You can easily make a sundial of almost any shape if you place it in the plane of the earth's equator. All you need to do is to mark off 15 degree segments around whatever you are using as a gnomon. Below is a picture of a conical sundial, which is a variation on the equatorial ring-type sundial. The dark triangle is the gnomon. The lines indicating the axis and edges of the cone have been added for illustration, but would not be part of the actual dial. You may think of it as a stack of progressively smaller equatorial ring dials.
Sometimes, parts of the dial itself become gnomons for other parts of the dial. Popular sundials of this type are shaped like a cross or a many-pointed star. The star example is shown below.
In a polar dial, time is kept by the shadow a block casts on a flat surface. This sundial is really a variation on the equatorial dial. In this case, the inclined plane and the gnomon are aligned with the the direction to the North Celestial Pole - that is, they are inclined to an angle equal to your latitude.
This can be a fun type of dial to construct in a garden with a suitable south-facing slope. The slope will receive maximum solar heating around the equinox (when the sunlight will come in perpendicular to the slope) so it may be a good site for early spring flowers.
The hour markers on this type are very unevenly spaced. For those interested, the formula is h / x = tan(hour angle), where 'h' is the hour and 'x' is the position on the X-axis.
Sundials and the Shepherd's Dial
In times past, shepherds out tending flocks and others who needed portable sundials often used a sundial based on the length of the shadow, not the angle of the shadow. The length of the shadow of an object depends on the altitude of the sun in the sky. This type of sundial, however, is more sensitive to seasonal changes. As you can see in the charts at the end of this section, the altitude of the sun (from Ames, Iowa) is the same at noon in December as at about 5 P.M. in June. Below are two sun dials: a pillar dial on the left and a shepherd's dial on the right.
A spherical sundial shows just how the sunlight is falling on the earth at any moment. You can use any globe for a spherical sundial, including the small earth globe that you made in the Unit 2 section "Make an Earth." Mount the globe with its North Pole pointing towards the North Celestial Pole.
The hours are marked around the equator, and the time is read (on two sides) by the edge of the illuminated portion as demonstrated below.