OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 7 — Jul. 1, 2014
  • pp: 1645–1656

Accuracy of sun localization in the second step of sky-polarimetric Viking navigation for north determination: a planetarium experiment

Alexandra Farkas, Dénes Száz, Ádám Egri, Miklós Blahó, András Barta, Dóra Nehéz, Balázs Bernáth, and Gábor Horváth  »View Author Affiliations


JOSA A, Vol. 31, Issue 7, pp. 1645-1656 (2014)
http://dx.doi.org/10.1364/JOSAA.31.001645


View Full Text Article

Enhanced HTML    Acrobat PDF (1135 KB) | SpotlightSpotlight on Optics Open Access





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

It is a widely discussed hypothesis that Viking seafarers might have been able to locate the position of the occluded sun by means of dichroic or birefringent crystals, the mysterious sunstones, with which they could analyze skylight polarization. Although the atmospheric optical prerequisites and certain aspects of the efficiency of this sky-polarimetric Viking navigation have been investigated, the accuracy of the main steps of this method has not been quantitatively examined. To fill in this gap, we present here the results of a planetarium experiment in which we measured the azimuth and elevation errors of localization of the invisible sun. In the planetarium sun localization was performed in two selected celestial points on the basis of the alignments of two small sections of two celestial great circles passing through the sun. In the second step of sky-polarimetric Viking navigation the navigator needed to determine the intersection of two such celestial circles. We found that the position of the sun (solar elevation θS, solar azimuth φS) was estimated with an average error of +0.6°Δθ+8.8° and 3.9°Δφ+2.0°. We also calculated the compass direction error when the estimated sun position is used for orienting with a Viking sun-compass. The northern direction (ωNorth) was determined with an error of 3.34°ΔωNorth+6.29°. The inaccuracy of the second step of this navigation method was high (ΔωNorth=16.3°) when the solar elevation was 5°θS25°, and the two selected celestial points were far from the sun (at angular distances 95°γ1, γ2115°) and each other (125°δ145°). Considering only this second step, the sky-polarimetric navigation could be more accurate in the mid-summer period (June and July), when in the daytime the sun is high above the horizon for long periods. In the spring (and autumn) equinoctial period, alternative methods (using a twilight board, for example) might be more appropriate. Since Viking navigators surely also committed further errors in the first and third steps, the orientation errors presented here underestimate the net error of the whole sky-polarimetric navigation.

© 2014 Optical Society of America

OCIS Codes
(000.4930) General : Other topics of general interest
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(260.1180) Physical optics : Crystal optics
(260.5430) Physical optics : Polarization
(330.5510) Vision, color, and visual optics : Psychophysics
(330.7321) Vision, color, and visual optics : Vision coupled optical systems

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: April 17, 2014
Manuscript Accepted: May 13, 2014
Published: June 30, 2014

Virtual Issues
August 26, 2014 Spotlight on Optics

Citation
Alexandra Farkas, Dénes Száz, Ádám Egri, Miklós Blahó, András Barta, Dóra Nehéz, Balázs Bernáth, and Gábor Horváth, "Accuracy of sun localization in the second step of sky-polarimetric Viking navigation for north determination: a planetarium experiment," J. Opt. Soc. Am. A 31, 1645-1656 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-7-1645


