2.1 Methodology
The methodology is very straightforward; photos of the spiral are selected with distinct background topography (i.e. mountains, islands, etc.) and visually mapped to the same view in the Google Earth terrain mode.  Lay lines or vectors are then drawn towards the center of the spiral and the origin (assumed sea level) then projected downrange a sufficient length to cross with adjacent lay lines at other mapped locations.  First it must be pointed out, that the phenomenon described by some as stationary, was actually moving as identified in both video and still shots.  One of the best examples is from the well known series of photographs taken by Jan-Petter Jørgensen from the vicinity of the north breakwater at Skjervoy, showing the dramatic growth and dissipation of the spiral (note photos #1 through #5 below all at same scale).
 
   

  

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. 

 

Photos #7 & 8)  © Vidar Bjørkli near Lysnes taken towards the end of the event.

Image #9) Superposition of above 2 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 dissipated).

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 lay 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 Lay Line Analysis
The image overlays with 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 lay 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 lay lines.

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

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

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 lay line.  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.

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2.3 Initial Locations Results
The results of the lay line 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 results of the lay line 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 lay line 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 lay lines were 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 lay line 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 lay 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 lay 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 lay line giving an elliptical error boundary of 40 by 100 miles (64 by 160 km). 

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 lay line 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 lay lines 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 for a 3D trajectory).  Combined with the initial spiral location, these four points from a consistent arcing 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
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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 the table below, with the elevation from a flat horizontal 2D surface projected tangent from the observer and computed for each location A through E. 

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 Shuttles is generally in the range from 186 to 242 miles (300 to 390 km) above the Earth, with the top of the dissipating spiral and void clearly into this range.  These results in Figure #37 combined with the 2D path in Figure #34, thus defines the 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.

Image #38) Trajectory, 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. Summary & Discussion
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From this lay line analysis and the subsequent determination of the approximate location, trajectory, size, and altitude of the "Norway Spiral" phenomenon, the following is noted:

• Contrary to some assertions that have placed this event over Norway or Finland, the lay line analysis clearly 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] with the considered error range.
  

• Through the lay line vectoring and altitude analysis, 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.
  

• 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 138 miles (222 km) northeast of its initial development and some 70 miles (113 km) offshore and 166 miles up (267 km).  From an observer at Skjervoy, this movement of the spiral was primarily translating sideways (right to left) and away 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 at approximately 391 miles (629 km), with the upper edge of the spiral at a very high altitude of about 351 miles (565 km), well within the orbital range of the Space Shuttle.  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.

• This analysis shows the initial spiral most likely forming in front of (west of) the blue beam, but when considering error 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.

• 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 lay line 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 lay lines, and a corresponding elevation/size error range of ± 10 miles (± 16 km).  While these estimates may be considered large, this range does not negate the general conclusions of this analysis, although the locations, trajectory, and altitude may indeed vary from the results presented.
  

This phenomenon observed over the Norway skies 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 and geometrics of this visually stunning event.

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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: 

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

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