created by Carl Sabanski
Shadow Plane Sundial
Shadow Plane Sundial: a class of dial in which the gnomon is movable and is set by the observer so that it, and its shadow, lie in the sun's hour plane. The gnomon may be a plane, line or point. The dial plate can, if required, be any surface.
Hour Plane: the plane which, at any instant, contains the sun, the observer and the north celestial pole. The style and the appropriate hour line lie in the hour plane.
Style: the line in space which generates the shadow edge used to indicate the time on the dial plate.
Each moment of the day has its own unique hour plane. As the sun moves across the sky so does its hour plane. You cannot see this plane but it can be used to tell the time of day. If the style of a sundial's gnomon is located on this plane, it can be used to indicate the time by casting a shadow on the dial's hour line.
Figure 1 illustrates the sun's hour plane. This figure shows both a horizontal and vertical sundial with a common style. This is a diptych sundial. The image is taken at 10 am on June 21. The hour plane passes through the style and the 10 am hour lines of both sundials. If this plane were extended, the back top corner would intersect the north celestial pole and the front top corner would intersect the sun. For the particular location of these sundials, this will be the orientation of the sun's hour plane at 10 am every day of the year.
Figure 1: The Sun's Hour Plane - Horizontal/Vertical Sundials (ZW2000CAD)
Imagine the sun moving towards noon, local apparent time. At solar noon, when the sun is directly overhead, the hour plane will be perpendicular to both dial plates. The hour plane angle relative to a horizontal plane will be at its minimum at sunrise and sunset. This minimum angle will vary with latitude.
To further illustrate the sun's hour plane Figure 2 shows horizontal and equatorial dials with a common style. This image was taken at 9 am on June 21. This being between the Spring and Fall Equinoxes means that you are looking at the top face of the equatorial sundial, which faces north. The equatorial sundial is at an angle to the horizontal equal to the co-latitude. The common style is at an angle equal to the latitude relative to the horizontal sundial's plate. When the style is extended to intersect the equatorial sundial it is perpendicular to its plate.
Figure 2: The Sun's Hour Plane - Horizontal/Equatorial Top Sundials (ZW2000/CAD)
Figure 3 shows another combination of horizontal and equatorial sundials with a common gnomon. These are exactly the same dials as in Figure 2 but this image was taken at 10 am on December 21. This being between the Fall and Spring Equinoxes means that you are looking at the bottom face of the equatorial sundial, which faces south. This figure shows more clearly the intersection of the style with the two dial plates.
Figure 3: The Sun's Hour Plane - Horizontal/Equatorial Bottom Sundials (ZW2000/CAD)
The hour lines of the equatorial sundial are spaced apart at 15° intervals. Each of these intervals indicates the passage of one hour of time. As the hour passed from 9 am to 10 am the sun moved 15° and as a result so did its hour plane as seen by comparing the hour planes on the equatorial dial. However, the hour plane did not move 15° degrees on the horizontal dial. The angle that the hour plane moves on the horizontal dial depends upon the latitude.
What these two figures show is that the hour lines of the horizontal sundial are the projection of the hour plane that passes through the hour lines of the equatorial sundial. In fact, the equatorial sundial can be used to graphically layout the hour lines for a number of sundials.
Now to the design of the shadow plane sundial.
It is relatively easy to create a horizontal or vertical shadow plane sundial. This description refers to Figure 1 as the example. The dial plate is made by rotating the dials 180° about the origin. The hour lines are then numbered in reverse order. The style can be a length of string. It must be terminated along the existing style so that it lies on a point on the hour plane that is common to all times of the day. It should be long enough to extend beyond the outer limit of the dial's hour lines. There is no fixed length. Figure 4 illustrates these steps having been done for a horizontal shadow plane sundial. The same termination point could be used for a vertical shadow plane sundial. To indicate the correct time the string is pulled taut and moved until its shadow falls across the dial's origin, i.e. the point at the base of the original style. The string will then lie in the desired hour plane and its shadow will indicate the correct moment in time as shown in Figure 4..
Figure 4: Horizontal Shadow Plane Sundial (ZW2000/CAD)
A practical dial would not be left as shown. The original gnomon is removed and a pole could be used to hold the termination point of the string style in the correct position. The origin of the sundial must be known so this point must be marked in some manner. And finally, the original horizontal or vertical dial can be removed. For an image of the completed horizontal shadow plane dial click here.
On a large scale this type of dial can become an interesting interactive sundial. All you need is a post, a flat area and a rope.
If you found this page on shadow plane sundials interesting, you will certainly want to see the next one.