Capricorn: Dec.22-Jan.29 The Sundial Primer
created by Carl Sabanski
Capricorn: Dec.22-Jan.29

The Sundial Primer Index

DeltaCad Sundial Macros - Steve Lelievre

Steve Lelievre wrote a DeltaCad macro that will create a Standard Time horizontal sundial using an azimuth or polar style. It has hour lines drawn at 15 minute intervals. You can get it here. The sundial has very unique hour lines as a result of being corrected for the Equation of Time. It is also corrected for longitude. This sundial is also called a "spider" sundial.

This macro can be used to design sundials in the latitude range of 25 to 65 for both the Northern and Southern Hemispheres. Steve indicated there is a problem with the Southern Hemisphere drawings but could not recall what it exactly was. If you discover something please let me know and I will post it. Steve plans to revisit his macro and update it at some time in the future.

SCADD

Figure 1 illustrates the input screen for this macro. As stated use negative degree values for south "Latitude" and east "Longitude" and "Timezone". Select either a "Polar axis" or "Upright" gnomon. "Roman" or "Standard" style numbers can be selected for the hour labels. The labels can be inverted so the sundial can be read when you are facing the sun. This will prevent you from casting a shadow on the dial plate when reading the time. The sundial has date circles that are required for determining the correct time. They are not labelled but January is by default placed on the inner circle but can be selected to go on the outer circle.

Figure 1: SCADD Macro - Horizontal Sundial

Figure 1: SCADD Macro - Horizontal Sundial

Figure 2 shows the horizontal sundial drawn for the inputs given in Figure 1. The January circle is on the inside. A "Polar axis" gnomon was selected and it can be drawn as a triangular piece rising from the centre of the sundial at an angle equal to the latitude.

Figure 2: SCADD Horizontal Sundial - January Inside

Figure 2: SCADD Horizontal Sundial - January Inside

Figure 3 shows a horizontal sundial with the same inputs as in Figure 1 but with "January outside" selected. Notice the difference in the hour lines and the boundary lines.

Figure 3: SCADD Horizontal Sundial - January Outside

Figure 3: SCADD Horizontal Sundial -  January Outside

The horizontal sundials in Figure 4 are designed for the same inputs given in Figure 1 but for the Southern Hemisphere. The sundial on the left has January on the inside and the one on the right has January on the outside. These are very different from the ones shown above.

Figure 4: SCADD Horizontal Sundials - Southern Hemisphere

Figure 4: SCADD Horizontal Sundials - Southern Hemisphere

The horizontal sundials in Figure 5 have "Upright" gnomons. This is actually an azimuth sundial. The gnomon can be a wire or cylindrical rod rising vertically from the centre of the sundial. The sundials on the left has January on the inside and the one on the right has January on the outside. The top sundials are designed for the Northern Hemisphere and the bottom sundials for the Southern Hemisphere.

Figure 5: SCADD Horizontal Sundials - Upright Gnomon - Northern Hemisphere

Figure 5: SCADD Horizontal Sundials - Upright Gnomon - Southern Hemisphere

Figure 5: SCADD Horizontal Sundials - Upright Gnomon

It is possible to adjust the hour lines on these sundials for a wide gnomon. Extend the horizontal and vertical lines to the outer boundary of the sundial. Draw the gnomon with the correct width and centred at the centre of the sundial. This will create two new dial centres. The positioning of the hour lines is as discussed in The Wide Gnomon page of The Sundial Primer. Note that a number of hour lines will be cut by the horizontal line and the portions above and below this line will be moved in opposite directions.

The original version of the SCADD macro is included as "SCADD_orig.bas". It has an entry for "Gnomon width" to deal with the wide gnomon but does not carry out the redrawing of the hour lines entirely correct. But it does get you started. The macro moves all morning hour lines to the left a distance equal to half the width of the gnomon and the afternoon hour lines to the right an equal distance. This is not correct for the portions of the hour lines located below the horizontal line passing through the centre of the sundial. The early morning hours should be moved back to the right a distance equal to the width of the gnomon and the late afternoon hours should be move to the left an equal distance. It's done!

