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Royal Society Open Science
Open AccessResearch article

Success of sky-polarimetric Viking navigation: revealing the chance Viking sailors could reach Greenland from Norway

Published:04 April 2018https://doi.org/10.1098/rsos.172187

    Abstract

    According to a famous hypothesis, Viking sailors could navigate along the latitude between Norway and Greenland by means of sky polarization in cloudy weather using a sun compass and sunstone crystals. Using data measured in earlier atmospheric optical and psychophysical experiments, here we determine the success rate of this sky-polarimetric Viking navigation. Simulating 1000 voyages between Norway and Greenland with varying cloudiness at summer solstice and spring equinox, we revealed the chance with which Viking sailors could reach Greenland under the varying weather conditions of a 3-week-long journey as a function of the navigation periodicity Δt if they analysed sky polarization with calcite, cordierite or tourmaline sunstones. Examples of voyage routes are also presented. Our results show that the sky-polarimetric navigation is surprisingly successful on both days of the spring equinox and summer solstice even under cloudy conditions if the navigator determined the north direction periodically at least once in every 3 h, independently of the type of sunstone used for the analysis of sky polarization. This explains why the Vikings could rule the Atlantic Ocean for 300 years and could reach North America without a magnetic compass. Our findings suggest that it is not only the navigation periodicity in itself that is important for higher navigation success rates, but also the distribution of times when the navigation procedure carried out is as symmetrical as possible with respect to the time point of real noon.

    Footnotes

    Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.4035236.

