Estimation of the Location, Trajectory, Size, and Altitude
of the "Norway Spiral" Phenomenon

"...... The first thing that jumps out here is that if the missile malfunctioned over the White Sea as reported, it should have been visible in northern Russia, Finland and Sweden as well as Norway -- yet the island of Tromsø, .......... was where it was the most visible, and no sightings were reported in Finland or Russia........"

"...... The EISCAT facility is absolutely dead-center on Amini's line from Tromsø ...... At this point there can be no doubt. EISCAT definitely was responsible for the Norway Spiral. X marks the spot."

Photos #1 - 5) © Jan-Petter Jørgensen at Skjervoy, all equally scaled by the background Kvanangstinder mountains showing both significant movement and growth of spiral.

Image #6) Scaled superposition of the above first four photos showing the trajectory and dramatic growth.

In Image #6 above, the first four photos from Skjervoy have been scaled and superimposed, showing the obvious growth and movement of the spiral.  This brings to question, is it coming closer, moving away, or translating sideways relative to the observer?  These are questions we will attempt to answer in the following analysis.  Another example photographed near Lysnes, 28 miles (45 km) southwest of Tromsø, also showing a similar progression of this event:

Photos #7, 8, & 9)  Progressive void and spiral expansion near Lysnes (at same scale) © Vidar Bjørkli.

Image #9a) Superposition of above 3 photos.

Because the phenomenon was in motion, in order to pinpoint the location with some accuracy, the photo analysis should consider the stage at which the spiral has progressed.  If different stages of the spiral evolution can additionally be vectored, an approximate trajectory may be obtained.  Most of the photos used in this analysis were taken near the beginning stage of the spiral development, similar to the photograph taken from Skjervoy in Photo #1.  Initially five locations were identified in an attempt to "triangulate" an initial position to the center of the spiral, the tail end of the blue beam, and the origin assumed at sea level.  There were four locations chosen in Norway, including Skjervoy, Storsteinnes, Highway E6 near Markenes, and Harstad, and one in Sweden; Road BD-870 near Puoltsa as shown in the map below with corresponding photos.

Figure #10) Location map showing initial 5 locations with good photographic representation.

Photo #11) © Jan-Petter Jørgensen behind Skjervoy north breakwater.

Photo #12) © Knut Anders Karlsen near Markenes (Hwy E6).

Photo #13) © Stian Michalski at Storsteinnes.

Photo #14) © Lars Sivertsen at Harstad (spiral already dissipating).

Photo #15) © Patrik Öhman near Puoltsa, Sweden on Road BD-870.

Note the almost identical shape of the spiral for both the northernmost and southernmost locations (Skjervoy and Puoltsa), suggesting that this event was a very long distance away.  Unfortunately this southern location in Sweden, along Road BD-870 near Puoltsa, could not be accurately located in Google Earth without any discernible landmarks, and thus was omitted from the analysis.  Although vector lines to the spiral could easily be matched to the road, this in effect would have been force-fitting the data to the desired results. This photo however distinctly shows the lower missile contrail back lit by the sun, which is blocked by mountains at most of the other locations.  A closer view of the contrail is shown below, seemingly marking the upper limits of the atmosphere.

Photo #16) © Tommy Guttormsen showing contrail viewed from the Vardfjellet Mountains, Norway.

2.2 Convergence Analysis

The image overlays with vectors or "lay lines" are shown below for the selected locations in Norway.  For brevity only the views aligned with the spiral and blue beam are shown, although additional views were also verified for the vector lines leading to the origin at sea level.  Note that the photograph frames are raised slightly above the Google Earth terrain so that the image silhouettes are verified as matching.  The next four image frames align to the center of the developing spiral:

Image #17) Photo © Jan-Petter Jørgensen overlayed with Google terrain at Skjervoy north breakwater using green vectors.

Image #18) Photo © Knut Anders Karlsen overlayed with Google terrain near Markenes (Hwy E6) with white vectors.

Image #19) Photo © Stian Michalski overlayed with Google terrain at Storsteinnes with red vectors.

Note in the next overlay at Harstad, chosen for the excellent correlation with background terrain, the spiral had dissipated at the time of the photograph. Thus the progression of the spiral through time, as noted at the Skjervoy location was added and scaled as additional layers, effectively backtracking where the center of the earlier spiral would have most likely occurred (point labeled B).  Essentially, photos from Skjervoy were superimposed with the Harstad location and scaled by the blue beams in photo #4 (Skjervoy) and #14 (Harstad).  The remaining photos from Skjervoy were easily scaled by the background mountains as was shown previously in Image #6.