This correction of the hour lines should not be done for the "Upright" gnomon. Because this gnomon is cylindrical in shape, the sun will cast a shadow from a different part of the surface throughout the day. Moving the hour lines as discussed above will not be effective in this case. Instead, the diameter of the gnomon should be as small as practical and the tine read from the centre of the shadow.

It is very easy to make a model of a SCADD horizontal sundial with upright gnomon or azimuth sundial. After completing the design print out the dial plate to the desired size and laminate it if it is to be protected. Glue the dial plate on to a 1/2-inch  thick piece of rigid styrofoam. Drill a 1/2-inch hole at the centre of the dial plate. Cut a 1/2-inch length of 1/2-inch wood dowel. Drill a hole in the centre of the dowel the diameter of a wire clothes hanger. Insert the dowel into the dial plate and a length of clothes hanger into the dowel. The clothes hanger will be vertical and acts as the gnomon.

Now, just how long does the gnomon need to be to ensure its shadow will intercept all the date lines throughout the year? Let's look at the worst case scenario but first a few general pieces of information.

The following equation is used to calculate the length "L" of the vertical gnomon required to cast a shadow of length "S" for any given day. The calculation is done at solar noon.

L = S x tan (Sun's Altitude) = S x tan (90 - Latitude + Sun's Declination)

The length of the shadow "S" required to intercept any given date circle is given by the following equations.

January Inside: S = Inner Radius + (Outer Radius - Inner Radius) x [(Day Number -1) / 364]

January Outside: S = Outer Radius - (Outer Radius - Inner Radius) x [(Day Number -1)  / 364)

Where the "Day Number" assumes January 1 is "1" and December 31 is "365".

The scenarios will assume the inputs shown in Figure 1 and will start with a sundial in the Northern Hemisphere. January on the inside gives the worst case. One might assume that since the furthest point is on the December 31 (Day Number 365) circle this circle must define the length of the gnomon.

S = 2 + (4 -2) x (364 / 364) = 2 + 2 = 4

L = 4 x tan (16.764) = 1.2049 units

Now remember the sun is highest, and therefore the gnomon's shadow the shortest, on the summer solstice or June 21 (Day Number 172). Let's check this out.

S = 2 + (4 - 2) x (171 / 364) = 2 + 0.9396 = 2.9396

L = 2.9396 x tan (63.29) = 5.8422 units

Amazing! It takes a gnomon almost 6 times longer to reach just beyond the centre of the date circles band than to reach the outer date circle.

The next sundial is located in the Southern Hemisphere. Again, January on the inside gives the worst case. Remember that December is summer where we are now. Will the summer solstice on December 21 (Day Number 355) give the longest gnomon again?

S = 2 + (4 - 2) x (354 / 364) = 2 + 1.9451 = 3.9451

L = 3.9451  x tan (63.29) = 7.8405 units

Again the furthest point is on the December 31 (Day Number 365) circle.

S = 4

L = 4 x tan (62.936) = 7.8288 units

For the Southern Hemisphere the gnomon's length is also determined by the distance to the summer solstice circle.

In any case, for a sundial with a diameter of 8 units, the gnomon must be relatively long for its shadow to intercept all the date circles. Perform these calculations for your particular latitude and sundial design to determine the required gnomon length. As the latitude decreases the gnomon's shadow shortens and the gnomon's length needs to be increased.

There is a way to keep the gnomon to a reasonable length. A pointer can be designed and used to determine the time. Figure 6 illustrates one possible design. The diameter of the circle is equal to the "Inner radius" or slightly less if the hour line numbers are to be displayed. A hole is placed at the centre with a diameter equal to the gnomon or for the model described above a diameter equal to the dowel. The pointer rotates on the gnomon or the dowel. If the dowel is used it must extend slightly above the surface of the dial plate. After positioning the sundial rotate the pointer until gnomon's shadow is centred on the green line. Find where the edge of the pointer, which extends beyond the green line, crosses the appropriate date line. Read the time at that point.

Figure 6: SCADD Azimuth Sundial Pointer

Figure 6: SCADD Azimuth Sundial Pointer