created by Carl Sabanski
DeltaCad Sundial Macros - Robert Hough
Robert Hough wrote a DeltaCad macro that will indicate the duration the sun illuminates any arbitrary surface at any location. You can get it here. This is an extremely useful macro for anyone wanting to design a sundial.
Figure 1 illustrates the input screen for this macro.
Figure 1: Duration Macro
Robert provides a complete description of his macro in the macro itself. This description is repeated below for those who are not comfortable accessing the macro. Read it carefully.
"When designing a sundial, the dialist should consider the earliest and latest sunlight on the face of the dial for the purpose of knowing what hours to use. The designer should also consider showing the client, or user, the limitations to avoid them having unrealistic expectations.
The theoretical duration of sunlight on a horizontal dial covers the time between sunrise and sunset at that site and these times can be easily computed. If the face is inclined from horizontal, the duration is reduced during certain portions of the year. Any declination of an inclined dial shifts the start and end times of that shortened duration.
If the dial is facing away from the equator, there can be two periods of the daylight striking the face.
An inclined/declined dial faces the celestial sphere at a particular direction (azimuth and altitude). There is another location on the earth's surface where a horizontal dial would face in that same direction. The latitude and longitude of that location can be determined and the sunrise/set times of that horizontal dial can be easily computed.
The sun will shine on our dial face between sunrise and sunset on both dials. The duration is from the latest of the two sunrises to the earliest of the two sunsets. In the case of two periods of the day when the sun shines on our dial, the first duration is from the first sunrise to the first sunset, and the second duration is from the second sunrise to the second sunset.
This macro plots sunrise/set lines for this site and also for the other location, called dial 2. It also fills the duration of sunlight with color to make it easier to interpret the duration.
The input values for Latitude, Longitude, and Standard Time Zone Meridian are self-explanatory. The values for Declination and Inclination need to be understood.
Declination is the Azimuth of the dial face, measured from the South (even in the southern hemisphere), South is 0, East is negative, West is positive, around to North which can either 180 or -180. If you stand with your back toward the dial face, you are looking toward the Azimuth (Declination). A horizontal dial always has a Declination of 0.
Inclination is always positive. A horizontal dial has an Inclination of 0. A vertical dial has an Inclination of 90. If you face the dial and it leans away from you, the Inclination is between 0 and 90. If the dial leans toward you, it has an Inclination between 90 and 180. For example, all vertical dials have an Inclination of 90. Vertical, south-facing dials have a Declination of 0, east-facing -90, west-facing +90, north facing 180 or -180.
Polar dials have an Inclination equal to the absolute value of the Latitude, in the northern hemisphere the Declination would be 0, in the southern hemisphere it would be 180.
An equatorial dial at Latitude 40 N has its upper (summertime) face described as a Declination of 180 and an Inclination of 50 (90 - 40), while its lower (wintertime) face has a Declination of 0 and an Inclination of 130 (90 + 40)."
The date entered in Figure 1 is for a horizontal sundial and results in the output shown in Figure 2. The time indicated is "Standard Time" and is corrected for both longitude and the Equation of Time. In many cases sundials are designed to show local apparent or solar time and if that is what your sundial is to show then select "Local Apparent Time". This will help you to determine the range for the hour lines to be shown on the sundial's dial plate.
Figure 2: Duration - Horizontal Sundial
The output for a horizontal sundial is shown for the selected location. because it is a horizontal sundial the output for Dial 2 is identical.
Figure 3 shows some additional outputs from "Duration" for the same location used in Figure 1. These are for the following sundials; vertical direct south, polar, vertical direct east and vertical direct west.
Figure 3: Vertical Direct South, Polar, Vertical Direct East & West Sundials
The area in yellow is the period the particular sundial will be illuminated by the sun during the year.