National Flag Vertical Sundial

Much effort has been put into this design so please leave a like or comment—it would mean a lot to me!  And if you have any feedback, I’d love to hear it!

Main Features

1. Choose your own flag!;
2. Completely customizable design for your Latitude & Longitude;
3. Supports both Northern & Southern Hemispheres;
4. Automatically corrects for the Equation of Time (EoT), including any standard time meridian offsets, therefore, directly displaying Standard Local Time;
5. Rotatable 2-sided plate design to cover both halves of the year;
6. Horizontal sliding “dual-gnomon” to select the date & display time; 
7. No complicated adjustments or alignments required other than levelness & orientation to the sun.

A Python script auto-generates the sundial hour curves based on a users input parameters, including the provision of a fully interactive output plot.  Here is an example:  

See attached documentation for more details on how to use the program & configure your own custom flag sundial.

How was it Designed

Each curve on the plot represents the shadow length of a horizontal gnomon over a range of days and for a specific hour. The gnomon is perpendicular to the dial plate & slides along the date scale located at the top edge of the sundial plate. The plate is mounted vertically and is designed to rotate horizontally around a pole in order to allow a user to face the plate towards the sun.  In this design, the height of the sundial plate is related to the length of the gnomon and is determined by the longest shadow that would be cast over the course of a year, which occurs during the summer solstice & when the sun's altitude is at its maximum. The height of the computed output chart "H" is, therefore, determined as follows:

     H= G∙tan (90 - ø +23.44) = G∙tan (113.44 - ø)

where ø is the latitude of the location of the sundial and G is the length of the gnomon.

Knowing the dimensions of the chart, the width is divided into 12 vertical bands representing the 12 months. Additional subdivisions are added to the months to represent 5 day periods.

The sun's altitude "a" must then be determined for a given hour (True Solar Time), for a particular day. The distance "D" of the hour line from the top of the chart is determined as follows:

     D= G∙tan a

Finally, the hour lines are calculated and corrected for the Equation of Time (EoT) to provide Local Mean Time (LMT), then further corrected for the user’s longitude so that Standard Local Time can be displayed directly on the sundial.  In summary, the relationship for the different types of times is as follows:

True Solar Time + EoT → Local Mean Time + Longitudinal Time Correction → Standard Time 

Please note that the sundial does not compensate for Daylight Savings Time & so the user needs to mentally add an hour extra to the time displayed by the sundial. 

The program allows the plot to be saved as an SVG, which is then imported into an image editor like Inkscape to remove any extraneous plot elements.  The final step is to convert the plot into a 3D object by assigning it height using Blender. The 3D plot is then used to create the required sundial features over a reference (blank) rectangular plate.  

How was it Printed

In this example, the sundial plate was printed in 3 different colors; i.e. main dial plate background in white, text & curves in black & flag in red & white.  Additionally, the plate is double-sided meaning that there is text & graphics on both sides.  

The best approach to follow for printing is to have your colors defined as separate objects which can then be implemented as multiple prints, or as a single print.  In either situation, each object needs to have its own STL file & the combining of these objects is achieved thru your slicer program.  It is essentially the equivalent of having multiple objects “dropped” into a main part to create a complete assembly. The results are cleaner & clearer boundaries, with smooth surfaces and no emboss or deboss features.  There at two common techniques to this approach:

1. Multi-Pass: Each object is printed individually as separate prints, with filament swaps occurring when new objects are uploaded to the printer.  Only one extruder is assigned in the slicer program & all parts remain on the print bed until all subsequent objects are printed around, or overtop existing parts;
2. Single-Pass: Objects are printed all together by assigning “virtual” extruders to each object or part in the slicer program & using filament change G-code commands instead of tool changes.  This is essentially “tricking” the printer into thinking that it has multiple extruders.  This technique also allows one to change filament color for different areas of the print bed, including on the same layer, therefore, making it possible to print all objects in one print job.  It is also the preferred method if you don't own an MMU.

In this design, text & graphics where assigned to individual objects each having 0.4mm heights.  Subsequently, each object was assigned to an extruder based on their color.  During printing, the objects where placed over their corresponding 0.4mm deboss areas located on the main dial plate. 

For optimal print quality, it is always best to have text & graphics against the print bed.  In this situation, this would result in printing two separate plates of half the total thickness which get sandwiched together during assembly to create a double sided part.  

Both single & dual-plate design options are provided in the file section.  More details are also available in the downloadable design instructions.

How to Use

1. Adjust the top horizontal edge of the sundial plate for levelness.  Rotate the flag by 90 degrees & repeat.  If you implemented the pole cap with a bubble level, you can use that to simplify adjustments;
2. One side of the sundial plate covers from January 1st to June 30th; whereas the other side is from July 1st to December 31st.  Slide the gnomon to the appropriate month & date;
3. By keeping the gnomon position fixed (use the lock screw on top of the gnomon), only rotate the sundial plate in azimuth so that it is facing the sun.  Adjust the plate position so that the gnomon casts the sharpest shadow against the plate; 
4. The time is read where the tip of the shadow intersects the hour lines on the plate. 

Thanks again for your support!