Horizontal Sundial

Horizontal Sundial: the common or garden sundial with a horizontal dial plate and polar-pointing gnomon.

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 horizontal dial, the angle increases clockwise.

The horizontal sundial must be designed for the particular latitude (�) where it is to be used. The style height (SH) of the gnomon is equal to the latitude. The hour line angles (X, HLA) can be calculated as follows:

X = arctan {sin � * 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 horizontal sundial will show the time whenever the sun is above the horizon. The dial must include all the hour lines from the time of earliest sunrise to the time of latest sunset.  At any latitude, the earliest sunrise and latest sunset will occur in mid to late June and on different days. Table 1 lists the local mean time of the earliest sunrise and latest sunset at a number of latitudes. Local mean time is solar time corrected for the Equation of Time but not for longitude. To determine these times for your location use "The Dialist's Companion". It gives both "Sunrise" and "Sunset" time. By entering a series of dates you can find the dates of the earliest sunrise and latest sunset. You can then use the corrections, "Equation of Time" or "Longitude Correction", to convert these to local apparent (solar) time or clock time. Determining these times for the summer solstice, June 21, is adequate for laying out the hour line range.

Table 1: Earliest Sunrise and Latest Sunset - Local Mean Time

Table 2 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 2: Hour Line Angle Calculations

Figure 1 is a plot of the hour lines for a horizontal 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: Horizontal 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: Horizontal sundial with gnomon 5 units high . (SHADOWS)

Figure 3: Horizontal 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 large gnomon the shadow will extend beyond the north end of the dial plate for the entire year. The sundial software package "SHADOWS" generates sundial layouts very quickly and is very good for doing this type of design comparison.

The following figures illustrate the effect of latitude on the sundial layout. All the sundials have the same plate dimensions and all the gnomons are 25 units high. At 0� latitude the sundial is a polar dial, the dial plate is parallel with the polar axis., and at 90� latitude it is an equatorial dial, the dial plate is parallel with the equator. At 0� latitude the gnomon is parallel to the dial plate and at 90� latitude it is perpendicular to the dial plate. As the sundial moves further north the shadow of the gnomon becomes longer until it extends beyond the top edge of the dial plate. Very low latitudes create problems with the design of a dial. For one thing the origin is located a long distance away.  Also, as the 10� N latitude drawing shows in Figure 5, the shadow will be not always be north of the gnomon. It will move south of it.

For an image complete with shadow click here.