Mathematical model of inverted analemmatic sundial on the example of Belogorsk sundial of the Bronze Age

TL;DR

This paper develops a mathematical model for an inverted analemmatic sundial, demonstrating its accuracy and suggesting its historical significance in improving Bronze Age time measurement methods.

Contribution

It introduces formulas for calculating hour marker coordinates on an inverted analemmatic sundial and applies them to the Belogorsk sundial to assess its accuracy.

Findings

Accuracy of 5-6 minutes for the Belogorsk sundial

Higher precision than Bronze Age water clocks

Supports hypothesis linking sundial invention to improved time measurement

Abstract

This article proposes a mathematical model of an inverted analemmatic sundial, provides formulas for calculating the coordinates of their hour markers. On the example of the Belogorsk sundial, a method is described for determining the accuracy of time measurement using an inverted analemmatic sundial, in which cup marks are used as hour markers. The obtained value of the accuracy of time measurement with the help of the Belogorsk sundial is 5 - 6 minutes and is quite good for a measuring instrument of the Bronze Age, and is also higher than the accuracy of time measurement with the help of a water clock. As a result, it is concluded that the hypothesis is confirmed that the invention of the sundial was associated with the need to improve the accuracy of time measurement using a water clock.