This now gives us points A through E that define the progression and trajectory of the spiral, where A is the origin of blue beam, B is the initial location of spiral formation (photo #1), C is the approximate location of the beginning of dissipation (photo #3), D locates increasing dissipation from Harstad (photo #14), and E, the largest measurable dissipation from Skjervoy (photo #4).  Note that although we can scale and superimpose these photos relative to each other in this manner, at this point we still have no idea as to the actual size of the phenomenon.

Image #20) Photos © Lars Sivertsen and © Jan-Petter Jørgensen overlayed with Google terrain at Harstad with blue vector.  Note blue circle at C is initial void at Skjervoy (photo #3), red circle at D corresponds to void for this photo (#14), and blue circle at E is final void at Skjervoy (photo #4).

Due to the poor photo quality at many of the sites, the tail end of the blue beam (pointing towards the Earth) could only be accurately located at the Skjervoy and Harstad locations as follows:

Image #21 & 22) Alignment to tail end of "blue beam" in Google terrain.  Photos © Jan-Petter Jørgensen at Skjervoy and © Lars Sivertsen at Harstad.

2.3 Initial Locations Results

The results of the convergence from the vector projection at both the center and origin of the spiral, based on the above superposition of photographs over Google Earth's terrain model, is presented in plan view below in Figure #23.  Due to the complexity of all the intersecting lines, the location analysis of the blue beam is omitted from this presentation for clarity, but is shown in the next section with the error analysis.  Using Skjervoy as our reference point, the resulting intersections (denoted by the orange dots) locate the center of the spiral ranging from about 481 to 508 miles (774-818 km) downrange, and the origin about 446 to 532 miles (718-856 km) downrange.  Russia's Coastal Warning for the Southern White Sea Rocket (missile) Launch Area [6] is also shown and overlaps with the projected location of the origin.

Figure #23) Results of convergence analysis showing probable locations of the origin and center of spiral during its early stage (click to enlarge).

2.4 Error Estimation

Error is of course apparent as displayed in the range of scatter, and this is primarily due to the subjective nature of superimposing the photos onto Google Earth's terrain map (human error).  The error is also likely variable dependent on the location where the vectors were sighted and projected.  For example, the Skjervoy location is believed to have a low error on the vector alignment, as the photographer's position is well known behind the north breakwater, with the distinctive peaks in the background mountains providing a very accurate projection.  Similarly, at Harstad, the expanse of mountains coupled with small foreground islands provided a very high confidence in the alignment.  At other location such as Markenes and Storsteinnes, the photographer's exact location is not known, and thus must be approximated by moving the observation point (beginning of the vector line) in a trail and error method, to match the background image in Google Earth's terrain map.

Error is especially evident in the vectoring at the above mentioned sites at Markenes and Storsteinnes, as these lines are divergent and never cross.  If we neglect the location at Storsteinnes, we effectively eliminate the outermost points (upper and lower bounds) at both the origin and spiral locations with a much tighter grouping, perhaps representing a more accurate result as shown below in Figure #24.  Allowing a generous error range of 5 degrees total (± 2.5 degrees on either side of the line) results in about ± 20 miles (32 km) on either side of the line at approximately 500 miles (805 km) downrange and ± 50 miles (80 km) along the line giving an elliptical error boundary of 40 by 100 miles (64 by 160 km).  Thus expressed as a percentage this downrange convergence error is approximately ± 10%.

With only five vector crossings per location representing a small sample, eliminating two may not be considered statistically advisable.  Yet in this case it appears to have little effect on the average center locations at both the origin and the spiral.  In addition, the location of the tail end of the blue beam is also shown, and assumed to have approximately the same error envelope although only two sites were involved (one intersection).

Figure #24) Revised convergence analysis with blue beam location and reported "missile launch corridor."

Based on the above, the distances from Skjervoy, including the aforementioned error bounds, ranges from 447 to 547 miles (719-879 km) to the spiral, 428 to 528 miles (689-849 km) to the origin, and 476 to 576 miles (766-926 km) to the observed tail end of the blue beam.  Averaging to the center of the error ranges we get approximately 497, 478, and 526 miles (800, 769, and 847 km), respectively, to the spiral, origin, and blue beam.

2.5 Evolution of Spiral Dissipation

From the many photographs it often appears as if the spiral was traveling away from our viewpoint (Norway) with the blue beam in front of (west of) the spiral.  Yet from this analysis, the blue beam has been most likely located behind the initial spiral location (east of), yet considering the error bounds may in fact range from in front, to behind, or perhaps in the same plane as the spiral.  The possibility of the beam being behind the spiral had previously been suggested in some forum discussions, with the observed helical nature of the beam being a product of refraction or modulation through the spiral bands as viewed from the west.  To further expound on this question, we will attempt to triangulate the position of the spiral over the progression at dissipation (or expansion of the center "void") and the path of movement.

