Note: dial46.5degreesN.stl is a dial for my latitude. See "How I Designed This" for instructions on how to make a dial for your latitude.
A Hemispherium is a type of sundial that places the shadow of the sun on a partial sphere, making it easy to understand the motion of the earth around the sun, the apparent motion of the sun through the day and through the year, Daylight Saving Time (Summer Time), the solstices and equinoxes, and the development of calendars.
It demonstrates how sundials are good for finding the time of the year as well as the time of day.
The long line marks the celestial equator. When the shadow of the gnomon crosses this line, it's the Spring (Vernal) or Fall (Autumnal) Equinox.
The upper edge of the partial sphere marks the Tropic of Capricorn. When the shadow of the gnomon touches this edge, it's the Winter Solstice (in the Northern Hemisphere), and the sun is at its lowest in the sky.
The lower edge of the partial sphere marks the Tropic of Cancer. When the shadow of the gnomon touches this edge, it's the Summer Solstice (in the Northern Hemisphere), and the sun is at its highest in the sky.
The short lines mark the hours. Notice that they evenly divide the partial sphere. The 24 hours of the day divide the sphere into 24 parts of 15 degrees each (360/24 = 15).
The gap in the partial sphere marks solar noon. Each day when the gnomon's shadow falls into this gap, the sun is at its highest in the sky for that day.
Watches and clocks show Standard Time (or Summer Time) rather than Solar Time. The difference is a complicated subject. It's possible to make sundials that show Standard Time, but they're a bit complicated. In contrast, a solar time sundial nicely models the movement of the sun through the sky.
Print in a light color filament, so you can easily see the shadow of the gnomon on the dial.
I designed this dial to be printed in PLA. If you print in ABS instead, you may have to deal with warping and shrinkage.
Carefully remove the support material, then mount the sundial. You may want to use a black, permanent marker to paint the numbers for 9am, noon, and 3pm.
To mount the sundial:
1) Find a level spot that faces south, and gets sunlight much of the day. A south-facing window sill is often a good choice.
2) Set the dial so the slot points due north. I find it easiest to use a magnetic compass and your local magnetic declination - the difference between where the compass points and true, geographic north. (see https://www.ngdc.noaa.gov/geomag/declination.shtml to find your local declination).
3) fix the dial in place with removable adhesive or nails.
A hemispherium is an easy sundial to construct in a CAD application: I just created a partial sphere with its top and bottom each 23.5 degrees (the tilt of the earth's axis) from horizontal. I then made the equator marker and the hour markers. Then I added the extruded digits for 9am, noon, and 3pm.
As I mentioned above, dial46.5degreesN.stl is a sundial for my latitude. To create a hemispherium sundail for your latitude:
1) import unrotatedDial.stl into your CAD application
2) rotate that dial in the XZ plane by the co-latitude of your location. The co-latitude is just 90 degrees minus your latitude. For example, my latitude is about 45.6 degrees North, so my colatitude is 90 - 45.6 = 44.4 degrees.
3) import horizonCutter.stl, basePlate.stl, and baseCutter.stl
4) Subtract (Cut) the horizonCutter from the rotated Dial. This subtraction gets rid of the part of the sphere that the sun's shadow will never strike.
5) adjust the Z height of the basePlate and baseCutter so that the base plate is just touching the bottom of your rotated dial, and the baseCutter is even with the bottom of the basePlate.
6) Subtract (Cut) the baseCutter from the rotated dial.
7) Add (Fuse) the basePlate to the cut, rotated dial..
8) export the fused result for printing.