June 6, 2025
Description
The design auto-generates plots using a Python script based on the user's entered latitude. Other parameters of the sundial can also be modified; i.e. size of main dial, number of hours to display, start of January ring from center, ½ & ¼ hour lines, text size, etc. using a text editor like Notepad++. The script is well documented so you won't have any problems following the code. Once executed, the script will automatically display the plot on your computer screen & save it to an SVG file. The saved SVG can then be modified in an image editor like Inkscape to remove any extraneous plot elements, then brought into Blender to give the plot height for conversion into an STL. The STL can then be used to create the required dial features over a blank plate. Further modifications can then be made to the dial like adding a center hole for the gnomon; i.e. recommend using a 3mm stainless steel rod. Don't forget to add the cap at the end of the rod to protect your eyes!
The length of the gnomon will depend on the diameter of the dial. It needs to be long enough to cast a shadow across the outer arcs and proportional to the altitude of the sun at noon, or one hour after noon during the summer solstice. This condition could make the gnomon impractically too high for some dial designs. Therefore, the shadow of a shorter gnomon can be extended by eye to the date arc during the period when the shadow does not fall on the outer arcs. In the provided design example, the max & min gnomon heights are calculated & presented in the output plot; i.e.
Example: Max & Min Gnomon Height (as calculated by the Python script):
Therefore, in this example, a reasonable gnomon length would be between 150 & 175mm.
The calculation of the sun's azimuth is given by the following equation:
A = arctan { sin (h) / [ sin ø cos (h) - cos ø tan δ ] }
where h is the hour angle, ø is the latitude and δ is the sun's declination.
The dial plate consists of 13 concentric circles that represent the 12 months of the year. The center of these circles is the location of the vertical gnomon.
For a given gnomon length, the two extremes for the shadow length is:
where G is the height of the gnomon.
The gnomon height required for the shadow to reach a given date circle can be determined as:
G = r tan a
where r is the radius of the date circle and a is the sun's altitude. The calculation can be performed for the two extremes given above.
The gnomon of this horizontal sundial is located at the center of the concentric month lines and perpendicular to the dial plate. The center is highlighted by a cross-hair mark on the output plot. The inner most month circle is January, the next is February, etc. up to December, which is the outer circle. In the case of a Horizontal Azimuth sundial, the term “spider” refers to the shape of the hour lines. The Sun's azimuth is used for indicating the time & the sundial's design makes it independent of the Sun's altitude in the sky.
Worth mentioning also that the hour lines are corrected for the Equation of Time, meaning that the sundial will display Local Mean Time. It won't, however, correct for any longitude offsets from your Standard Time meridian so you will need to make the mental conversion.
Since I don't own an MMU printer, “virtual” extruders where assigned to each color in the slicer program & the filament change G-code command (M600) was issued instead of extruder changes. This is a commonly used technique which essentially tricks the printer in thinking it has multiple extruders. This technique also allows one to change filament color for different areas on the same print layer, therefore, making it possible to print all colors in one print job. Print the surface with text & graphics against the bed for best quality.
Place the sundial on a level surface with the month labels in vertical alignment with the direction of your southern meridian (if your in the northern hemisphere). The 12 o'clock hour mark would therefore be facing in a northerly direction.
The time is read at the intersection point of the shadow of the gnomon with the circle of the current month. For finer resolution, one could interpolate between the month circles; example: 15th of the month would be half-way between two months, etc.
The example included in the file section is for a latitude of 50.3 degrees north.
References:
License:
Creative Commons — Attribution — Noncommercial — Share Alike
3DMason