Using the superimposed photographs that were established previously at the Harstad location (Image #20), defining the spiral sequence through points A through E, we now align vectors from both the Skjervoy and Harstad locations for point C, D, and E, representing the final progression of dissipation.  For completeness these photos at dissipation are shown again below (not to scale):

Photos #25. 26 & 27) Sequence of dissipation at Skjervoy (C), Harstad (D), and Skjervoy again (E). © Jan-Petter Jørgensen at Skjervoy and © Lars Sivertsen at Harstad.

The same basic procedure presented in the Methodology (Section 2.1) is again repeated for the Skjervoy and Harstad locations for this sequence of points representing the evolution of the dissipation.  The Skjervoy and Harstad locations may best represent the median of the results, as their lines cross near the center of the data points in both the origin and spiral locations, and these locations are by far the most accurate to overlay with the Google terrain mapping, due to their distinctive and numerous background features previously discussed.  Below are the overlayed photos in Google Earth for each location at C, D, and E (not to scale):

Image #28 & 29) Alignment with first dissipation point C.  © Jan-Petter Jørgensen at Skjervoy and © Lars Sivertsen at Harstad.

Image #30 & 31) Alignment with second dissipation point D.  © Jan-Petter Jørgensen at Skjervoy and © Lars Sivertsen at Harstad.

Image #32 & 33) Alignment with final dissipation point E.  © Jan-Petter Jørgensen at Skjervoy and © Lars Sivertsen at Harstad.

The two projected vectors at each location C, D, and E, are extended downrange to a crossing location and superimposed with the previous results from Figure #24 and presented below in Figure #34.

Figure #34) Movement of spiral tracking towards northeast showing path of dissipation (spiral sizes calculated in following sections).

For consistency, only the locations at Skjervoy and Harstad are shown at all crossings, but still adopting the same error range as before, namely an approximate elliptical error boundary of 40 by 100 miles (64 by 160 km).  From this analysis, the movement of the spiral from its starting point (B) to the final dissipation point (E) is estimated at 138 miles (222 km) to the northeast in the 2-dimensional x-y plane (variations in altitude, z, will be considered in the next section).  Combined with the initial spiral location, these four points form an approximate path towards the northeast, taking the spiral across the Kola Peninsula then out over the Barents Sea some some 70 miles (113 km) offshore.

3. Trajectory, Size, and Altitude

3.1 Methodology

From the preceding section, the distances of the spiral from Skjervoy were determined in the x-y plane, yet to estimate altitudes and sizes, we will need a reference dimension from one of the photographs to establish known angles to the center of each spiral location.  Luckily, such a reference dimension is easily obtained from the background mountains at the Skjervoy location following the same basic methodology as shown in Kevin Martin's video. [5]  Measuring the distance from the observer at Skjervoy across the open waters to the Kvanangstinder mountains, and the height of a selected peak, we can then establish an angle to the top of that peak.  Using this angle scaled by the photograph, it is thus straightforward to infer the angles by direct line-of-sight to the center of the spiral through its entire evolution as depicted below in Figure #35, referencing the same established points A through E.

Figure #35) Geometry describing the relative line-of-sight angles from observer at Skjervoy based on an over water distance to, and height of mountain.

The most northwest ridge or peak was selected from the Kvanangstinder mountains (also known as the saw back mountains) with the elevation and distance obtained in Google Earth of 2,538 ft (719 m) and 45,186 ft (13.77 km), respectively.  This set the reference angle to the mountain of 2.97° assuming the observer (photographer) was approximately 6 ft above the water upland, and about 6 ft tall for a total elevation of 12 ft (3.7 m).  Note Kevin Martin used one of the larger peaks to the southeast in his analysis with a corresponding reference angle of 4°.

3.2 Results

With the resulting angle, (ө) and distance, (l ) to the initial and dissipated spiral locations now established, the above geometric relationships are first solved for the hypotenuse, which defines the line-of-sight distance, h = l / cos(ө), and then for the elevation, z = h sin(ө).  These results are presented in Table #1 below, with the elevation from a flat horizontal 2D surface projected tangent from the observer and computed for each location A through E.

Table #1: Geometric scaling of spiral progression.

1.  Measured from projected horizontal 2D plane (Earth's curvature not accounted for).
2.  As seen from Skjervoy.
3.  As seen from Harstad.

Knowing the elevation, z, at each spiral location, taken from this projected tangential surface, this value can then be used to scale the different photos to obtain an estimate on the spiral and void diameters.  An example of this simple procedure for the initial spiral location, B, is shown below in Image #36:

Image #36) Example of procedure for scaling of initial spiral.

