The time (the hour angle) can be determined by the direction from which the sun shines. That is why the most important part of most sundials is a shadow thrower (gnomon).
Due to the inclination of the earth's axis and the different speed of the earth's movement around the sun, there are deviations of up to ± 5 minutes in summer and up to ± 15 minutes in winter.
"The sundial always goes right,
the wheel clock is taken too seriously. "
(The deviations of a maximum of ± 15 minutes hardly played a role until the end of the 19th century.
The highest point of the sun (zenith) was set as 12 o'clock. The clocks were set according to the sun.)
Calculation of the maximum sun height σ
The graphic shows the position of the sun on March 20, 2023 and September 23, 2023 – vertically above the equator. Since the sun is 109 times larger than the earth, the sun's rays hit the earth almost parallel. The sketch shows that the elevation angle σ is calculated from the latitude φ as follows:
σ = 90º - φ
For Saarbrücken, this results in the maximum height of the sun at the equinox: σ = 90º – 49.2º = 40.8º
If the earth's axis inclines by ± 23.4º over the course of a year, the maximum sun elevation in Saarbrücken is 64.2º for the summer solstice and 17.4º for the winter solstice.
This calculation is the true height of the sun. Due to the refraction of the sunlight in the atmosphere, it appears to be higher, i. e. you can see the sun about a quarter of an hour longer in the evening, although it is actually already partly below the horizon, and about a quarter of an hour earlier in the morning, although it is still below the horizon. This accounts for about +0.5º. When the sun is at its highest, the path of sunlight through the air is shorter and this effect is much smaller.
Since the path of the sunlight through the atmosphere varies, the spherical shape of the sun is flattened near the horizon.
If you take the date into account, you can also determine the time from the apparent height of the sun or, if you know the time, the date.
The invention of the cylinder sundial is attributed to Hermann the Lame (1013-1054), a monk in the Reichenau Monastery (Lake Constance), in 1050. It was widespread from the end of the Middle Ages to modern times. It is easy to use and does not depend on the north-south direction, so no compass is required. The cylindrical body has a rotatable head with a pair of collapsible shadow throwers. Around the cylinder there are 2 rings at the top and bottom with monthly and daily data for the first and second half of the year.
If you set the summer gnomon (short) or the winter gnomon (long) to the date and align the clock so that the shadow is pointing straight down, you can read the time on the lines.
The predecessor was the Chinese pilgrim's staff (on the right wall).
Gnomonic equatorial clock
The sundial is a true copy of an instrument built by Philipp Pfeffenhauser (1654 - 1733) in Augsburg (Germany). If the time is to be read, the plumb balance is first set up and the instrument is placed horizontally with the aid of the two adjusting screws. Now the quarter circle of the latitude quadrant is set up, the equatorial plane is pushed over it and the geographical latitude is set. Incidentally, the latitudes of some large European cities are engraved on the top of the instrument. The bottom line then reads: Philipp Pfeffenhauser Augsburg 48. Finally, the height of the semicircular shadow projector on the slider is set according to the current month. Now the sundial is rotated until the tip of the shadow cast by the shadow thrower falls on the line of one of the two dials. The dials show the hours of the morning and the hours of the afternoon.