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Sundials : Calculation & Design

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Sundial & Birdbath Combination
A horizontal dial with a fabric-formed pedestal, when pair with a similarly designed birdbath, can offer an appealing addition to a backyard setting. Throw in a few custom flower pots (from single-use plaster molds) for even greater appeal.
The dial to the right (vertical, south-facing, polar-gnomon) was made using a combination of design techniques. Debossing was used for denoting hour line values, dial location and latin inscription (loosely translated as "The hours rush") as well as the upper and lower limits of the gnomon shadow throughout the year. Different colored concrete (white and light gray) was used to lay out the hour lines as well as the position of the gnomon's shadow during the equinoxes, which will trace a horizontal path. Finally, the EOT inset ("Equation of Time") is a precast element (made from a reusable rubber mold) attached to the dial as the final step during fabrication.
In the design phase, it can be useful to have software to help with the heavy lifting in the event the sundial incorporates more than just the standard polar gnomon and hour lines.  I've used the following from time to time to work out details of some of the dials I've worked on:
Calculator Screen Shot
A more comprehensive calculator is available at: Sun Dial Calculator. It's an XHTML file which loads and runs in a browser as a "stand alone" utility just like any garden variety web page.  With this utility one can calculate analemmatic and cylinder dials as well as classic and bifilar dials. It is also available via download (ZIP file):  XHTML Dial Calculator . 
Vertical Sundial
The dial to the right represents a vertical, south-facing dial (1-inch perpendicular gnomon) made early in the process of working out the use of plaster molds and debossing.  This piece was also made using acrylic polymer and GFRC (glass-fiber reinforced concrete).


Vertical, West-facing Dial
Another early attempt at debossing is shown at the right. This one is a vertical, west-facing dial with a two-inch long, ¼-inch diameter brass gnomon.
This dial (vertical, south-facing), also a sundial constructed early in my experiments with debossing (look at the "7" in the upper layout!), has two layouts. Each layout corresponds to a six month period, one from winter to summer solstice and one from summer to winter solstice. The curved lines are a departure from the more traditional straight hour lines typically seen on dials, and are designed to take into account the variable motion of the sun throughout the year. While variable, the solar motion can still be calculated and incorporated into a dial (assuming one doesn't mind the extra work;).
 
My earliest dials adopted a precast approach (the molds were made using the same technique outlined elsewhere).  Both of the dials shown below were designed for a latitude of 37 degrees north (or south).  The unusual shape of one of the dials shown is just a variation of an armillary sphere.  The "flaring" arms are ellipses with an eccentricity determined by the dial latitude (i.e. 37 degrees).

Early Dials


After precast dials became a little boring (didn't take long), next attempts were created using an approach similar to early table tops (i.e. hours marker patterns were prepositioned on a piece of formica before casting the dial face).  The gnomon (3/8" square brass) was generally added afterward (removable elements in the dial face allowed insertion of the gnomon after the concrete had cured).