Year 2010

Article of the month June

Mirror sundials 1

Theory
When a small mirror is fixed anywhere, we can observe the reflected sunlight.
We can call this mirror a "reflecting nodus". The attitude of the reflecting nodus may be chosen freely.

How can we easily draw the hour lines for a reflecting nodus sundial?

A simple way to recognize what the hour lines of such a sundial will be, is by looking at the orientation of the mirror image of the pole style.
Imagine a laser beam, parallel to the Earth's axis, incident on the mirror.
The reflected beam will represent the location and direction of the reflected pole style.

Some examples
The following figure shows an equatorial sundial (left). The conventional nodus on the pole style defines the well known homogeneous hour line pattern on the equatorial plane.
If we place a reflecting nodus parallel to the equator, then the reflected pole style remains parallel to the actual pole style.
The homogeneous pattern now appears on the sundial surface which is parallel to the equatorial plane.

In the next figure, the reflected pole style is brought straight up.
The reflected pole style continues to operate as a real pole style, and a homogeneous pattern appears on the horizontal sundial surface perpendicular to the pole style.

In order to aim the reflected pole style towards the zenith, it must be rotated through 38 degrees.
To do this, the reflecting nodus mirror is rotated by half this angle, or 19 degrees.

The pole style could also be aimed straight down, as shown in the last figure.
In this case also, you will have a homogeneous pattern on the horizontal plane.
To this end, the mirror is rotated an extra 90 degrees, making the reflected pole style turn through another 180 degrees.

General
We can now write down some general comments on the above principle.

1. A properly aligned reflecting nodus can project any sundial onto any plane.

2. The properties of the projected sundial are essentially equal to those of the actual sundial.

3. Each sundial is one of a pair, with the orientations of the mirrors differing by 90 degrees, and those of the pole styles 180 degrees; the respective hour lines are numbered in opposite directions.

4. It may be that over the year, the sun shines on both sides of the reflecting nodus. In general therefore, the nodus should reflect on both sides.

5. The principle described above applies to a single nodus. A complete style can be built from a number of reflecting nodi.

Next month, we will show some practical examples of reflecting nodus sundials.

Hendrik Hollander.

English translation: RH