Vertical Sundial - Direct South

Vertical Sundial: any dial in which the dial plate is vertical.

Latitude: is the angular position of a place north or south of the equator. Positive values in the Northern hemisphere, negative in the Southern hemisphere.

Style Height / Style Angle (SH): of a polar style is the angle that the style makes with the sub-style line.

Sub-Style (line): the line lying in the dial plane which is perpendicularly below (or behind for a vertical dial) the style.

Hour Line: the line on a dial plate indicating the shadow position at a particular time (includes fractional as well as whole hours).

Hour Angle (h, HA): the angle corresponding to the sun's position around its daily (apparent) orbit. Measured westward from local noon, it increases at a rate of 15° per hour. Thus 3 pm (Local Apparent Time) is 45° and 9 am is -45°

Hour Line Angle (X, HLA): the angle that an hour line on a dial plate makes with the noon line. For a vertical dial, the angle increases counter-clockwise.

The vertical sundial must be designed for the particular latitude (ø) where it is to be used. The style height (SH) of gnomon is equal to the co-latitude or 90° minus the latitude. The hour line angles (X, HLA) can be calculated as follows:

X = arctan {cos ø * tan (h)}

where h is the hour angle, in degrees, given by:

h = (T₂₄ - 12) * 15°

and T₂₄ is the time in 24-hour clock notation (hours after midnight) in decimal hours.

The sun can only shine on a vertical direct south sundial in the Northern Hemisphere and a vertical direct north sundial in the Southern Hemisphere between 6 A.M. and 6 P.M. Visit the "Sun Charts" page for some interesting information. 

Table 1 shows the calculation performed for a sundial located at latitude 50°N. Notice that the hour line angles for the am and pm hours are symmetrical about the noon hour line. Click here to download a spreadsheet that will perform these calculations for you.

Table 1: Hour Line Angle Calculations

Figure 1 is a plot of the hour lines for a vertical direct south sundial in 15-minute intervals. A drawing like this can be used as a template to lay out a dial plate. It also shows the dial mounting details.

Figure 1: Vertical Direct South Sundial (ZW2000/CAD)

When you have determined how large a dial plate you want then you must give some consideration to how large the gnomon should be. The height of the gnomon will determine the path the shadow will take over the dial plate throughout the year. The following three figures illustrate this for three gnomon heights using a dial plate that is fixed in size.

Figure 2: Vertical sundial with gnomon 5 units high . (SHADOWS)

Figure 3: Vertical sundial with gnomon 15 units high . (SHADOWS)

Figure 4: Horizontal sundial with gnomon 25 units high . (SHADOWS)

As the gnomon height increase the shadow covers more of the plate yet remains on the dial plate. For a very large gnomon the shadow will extend beyond the end of the dial plate for portion of the year. The sundial software package "SHADOWS" generates sundial layouts very quickly and is very good for doing this type of design comparison.