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. H. McGovern, “The archeology of the Norse North Atlantic,” Annu. Rev. Anthropol. 19, 331–351 (1990).
  2. O. Olsen and O. Crumlin-Pedersen, Five Viking Ships from Roskilde Fjord (National Museum, 1978).
  3. S. Thirslund, Viking Navigation: Sun-Compass Guided Norsemen First to America (Gullanders Bogtrykkeri a-s, 2001).
  4. B. Bernáth, M. Blahó, Á. Egri, A. Barta, and G. Horváth, “An alternative interpretation of the Viking sundial artefact: an instrument to determine latitude and local noon,” Proc. R. Soc. A 469, 20130021 (2013). [CrossRef]
  5. B. Bernáth, A. Farkas, D. Száz, M. Blahó, Á. Egri, A. Barta, S. Åkesson, and G. Horváth, “How could the Viking sun-compass be used with sunstones before and after sunset? Twilight board as a new interpretation of the Uunartoq artefact fragment,” Proc. R. Soc. A 470, 20130787 (2014). [CrossRef]
  6. T. Ramskou, “Solstenen,” Skalk 2, 16–17 (1967).
  7. P. G. Foote, “Icelandic sólarsteinn and the Medieval background,” J. Scandinavian Folklore 12, 26–40 (1956).
  8. A. Le Floch, G. Ropars, J. Lucas, S. Wright, T. Davenport, M. Corfield, and M. Harrisson, “The sixteenth century Alderney crystal: a calcite as an efficient reference optical compass?” Proc. R. Soc. A 469, 20120651 (2013). [CrossRef]
  9. K. L. Coulson, Polarization and Intensity of Light in the Atmosphere (A. Deepak, 1988).
  10. B. Bernáth, M. Blahó, Á. Egri, A. Barta, G. Kriska, and G. Horváth, “Orientation with a Viking sun-compass, a shadow-stick and calcite sunstones under various weather situations,” Appl. Opt. 52, 6185–6194 (2013). [CrossRef]
  11. C. Roslund and C. Beckman, “Disputing Viking navigation by polarized skylight,” Appl. Opt. 33, 4754–4755 (1994). [CrossRef]
  12. I. Pomozi, G. Horváth, and R. Wehner, “How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation,” J. Exp. Biol. 204, 2933–2942 (2001).
  13. L. K. Karlsen, Secrets of the Viking Navigators (One Earth, 2003).
  14. B. Suhai and G. Horváth, “How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study,” J. Opt. Soc. Am. A 21, 1669–1676 (2004). [CrossRef]
  15. A. Barta, G. Horváth, and V. B. Meyer-Rochow, “Psychophysical study of the visual sun location in pictures of cloudy and twilight skies inspired by Viking navigation,” J. Opt. Soc. Am. A 22, 1023–1034 (2005). [CrossRef]
  16. R. Hegedüs, S. Ǻkesson, R. Wehner, and G. Horváth, “Could Vikings have navigated under foggy and cloudy conditions by skylight polarization? On the atmospheric optical prerequisites of polarimetric Viking navigation under foggy and cloudy skies,” Proc. R. Soc. A 463, 1081–1095 (2007). [CrossRef]
  17. G. Horváth, A. Barta, I. Pomozi, B. Suhai, R. Hegedüs, S. Ǻkesson, V. B. Meyer-Rochow, and R. Wehner, “On the trail of Vikings with polarized skylight: experimental study of the atmospheric optical prerequisites allowing polarimetric navigation by Viking seafarers,” Phil. Trans. R. Soc. B 366, 772–782 (2011). [CrossRef]
  18. G. Ropars, G. Gorre, A. Le Floch, J. Enoch, and V. Lakshminarayanan, “A depolarizer as a possible precise sunstone for Viking navigation by polarized skylight,” Proc. R. Soc. A 468, 671–684 (2012). [CrossRef]
  19. G. P. Können, Polarized Light in Nature (Cambridge University, 1985).
  20. G. Horváth, B. Bernáth, B. Suhai, A. Barta, and R. Wehner, “First observation of the fourth neutral polarization point in the atmosphere,” J. Opt. Soc. Am. A 19, 2085–2099 (2002). [CrossRef]
  21. G. Horváth and D. Varjú, Polarized Light in Animal Vision—Polarization Patterns in Nature (Springer Verlag, 2004).
  22. E. Batschelet, Circular Statistics in Biology (Academic, 1981).
  23. A. E. J. Ogilvie, L. K. Barlow, and A. E. Jennings, “North Atlantic climate c. ad. 1000: millennial reflections on the Viking discoveries of Iceland, Greenland and North America,” Weather 55, 34–45 (2000). [CrossRef]
  24. R. Hegedüs, S. Ǻkesson, and G. Horváth, “Polarization patterns of thick clouds: overcast skies have distribution of the angle of polarization similar to that of clear skies,” J. Opt. Soc. Am. A 24, 2347–2356 (2007). [CrossRef]
  25. R. Kammann, “The overestimation of vertical distance and slope and its role in the moon illusion,” Perception Psychophys. 2, 585–589 (1967). [CrossRef]
  26. M. Hershenson, The Moon Illusion (Erlbaum, 1989).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited