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

According to Thorkild Ramskou's theory proposed in 1967, under overcast and foggy skies, Viking seafarers might have used skylight polarization analysed 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, respectively, 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 that 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.