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

The Sundial Primer Index

DeltaCad Sundial Macros - Simon Wheaton-Smith

Simon Wheaton-Smith has written numerous DeltaCad sundial and dialling related macros. Simon has provided detailed notes within many of these macros to help those of you who are interested in learning how to program your own macros.  If you are new to programming open these files in the DeltaCad macro editor by selecting the "Macro" Tab and then the "E" button, and study the programs and the notes.

You can download all 27 of Simon's macros here. Two pdf files are also included:

"DeltaCADmacroREADME.pdf": summarizes the macro files as well as providing some important notes.

"NotesOnProgrammingDeltaCAD.pdf": is an introduction in programming DeltaCad macros that you will find very useful.

Be sure to check the Illustrating Shadows DeltaCad Macros page for the most recent versions. This page will take to you to many others where Simon has created programs to draw sundials using various languages. Who knows, you may just find what you are looking for.

A more recent version of Simon's macros can be obtained here. Some of these macros combine similar sundials described below to make them easier to use. There are also other improvements incorporated into some of the macros. Check them out!

The following is an overview of the macros Simon has developed. For more information on the various sundials and tools presented here visit Illustrating Shadows. You will be pleasantly surprised by all the dialling information you will find there. A lot of information regarding all these items are available in Simon's two books Illustrating Shadows and Illustrating More Shadows. They are a great value! Show that you appreciate Simon's work by purchasing them either in print or on CD.

And as Simon says:

"Some of the key features in my DeltaCAD macros include:

  • north and south hemisphere for most dials

  • animation of shadows or calendar lines

  • animation for shepherd and azimuth dials

  • astrolabe for any latitude (planispheric)

  • the infamous inclined decliner"

Simon uses the term "calendar line or curve" but keep in mind this is equivalent to "declination line" and the terms can be used interchangeably.

Macros for both Hemispheres provide an entry box for "N" or "S". Western longitudes are positive.

SIMPLE PROGRAMS

These macros demonstrate the programming techniques involved in the creation of some simple sundials.

Simple Horizontal Sundial - DC-basic-h-dial

This macro draws a basic horizontal sundial based on the "latitude",  "longitude" and "ref longitude" entered by the user. One of three time intervals between hour lines can also be selected; "1" for 60 minutes, "2" for 30 minutes and "4" for 15 minutes.

Figure 1 shows the drawing created by this macro. The hour lines are corrected for longitude. There is also a table of hour line angles for the full hours.

Figure 1: Simple Horizontal Sundial

Figure 1: Simple Horizontal Sundial

Simple Vertical Sundial - DC-basic-v-dial

This macro draws a basic vertical direct south sundial. The inputs are the same as the for the previous sundial.

Figure 2 shows the drawing created by this macro. The hour lines are corrected for longitude. There is also a table of hour line angles for the full hours.

Figure 2: Simple Vertical Sundial

Figure 2: Simple Vertical Sundial

Simple Shepherd's Sundial - DC-basic-s-dial-a

This macro draws a basic Shepherd's sundial based on  the "latitude" entered by the user. One of three time intervals can also be selected. The gnomon length "Gnomon ln ht" is adjustable. The points on the hour lines can be joined using either splines "S" or lines "L". Splines will result in smoother curves.

If the value 0 is chosen for the "latitude" the macro will create an animation. It will successively draw a Shepherd's sundial for latitudes between 25 and 90 at intervals of one degree and then stop.

Figure 3 shows the drawing created by this macro.

Figure 3: Simple Shepherd's Sundial

Figure 3: Simple Shepherd's Sundial

Simple Horizontal Bifilar Sundial - DC-basic-bifilar-a

This macro draws a basic bifilar sundial based on the "latitude",  "longitude" and "ref longitude" entered by the user. One of three time intervals between hour lines can also be selected.

A bifilar sundial has two gnomons parallel to the dial plate and they are both at different heights above the dial plate. They can be thin wires with one running east-west and the other north-south. This particular bifilar sundial is designed to have equiangular hour lines, i.e. the full hour line angles are 15 apart. This requires a specific relationship between the the gnomons and this is given in the drawing.

If the value 0 is chosen for the "latitude" the macro will create an animation. It will successively draw a bifilar sundial for latitudes between 10 and 80 at intervals of one degree and then stop. The only change in the dial plate is the position of the east-west gnomon.

Figure 4 shows the drawing created by this macro. The hour lines are corrected for longitude. There is also a table of hour line angles for the full hours. The position and height of the two gnomons is also shown. The table on the left indicates for given heights of the north-south gnomon "N:S ht" the required Y co-ordinate "E:W y" and height "E:W ht" of the east-west gnomon.

