created by Carl Sabanski
DeltaCad Sundial Macros - Valentin Hristov - Super Box Sundial
The previous polar box sundial "sdbox" designs a sundial that can be used in three configurations as was discussed. In this macro, Valentin Hristov creates a "super" box sundial. It can be designed for any orientation. Amazing!
The package of files made available for download includes a text file "sdboxarb.txt". There is a discussion about the use of this macro and you should read it. Some of the configurations discussed are illustrated below.
Box Sundial with Arbitrary Orientation - sdboxarb
Figure 1 shows the entries available to the user. The previous entries for "Latitude", "Longitude", Central meridian" and "Place" are available. Selections to include corrections for longitude and the Equation of Time are now available. Longitude correction can be removed by entering the same value for "Longitude" and "Central meridian". Also the hour lines can be drawn at 15 and 30 minute as well as 1 hour intervals.
Figure 1 - Box Sundial with Arbitrary Orientation Macro
However it is the entries for the declination, inclination and rotation of the box that give the macro a great deal of flexibility. The box sundial can now be designed for any orientation.
The "Declination of the plane of the box", "Inclination of the plane of the box" and "Rotation of the box" are a bit tricky to visualize. Figure 2 illustrates these three inputs. The position defined by Decl = 0, Inc = 0 and Rot = 0 places the box parallel to the E-W axis. The 3 rectangles in the figure are the dial plane as it is being manipulated by the 3 variables. The yellow dial plane shows the effect of changes to the "Declination of the dial plane", the cyan to changes in the "Inclination of the dial plane" and the green to changes in the "Rotation of the dial plane". These three variables allow the sundial to be placed in any orientation. To help further visualize the box's orientation draw a rectangle on a sheet of paper to represent the box. Turn this sheet as required for the Decl, Incl and Rot.
Figure 2: Positioning the Box in an Arbitrary Position
The sundial drawn by the previous macro "sdbox" could be used as a polar, vertical direct east or vertical direct west sundial. These same sundials can be designed using this macro using the following entries.
Polar Box Sundial
Hemisphere: Declination = 0, Inclination = latitude, Rotation = 0
Vertical Direct East Box Sundial
Declination = -90, Inclination = 90, Rotation = -90 + latitude
Vertical Direct West Box Sundial
Hemisphere: Declination = 90, Inclination = 90, Rotation = 90 - latitude
The entries in Figure1 are for a polar box sundial. Figure 3 shows the drawing of this sundial. The hour lines are only drawn for the times the sundial is illuminated by the sun. Base triangles are used only if the rotation is 0º or 180º, therefore they are not drawn. This can easily be done by creating a drawing using the macro "sdbox". The base triangles can be copied from that drawing and pasted into the "sdboxarb" drawing. The additional parts shown in Figure 3 are for a specific purposed that will be described later.
Figure 3 - Polar Box Sundial
Figure 4 shows this polar sundial as well as vertical direct east and vertical direct west sundials. They are of course not in the correct orientation for use but illustrate what the macro can do. The vertical direct east sundial's morning hours are confined to those that actually can be read. This is the same with the vertical direct west sundial's evening hours.
Figure 4 - Vertical Direct West, Polar and Vertical Direct East Box Sundial Models
The combinations are endless!
According to Valentin it is sufficient to make a combination of 3 sundials, 1 horizontal and 2 vertical adjusted to both sides of the horizontal, that can be self-orienting and used to find true north-south. True north-south is found if you rotate the whole construction of 3 sundials until the time readings on two of them are the same. This is discussed further in "sdboxarb.txt" but the values required to do this are as follows.
Sundial1(horizontal):: Declination = 0, Inclination = 0, Rotation = 0 and read from the south or Declination = 180, Inclination = 0, Rotation = 0 and read from the north and
Sundial 2 (vertical- adjusted to the northern end of the horizontal): Declination = 0, Inclination = 90, Rotation = 0 read from the south and
Sundial 3 (vertical- adjusted to the southern end of the horizontal): Declination = 180, Inclination = 90, Rotation = 0 read from the north
These combinations work best at latitudes in the range of 30º to 60º. The text file discusses a design option for lower latitudes (suitable inclination 45º instead of 90º) as well as giving additional information of interest such as the sundial combinations to be used for the Northern and Southern Hemispheres. Normally one would expect a direct south facing vertical sundial in the Northern Hemisphere and a direct north facing sundial in the Southern Hemisphere to appear as mirror images. That is not the case with these sundials. They will be different because June always remains at the centre of the sundial and when it is summer in one Hemisphere it is winter in the other.
Figure 5 shows the four sundials described above. The first horizontal sundial shows the parts that would hold the vertical sundial in place.
Figure 5 - Sundial 1 South, Sundial 1 North, Sundial 2 and Sundial 3
Normally only 2 of the 3 sundials, the horizontal and one of the verticals, are required to cover the majority of the time the sundials are illuminated during the day. The third is required if you are interested in hours very early in the morning or late in the evening when the sun's azimuth is north (Northern Hemisphere) or south (Southern Hemisphere) of the true east- west line. Figure 6 shows a self-orientating sundial for the Northern Hemisphere consisting of a horizontal sundial (Sundial 1 South) and a vertical sundial (Sundial2).
Figure 6 - Self-Orientating Sundial: Northern Hemisphere