    References

    • 1
      McGovern TH. 1990The archaeology of the Norse North Atlantic. Ann. Rev. Anthropol. 19, 331–351. (doi:10.1146/annurev.an.19.100190.001555) Crossref, Google Scholar
    • 2
      Ingstad H, Ingstad AS. 2000The Viking discovery of America: the excavation of a norse settlement in L'Anse aux Meadows, Newfoundland. St John's, Canada: Breakwater Book Ltd. Google Scholar
    • 3
      Thirslund S. 2001Viking navigation: sun-compass guided norsemen first to America. Humlebæk, Denmark: Gullanders Bogtrykkeri a-s, Skjern. Google Scholar
    • 4
      Thirslund S. 1997Sailing directions of the North Atlantic Viking age (from about the year 860 to 1400). J. Navig. 50, 55–64. (doi:10.1017/S0373463300023584) Crossref, Google Scholar
    • 5
      Karlsen LK. 2003Secrets of the Viking navigators. Seattle, WA: One Earth Press. Google Scholar
    • 6
      Thirslund S.1991A presumed sun compass from Narsarsuaq. In The church topography of the eastern settlement and the excavation of the Benedictine Convent at Narsarsuaq in the Uunartoq Fjord (ed. Vebæk CL), pp. 65–71. Monographs on Greenland, vol. 278, Man & Society, vol. 14. Copenhagen, Denmark: Museum Tusculanum Press. Google Scholar
    • 7
      Thirslund S. 1993The discovery of an early bearing-dial: further investigations. J. Navig. 46, 33–48. (doi:10.1017/S0373463300011292) Crossref, Google Scholar
    • 8
      Ramskou T. 1967Solstenen. Skalk 2, 16–17. Google Scholar
    • 9
      Pomozi I, Horváth G, Wehner R. 2001How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation. J. Exp. Biol. 204, 2933–2942. PubMed, Google Scholar
    • 10
      Suhai B, Horváth G. 2004How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study. J. Optic. Soc. Am. A 21, 1669–1676. (doi:10.1364/JOSAA.21.001669) Crossref, Google Scholar
    • 11
      Hegedüs R, Åkesson S, Horváth G. 2007Polarization patterns of thick clouds: overcast skies have distribution of the angle of polarization similar to that of clear skies. J. Optic. Soc. Am. A 24, 2347–2356. (doi:10.1364/JOSAA.24.002347) Crossref, Google Scholar
    • 12
      Hegedüs R, Åkesson S, Wehner R, Horváth G. 2007Could 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. (doi:10.1098/rspa.2007.1811) Link, Google Scholar
    • 13
      Horváth G, Barta A, Pomozi I, Suhai B, Hegedüs R, Åkesson S, Meyer-Rochow B, Wehner R. 2011On 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. (doi:10.1098/rstb.2010.0194) Link, Google Scholar
    • 14
      Horváth G, Barta A, Hegedüs R. 2014Polarization of the sky. In Polarized light and polarization vision in animal sciences (ed. Horváth G), pp. 367–406. Berlin, Germany: Springer. Google Scholar
    • 15
      Horváth G, Farkas A., Bernáth B. 2014Sky-polarimetric Viking navigation. In Polarized light and polarization vision in animal sciences (ed. Horváth G), pp. 603–635. Berlin, Germany: Springer. Google Scholar
    • 16
      Barta Aet al.2014Polarization transition between sunlit and moonlit skies with possible implications for animal orientation and Viking navigation: anomalous celestial twilight polarization at partial moon. Appl. Opt. 53, 5193–5204. (doi:10.1364/AO.53.005193) Crossref, PubMed, Google Scholar
    • 17
      Horváth G, Takács P, Kretzer B, Szilasi S, Száz D, Farkas A, Barta A. 2017Celestial polarization patterns sufficient for Viking navigation with the naked eye: detectability of Haidinger's brushes on the sky versus meteorological conditions. R. Soc. open sci. 4, 160688. (doi:10.1098/rsos.160688) Link, Google Scholar
    • 18
      Száz D, Farkas A, Blahó M, Barta A, Egri Á, Kretzer B, Hegedüs T, Jäger Z, Horváth G. 2016Adjustment errors of sunstones in the first step of sky-polarimetric Viking navigation: studies with dichroic cordierite/tourmaline and birefringent calcite crystals. R. Soc. open sci. 3, 150406. (doi:10.1098/rsos.150406) Link, Google Scholar
    • 19
      Farkas A, Száz D, Egri Á, Blahó M, Barta A, Nehéz D, Bernáth B, Horváth G. 2014Accuracy of sun localization in the second step of sky-polarimetric Viking navigation for north determination: a planetarium experiment. J. Optic. Soc. Am. A 31, 1645–1656. (doi:10.1364/JOSAA.31.001645) Crossref, Google Scholar
    • 20
      Száz D, Farkas A, Barta A, Kretzer B, Egri Á, Horváth G. 2016North error estimation based on solar elevation errors in the third step of sky-polarimetric Viking navigation. Proc. R. Soc. A 472, 20160171. (doi:10.1098/rspa.2016.0171) Link, Google Scholar
    • 21
      Száz D, Farkas A, Barta A, Kretzer B, Blahó M, Egri Á, Szabó G, Horváth G. 2017Accuracy of the hypothetical sky-polarimetric Viking navigation versus sky conditions: revealing solar elevations and cloudinesses favourable for this navigation method. Proc. R. Soc. A 473, 20170358. (doi:10.1098/rspa.2017.0358) Link, Google Scholar
    • 22
      Bernáth B, Blahó M, Egri Á, Barta A, Kriska G, Horváth G. 2013Orientation with a Viking sun-compass, a shadow-stick, and two calcite sunstones under various weather conditions. Appl. Opt. 52, 6185–6194. (doi:10.1364/AO.52.006185) Crossref, PubMed, Google Scholar
    • 23
      US National Geospatial-Intelligence Agency. 2017Pilot chart of the North Atlantic Ocean. See https://msi.nga.mil/MSISiteContent/StaticFiles/NAV_PUBS/APC/Pub106/106oct.pdf. Google Scholar
    • 24
      Walker J. 1978The amateur scientist: more about polarizers and how to use them, particularly for studying polarized sky light. Sci. Am. 238, 132–136. (doi:10.1038/scientificamerican0178-132) Crossref, Google Scholar
    • 25
      Können GP. 1985Polarized light in nature. Cambridge, UK: Cambridge University Press. Google Scholar
    • 26
      Roslund C, Beckman C. 1994Disputing Viking navigation by polarized skylight. Appl. Opt. 33, 4754–4755. (doi:10.1364/AO.33.004754) Crossref, PubMed, Google Scholar
    • 27
      Schaefer BE. 1997Vikings and polarization sundials. Sky Telescope 93, 91–94. Google Scholar
    • 28
      Wild W, Fromme B. 2007Der Sonnenstein der Wikinger: Navigation mit polarisiertem Himmelsicht. Praxis der Naturwissenschaften - Physik in der Schule 56, 33–38. Google Scholar
    • 29
      Hawthorne CF, Dirlam DM. 2011Tourmaline the indicator mineral: from atomic arrangement to Viking navigation. Elements 7, 307–312. (doi:10.2113/gselements.7.5.307) Crossref, Google Scholar
    • 30
      Ropars G, Gorre G, Le Floch A, Enoch J, Lakshminarayanan V. 2012A depolarizer as a possible precise sunstone for Viking navigation by polarized skylight. Proc. R. Soc. A 468, 671–684. (doi:10.1098/rspa.2011.0369) Link, Google Scholar
    • 31
      Le Floch A, Ropars G, Lucas J, Wright S, Davenport T, Corfield M, Harrisson M. 2013The sixteenth century Alderney crystal: a calcite as an efficient reference optical compass?Proc. R. Soc. A 469, 20120651. (doi:10.1098/rspa.2012.0651) Link, Google Scholar

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