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

The Sundial Primer Index

DeltaCad Sundial Macros - Valentin Hristov - Cylinder Sundial

The macro discussed below opens the door to an additional variety of cylinder sundials. It is extremely versatile!

Cylinder Sundial: Type 2 - cylarb2

This macro draws four basic kinds of cylinder sundial as determined by the combinations of the selections for "Type of top circular base" and "Read time from". The sundials are as follows:

  1. A sundial that indicates the time on hour lines read from inside a cylinder by a beam of light passing through a concentric hole or a almost point aperture on the top of the cylinder. The aperture acts like a nodus when casting its beam of light on the inner surface of the cylinder where the hour lines are positioned. 
  2. A sundial that indicates the time on hour lines read from outside a cylinder by a beam of light passing through a concentric hole or aperture on the top of the cylinder. 
  3. A sundial that indicates the time on hour lines read from inside a cylinder by the shadow cast by an arbitrary nodus point on the top of the cylinder.
  4. A sundial that indicates the time on hour lines read from outside a cylinder by the shadow cast by an arbitrary nodus point on the top of the cylinder.

The hole is concentric with the cylinder but the nodus point can be placed anywhere on the top of the cylinder. The cylinder can be placed in any orientation. It is possible to use this macro to create the sundials that were designed by the previous cylinder sundial macro "cylarb1".  This will be discussed later.

This cylinder 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 at intervals of 15, 30 and 60 minutes are available. The "Period" over which the sundial will be designed must also be selected. The hour lines can be adjusted for the longitude and the Equation of Time.

Figure 1: Cylinder Sundial Macro - Nodus Point

Figure 1: Cylinder Sundial Macro - Nodus Point

The "Declination of the base plane", "Inclination of the base plane" and "Rotation in the base plane" are illustrated in Figure 2. It is important to note that these entries relate to the "top circular base" of the cylinder. The reference position defined by Decl = 0, Inc = 0 and Rot = 0 results in a vertical cylinder perpendicular to the horizontal plane with a horizontal top circular base. The 2 rectangles in the figure are the base plane as it is being manipulated by 2 of the 3 variables. The yellow base plane shows the affect of changes to the "Declination of the dial plane" and the cyan to changes in the "Inclination of the dial plane". The magenta arrows show how the top circular base is affected by changes in the "Rotation in the dial plane". These three variables allow the sundial to be placed in any orientation. For latitudes in the Southern Hemisphere it is natural to start by setting the "Declination of the base plane" to 180.

Figure 2: Positioning the Cylinder in an Arbitrary Orientation

Figure 2: Positioning the Cylinder in an Arbitrary Orientation

"Time read from the inside" draws the cylindrical surface of the sundial so it can be read from the inside of the cylinder. "Time read from outside" assumes the cylinder is transparent and draws the sundial so it can be read from the outside of the cylinder looking through the transparent wall.

"Type of top circular base" permits the selection of one of two available bases. The first is a "Concentric hole" . 

Figure 3 shows the parameters that can be selected for the concentric hole. The "Hole radius" determines the radius "R" of the hole in the top circular base. The red line, when the cylinder is its reference position as defined above, has the top of the line to the north. The reference point of the hole is important to determine as it must be kept track of as the base plane is being manipulated to move the sundial into the desired position. A radius of "0" represents a small hole at the centre of the base and the reference point is at the centre of the red line. A radius equal to the cylinder's radius eliminates the top circular base and the edge of the cylinder is used to indicate the time. In this case the reference points are the points on the circumference of the cylinder. If a thick circular base is used with any intermediate radius there are two options available for reading the sundial. The "Time at the lowest point of the light spot" option is shown in the centre of Figure 3. Note that the thicker the top circular base is a larger portion of the sundial becomes unusable. The "Time at the highest point of the light spot" option is shown at the right of Figure 3. The reference point for each of these options will fall somewhere on the circumference of the hole.

Figure 3: Concentric Hole Parameters

Figure 3: Concentric Hole Parameters

The second "Type of top circular base" is a "Nodus point". In the drawings, except for those generated by the macro, the nodus is represented by a pie section but it can be any suitable point.

Figure 4 shows the parameters that can be selected for the nodus point. The "Radius" determines the distance "R" the nodus is away from the centre of the cylinder base. The red line, when the cylinder is in its reference position as defined above, has the top of the line to the north.  A radius of "0" places the nodus at the centre of the top circular base and the reference point is at the centre of the red line. A radius equal to the cylinder's radius places the nodus on the circumference of the cylinder. The "Angle" will rotate the nodus clockwise from 0 to 360 similar to azimuth.  Note that a thick nodus must be placed above the base of the cylinder.

Figure 4: Nodus Point Parameters

Figure 4: Nodus Point Parameters

Keeping track of the position of the reference point is very important. Having a small cylinder model such as a dowel can be very helpful. The reference point can be marked on the top of the model and its declination, inclination and rotation, as well as the nodus angle, can be changed to help visualize where the reference point ends up and the final orientation of the cylinder.

The dimensions of the cylinder are defined by the "Cylinder radius" and the "Maximal length below the base" and "Maximal length above the base". The "Cylinder radius" is self explanatory. By default the circular base is assumed to be at the top of the cylinder and the "Maximal length above the base" is set to "0". The "Maximal length below the base" is the maximum length the cylinder can be below the top circular base. If the drawing does not require this entire length it is automatically reduced. Some cylinder orientations will result in the hour lines going beyond the base and into an area where no cylinder exists. For example, this can occur if the macro is used to design the cylinder sundials from the previous macro "cylarb1" that are in the horizontal position. In such cases positive values of "Maximal length above the base" will extend the cylinder on the opposite side of the base (upwards on the drawing) and allow the hour lines on that side to be drawn. An example will be given later.