To estimate a general error range we can consider the initial spiral which is approximately 500 miles away with a ± 50 miles established in Section 2.4.  This gives a minimum and maximum range from approximately 450 to 550 miles and corresponding elevation of about 70 to 85 miles, or ± 7.5 miles deviation.  Thus based on this, the error for elevation and size measurements is conservatively estimated at approximately ± 10 miles (± 16 km).

We now account for the effects of the Earth's curvature, which becomes very significant over these large distances of sight.  Projecting the line-of-site values downrange over an imaginary flat 2D surface, as was described above, the altitudes are taken perpendicular to the Earth's surface resulting in values A through E of 79, 107, 146, 160, and 166 miles (127, 172, 235, 257, and 267 km).  Note that the typical orbit for the Space Shuttle is generally in the range of 186 to 242 miles (300 to 390 km) and the International Space Station at 220 miles (355 km), with the majority of the dissipating spiral and void clearly into or beyond these orbital ranges.  These results in Figure #37 combined with the 2D path in Figure #34, thus defines the approximate 3D trajectory of the center of the spiral.

Figure #37) Elevation view showing adjustment for curvature of the Earth with line-of-site values (h) and progression and sizes of spiral.

3.3 Estimation of Size

From the work of the previous sections, we now have obtained all the necessary data to scale the important features of the photographs to get an idea of the evolution of the size of the phenomenon ranging from the initial spiral formation to the final dissipation.

We can now piece together this information with the popular series of photos from Skjervoy, and the Harstad photo as shown below in Images #38, #39, and #40 with the superposition of both the initial and dissipating spirals extended from the tail end of the blue beam.  These series of photos completes the spiral evolution and dissipation from points B through E.  The initial spiral was scaled at approximately 95 miles (153 km) in width at point B, expanding to 190 miles (306 km) at the beginning of dissipation at point C, and 391 miles (629 km) near the end of dissipation at point D.  Even though we have one additional photo at point E, the spiral has significantly dispersed with the fringes outside of the picture frame (photo #40) and thus undetermined but likely immeasurable in any case.

Similarly, the progression of the void occurs initially at 33 miles (53 km) across at point C, 106 miles (171 km) at point D, and 170 miles (274 km) at point E.  It also appears in the photos that the void beyond this range disperses quickly losing any definable shape (see photo #5).  In terms of elevation the initial spiral forms at approximately 107 miles (172 km) above sea level and climbs to an elevation of about 166 miles (267 km) as it moves northeasterly, dissipating over the Barents Sea.

It should be noted in Image #38, that the separate dimensions are referenced and scaled accordingly to each of the sequential locations B, C, and E (which are moving away from the observer), and thus the image as a whole does not have a single scale factor but actually three corresponding to the three different vertical perpendicular planes of B, C, and E.  The dimension of 143 miles (230 km) between B and E thus represents the projection of the horizontal translation both to the left (north) and into the picture (east).

Image #38) Size, and altitude results for the observed spiral progression at Skjervoy (photos © Jan-Petter Jørgensen).
Note that center of closest spiral at point B is approximately 503 miles (810 km) away from photographer.

In the following photo from Harstad, the initial and ending void sizes from Skjervoy have been superimposed, showing the growth or progression of the void northerly while the southern edge remains nearly stationary.  This photo is almost identical to the one taken at Lysnes (photo #8) and is believed to be close to the maximum size of the spiral before dispersion.  Although the spiral appears to be touching the ground in this photo, the bottom edge is actually calculated some 20 miles (32 km) or more above sea level once the curvature of the Earth is accounted for.

Image #39) Overlay of large dissipated spiral taken from Harstad (red void) scaled from spiral at Skjervoy (blue voids) with estimated dimensions.
Note that center at point D is approximately 562 miles (904 km) away from reference location at Skjervoy (photo © Lars Sivertsen).

Image #40) Size, and altitude results for the final observed spiral dissipation at Skjervoy (photo © Jan-Petter Jørgensen).
Note that center of void is approximately 565 miles (909 km) away from photographer.

4. Void Expansion and Translation Velocities

4.1 Methodology

In section 3.2 and 3.3 we examined the progression of the void expansion in terms of size and location in space, but with no reference to time.  In this section the objective is to estimate the velocity of the void expansion and translation by correlating frame captures of video footage with the previously scaled images.  Shown below is the video that was chosen for this analysis which was shot from Tromsø.  This video has been uploaded to YouTube by multiple users [7] (author is unknown), and exist in both the original format at a 16:9 ratio and also a compressed version (distorted) at 4:3 ratio.  The location was identified by the "Arctic Cathedral" located in the foreground (near the end of the video) and the mountainous backgrounds that were also verified in Google Earth (as in Section 2.2).  Although lacking the initial development of the spiral, it displays an excellent progression of the void expansion and general trajectory both horizontally to the north (left) and vertically (up).

