Region

Town

Location

Latitude

Longitude

Cyprus

34° 40' N

32° 55' E

Digital Simulation of the Kourion Sundial.

In the courtyard of the Kourion Museum, near the town of Episkopi, stands a Roman marble sundial. It was discovered in the ruins of the site of Kourion.

Chrysanthos Kanellopoulos, with the assistance of Platon Konstantopoulos, has created a digital model of the sundial and has worked on simulation of gnomon's shadow. The model has been "virtually" placed in a number of theoretical locations as well as Kourion's latitude itself and also in different times, particularly in the period in which Kourion was built. Shadows cast during the Equinoxes and Solstices are compared with the corresponding calendar circles on the dial's reading surface.

Find Location of the Sundial

The perfection in execution, details and calculations combined with the find spot of our example, the Agora of Kourion, betrays that it was perhaps public property, installed and intended to regulate the most demotic space of a town: the actual heart, the Agora itself. The Agora of Kourion dates from the Severan era (C.E. 193-235); specifically, its construction period dates from the beginning of the 3rd century C.E. (Christou 1996: 45). The presence of distance 0.29 – 0.295 m. in four of the dial’s principle dimensions suggests the use of the standard Roman foot (pes), here measured as 0.296 m.,(Jones 1989, 37) a variation of the ancient Greek Attic or so-called Soloneian foot of 0.29387 – 0.294 m. (Büsing 1982: 25) or Ionian pous of 0.296 m. (0.295 and 0.296, or 0.2972 m.). A similar sundial, with a nearly identical moulded base, was found in Palaepaphos, by Phil Walker, and is now exhibited in the Kouklia Museum. It is tentatively dated in the Roman period, however it is much simpler with only two calendar circles. Like in the Kourion example, the line of the Winter Solstice is rather composed of two closely spaced arcs (A and B).

Physical Details of the Sundial

Inventory no: AM 150, Kourion Museum, provenance: Kourion Agora, collected by McFaden. Now displayed at the courtyard of the Kourion Museum, Episkopi, Cyprus..

Material : marble. The base is carved with a cyma recta – S shaped molding.
The dial’s reading concave surface is designed on the basis of a cone, in the form of a circular equilateral triangle with sides 0.46. Cone Diameter: 0.46, Cone height: 0.40. The axis of the cone is at the angle of 30 degrees from the horizontal; thus its base and the reading conical surface are tilted 60 degrees from horizontal plane (Neugebeuger 1948).The lower surface is cut off by the cone at 194.5 degrees of a circle, that is as a horse shoe shaped arc of 12 out of 22 sections of the circle. The 12 hour sections are marked on the reading surface with 11 lines, which meet 0.035 above the dial’s upper surface, clearly off the axis of the cone. A dial of this kind would normally have 3 canonical calendar lines, which correspond to the winter solstice, equinoxes and summer solstice (tropai) respectively, like the example from Samos (Gibbs 1976: 44 and : http://www.math.uni-hamburg.de/math/ign/xyz/ca00-v5.htm#tth_sEc1 (fig. 1) ). More detailed than other examples, the scaphe of Kourion, is carved with a total of 7 calendar circles (A-G in the Figure opposite) and it is at the angle of exactly 60 degrees from all sides.

The cone of the scaphe is at 30 Degrees from the vertical plane, as described above. A "hemicyclium" should be designed to be the same angle as the latitude of the place. Kourion's latitude is approximately 34° 40' N , so it is a bit out, however it is suspected that many ancient sundials were a little inaccurate (Phil Walker, via letteris). It can be speculated that it was manufactured in somewhere in Egypt, which indeed has a latitude of 30 degrees and was somehow imported to Cyprus. There is at least one well known parallel case. In 263 B.C.?., a sundial came to Rome from Catania in Sicily, thanks to Consul Valerius Messala. This confiscated Greek sundial was erected on the Campus Martius without recognizing the error due to the difference in latitude of 4.5° (Wolfschmidt 2000). Ideally, the Kourion sundial would work accurately in Cairo (Roman Babylon) or Petra, Jordan which have a latitude identical to the angle of the cone and the reading surface (30°).

A three dimensional digital model of the Kourion sundial was built on MAX, by Platon Konstantopoulos. The model was placed at Cairo's and Kourion's latitudes and was rendered to simulate sun's orbit and shadow of the pin (gnomon) at desired days of the year and hours of the day. The model of the sundial was orientated with the gnomon pointing North/South. These adjustments can be operated in the software. The readings were right with a length of the pin equal to 0.1846, when the sundial was operated in Kourion, and with a pin length of 0.1673 m., with the sundial placed in Cairo. When the shadow of the gnomon is, on Equinoxes, cast on the middle Circle (Line D), it is cast right on lines A-B and G during the Solstices. The renders yield more accurate readings/ better results with the sundial placed in the latitude of Cairo.

