The
Sundial Primercreated by Carl Sabanski |

The analemmatic sundial presented here is a horizontal azimuth sundial with a moveable vertical gnomon. It uses the azimuth of the sun to indicate the time. The determination of the hour points on the ellipse requires that you know the latitude (ø) where the sundial is to be located. To calculate the dimensions of the scale of dates you will need to know the sun's declination on particular dates for each month. Figure 1 illustrates an analemmatic sundial with its scale of dates.
Figure 2 illustrates the design layout for the sundial. It is assumed that the semi-major axis of the ellipse, OC or OD and designated as M, is 1. When the calculations are complete a series of numbers will be established that will be multiplied by the actual semi-major axis dimension to establish the position of the hour points. The semi-minor axis of the ellipse, m, is the line OE and determined as follows. m = sin ø where ø is the latitude. There will be two methods for positioning the hour points available. These include: - The horizontal dimension "X" that lies on the east-west line and the vertical dimension "Y" that lies on the north-south line.
- The central angle "A" and the dimension "Z".
The horizontal dimension "X" from point "O" is: X = sin h where h is the hour angle, in degrees, given by: h = (T and T The vertical dimension "Y" from point "O" is: Y = sin ø * cos h Note that the calculation of "X" only requires the hour angle and would be the same for a dial at any latitude. The dimension "Y" is dependent upon the latitude. The central angle "A" is: A = arctan {(tan h) / (sin ø)} The dimension "Z" from point "O" to the hour point, in this example 1, is: Z = (sin h) / (sin A) 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.
The next step is to establish the scale of dates. This is the scale that is used to determine the position of the gnomon on a given day of the year. The scale point is determined for the first day of each month and for the two extremes at the time of the solstices. To do this, the sun's declination is required for each of these dates. The values used were obtained from "The Dialist's Companion". The scale of dates is determined as follows: S = tan (dec) * cos ø where "dec" is the sun's declination. In Table 2 the calculation is performed for the same sundial. The spreadsheet offered above will perform this calculation if you wish to use different days or different declination values.
The layout of the scale of dates begins at point "O". Positive numbers are measured up the "Y" axis and negative numbers down the "-Y" axis. Figure 3 illustrates a layout for the scale of dates.
Now that the multipliers are established all that is required is to establish the length of the semi-major axis. Remember that if you are building an interactive sundial, where a person acts as the gnomon, you do not want the dial to be of unreasonable size or it will be difficult to determine where the shadow is pointing. Once done, then you can calculate all the dimensions required to lay out the hour points and the scale of dates.
For an image complete with shadow
click here. |