created by Carl Sabanski
DeltaCad Sundial Macros - Valentin Hristov - Bifilar Sundial
This macro draws a sundial that indicates the time by the intersection of the shadows of two wires on the dial plate. The wires are stretched above the dial plate and parallel to it. One wire will normally run from the top to the bottom of the dial plate and the second from one side to the other, thus being perpendicular to each other. The wires are also normally at different heights. The gnomons could be thick parallelepipeds, but then the print out must be cut along the indicated projections of the wires and the quarters must be properly adjusted.
The sundial can be designed for any orientation.
As mentioned above, this particular macro is used to design a "classical bifilar" sundial, which is recognized as having the two wire gnomons, both parallel to the dial plate and perpendicular to each another. Valentin has taken this macro to the next level where the wires can be given any arbitrary orientation. This allows the design of bifilar sundials with "almost infinitely" many possibilities. Be sure to check this macro out!
Classical Bifilar Sundial - sdabifil
This bifilar sundial is generated after the user enters the "Latitude", "Longitude" and "Central meridian" of the sundial's location as shown in Figure 1. A "Place" descriptor can also be included. Hour lines intervals of 15 and 30 minutes and one hour are available. The "Period" over which the sundial will be designed must also be selected. The hour lines can be adjusted for longitude and the Equation of Time. Longitude correction can be removed by entering the same value for "Longitude" and "Central meridian". However it is the entries for the declination, inclination and rotation of the dial plane that give the macro a great deal of flexibility. The bifilar sundial can now be designed for any orientation. Additionally the choice of the rectangular area is also a big advantage.
Figure 1 - Bifilar Sundial Macro
The values for the "Heights of the gnomons" must be determined. These values define how high the two gnomons, generally being wires, are above the dial plate. If the two heights of the gnomons are suitably chosen the hour lines will be equiangular, 15º per hour. If Declination = 0, Inclination = 0 and Rotation = 0, then the value of the ratio between the two heights of the two gnomons should be equal to "sin (Latitude)". The "Rectangular area" of the dial plate must be defined. This allows the more hour lines to be shown on the dial plate without decreasing the height of the gnomons too much. It can also be used to decrease the white space on the dial plate.
The sundial drawn with this macro is shown in Figure 2. This sundial has equiangular hour lines but they are drawn with the EoT correction so this may be difficult to see. The four triangular pieces define the position and height of the gnomons. A taut string between the top of each of the opposing two triangles would serve as the styles. The layer "ShadowCastingPoints" shows all points on the gnomons which cast a shadow on the hour lines inside the rectangular area. Also the common point of the extensions of the hour lines without EoT correction is shown in this layer as a small circle. Remember to turn off this layer before printing the sundial.
Assume that the "Left-Right" gnomon has a height equal to the "sin (Latitude)" times the height of the "Up-Down" gnomon. It is interesting to note, for this particular sundial, the "Left-Right" gnomon is a distance equal to "cos (latitude)" times the height of the "Up-Down" gnomon above the common point of the hour lines.
Figure 2 - Horizontal Bifilar Sundial
The macro also draws the declination line the 1st, 11th and 21st days of each month.
Many variations of the bifilar sundial can be created with this macro. To get additional hour lines on the dial plate reduce the heights of the gnomons or increase the rectangular area. If you want to have full analemma as hour lines select "Whole year" for the period. Be careful not to select too small a "Time interval" as many of the analemma will cross and the sundial will become confusing.
It is also possible to use this macro to create a number of other sundials. In particular, by placing both gnomons at the same height a nodus is created at the intersection of the two styles. In fact styles are not needed because all shadow points will be cast upon the dial plate by this single point. By entering the appropriate values for the declination, inclination and rotation of the dial plane many different sundials can be designed. These are shown in the table in Figure 3, where the southern latitudes are entered as negative numbers.
Figure 3: Sundial Configuration Table
For any of these sundials the triangles indicate the height of the nodus. The location of the nodus is given by the small dark circle located at the intersection of the horizontal and vertical lines drawn between the tips of the four triangles. The origin of the hour lines, if one exists, is given by the small circle.
Figure 4 illustrates a number of these sundials for the location shown in Figure 1 in the Northern Hemisphere. In all the examples below the height of the two gnomons was set to 1 (the case of the nodus sundial) and the EoT correction was switched off for clarity.
Equatorial Sundial - Top & Bottom
Polar & Horizontal Sundials
Vertical Direct South & North Sundials
Vertical Direct East & West Sundials
Vertical Declining East & West Sundials
Figure 4: Various Sundials
The images of the sundials above show the extreme versatility of this macro. It is an amazing piece of work!