The parameter "How to draw" allows lines to be drawn as "short segments" or "splines". Normally "splines" is selected". There will be certain situations when the drawing will contain unwanted horizontal lines when splines are used. This will occur for sundials designed for latitudes in the polar zones as well as certain other situations when Longitude" and "EoT" correction are applied. These lines will be obvious as they connect the splines from one side of the dial to the other. DeltaCad has no way of removing these lines but some other CAD software can. To remove these unwanted lines select "short segments".

The parameter "Angles between" is used to define only a portion of a cylinder. This is useful if a sundial is being placed on a large part of a circular wall that does not wrap around 360 such as a bay. The two ranges are 0 to -180 and 0 to 180. The drawing shows the complete sundial but there are vertical lines that define the portion of the cylinder that fits in the bay.

The sundial drawn with this macro using the information in Figure 1 is shown in Figure 5. This is a vertical nodus type cylinder sundial with the nodus radius "0". In this case the angle could be arbitrary. The bottom portion of the drawing is the dial surface. The magenta lines show the outer boundaries of the cylinder set by "Angles between". The first small dot above dial surface represents the nodus as it relates to the sundial drawing. With these parameters it just happens to fall visually on the circumference of the circle. The circle represents the sundial and the small dot in the centre shows the position of the nodus within the cylinder base. The two green arrows show the relationship between the drawing and how it applies to the cylinder sundial. The cardinal directions "NESW" are shown only when the "Inclination of the base plane" is set to "0" resulting in the top circular base being in a horizontal plane. In other cases it is not shown as it would not represent the sundial's orientation in a meaningful way.

Figure 5: Nodus Type Cylinder Sundial

Figure 5: Nodus Type Cylinder Sundial

For comparison Figure 6 shows the same sundial as in Figure 5 but with "Read time from outside (transparent)" selected. In this case the time is read from the outside of the cylinder through a transparent wall. Note that both the hour lines and east-west directions are reversed.

Figure 6: Nodus Type Cylinder Sundial - Transparent

Figure 6: Nodus Type Cylinder Sundial - Transparent

Figure 7 shows the macro set up to draw a concentric hole type cylinder sundial.

Figure 7: Cylinder Sundial Macro - Concentric Hole

Figure 7: Cylinder Sundial Macro - Concentric Hole

Both sundials shown in Figure 8 are concentric hole type cylinder sundials with a hole radius of "0.5" and full radius of "1".. The sundial on the left uses the "Time at the lowest point of the light spot" option and the one on the right the "Time at the highest point of the light spot" option. The sketches at the top of the drawing represent these two options for a thick top circular base and are similar to those shown in Figure 3. These sketches appear only when the hole radius is greater than 25% of the cylinder radius. If the hole is small in a thick base then only a small portion of the sun's rays will make it through the hole and a large area of the sundial is unusable. However it is still possible to select either of the two "Time at the" options and the sundial drawings will be different. The "lowest" variant is suitable for higher latitudes and the "highest" variant for lower ones.

Figure 8: Concentric Hole Type Cylinder Sundial

Figure 8: Concentric Hole Type Cylinder Sundial

Let's look at how this macro can be used to design a sundial presented in the previous cylinder sundial macro "cylarb1". Figure 9 shows an east-west horizontal cylinder sundial with the hole pointing to celestial south designed with the macro "cylarb1".

Figure 9: E-W Horizontal Cylinder Sundial with Hole to Celestial South Figure 9: E-W Horizontal Cylinder Sundial with Hole to Celestial South - cylarb1

Figure 9: E-W Horizontal Cylinder Sundial with Hole to Celestial South - cylarb1

Figure 10 shows the required parameters for the "cylard2" macro configured to produce this sundial. This is where the cylinder sundial model comes in very useful. First note that a nodus point sundial with a radius of "1" is selected. This places the nodus on the north edge of the horizontal base of the vertical cylinder. The "Declination of the base plane" is set to 90, which rotates the nodus to the east. The "Inclination of the base plane" is set to 90, which places the top circular base vertically, the cylinder horizontally and the nodus at the top. The "Rotation of the base plane" is set to "180 - Latitude" or 129.8512, which rotates the central line of the drawing to a position that is opposite to the south in the celestial equatorial plane. The "Nodus point Angle" is set to 180, which is opposite to the central line. At this point the cylinder is situated as shown in Figure 9 but assuming the "Maximal length above the base" is set to "0" only the portion of the cylinder to the east of the hole is present. By setting this parameter to be positive the west part of the cylinder is added.

Figure 10: E-W Horizontal Cylinder Sundial with Hole to Celestial South Macro

Figure 10: E-W Horizontal Cylinder Sundial with Hole to Celestial South Macro

Figure 11 shows the sundial drawing produced by the macro. The sundial drawing is the same as in Figure 9 but west is at the top and east is at the bottom. Another difference is that here corrections for latitude and the Equation of Time are included. To reverse the directions of east and west set the "Declination of the base plane" to -90 and the "Rotation of the base plane" to "-(180 - Latitude)".

Figure 11: E-W Horizontal Cylinder Sundial with Hole to Celestial South - cylarb2

Figure 11: E-W Horizontal Cylinder Sundial with Hole to Celestial South - cylarb2

The other sundials created with "cylarb1" can also be drawn using this macro. Try some of them.

Before printing the sundial turn off the layer "Scheme" to prevent the drawing of the sundial that includes the green arrows from being printed. If the layer "DateLines" is turned off the declination lines will not be printed.

Try making a transparent cylinder sundial from a glass. If you happen to have a portion of a circular wall or bay available you can now design a sundial for it no matter which direction it faces.