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How To Make A Sundial

This document explains how to make Safalra’s Sundial, a cross between a normal sundial and an armillary sphere. As well as telling the time, it lets you know the location and time of midsummer and midwinter sunrise and sunset. If you want to know about the theory behind sundials, and how to make various other kinds of sundial, I suggest reading the excellent book Sundials: Their Theory And Construction:

Safalra’s Sundial consists of four arcs:

First you need to make the polar and equatorial arcs, as show in the diagram below. Choose an inner radius and outer radius for the two circles, and make the angle in the triangle equal to your latitude. The blue area is your polar arc, and the green area is your equatorial arc.

Next you need to make the tropical arcs, as shown in the diagram below. These also form a complete circle.

The inner and outer radii of this circle are different from those of the polar/equatorial circle. If your browser has Javascript enabled, you can use the form below to calculate the inner and outer radii for this circle.

If you live inside the arctic or antarctic circles, you only need one tropical arc — a complete circle. Otherwise, you need to divide the circle into two arcs, as shown in the diagram. If your browser has Javascript enabled, you can use the following form to calculate the angles from the horizontal shown in the diagram:

degrees — for example, enter 50.5 for 50 degrees 30 minutes north or south

Now you need to assemble the arcs, as shown in the picture at the top of this page. The polar arc is aligned along a north–south line, with the gnomon at the north if you live in the northern hemishpere, or the south if you live in the southern hemisphere. The equatorial arc is aligned along an east–west line, but is tilted — the angle between the arc and the vertical is equal to your latitude, so the angle between the arc and the gnomon is a right angle. The tropical arcs are parallel to the equatorial arc, 23.5 degrees further around the polar arc. You can attach the arcs together in two ways — either cut the equatorial and tropical arcs in half and attach them to the sides of the polar arc, or cut slots in the arcs to attach them together.

To use the sundial to tell the time, you need to calculate the angles at which to draw the hour lines. If your browser has Javascript enabled, you can use the following form to calculate the angles of the hour lines relative to the gnomon (noon): If you live in the northern hemisphere, number the lines clockwise. If you live in the southern hemisphere, number the lines anti-clockwise.

degrees — for example, enter 50.5 for 50 degrees 30 minutes north or south

The sundial can be used not only to tell the time, but also to calculate the location and time of midsummer and midwinter sunrise and sunset. On midsummer’s day, the shadow of the higher tropical arc falls on the point of the gnomon. At the equinoxes, the shadow of the equatorial arc falls on the point of the gnomon. On midwinter’s day, the shadow of the lower tropical arc falls on the point of the gnomon.