Latitude and Longitude

Latitude (ø): is the angular position of a place on the Earth's surface measured north or south of the equator. Positive values in the Northern hemisphere, negative in the Southern.

Longitude (λ): is the the angular location of a place on the Earth's surface measured east or west of the Prime meridian through Greenwich. Longitudes west are positive and east are negative.

Figure 1: Lines of Latitude and Longitude

To design a sundial its location must determined. Sundial design requires that you know the latitude of the sundial's location. With this information the sundial will indicate "local apparent time" or solar time. Unless the sundial is located on the standard meridian for a particular time zone, and you wish to correct for this, the longitude must be known. Knowing the longitude, the sundial design can be adjusted to indicate "zonal solar time" or the correction can be manually applied by adding or subtracting from the "local apparent time". This topic is discussed in further detail in the next section.

The following data and equations come from an old astronomy handbook.

Earth:
Equatorial Radius: 6378.140 kilometers
Polar Radius: 6356.755 kilometers
Mean Radius: 6371.004 kilometers

Latitude:

1° of latitude = 111.133 - 0.559 cosine (2 x latitude)  kilometres
The following table shows the distance between 1° (degree), 1' (minute) and 1" (second) of latitude as the latitude changes.

Table 1: Latitude Distance vs Latitude

Longitude:

1° of longitude = 111.413 cosine (latitude) - 0.094 cosine (3 x latitude)  kilometres
The following table shows the distance between 1° (degree), 1' (minute) and 1" (second) of longitude as the latitude changes.

Table 2: Longitude Distance vs Latitude

The latitude and longitude of your location can be determined from a map. There are also web sites that provide this information. If you own or know someone with a GPS (Global Positioning Systems) unit, you can probably find your latitude and longitude to the nearest second.

But just how accurately must you determine your latitude and longitude? 1° of longitude is equivalent to 4 minutes of time. If you determine the longitude to within 1', the error introduced is 4 seconds. From Table 2 the sundial could be positioned anywhere in a small community (like ours). Latitude error is more difficult to illustrate but the following table is a list of the hour angles, in degrees,  for a horizontal sundial calculated at 50°, 50° 1' and 51° latitude. This comparison would change at different latitudes but probably illustrates a point.

Table 3: Latitude Effects

Note that 1' = 0.0166667° and 1" = 0.000277778°. From the table, a 1' error in latitude affects the second decimal place of the hour angles. Also consider that a sharp pencil will draw a line approximately 0.5mm wide. If you draw an hour line 12 inches long with this pencil, the angle width of the line at 12 inches from a point at the origin will be about 0.094°. This is significantly more than the change caused by a 1' latitude error. The point would be that if you are hand crafting your sundial being a few minutes off won't make much of a difference.