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

Bernáth, Balázs; Farkas, Anna; Száz, Dénes; Blahó, Miklós; Egri, Ádám; Barta, András; Åkesson, Susanne; Horváth, Gábor

doi:10.1098/rspa.2013.0787

Cited by 17 publications

(36 citation statements)

References 14 publications

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“…These instruments bear gnomonic lines valid at a given latitude on prominent dates (e.g., spring equinox, summer solstice) and provide compass directions with the aid of the gnomon shadow [3]. Recently, two alternative interpretations of the Uunartoq artifact were demonstrated: it was interpreted as an instrument to determine latitude and local noon [4], or as a twilight board [5]. It is a frequently cited and often criticized hypothesis that Vikings were able to locate the sun and perform solar navigation even under cloudy or foggy conditions with a three-step sky-polarimetric navigation [6]:…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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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 θ(S), solar azimuth φ(S)) 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 (ω(North)) was determined with an error of -3.34°≤Δω(North)≤+6.29°. The inaccuracy of the second step of this navigation method was high (Δω(North)=-16.3°) when the solar elevation was 5°≤θ(S)≤25°, and the two selected celestial points were far from the sun (at angular distances 95°≤γ(1), γ(2)≤115°) and each other (125°≤δ≤145°). 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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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“…This fragment turned out to be a remnant from the Viking era, and, according to the most possible assumptions, it was part of a Sun compass, a device used for marine navigation that determines the direction of geographical North with the help of the shadow cast by a vertical gnomon onto the horizontal dial surface in sunshine. Its alternative function and usage was proposed by Bernáth et al [14,15].…”

Section: Introductionmentioning

confidence: 99%

“…The estimation of the solar elevation was most possibly performed by using numbers of his own fists and fingers to measure it, as described by Bernáth et al [31]. Knowing the solar elevation, the shadow of the occluded Sun had to be replaced by a shadow-stick, as described in detail by Bernáth et al [15,31].…”

Section: Introductionmentioning

confidence: 99%

North error estimation based on solar elevation errors in the third step of sky-polarimetric Viking navigation

et al. 2016

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The theory of sky-polarimetric Viking navigation has been widely accepted for decades without any information about the accuracy of this method. Previously, we have measured the accuracy of the first and second steps of this navigation method in psychophysical laboratory and planetarium experiments. Now, we have tested the accuracy of the third step in a planetarium experiment, assuming that the first and second steps are errorless. Using the fists of their outstretched arms, 10 test persons had to estimate the elevation angles (measured in numbers of fists and fingers) of black dots (representing the position of the occluded Sun) projected onto the planetarium dome. The test persons performed 2400 elevation estimations, 48% of which were more accurate than ±1°. We selected three test persons with the (i) largest and (ii) smallest elevation errors and (iii) highest standard deviation of the elevation error. From the errors of these three persons, we calculated their error function, from which the North errors (the angles with which they deviated from the geographical North) were determined for summer solstice and spring equinox, two specific dates of the Viking sailing period. The range of possible North errors Δ ω N was the lowest and highest at low and high solar elevations, respectively. At high elevations, the maximal Δ ω N was 35.6° and 73.7° at summer solstice and 23.8° and 43.9° at spring equinox for the best and worst test person (navigator), respectively. Thus, the best navigator was twice as good as the worst one. At solstice and equinox, high elevations occur the most frequently during the day, thus high North errors could occur more frequently than expected before. According to our findings, the ideal periods for sky-polarimetric Viking navigation are immediately after sunrise and before sunset, because the North errors are the lowest at low solar elevations.

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“…The navigation method deduced by Bernáth et al . [31] based on the Uunartoq artefact fragment functioning as a twilight board is useful also during twilight and under clear skies, when the sun is close to the horizon (when −8° ≤ θ ≤ +10°). Using a twilight board, a shadow-stick and sunstone crystals could have allowed Vikings to navigate during long twilight periods on the basis of polarization patterns of clear skies.…”

Section: Discussionmentioning

confidence: 99%

Celestial polarization patterns sufficient for Viking navigation with the naked eye: detectability of Haidinger's brushes on the sky versus meteorological conditions

et al. 2017

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If a human looks at the clear blue sky from which light with high enough degree of polarization d originates, an 8-shaped bowtie-like figure, the yellow Haidinger's brush can be perceived, the long axis of which points towards the sun. A band of high d arcs across the sky at 90° from the sun. A person can pick two points on that band, observe the yellow brushes and triangulate the position of the sun based on the orientation of the two observed brushes. This method has been suggested to have been used on the open sea by Viking navigators to determine the position of the invisible sun occluded by cloud or fog. Furthermore, Haidinger's brushes can also be used to locate the sun when it is below the horizon or occluded by objects on the horizon. To determine the position of the sun using the celestial polarization pattern, the d of the portion of the sky used must be greater than the viewer's degree of polarization threshold d* for perception of Haidinger's brushes. We studied under which sky conditions the prerequisite d > d* is satisfied. Using full-sky imaging polarimetry, we measured the d-pattern of skylight in the blue (450 nm) spectral range for 1296 different meteorological conditions with different solar elevation angles θ and per cent cloud cover ρ. From the measured d-patterns of a given sky we determined the proportion P of the sky for which d > d*. We obtained that P is the largest at low solar elevations θ ≈ 0° and under totally or nearly clear skies with cloud coverage ρ = 0%, when the sun's position is already easily determined. If the sun is below the horizon (−5° ≤ θ < 0°) during twilight, P = 76.17 ± 4.18% for dtruemin∗=23normal% under clear sky conditions. Consequently, the sky-polarimetric Viking navigation based on Haidinger's brushes is most useful after sunset and prior to sunrise, when the sun is not visible and large sky regions are bright, clear and polarized enough for perception of Haidinger's brushes.

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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

Cited by 17 publications

References 14 publications

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

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

North error estimation based on solar elevation errors in the third step of sky-polarimetric Viking navigation

Celestial polarization patterns sufficient for Viking navigation with the naked eye: detectability of Haidinger's brushes on the sky versus meteorological conditions

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