Accuracy of the hypothetical sky-polarimetric Viking navigation versus sky conditions: revealing solar elevations and cloudinesses favourable for this navigation method

Abstract

Changes performed along the comments of Referee 1 are marked by violet.Changes performed along the comments of Referee 2 are marked by green.Sky conditions favourable for Viking navigation RSPA-2017-0358-R2 Száz et al. 2 AbstractAccording to Thorkild Ramskou's theory proposed in 1967, under overcast and foggy skies Viking seafarers might have used skylight polarization analyzed with special crystals called sunstones to determine the position of the invisible Sun. After finding the occluded Sun with sunstones, its elevation angle had to be measured and its shadow had to be projected onto the horizontal surface of a sun-compass. According to Ramskou's theory, these sunstones might have been birefringent calcite or dichroic cordierite or tourmaline crystals working as polarizers. It has frequently been claimed that this method might have been suitable for navigation even in cloudy weather. This hypothesis has been accepted and frequently cited for decades without any experimental support. In this work we determined the accuracy of this hypothetical sky-polarimetric Viking navigation for 1080 different sky situations characterized by solar elevation θ and cloudiness ρ, the sky polarization patterns of which were measured by full-sky imaging polarimetry. We used the earlier measured uncertainty functions of the navigation steps 1, 2 and 3 for calcite, cordierite and tourmaline sunstone crystals and the newly measured uncertainty function of step 4 presented here.As a result, we revealed the meteorological conditions under which Vikings could have used this hypothetical navigation method. We determined the solar elevations at which the navigation uncertainties are minimal at summer solstice and spring equinox for all three sunstone types. On average, calcite sunstone ensures a more accurate sky-polarimetric navigation than tourmaline and cordierite. However, in some special cases (generally at 35° ≤ θ ≤ 40°, 1 okta ≤ ρ ≤ 6 oktas for summer solstice, and at 20° ≤ θ ≤ 25°, 0 okta ≤ ρ ≤ 4 oktas for spring equinox) the use of tourmaline and cordierite results in smaller navigation uncertainties than the use of calcite. Generally, under clear or less cloudy skies, the sky-polarimetric navigation is more accurate, but at low solar elevations its accuracy remains relatively large even at high cloudiness. For a given ρ, the absolute value of averaged peak North uncertainties dramatically decreases with increasing θ until the sign (+/-) change of these uncertainties. For a given θ, this absolute value can either decrease or increase with increasing ρ. The most advantageous sky situations for this navigation method are at summer solstice when the solar elevation and cloudiness are 35° ≤ θ ≤ 40° and 2 oktas ≤ ρ ≤ 3 oktas. Media SummaryAccording to Ramskou's theory, under overcast/foggy skies Vikings used skylight polarization analyzed with sunstone crystals to determine the sun position. After finding the occluded Sun, its elevation had to be measured and its shadow had to be projected onto a sun-compass. It has frequently b...

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

“…The effect of consistent overestimations/underestimations of the deduced solar elevation was measured by Száz et al . [ 20 ] and was included in the computation of the θ−ρ matrix of the north uncertainties [ 21 ]. — Further simulations could also answer the question: How robust are the very high navigation success rates obtained, with respect to altering various parameters and environmental/meteorological conditions?…”

“…The effect of consistent overestimations/underestimations of the deduced solar elevation was measured by Száz et al . [ 20 ] and was included in the computation of the θ−ρ matrix of the north uncertainties [ 21 ].…”

“…Using the measured uncertainties of the four navigational steps, Száz et al . [ 21 ] determined the accuracy of sky-polarimetric navigation for 1080 different celestial situations characterized by the solar elevation angle θ and the cloudiness ρ (in oktas = 1/8 units), the sky polarization patterns of which have been measured by full-sky imaging polarimetry. As a result, they obtained the average ± standard error of the angular deviation from the north direction for the 1080 different sky situations (i.e.…”

“…This method is the so-called sky-polarimetric Viking navigation, the atmospheric optical prerequisites of which have been intensely studied [9][10][11][12][13][14][15][16][17]. The uncertainties of the four main steps of this navigation method have been measured on test persons in psychophysical experiments in a laboratory and a planetarium [18][19][20][21][22].…”

A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere

“…It is reported that the Vikings possibly used the polarization patterns of skylight for solving challenging navigation tasks, such as sailing to Greenland from Norway. The authors determined the accuracy [22] of hypothetical sky-polarimetric Viking navigation for 1080 different sky conditions that were characterized by parameters such as solar elevation and cloudiness [23]. A simulation based on a large amount of actual data [23], obtained using imaging polarimetry, shows that Viking sailors could have travelled to Greenland from Norway using polarization information [24].…”