high speed of the UFO, the rotation speed of the radar beam (120° / second), and the finite radar beam width.
We will ignore the actual angular beam width of the B-52 radar in azimuth, in order to be able to estimate the enlargement of the echo as a result of the finite beam width. We do know that the radar distance resolution was about 120 feet (36.6 m).
It is therefore probable that the radar angular (azimuth) resolution was such that at one nautical mile distance the resolution in distance and azimuth was of the same order of magnitude, corresponding to an angle of 1.13 degrees in azimuth, elapsed by the rotation of the antenna in only 9 milliseconds. Given the highest speed we have calculated (20466 km / h), the maximum lateral displacement of the UFO at a distance of 1 nm would have been only 51 meters during the 9 milliseconds of beam sweep. We can therefore infer that the dimensions of the echo were not dramatically altered (less than 20 %) by the relative speed of the UFO and the sweep-speed of the radar beam.
Since the radarscope photographs record only instantaneous positions, it is probable that the actual UFO movements correspond to a spiraling trajectory around a vertical axis beneath the B-52. As we will see, the orientation of the main axis of the UFO has nothing to do with the successive positions of the echo on the photographs, because the real trajectory of the UFO between the photos is unknown.
Witness accounts suggest that the UFO likely had a distinctly ovoid shape, which is also discernible in the radar photographs. It is intriguing to compare the orientation of the long axis of the echo (green color) with the trajectory of the UFO (blue color), as well as to the positions of the B-52, which is moving along the blue line from the upper left to the lower right at a speed of about 460 km/ h (285 mph). In the following illustration, the UFO is assumed to be at the same altitude as the B-52. This being the case, we can now extend the UFO trajectory radially at this scale.
We observe that the successive orientations of the main axis of the UFO are virtually never parallel to the straight trajectory of the B-52. In numerous photos (especially photos 776 to 782), the axis of the UFO echo is nearly perpendicular to the trajectory of the B-52.