created by Carl Sabanski
Window Sundial (or projecting dial): a dial in which the hour lines are marked on a window in such a way that their shadows fall across a single reading point inside the room. The lines, as drawn on the window, form an inverted, mirror-imaged vertical dial.
Figure 1 illustrates the layout for a window dial. This is a sundial for a window facing directly south. Note that this is a view of the sundial as it would appear looking at it from inside the room. It is most likely that the sundial would be located on the inside of the window.
Figure 1: Window Sundial Layout (ZW2000/CAD)
Determining the location of the reading point that marks the time within the room is not difficult but getting it so that it will be on the floor, wall or other stationary surface may take a little effort. The size and location of the window as well as how large the dial is all affect the position of the reading point and how many of the hour lines will actually cast a shadow on the point. The reading point can be in numerous positions but they are all located on a single line. This line is the imaginary style of the original vertical sundial's gnomon that has also been inverted and mirror-imaged. As a result the style originates from the centre of the dial and moves up and out into the room as shown in Figure 1. The reading point can be located anywhere along this line. To move the reading point into the room it is necessary to move up the sundial and as result all the hour lines will not be included. Imagine the horizontal lines in the figure to be various locations for the floor of the room with the window starting at floor level.
The distance H from the wall to the reading point is determined as follows:
tan (90 - ø) = H / V
where V is the vertical distance above the centre of the dial to where the hour lines will begin. This line would be located at the bottom of the window. This design assumes that the floor is located at the bottom of the window.
In order that the reading point is not too close to the window the number of hour lines used can be decreased or the sundial can be scaled up. There is a limitation imposed by the window size. It is easier to move further away from the window at lower latitudes.
Figure 2 shows a window sundial designed for a latitude of about 50° N. The window is 36 inches high and 60 inches wide. The earliest hour line is 6:45 am and the latest 5:15 pm. The hour lines begin at a horizontal line 6 inches above the centre of the sundial. The reading point, which is actually located on the floor, is only about 5 inches away from the window.
Figure 2: Window Sundial (ZW2000/CAD)
The hour lines on this sundial get quite tight and make reading it a little difficult. Actually for this sundial, the shadows from the shorter hour lines early in the morning and late in the afternoon only appear for periods in late spring and early fall and then are usually too short to reach the reading point. In mid summer the sun remains almost directly east in the early morning and directly west in the late afternoon and as a result there are no shadows. In the winter there just is no sun.
Figure 3 illustrates the range that the shadows cast by the hour lines will span at noon.
Figure 3: Window Sundial - Noon in June / December (ZW2000/CAD)
Figure 4 shows the dial's shadows at 10 am in July. The !0 am hour line's shadow passes directly through the reading point.
Figure 4: Window Sundial - 10 AM in July (ZW2000/CAD)
By reducing the number of hour lines for this dial the reading point could be moved further out and it would be easier to read. Although not many hours would be available it would still make an interesting dial.
It is obvious that a sundial such as this requires careful consideration of the window location and size as well as the placement of the reading point within the room. This in turn will affect the hour lines whose shadows will reach this point and thus the sundial itself.
If the sundial illustrated above was constructed in such a way that it could be mounted in an opening where it would be located in free air the hour lines' shadows would be projected as shown. However, if it is to placed on a piece of glass, it may not function exactly as expected. One factor that has not been taken into consideration in the above discussion is the refraction of light that occurs as the sunlight passes through glass. Check out the Refraction of Light page for more details.
In the case of a window sundial the sunlight must first enter the glass at which point it is refracted or bent in a given direction. As the sunlight passes out of the glass on the inside it is bent back. The sunlight does not however return to its original angle. Also, as the sunlight passes through the glass it is shifted slightly because of the new angle. This shift depends upon the thickness of the glass.
Figure 5 illustrates the affect on light as it passes through a single layer of glass. The refractive index of air is 1.0002926. There are many types of glass and the refractive index varies. A value of 1.51714 was used. This figure compares the angle of incidence of the incident light ray on one side of the glass to the angle of refraction of the refracted light ray on the other side of the glass. There is always a slight difference but it becomes greater with an increasing angle of incidence, i.e. as the light becomes more parallel to the glass.
Figure 5: Light Passing Through Glass
The angle of incidence of sunlight at the air to glass boundary on the outside of the window will depend upon the sun's azimuth and altitude. Both of these factors will affect how the sunlight is refracted as it moves through the window. As the sun moves horizontally across the window from east to west it also moves up an down the window. The angle of incidence increases in the morning and evening due to the sun's azimuth and towards noon due to the sun's altitude.
As the the angle of incidence of the sunlight to the window is greatest earlier in the morning and later in the afternoon this would probably result in the largest error. Because of the design of this sundial, it is likely that these hour lines would not even be included.
Remember that this is only
a single pane of glass. Some windows have two or three panes of
glass and for energy efficiency in cold climates, Low E coatings. This will all affect the
sunlight as it attempts to cast a shadow from the sundial located on the window.