Work of our members

Equatorial sundial with optical disk

The essential component of this sundial is a circular disk of Perspex which lies in the equatorial plane. Sunlight entering one side of the disk exits the other side and falls, more or less focused, on an adjustable screen with an index line reading the time.

It is only for constructional reasons that this sundial has something resembling a polar gnomon at all: the opaque pin fixing the Perspex disk. While its shadow is useful in positioning the index, it is really not necessary.

This sundial functions at every declination of the sun. In fact, it would accommodate declinations far greater than 23.5 degrees. Any light entering the cylinder surface can only exit through that surface. Likewise, light entering through the top can only leave through the bottom.

This is because these surfaces are perpendicular to each other and because the index of refraction for Perspex is sufficiently high at n=1.5. As a result, the critical angle is less than 45 degrees.
Any ray entering the Perspex, once inside, must be less than the critical angle from normal. Therefore, if it tried to exit through a surface at right angles to the first, it would be more than the critical angle from its respective normal, and therefore suffer total reflection.
This is true for any ray, even at grazing incidence. The light follows a zig-zag path between upper and lower surface.

For every solar declination, the light exits approximately in the equatorial plane. In summer, the daily arc exceeds 180 degrees. A fixed screen with an hour scale is therefore not practical, because it would have to be so big as to be in the way during early mornings and late evenings. For this reason, the sundial has a small screen with index, that rotates about the axis of the optical disk. The index line is placed in the middle of the slightly focused beam leaving the disk. An extension of the index line reads the time on the hour scale.

The sundial is made for 52 degrees latitude; the equatorial plane inclines by 38 degrees.
It may be adjusted for longitude, equation of time, and standard or summer time.
This is done using an auxiliary disk with the necessary scales, between the base and the hour disk. This disk is set to longitude. Then, the hour disk is set to summer or standard time, and to the equation of time.