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

Normally the cylinder sundial is perceived to be a vertical cylinder with a moveable horizontal gnomon, also known as a Shepherd's sundial. Valentin has written two sundial macros that allow you create a very interesting and unique cylinder sundials. They are quite amazing!

The first type of cylinder sundial is described below. The second type can be found by following this link. It's worth a visit!

Cylinder Sundial: Type 2

Cylinder Sundial: Type 1 - cylarb1

This macro draws a sundial that indicates the time on hour lines inside a cylinder by a beam of light passing through a small hole or aperture on the cylinder. The aperture acts like a nodus when casting its small beam of light on the inner surface of the cylinder where the hour lines are positioned. The cylinder, and therefore the hole, can be placed in any orientation.

Valentin provided some insight into the development of this macro. The cylinder sundial macro started with a modification to the bifilar sundial macro where "only some new formulae are included". By starting with an existing macro and introducing the appropriate new formulae Valentin states that "I have at once the the whole flexibility in a new situation. Of course, the analytical geometry is also needed to find the formulae...". The following sketch illustrates Valentin's preparation for this new and exciting macro. For Valentin the fun is first achieving the final result. The rest is the icing on the cake.

Figure 1: The Beginning of a New Macro

Figure 1: The Beginning of a New Macro

This cylinder sundial is generated after the user enters the "Latitude", "Longitude" and "Central meridian" of the sundial's location as shown in Figure 2. 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. The "Left end" and "Right end" entries define the length of the cylinder over which the hour lines are drawn. The "Cylinder radius" determines the size of the cylinder.

Figure 2 - Cylinder Sundial Macro

The "Declination of the dial plane", "Inclination of the dial plane" and "Rotation of the dial plane" are a bit tricky to visualize. Figure 3 illustrates these three parameters. The position defined by Decl = 0, Inc = 0 and Rot = 0 places the cylinder parallel to the E-W axis with the hole at the top aligned with the Zenith. 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 cylinder's orientation draw a rectangle with a small circle at its centre, to represent the cylinder, on a sheet of paper. Turn this sheet as required for the Decl, Incl and Rot.

Figure 3: Positioning the Cylinder in an Arbitrary Orientation

Figure 3: Positioning the Cylinder in an Arbitrary Orientation

Figure 4 shows the orientation of the cylinder sundial as specified in Figure 2. Note the cylinder is on the E-W line and the hole is located at the top of the cylinder.

Figure 4: Cylinder Orientation

Figure 4: Cylinder Orientation

The sundial drawn with this macro using the information in Figure 2 is shown in Figure 5. The length of the vertical line is equal to the circumference of the inner surface of the cylinder. The two ends of this line would be located at the top of the cylinder. The hole is located where the ends of this line meet. The length of the horizontal line is equal to the length of the cylinder. This length will determine the number of hour lines that can be drawn. Note that no consideration is given for the thickness of the cylinder wall. This will affect how many hour lines will be available so try to make the wall in the area of the hole as thin as possible.

Figure 5: Cylinder Sundial

Figure 5: Cylinder Sundial

Figure 6 shows the same sundial as above with a couple of modifications. Both sundials have time intervals of 30 minutes. The sundial on the left is for the period of June 21 to December 21 and the hour lines are corrected for both the Equation of Time and longitude. The sundial on the right is the same except the period is for a whole year and the one additional layer available "DateLines" is turned off.

images/Valentin_Hristov_SDCYLARB_Sundial1a.gif

Figure 6 : Cylinder Sundial with a Twist

Figure 7 provides a table showing a number of possible configurations for the cylinder sundial. These are for the Northern Hemisphere.


Northern Hemisphere
CYLINDER TYPE DECL INCL ROT
E-W Horizontal, hole to Zenith 0 0 0
same as above but a mirror image 180 0 0
E-W Horizontal, hole to South 0 90 0
E-W Horizontal, hole to Celestial South 0 LAT 0
N-S Horizontal, hole to Zenith 90 0 0
same as above but a mirror image -90 0 0
N-S Horizontal, hole to West 90 90 0
N-S Horizontal, hole to East -90 90 0
Vertical, hole to South 0 90 90
Vertical, hole to West 90 90 90
Vertical, hole to East -90 90 90
Polar, hole to Celestial South 0 LAT 90
Polar, hole to West 90 90 -LAT
(180-LAT)
Polar, hole to East -90 90 LAT
(LAT-180)

Figure 7: Cylinder Sundial Configuration Table

There are obviously many more combinations that can be tried.

Some Examples of Cylinder Sundials

The following figures illustrate some of the examples of cylinder sundials given in Table 6. The first example of a horizontal cylinder sundial positioned on the east-west line with the hole located at the top, DECL = 0, INC = 0 and ROT = 0 was discussed above. In these examples the default values for "Left end" and "Right end" are used.

E-W Horizontal Cylinder, Hole to South - DECL = 0, INCL = 90, ROT = 0

Figure 8: E-W Horizontal Cylinder Sundial with Hole to South - Cylinder Orientation Figure 8: E-W Horizontal Cylinder Sundial with Hole to South

Figure 8: E-W Horizontal Cylinder Sundial with Hole to South

E-W Horizontal Cylinder, Hole to Celestial South - DECL = 0, INCL = LAT, ROT = 0

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

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

N-S Horizontal Cylinder, Hole to Zenith - DECL = 90, INCL = 0, ROT = 0

Figure 10: N-S Horizontal Cylinder Sundial with Hole to Zenith - Cylinder Orientation Figure 10: N-S Horizontal Cylinder Sundial with Hole to Zenith

Figure 10: N-S Horizontal Cylinder Sundial with Hole to Zenith

N-S Horizontal Cylinder, Hole to West - DECL = 90, INCL = 90, ROT = 0

Figure 11: N-S Horizontal Cylinder Sundial with Hole to West - Cylinder Orientation Figure 11: N-S Horizontal Cylinder Sundial with Hole to West

Figure 11: N-S Horizontal Cylinder Sundial with Hole to West

Vertical Cylinder, Hole to South - DECL = 0, INCL = 90, ROT = 90

Figure 12: Vertical Cylinder Sundial with Hole to South - Cylinder Orientation Figure 12: Vertical Cylinder Sundial with Hole to South

Figure 12: Vertical Cylinder Sundial with Hole to South

Vertical Cylinder, Hole to West - DECL = 90, INCL = 90, ROT = 90

Figure 13: Vertical Cylinder Sundial with Hole to West - Cylinder Orientation Figure 13: Vertical Cylinder Sundial with Hole to West

Figure 13: Vertical Cylinder Sundial with Hole to West

Polar Cylinder, Hole to Celestial South - DECL = 0, INCL = LAT, ROT = 90

Figure 14: Polar Cylinder Sundial with Hole to Celestial South - Cylinder Orientation Figure 14: Polar Cylinder Sundial with Hole to Celestial South

Figure 14: Polar Cylinder Sundial with Hole to Celestial South

Polar Cylinder, Hole to West - DECL = 90, INCL = 90, ROT = -LAT

Figure 15: Polar Cylinder Sundial with Hole to West - Cylinder Orientation Figure 15: Polar Cylinder Sundial with Hole to West

Figure 15: Polar Cylinder Sundial with Hole to West

The cylinder sundial can be used in a playground. Many playgrounds have concrete cylinders that the children play in. Why not paint some hour lines inside one of these? If you have a cylindrical tower as part of your home a cylinder sundial would make a great conversation piece. Just use your imagination!