Figure 4: Simple Horizontal Bifilar Sundial

Figure 4: Simple Horizontal Bifilar Sundial

Simple Sun Declinations - DS-basic-calendar

This macro will draw declination lines or calendar curves based on the "SH style height" and the vertical gnomon height "Gnomon lin ht" entered by the user. The style height, normally the latitude, and gnomon height define the position of the nodus or shadow casting point. Two "solar declinations" can be entered in addition to 23.5, which defines the solstices. A "Decl" value other than 0 will result in an animation that will show the path of the nodus' shadow for the declination entered.

Figure 5 shows the drawing created by this macro. It explains how to align the calendar curves on a sundial drawn by one of the sundial macros.

Figure 5: Sun Declination Lines

Figure 5: Sun Declination Lines

HOUR ANGLE SUNDIALS

These macros draw sundials that use the sun's hour angle to indicate the time.

Horizontal Sundial - Northern and Southern Hemispheres - DC-h-dial-NandS

This macro draws a horizontal sundial similar to the simple horizontal sundial above except the user can now select a location in the Northern "N" or Southern "S" Hemisphere.

Figure 6 shows the drawing created by this macro.

Figure 6: Horizontal Sundial - Northern and Southern Hemispheres

Figure 6: Horizontal Sundial - Northern and Southern Hemispheres

Horizontal Sundial with Calendar Lines Based on Sub-Style Length - DC-h-dial-ssl-a

The entries for this macro are similar to those for the simple horizontal sundial. There is also any entry for the gnomon's sub-style length "Gnomon sub st len". This length is used to determine the position of the nodus used to draw the 7 calendar lines for the dates of the Zodiac.

If the value 0 is chosen for the "latitude" the macro will create an animation. It will successively draw the 3 calendar lines for the solstices and equinoxes for latitudes between 10 and 60 at intervals of one degree and then stop.

Figure 7 shows the drawing created by this macro. The default value of the sub-style length was used and as a result only 6 calendar lines are visible. If a smaller value such as "0.15" is used all 7 calendar lines would be visible.

Figure 7: Horizontal Sundial with Calendar Lines Based on Sub-Style Length

Figure 7: Horizontal Sundial with Calendar Lines Based on Sub-Style Length

Horizontal Sundial with Hour Lines Based on Gnomon Linear Height - DC-h-dial-glh-a

This macro is similar to the previous one except here the variable is the linear length of the gnomon "Gnomon lin lt". This value is the height of the nodus above the dial plate and is used to determine the sub-style length.

Figure 8 shows the drawing created by this macro. The value of the gnomon's linear length will determine whether all 7 calendar lines will be drawn so be sure to check this out.

Figure 8: Horizontal Sundial with Calendar Lines Based on Gnomon Linear Length

Figure 8: Horizontal Sundial with Calendar Lines Based on Gnomon Linear Length

Horizontal Sundial with Animated Calendar Line Shadow - MAIN-DC-dial-cal-a-shadow

This macro is the same as the one above except only the calendar lines for the solstices and equinoxes are drawn. A "Decl" value other than 0 will result in an animation that will show the path of the nodus' shadow for the declination entered.

Figure 9 shows the drawing created by this macro. A "Decl" value of 11 was entered and the path of the nodus' shadow is clearly visible upon completion of the animation.

Figure 9: Horizontal Sundial with Animated Calendar Line Shadow

Figure 9: Horizontal Sundial with Animated Calendar Line Shadow

Vertical Direct North and South Sundials - DC-v-dial-NandS

This macro draws a vertical sundial similar to the simple vertical sundial above except the user can now select a location in the Northern "N" or Southern "S" Hemisphere. In the Northern Hemisphere the sundial will be a vertical direct south sundial and in the Southern Hemisphere it will be a vertical direct north sundial.

Figure 10 shows the drawing created by this macro.

Figure 10: Vertical Direct South Sundial - Northern Hemisphere

Figure 10: Vertical Direct South Sundial - Northern Hemisphere

Vertical Declining Sundial - MAIN-DC-v-dec-dial-a

The entries for this macro are similar to the simple vertical sundial. There is also an entry for the wall declination "Declination from S". Be careful to note the sign convention. The wall declination is limited to the range of -75 to 75. The sundial can be drawn only for the Northern Hemisphere.

