Tuhelj – scientific pastime 2022

Milutin Tadić (calculation, design) & Berislav Horvatić (making, testing, photos)

46° 05’ N, 15° 45’ E

Instead of ordering a not-so-cheap horizontal sundial on the Internet, on which the shadow also shows the time of afternoon Islamic prayer (ṣalāt al-ʿaṣr), as well as qibla, the direction to Mecca, we decided to have fun and calculate and make it by ourselves. For the locality we chose Tuhelj, a small village in Croatian Zagorje, where B. H. resides. (fig. 1).

*Figure 1*. A panorama of Tuhelj which, according to the 2021 census, has 195 inhabitants

*Figure 2.* The condition was to make use of only those material resources and aids that are available to everyone: a circular kitchen board (D = 30 cm), the tip of a bamboo skewer (h = 4 cm), paper glue, a spirit level and an accurate watch.

*Figure 3*. Glueing the gnomon and adjusting its verticality

Figure 4. Instructions leaflet glued to the bottom side of the dial

Figure 5. A bench at the bus stop in the vicinity of the local church (famous for the baptism of Josip Broz in 1892 – later better known as Tito) was chosen as the test site. The place was not chosen because of that, but because of the bench which is flat, almost perfectly horizontal, unshaded, and nearly always unoccupied. The sundial was placed horizontally and oriented precisely at true solar noon on December 23. It had been supposed to be “put into operation” on December 21, the winter solstice, but the sky over Tuhelj was cloudy on December 21 and 22 as well. (The motto on the sundial says “The sun shines for everyone”, not “The sun shines everywhere”…) . The difference in the path of the shadow on December 21 and 23 is practically negligible because the change in the sun’s declination is insignificant (–23.44°, –23.43°).

*Figure 6*. The bench chosen for solar testing happens to be a “solar bench” – quite literally, but only accidentally.

Figure 8. The calculation reduced the accuracy of the sundial to the equation of time (e) value, which on December 23 amounted to only +57 seconds. This means that on that day the shadow would have been fast for close to one minute. When the shot was taken at solar noon (11:56 a.m. CET), it turned out that everything was in place: the tip of the shadow barely touched the winter solstice hyperbola and fell on the corresponding segment of the analemma.

Figure 9. At 1:58 p.m. (CET) the shadow tip touched the first ʿaṣr line and silently marked the beginning of the afternoon Islamic prayer. It is defined as the moment when the length of the shadow of the gnomon equals the sum of the length of the midday shadow and the height of the gnomon. According to the calculation, on December 23, 2022, that moment is at 14:02 true solar time (locally, in Tuhelj), which means that the shadow indeed „obeyed“ the rules of gnomonics, as it should. In short, the sundial has proven fully functional.