Since Tromsø is only about 30 miles (48 km) further west from the spiral event than Skjervoy, and the vectors from both locations to the spiral diverge by only 3.6º, we can scale this video to the Skjervoy images without any significant geometric errors.  However, due to the low quality of the video (in comparison to the photos), scaling of the actual image overlays proved to be difficult, and thus the results herein should be viewed only as approximate.

At 31.4 seconds into the video, the shape of the "blue beam" and size of the void seem to closely match that of Photo #3 from Skjervoy, in which the dimensions were previously scaled in Section 3.3 (Image #38).  This correlation is shown below in Image #41 which approximately scales the video frame at this particular point in time by denoting the same helical pattern in the lower part of the blue beam and the center and diameter of the voids.  In addition to the obvious sideways and vertical translation, it is also moves away from the observer (Section 3.2) thus affecting the sequential scaling of frame captures.

Image #41) Scaled overlay of video capture and Skjervoy Photo #3.

To account for this change in scaling with time as the event tracks away from the observer, it would be desirable to correlate the video to established know locations in Section 3.2, with at least two locations correlating a frame capture with a known image to establish a trend.  The above scaled frame/image occurring at t = 31.4 seconds can be used for the first point, which also conveniently coincides with location C from the Section 3.2 analysis.  Unfortunately the video appears to never reach the point in time correlating to location D.  However, at the end of the video (t = 50.6 sec), the void is initially estimated at about 85 miles (137 km) in diameter, and this is located roughly 72% along the trajectory between the void diameters at location C and D.

Ignoring the horizontal and vertical translation motions for now (does not affect scaling), and taking 72% of the downrange translation of the void from C to D obtained from Table #1, gives us 12.5 miles or 20 km (74% of 17.4 miles or 28.0 km).  The corrections are then applied in CAD as a linear trend showing only a small change in void size and translation distances; resulting in scale factors of 0.961 at t = 0.17 seconds and 1.023 at t = 50.6 seconds, as referenced to the 1:1 scaled image at t = 31.38 seconds (Image #41).  These scale factors are small because the downrange movements are very small compared to the vast downrange distance to the observer, which is in excess of 530 miles (853 km).

The resulting scale-corrected sequential frame captures, with the estimated void radius, horizontal and vertical translations, are shown in Images #42 through #53.  Note that these dimensions are simply referenced to discernible foreground features in the video and do not relate to any particular datum.

Images #42 - 53) Video frame captures with translations and void radius scaled for velocity estimation.

4.2 Velocity Estimates

There are three aspects to the movement of this event in which we can attempt to estimate the velocities:

For reference we define the coordinate system where the x-axis points east (into the page), y-axis points north (to the left), and z-axis points up; with the corresponding velocity components, Vx, Vy, and Vz as shown in Figure #54.  The resultant velocity vector along the trajectory is thus:

Figure #54) Defined coordinate system for velocity vectors representing the spiral trajectory.

For the void expansion, the velocity is defined as Ve, relative to the center of the void and based on the rate of expansion of the void radius, r.  Although the exact plane of the void is uncertain, it has no discernible obliqueness in any of the photos or videos and is assumed to be in a plane approximately perpendicular to the observer.  In the scaled Images #42 - 53, the observable translation only represents the velocities in the horizontal (y) and vertical (z) directions and thus we have no accurate track of the easterly (x) movement downrange.  Yet this velocity, Vx (into the page) can be inferred from the estimated scaling that was done previously in Section 4.1, namely a 12.5 mile (20 km) difference between Image #50 and #53 (where dt = 50.62 - 31.38 = 19.24 sec.).  Accordingly, the downrange velocity is approximated as 12.5 mi / 19.24 s = 0.649 mi/s = 2,240 mph (3,690 kph).

From the 12 video captures above, both the horizontal (y) and vertical (z) translations of the center of the spiral is plotted together in Figure #55 and the expansion of the void radius, r, in Figure #56.  Fitting curves to these results we find that the y translation closely follows a 2nd order regression while the z translation is roughly linear.  The expansion of the void also follows a linear trend for about the first 20 seconds then appears to decrease past this point when the void radius is about 40 to 45 miles (64 to 72 km).

Figure #55) Horizontal, y (north) and vertical, z, translations obtained from video frame captures.

Figure #56) Expansion of void radius, r, obtained from video frame captures.

With Vx already estimated above, the remaining velocities are obtained from the regression equations by simply taking the derivatives:

A summary of the measured data, computed velocity components, and vector additions is shown in Table #2.

