created by Carl Sabanski
Vertical Sundial - Direct East and West
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.
The vertical direct east and west sundials are universal and can be used at any latitude. The vertical direct east sundial will indicate the hours from sunrise to noon and the west sundial from noon until sunset. Neither sundial will show the noon hour because they lie in the plane of the meridian. The hour lines are parallel to each other. The gnomon is positioned on the 6 o'clock hour line with its style parallel to the dial plate, similar to the gnomon of a polar dial. The dial plate for the vertical direct east sundial is rotated counter-clockwise an angle equal to the latitude so the gnomon points to the celestial pole. The dial plate for the vertical direct west sundial is rotated clockwise.
The distance between the hour lines and the sub-style can be calculated as follows. The sub-style is the 6 am hour line for an east sundial and 6 pm hour line for a west sundial. If the gnomon has an appreciable thickness, then a noon gap would appear and two sub-styles would exist. By choosing a gnomon height GH:
X = GH * tan (h)
where h is the hour angle, in degrees, given by:
h = (T - 6) * 15°
and T is the time in decimal hours.
Table 1 list the distance to the hour lines for 15-minute intervals assuming a gnomon height of 1. By selecting a gnomon height you can easily determine the distance to each hour line by using the multipliers. Click here to download a spreadsheet that will perform these calculations for you.
Table 1: Vertical Direct East & West Sundials Hour Line Distances
Note that the distance to the 9 am and 3 pm hour lines is equal to the height of the gnomon. As an example, selecting a gnomon height of 2.5 inches will result in a dial length of 19.99 inches for a vertical direct east sundial that indicates time between 6 am and 11:30 am or a vertical direct west sundial that indicates time between 12:30 pm and 6 pm.
Figure 1 illustrates the layout of the hour lines for both the vertical direct east and west sundials and how they must be installed to function correctly at any latitude.
Figure 1: Vertical Direct East and West Sundials (ZW2000/CAD)
Rather than using a plate for the gnomon, a vertical rod can be used to create a nodus. It is then possible to show the declination lines on the dial plate. Figure 2 illustrates such an example. The height of the nodus will affect the shadow path throughout the year and the number of hours that can be displayed on a dial plate of a given size.
Figure 2: Vertical Direct East & West Sundials with Declination Lines (SHADOWS)
For an image complete with
shadow click here.