In the digital model, the gnomon was rendered bronze, to be distinguished from its dark grey shadow. The calendar circles were painted red, for the same purpose. The hour lines were omitted, as they were confusing. The simulation and experimentation was a digital one; the sundial was virtually placed in Cyprus and Cairo, but operated from/ on our PC in Athens, Greece - or potentially, from anywhere in the globe, and with the sun at any desired position! The actual sundial could only be tested in the latitude of Kourion, and a physical replica would be required to be tested in Cairo while even such replica would be impossible to work and be studied in, say, Athens, London or Sydney. In contrast, with digital technology, it was possible to virtually install and test the ancient scaphe to Cairo, its "correct" place, and operate it from any place on earth. Discrepancies observed in Kourion, Cyprus were not insignificant as compared to the correct readings with the sundial "placed" in Cairo, the ideal site for this dial. Compare fig. 9 with fig. 10.

During the simulation, the issue of precession of the Equinoxes was taken into consideration. The earth's axis moves in a cone-shaped pattern, called a precession, with the celestial North Pole describing a full circle every 26,000 years or so. Hipparchus (c.120 BCE) proved that over extended periods of time there was a constant change in the constellation in which the equinoxes occurred, this was called the "precession of the equinoxes". This change in equinoxes occurs at a very slow pace - the constellation through which the equinox occurs changes only every 2,160 years. The entire zodiac is passed through about every 26,000 years.
2,000 years ago, during the Roman era, the equinox was in Aries and by 2,600 it will be in Aquarius. This was taken in account in the construction and render of our model.

The Vernal equinox is used to mark the beginning of Spring. Today, this occurs around March 21, but the date varies from year to year. Julius Caesar, in 46 B.C.E. (i.e. about the date of our sundial), reformed the calendar by switching its base from lunar to solar and the day on which the Vernal equinox occurred was defined as March 25. The Council of Nicea had in June 325 fixed the date of the equinox on March 21, thus adopting to the error of 4 days due to the "precession". In 45 CE, the Vernal Equinox would be March 24, in year 135 on March 23, in year 215 on March 22, and in 325 CE on March 21, as explained above. Had nobody adjusted the length of the pin in the Kourion overtime, there would have been a maximum deviation of 4 days, before the city was totally destroyed on 21 July 365 by a major earthquake.

The length of the gnomon was corrected accordingly. In the digital model the pin was given a length so that its shadow is cast on the Equinox line (Line D) on March 22-23, that is during the construction period of the Kourion Agora, in the early 3rd century C.E. Luckily, this averages the difference between the Equinox date in Julian's times (March 25) and the Equinox's position in 365 (July 21), when the Agora was destroyed and, most probably, the dial went out of use. Thus, dates throughout the entire Roman period can be taken with an average error of 2 days. Each day is represented on the reading surface between 0.00085 and 0.0013 m. Therefore, the discrepancy of 2 days is 0.0017 m., or 1.7 mm., with a maximum of 0.0026 m. or 2.6 mm. Accordingly, the maximum deviation of 4 days due to the "precession" between Julius Caesar's times and year 365 varies significantly between 3.4 mm. and 5.2 mm. (0.0034 and 0.0052 m.).

At the equinox, the sun rises directly in the east and sets directly in the west. Therefore, line D on the reading surface of the Kourion's dial should correspond to the tip of the pin with a theoretical, projecting length of the pin equal to 0.1846 m.
After these adjustments and calibration on the basis of the Equinoxes, it was found in numerous renders that the shadows corresponded to Lines A-B (Winter Solstice) and Line G (Summer Solstice) on December 21-25 and June 21-25 respectively.

The following parameters were taken in consideration, in the digital simulation and renders of the model:

JULIUS CAESAR'S TIMES (46 B.C.E.)
The sundial should be placed at a latitude of 30° (Cairo)
In year 46 B.C.E., the length of the pin (gnomon) should be such that its shadow is cast during the Roman Equinoxes (March 25) on Line D of the scaphe.
Length of pin: 0.1673 m.

The sundial should be placed at a latitude of 34° 40' (in Kourion)
In year 46 B.C.E., the length of the pin (gnomon) should be such that its shadow is cast during the Roman Equinoxes (March 25) on Line D of the scaphe.
Length of pin: 0.1846 m.

CONSTRUCTION PERIOD OF KOURION'S FORUM, ca. 200 C.E.
The sundial should be placed at a latitude of 30° (Alexandria, Petra or Cairo)
In year 180, the length of the pin (gnomon) should be such that its shadow is cast during the Vernal Equinox (March 23) on Line D of the scaphe.
Length of pin: 0.1673 m.

The sundial should be placed at a latitude of 34° 40' (in Kourion)
In year 180, the length of the pin (gnomon) should be such that its shadow is cast during the Vernal Equinox (March 23) on Line D of the scaphe.
Length of pin: 0.1846 m.

The sundial should be placed at a latitude of 30° (Alexandria, Petra or Cairo)
In year 2002, the length of the pin (gnomon) should be such that its shadow should be cast during the Equinoxes (March 20 - September 23) on Line D of the scaphe. Length of pin: 0.1673 m.

The sundial should be placed at a latitude of 34° 40' (in Kourion, Cyprus)
In year 2002, the length of the pin (gnomon) should be such that its shadow should be cast during the Equinoxes (March 20) on Line D of the scaphe.
Length of pin: 0.1846 m.
http://www.dragon.org/chris/dates.html

*** Renders by Chrysanthos Kanellopoulos and Platon Konstantopoulos