The most significant movement of the spiral is to the north (translating sideways) represented by the velocity component Vy, with a maximum of approximately 7,500 mph (12,070 kph) at the beginning of the video and decreasing to 4,200 mph (6,760 kph) near the end.  The easterly component Vx was assumed linear and coincidentally matches the vertical velocity Vz almost exactly at 2,240 mph (3,600 kph) with its resulting linear motion.

The maximum resultant velocity, V, of the spiral (from the vector sum of Vx, Vy, and Vz) occurs at the beginning of the video with the trajectory to the north-northeast at about 8,150 mph (13,110 kph) and decreasing to approximately 5,300 mph (8,530 kph) at the end (t = 50.6 sec) where the void diameter is about 94 miles (151 km).  The void expansion, represented by the velocity, Ve, appears to spread out at a linear rate at approximately 6,600 mph (10,620 kph) relative to the center for the initial 20 seconds, thereafter decreasing to around 4,500 mph (7,240 kph) near the end of the video (and likely continuing to decrease with further expansion).

The velocity of the leading edge of the void expansion (north side) as it is projected out from the center of the moving spiral, can simply be expressed as the sum of the two velocity vectors, V and Ve, resulting in a maximum velocity of the leading edge at approximately 13,350 mph (21,500 kph) at the start of the void expansion and decreasing to about 9,750 mph (1,570 kph) at t = 50.6 seconds.

Table #2: Summary of measured distances from video frames and the resulting velocity components and vectors.

1.  Measured distances from video frame capture -  Images #42 through #53.
2.  East velocity roughly estimated based on downrange distance differential and is assumed linear.

4.3 Verification and Error Estimation

Based on the large and somewhat unbelievable magnitude of the velocities of the spiral trajectory and void, these values are accordingly examined for possible scaling and methodology errors.

The largest assumption in this analysis and perhaps the most prone to error was the assumed downrange velocity Vx (Section 4.2), since this can not be measured from the video frames directly, due to the vector direction into the page.  In the worst case, if we completely ignore this velocity (Vx = 0), the resultant trajectory vector, V, would decrease to 7,840 mph (12,620 kph) which is only a 4% difference in the actual computed value of 8,154 mph (12,620 kph).  Of course we know that Vx is not zero, but even if it was as much as 50% larger or 50% smaller this would be an error of only ± 2%.

Another source of error is in the initial scaling of the video frame captures, based on this same downrange motion.  This scaling correction, obtained from two points in the spiral progression, location C and another point at t = 50.6 seconds, where the void diameter was initially estimated at about 85 miles (137 km).  Based on this size progression which was about 72% of the difference from location C to D (void diameters), a downrange distance of 12.5 miles (20 km) was obtained.  After the frames were actually scaled however, the void diameter at t = 50.6 seconds became 93.6 miles (150 km), or 83% of the difference from location C to D giving a 14.4 mile (23 km) downrange distance.  Although the difference between 12.5 and 14.4 miles is large, this must be added to the total downrange distance (+560 miles referenced at location C from Tromsø) to see the actual scaling affect.  For example, at the last frame where t = 50.6 seconds, the initial scale factor was 1.023 (Section 4.1) and the revised based on the 14.4 mile differential is 1.027, a difference of only 0.004 or 0.4%.  This small scaling error can thus be considered negligible.

As an additional check, the spiral at locations at B and C (Skjervoy Photo #1 and #3) are superimposed and scaled with the video frame at t = 31.4 seconds which is approximately at location C (Image #50), so we can now compare the track from B to C that was previously plotted in Figure #34.   In this superposition shown below in Image #57, the distance difference between location B and C is simply 141 - 58 miles = 83 miles (134 km).

Figure #57) Superposition of locations B and C from video and Skjervoy Photos #1 and #3.

Taking the downrange differential of 32.8 miles (52.8 km) from Table #1, the resultant horizontal distance is solved for d  = (83² + 32.8²) ^½ such that d = 89.2 miles (143.5 km).  From Figure #34 the corresponding horizontal track from B to C is measured at 83.2 miles (133.9 km).  Thus the error in the horizontal translation distance is approximately 7% in this case.  As noted earlier in Section 4.1, because of the low quality of the video we fully expected the scaling efforts to be difficult, and the error observed here in the x-y horizontal translation may be indicative of this uncertainty.

Looking at the regression curves generated from the video frame data (Figures #55 and #56), we see good R² values ranging from 0.993 to 0.999, and the relative standard error (RSE) of 2.1%, 1.4%, and 2.0% for the y, z, and r regression equations, respectively.

Thus based on the above error analysis and verification, it appears that the error associated with video frame scaling and the subsequent regression analysis are relatively small in the range of ± 2%.  However, from Figure #57, correlation to the earlier convergence analysis with the video frame captures, we see that this 7% error is in the same ballpark as the ± 10% established for the downrange convergence in Section 2.4.  Since the video scaling is based on this original vector convergence analysis, a conservative error range of ± 10% is also established for the velocity analysis.

