Vertical Sundial - Direct North

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.

Azimuth (A, AZ): the angle of the sun, measured in the horizontal plane and from true south. Angles to the west are positive, those to east, negative. Thus due west is 90°, north is ±180°, east is -90°.

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 will only shine on a vertical direct north sundial early in the morning and late in the afternoon. This will occur only in the spring and summer months and not at all in the fall and winter. The maximum number of hours that can be indicated on a vertical direct north sundial will occur on the summer solstice, June 20 or 21. In the morning this period will be from sunrise until the sun is due east and in the afternoon this period will be from when the sun is due west until sunset. "The Dialist's Companion" can be used to determine the periods of time that the sun shines on a direct north sundial. This program allows you to set any location, date and time. The image below shows that the program has been set for June 20, 2004 and the "Dial Time" is set to 12:00 pm. To accomplish this, the "Pinawa Central" time was entered as 12:00 pm and then the "End" key was selected to freeze the screen. As long as the "End" key is not selected again the "Pinawa Central" time can be adjusted to any time and the clock will remain frozen. Note that the time for "Solar Noon" is given as 12:25:12 pm. Entering this time will set the "Dial Time" to 12:00 pm. Note the following:

• The time for "Sunrise" is approximately 4:20 am. This is clock time. To get solar time or local apparent time, the "Total Correction" must be added. In this case the correction is approximately -25 minutes. Therefore, the earliest time of sunrise is 3:55 am.

• The time for "Sunset" is approximately 8:30 pm. Carrying out the same correction procedure, the latest time of sunset is 8:05 pm.

• The azimuth of the sun is 0° indicating that it is due south.

It is a little more work to obtain the latest morning and earliest afternoon hours. The latest morning hour is when the sun is due east or when the azimuth indicated on the screen below indicates 90° E. The earliest afternoon hour is when the sun is due west or when the azimuth indicated on the screen below indicates 90° W. The way to determine this is to change the time until each of these values is approached. Don't forget to apply the correction as discussed above to obtain solar time. This is easily done by recording the "DIAL TIME". You need not be overly accurate as the hour lines on the dial will extend beyond these points. It doesn't take a lot of time to do this.

Figure 1: Determining Earliest & Latest Morning & Afternoon Hours

Once you have established the morning and afternoon ranges for the hour lines, you can design your sundial. 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. This spreadsheet is the same one that is used to design a vertical direct south sundial.

Table 1: Hour Line Angle Calculations

Figure 2 is a plot of the hour lines for a vertical direct north 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 2: Vertical Direct North 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. Check out the figures in the "Vertical Direct South Sundial" page.