If the value 0 is chosen for the "Declination from S" the macro will create an animation. It will show the effect on the hour lines, SH and SD from changes in wall declination from -75 to 75.

Figure 11 shows the drawing created by this macro. The style height "SH" and sub-style angle "SD" are both shown in the drawing as well as tabulated values.

Figure 11: Vertical Declining Sundial - Northern Hemisphere

Figure 11: Vertical Declining Sundial - Northern Hemisphere

Vertical Declining Sundial Northern and Southern Hemispheres - DC-v-dec-NandS-a

This macro is the same as above except the user can now select a location in the Northern "N" or Southern "S" Hemisphere.

Figure 12 shows the drawing created by this macro.

Figure 12: Vertical Declining Sundial - Northern and Southern Hemispheres

Figure 12: Vertical Declining Sundial - Northern and Southern Hemispheres

Polar Aligned Vertical Declining Sundial - DC-v-dec-facing-pole

The entries for this macro are similar to the vertical declining sundial. However the value for "Declination fro S" is limited to the range of plus/minus 120 to 175. This results in the dial plate facing north.

Figure 13 shows the drawing created by this macro. It shows both early morning and evening hours.

Figure 13: Polar Aligned Vertical Declining Sundial

Figure 13: Polar Aligned Vertical Declining Sundial

East-West Vertical Declining Sundial - DC-v-dec-facing-EW

The entries for this macro are similar to the vertical declining sundial. However the value for "Declination fro S" is limited to the ranges of plus/minus 45 to 89 and 91 to 135. A vertical declining sundial facing close to east or west is known as a vertical great decliner.

A second box becomes available to enter the hour range desired.

Figure 14 shows the drawing created by this macro. In this case it shows only the afternoon hours. The hour lines are very close together but a box displayed when the macro is run describes how to deal with this.

Figure 14: East-West Vertical Declining Sundial

Figure 14: East-West Vertical Declining Sundial

Inclining-Declining Sundial - DC-inc-dec

This macro draws an inclining-declining sundial based on the "latitude",  "longitude" and "ref longitude" entered by the user. One of two time intervals between hour lines can also be selected. Entries are also required for the inclination and declination of the dial plate. Read the instructions included in the first box carefully.

Figure 15 shows the drawing created by this macro.

Figure 15: Inclining-Declining Sundial

Figure 15: Inclining-Declining Sundial

Meridian Sundial - MAIN-DC-m-dial

The meridian sundial is a vertical direct east or direct west sundial.

This macro draws a meridian sundial based on the "latitude",  "longitude" and "ref longitude" entered by the user. Entries for the gnomon's linear height "Gnomon lin ht" and to define whether the sundial faces east "E" or west "W" are required. One of three time intervals between hour lines can also be selected.

Figure 16 shows the drawing created by this macro. The solstice and equinox declination lines are also drawn.

Figure 16: Vertical Direct West Sundial

Figure 16: Vertical Direct West Sundial

Inclining Meridian Sundial - MAIN-DC-m-inc

This macro is the same as above except the user can enter a dial plate inclination.

Figure 17 shows the drawing created by this macro.

Figure 17: Inclining Vertical Direct West Sundial

Figure 17: Inclining Vertical Direct West Sundial

Polar Sundial - MAIN-DC-p-dial

This macro draws a polar sundial based on the "longitude" and "ref longitude" entered by the user. An entry for the gnomon's linear length "Gnomon lin lt" is required.

Figure 18 shows the drawing created by this macro. The solstice and equinox declination lines are also drawn.

Figure 18: Polar Sundial

Figure 18: Polar Sundial

Equatorial Sundial - MAIN-DC-q-dial

This macro draws an equatorial sundial based on the "latitude",  "longitude" and "ref longitude" entered by the user. An entry for the gnomon's linear length "Gnomon lin lt" is required. Entering "N" or "S" will result in drawings for the top and bottom of the dial plate.

Figure 19 shows the drawing created by this macro. This is the top of the sundial facing north. The sunrise/sunset line is used to determine the hour lines that will be removed. Declination circles are also shown.

Figure 19: Equatorial Sundial

Figure 19: Equatorial Sundial

ALTITUDE SUNDIALS

These macros draw sundials that use the sun's altitude to indicate the time.

Shepherd's Sundial - DC-s-dial-decl-a

This macro draws a Shepherd's sundial based on  the "latitude" entered by the user. One of three time intervals can also be selected. The gnomon length "Gnomon ln ht" is adjustable. This is a more accurate drawing than the simple Shepherd's sundial as the sun's declination is calculated every two days.