5. Summary & Discussion

From this convergence analysis and the subsequent determination of the approximate size, location, trajectory, and associated velocities of this unusual phenomenon, the following is noted:

• Contrary to some assertions that have placed this event over Norway or Finland, the vector analysis establishes the initial spiral over the Russian province of Murmansk and the Kola Peninsula with the origin (contrail) located in the vicinity of the western White Sea, and within the coastal warning for the Southern White Sea Rocket Launch Area (or simply "missile launch corridor") [6] within the considered error ranges.

  
  

• With respect to altitude, the apparent origin or tail end of the blue beam was located inland approximately near the northeast tip of missile launch corridor at an elevation of 79 miles (127 km).  The initial formation of the spiral was approximately 62 miles (100 km) north of the blue beam origin and 60 miles (97 km) inland, or west of the White Sea, with altitude and diameter of 107 and 95 miles (172 and 153 km), respectively.  With the Kármán line defining the approximate boundary between the upper atmosphere and outer space at 62 miles up (100 km), this puts the center of the spiral well into outer space with the lower edge of the spiral at about 60 miles (96 km) or approximately at the Kármán interface.  This is therefore an event that transpired primarily in space, and thus not significantly confined or influenced by atmospheric conditions.

  
  

• The path of the spiral was to the northeast and climbing in altitude, traveling across the peninsula and out over the Barents Sea.  The final dissipation of the spiral occurred approximately 143 miles (230 km) northeast of its initial development and some 70 miles (113 km) offshore and 166 miles up (267 km) (from sea level).  From an observer at Skjervoy, this movement of the spiral was primarily translating sideways (right to left), upwards, and downrange as it moved northeasterly over the Barents Sea.  However, the dramatic growth of the spiral gives the impression that it is moving closer to the observer.

  
  

• At the point of relatively rapid growth of the "void" and spiral, the upper limit of expansion scaled from photographs places the maximum photographed width of the spiral envelope at approximately 391 miles (629 km), with the upper edge of this envelope at a very high altitude of about 351 miles (565 km), well within the orbital range of space craft such as the Space Shuttle and International Space Station.  To gain a perspective on size, a medium size tropical cyclone is in the range of approximately 200 to 400 miles (322 to 644 km) across, so in a sense this spiral can be likened to a hurricane projected vertically on its side.

  
  

• From the video analysis, the movement of the center of the spiral towards the north-northeast trajectory is estimated with an initial velocity (at the beginning of the video) exceeding 8,000 mph (12,875 kph) and gradually decreasing towards the end of the video (near location D) to about 5,300 mph (8,530 kph).  The vertical component of this translation is approximately linear with an average velocity of 2,240 mph (3.600 kph).  The expansion of the void out from the center of the moving spiral is also nearly linear with an average velocity of 6,600 mph (10,620 kph) for about the first 20 seconds of the expansion, then gradually decreasing from this point on.  The velocity of the leading edge of the void (north side) from the combination of the expansion and  trajectory velocity is approximately 13,350 mph (21,500 kph) near the beginning of the void expansion.  Although the magnitude of these speeds seems somewhat incredible, they are consistent with the measured geometrics and movement, and the fact that the event was generally well above the atmosphere and not constrained by the propagation through a medium.  The substantial distance at which this event was observed (+500 miles) combined with the equally massive size of the spiral envelope, also gives the illusion of a more slowly moving object.

  
  

• This analysis shows the initial spiral most likely forming in front of (west of) the blue beam, but when considering the computed error ranges it may have been behind or in the same plane as the blue beam.  It had been suggested in some forum discussions that the helical nature of the blue beam was due to the light being refracted through the spiral bands.  Although in some photographs this theory seems plausible, other photographs seem to show this helical pattern still faintly present after dissipation, leaving this unconfirmed at this point.  If the blue beam is positioned in the same plane as the spiral, the helical feature may be a result of the modulation or shearing action from the rotating spiral bands.

  
  

• All the available photographs and videos are shot from very distant locations and mainly from the northwestern regions of Norway, suggesting perhaps some manner of illumination only visible to these western observers.  It may be possible that there was too much light present in the atmosphere from the easterly regions (Finland, Russia) such that the phenomenon was overpowered by the sun in these areas with an earlier sunrise.

