created by Carl Sabanski
Hours Before Sunset Sundial
Italian or Italic Hours: the number of hours elapsed since the most recent sunset (hour 0), with 24 equal hours per day. They were used in many European countries during the period 1200 to 1800. They are sometimes written "horae ab occasu solis" or "H.AB OCC." on dials. The two terms (Italian and Italic" are used synonymously in modern works but there is some evidence in older works that Italian hours were counted from 30 minutes after sunset.
The hours before sunset or HB4S sundial is simply a sundial showing Italian hours that have been slightly modified. An Italian hours sundial has hour lines numbered starting from sunset. The hour line one hour before sunset will be numbered as 23, before that 22 and so forth. Now, simply reverse this numbering scheme. The sunset hour line will still be 0 but the one before it will be 1, before that 2 and so on. In this way the hour lines are numbered in a countdown fashion to sunset. And you have an HB4S sundial.
Typically these sundials are positioned vertically and have a nodus some distance vertically from the dial plate. The reading is taken from the tip of the shadow cast by the nodus. The sundial is not affected by longitude or the Equation of Time.
Figure 1 illustrates a vertical HB4S sundial located at a latitude of 50º N and declining 45º W. The position of the nodus is indicated by the cross. The gnomon is a vertical pin with a given length used to determine the position of the hour lines. The sundial includes the solstice and equinox declination lines. It will indicate up to 9 hours before sunset during certain portions of the year.
Figure 1: Hours Before Sunset Sundial (ZW2000/DELTACAD)
There are a number of factors to take into consideration when designing an HB4S sundial. Because the sundial uses a nodus care must be taken in selecting how far above the dial plate the nodus is positioned. Depending upon the size of the dial plate, a nodus far above the dial plate will drive many of the hour lines off the plate and could severely limit the number available. The declination of the dial plate will affect the period of time each hour line is visible on the dial plate during the year. If the above sundial were to approach direct south more hour lines would be available but for very limited times of the year.
The HB4S sundial must be designed for the particular latitude where it is to be used. Assuming the sundial is vertical, the declination of the wall must be known as well as the gnomon length. Referring to Figure 1 it can be seen that in most cases the hour lines are bound by the solstice lines. For these lines the location of the nodus' shadow will define the hour line. The shadows co-ordinate calculations are performed at the summer solstice, when the sun's declination is 23.44º and at the winter solstice, when its declination is -23.44º. For hour lines that do not terminate at the two solstice lines some other suitable date and therefore declination must be selected.
For a given declination the first step is to calculate the hour angle for sunset. With this value it is a simple matter of subtracting 15º to determine the hour angle for each hour before sunset. Each hour angle will be used to determine the co-ordinates of that particular hour line. Using the hour angle and declination the sun's altitude is calculated. The altitude is checked to confirm the sun is above the horizon and if this not the case a different declination value is selected and the altitude calculation is performed again. Once the altitude shows the sun above the horizon the sun's azimuth is calculated. The azimuth is checked to confirm the dial plate is illuminated by the sun and if this is not the case a different declination value is selected and the azimuth calculation is performed again. Once the azimuth shows the sun illuminates the dial plate the difference between the azimuth of the sun and the declination of the sundial is determined. Now the co-ordinates for one point of the nodus' shadow for a given hour line can be calculated. These steps are repeated to obtain a second point for a given hour line and again for additional hour lines.
The information above describes the steps required to locate the hour lines for an HB4S sundial. Rather than going into further detail, Mac Oglesby has given permission to offer his manual for an hours before sunset sundial. This manual is very detailed and discusses the design and construction of the sundial. It includes background information, all the required equations and worked examples.
Design and Construction Manual for Flat Vertical Sundials
The hours before sunset sundial would be an excellent project for a small air field, a golf course or for avid gardeners who want to know how much time they can spend in their garden before the sun sets.
The hours before sunset sundial shown below is based on the sundial in Figure 1.
For an image complete with
shadow click here.