If the value 0 is chosen for the "latitude" the macro will create an animation. It will successively draw a Shepherd's sundial for latitudes between 25 and 90 at intervals of 2.5 and then stop.

Figure 20 shows the drawing created by this macro.

Figure 20: Shepherd's Sundial

Figure 20: Shepherd's Sundial

Dual Gnomon Shepherd's Sundial - DC-s-dial-decl-2g-a

This macro is the same as above except the user can enter a gnomon length for the winter 'Gnomon ln ht W" and one for the summer "Gnomon ln ht S". This results in the winter hour lines being more separated and as a result easier to read.

Figure 21 shows the drawing created by this macro. In this macro the sun's declination is calculated every day.

Figure 21: Dual Gnomon Shepherd's Sundial

Figure 21: Dual Gnomon Shepherd's Sundial

Horizontal Planispheric Astrolabe - DC-astrolabe

For further information on astrolabes visit Simon's web site. Also read the header in this macro. Here is an excerpt.

"This program is for educational purposes only, it works but its focus is on programming methods, the end result is usable but not intended to be used without the added human touch."

Figure 22 shows the drawing created by this macro.

Figure 22: Horizontal Planispheric Astrolabe

Figure 22: Horizontal Planispheric Astrolabe

Vertical Planispheric Astrolabe - MAIN-DC-astrolabe-v

The comments for the horizontal planispheric astrolabe apply here as well.

Figure 23 shows the drawing created by this macro.

Figure 23: Vertical Planispheric Astrolabe

Figure 23: Vertical Planispheric Astrolabe

AZIMUTH SUNDIALS

These macros draw sundials that use the sun's azimuth to indicate the time.

Winged Azimuth Sundial - DC-azimuth-a

This macro draws an azimuth sundial based on  the "latitude", "longitude" and 'ref longitude" entered by the user. One of three time intervals can also be selected. The points on the hour lines can be joined using either splines "S" or lines "L". Splines will result in smoother curves. The "Dial format" will place the summer solstice date circle on the outside when "N=normal" is selected and on the inside when "O=other" is selected".

If the value 0 is chosen for the "latitude" the macro will create an animation. It will successively draw an azimuth sundial for latitudes between 25 and 90 at intervals of one degree and then stop.

Figure 24 shows the drawing created by this macro.

Figure 24: Winged Azimuth Sundial

Figure 24: Winged Azimuth Sundial

MISCELLANEOUS DIALLING AIDS

Calendar Lines/Curves - DC-calendar-curves

This macro draws calendar lines for various sundials. By using the values for style height "SH" and sub-style angle "SD" it is possible to draw the calendar lines for vertical declining sundials. It is then a matter of overlaying and aligning the calendar lines on a sundial designed using one of the other macros. It will be left up to you to try various combinations of inputs and see what the results are.

Figure 25 shows the drawing created by this macro. This is for a horizontal sundial and so the "SH style height" is equal to the latitude. If the hour lines "H" are replaced by degrees "D" the dial plate hour lines are replaced by a protractor. When a value for "shift by SD" is entered the protractor is used as this would indicate the calendar lines are for a vertical declining sundial and they will need to be rotated on the dial plate.

Figure 25: Calendar Lines / Curves

Figure 25: Calendar Lines / Curves

Table Generator - DC-data-tables

This macro creates tables and graphs for a variety of important dialling information including:

  • Julian Day - report

  • EOT (2 wave) - report and graph

  • EOT (3 wave) - report and graph

  • Solar Declination (1 wave) - report and graph

  • Solar Declination (6 Waves) - report and graph

  • Sunrise/Sunset - report and graph

Some selections will result in a second box being displayed that will request additional information.

Figure 26 shows a graph for the Equation of Time drawn by this macro.

Figure 26: Graph of the Equation of Time

Figure 26: Graph of the Equation of Time

Almanac for a day - MAIN-DC-almanac

This macro creates a table of very useful information for the diallist and anyone interested in sunny matters. Enter the location of interest and the month and day and the almanac will give the following:

  • Julian Day

  • EOT (Equation of Time)

  • Long Corr (Longitude Correction)

  • Net Corr (EOT + Long Corr)

  • Declination (Sun)

  • Rise (Sunrise)

  • Set (Sunset)

  • Alt (Sun's Altitude using local apparent time)

  • Azi (Sun's Azimuth using local apparent time)

  • Hour line angles for a horizontal sundial

  • Hour line angles for a vertical direct south/north sundial

Figure 27: Almanac for a Day

Figure 27: Almanac for a Day