  
  

• Due to the subjective nature of the vector mapping, a generous error range was implemented producing an error envelope represented by an ellipse some 40 by 100 miles (64 by 160 km) at the crossing of multiple vectors, and a corresponding elevation/size error range of ± 10 miles (± 16 km).  This equates roughly to a ± 10% error in the downrange convergence and ± 7% in elevation.  Similarly, a ± 10% error range was adopted for the velocity estimates based on the above convergence error, although the velocity data regression and scaling errors were generally below ± 2%.  While these error estimates may be considered large, this range does not negate the general conclusions of this analysis, although these values may indeed vary from the results presented.

This phenomenon observed in the northwest regions of Norway has generated much debate as to its nature, origin, and purpose, and with many potential implications if the official missile report is dismissed.  Although it was not the intent of this paper to address such a scope of all possible theories, I am hopeful that this small but focused study at the very least, may dispel some of the disinformation and confusion as to the location, movement, and geometrics of this visually stunning event.

Footnotes:

1.   All photographs have been accredited to the photographer and location when known and are presented only for research purposes and in the spirit of the dissemination of open information and knowledge.  No profit or funds are involved in their use.  If you are an author of any of these photos and would like to have any corrections made or have them removed, please contact:

References:

1.   Virginia Wheeler and Vince Soodin, The Sun News, Spiral UFO puts Norway in a spin, Dec. 9, 2009, http://www.thesun.co.uk/sol/homepage/news/2764647/Spiral-UFO-puts-Norway-in-a-spin.html

2.   Michael d'Estries, Mother Nature Network, Mystery lights over Norway baffle residents, Dec. 10, 2009, http://www.mnn.com/technology/research-innovations/stories/mystery-lights-over-norway-baffle-residents

3.   Rense.com, Webbot Clif High talks about Norway Spiral on Jeff Rense Show, Dec. 10, 2009, http://www.youtube.com/watch?v=nbl1yheVqpU

4.   David Wilcock, Divine Cosmos, Disclosure Endgame: Free Ebook!, Dec. 2009,
http://divinecosmos.com/index.php/start-here/davids-blog/521-disclosure-endgame
http://www.scribd.com/doc/24613746/David-Wilcock-Disclosure-Endgame-E-Book

5.   Kevin Martin, Southern California Weather Authority, Norway Spiral debunked with math evidence - White Sea was the location in Russia, Dec. 14, 2009, http://www.youtube.com/watch?v=1GSa2wRtZRI

6.   Forum River Traveler, NAVTEX Russian missile launch area coordinates (in Russian) Dec. 2009, http://forum.flot.su/showthread.php?p=102072

ZCZC FA79
031230 UTC DEC 09
COASTAL WARNING ARKHANGELSK 94
SOUTHERN PART WHITE SEA
1.ROCKET LAUNCHING 2300 07 DEC TO 0600 08 DEC
09 DC 0200 TO 0900 10 DEC 0100 TO 0900
NAVIGATION PROHIBITED IN AREA
65-12.6N 036-37.0E 65-37.2N 036-26.0E
66-12.3N 037-19.0E 66-04.0N 037-47.0E
66-03.0N 038-38.0E 66-06.5N 038-55.0E
65-11.0N 037-28.0E 65-12.1N 036-49.5E
THEN COASTAL LINE 65-12.2N 036-47.6E

7.   http://youtu.be/PypwRaX-xQA, http://youtu.be/CxA0Asq2YDg, http://youtu.be/zsiSirIq4SA

News and Photo Links:

Norse Spiral Gallery -- Gizmodo

Lysfakkel på himmelen - Harstad Tidende

Lysfenomen over Nord-Norge

Märkligt ljussken över Kiruna

Spirals in the sky

Mysterious light spirals over Norway, and 100 years of weird stuff in the sky

Weird Spiral Lights Over Norway | Ghost Theory

Mystery as spiral blue light display hovers above Norway | Mail Online

Earthfiles.com Environment | Unexplained White and Blue Light Spirals in Norwegian Sky

Tandberg: – Missil ut av kontroll - Nordland - NRK Nyheter

Nytt mystisk lysfenomen i nord - Nyheter - yr.no

A "Nobel Torsion Message" Over Norway? - Richard C. Hoagland

On the Norway Spirals and their Physically Impossible "Ripple" Propagation (PDF)

Wikipedia: 2009 Norwegian spiral anomaly

Revision History:

12/29/2009: Initial draft posting.

01/03/2010: Initial finalized posting.

01/09/2010: Added location map.

01/12/2010: Temporarily pulled page down to incorporate new photos and information.

01/14/2010: Revised with two new photos from Skjervoy; additional vectoring and updating; resulting new trajectory over Barents Sea.

02/13/2010: Minor text revisions; revised Image #6; revised error ranges; replaced one expired reference link; added additional links.

07/21/2011: Added video analysis section on translation and void expansion velocities; minor revisions to dimensions; added additional reference/links.

© 2009-2011  SpellConsulting.com

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