Some didactic notes for those who approach gnomonics

You may imagine to travel to the North Pole to make there a sundial. Surely it is not a friendly place, and, moreover, may be an useless location to know what time it is.
From this place the Earth revolution allows you to watch that a celestial body is keeping the same altitude while turning over the horizon.
You may imagine to be there and observe a celestial body, you revolve yourself with regard to the Celestial Sphere but you feel as if the celestial body is describing a circle parallel to the horizon.

In a given day we may consider the Sun fixed in the Celestial Sphere (with a little approximation), then, like any other celestial body, it would describe a circle around the polar axis, that is a circle parallel to the horizon. As per this assumption it would be hard to define when it is noon, it would be always noon because it is not distinguishable neither by the Sun altitude, the altitude is costant all day long, nor by its direction, the Sun is always towards South.

Defying the outward useless of this sundial you may erect an obelisk over the Pole, then, remembering the Sun turns around the obelisk, that is around the polar axis, you may expect the obelisk to cast a shadow which revolves in a day. In particulary, the Sun will turn for 360° in 24 hours so that you may watch the shadow to turn 15° in an hour. This is a very interesting condition because the sundial doesn't indicate useful time but it shows the time while elapsing on a very simple dial, with the hour lines every 15° from the base of the obelisk. During the year the shadow changes its length because the Sun varies its altitude, anyway the obelisk casts the shadow on the same hour line when the Sun is the same hour plane, that is the plane which includes the hour line and the polar axis.

The simplicity of this dial encourage to study if it is possible to make a sundial with the same features in any other place.
To move the horizontal dial with its obelisk from the Pole to another place we may use a virtual truck; during the travel the obelisk will be keeping its vertical direction with regard the Earth's curvature and the dial will remain horizontal so that both of them shoudn't be parallel to their orientation to the Pole.

We can imagine to move the dial in a new place so that it remains parallel to the polar orientation, with the obelisk orthogonal to the dial. We can say the sundial has been transferred parallel to itself, the obelisk is still directed as the polar axis and the sundial lies shifted from its original position. The displacement is not important because the distance is insignificant if compared with the distance of the Earth from the Sun, therefore the sundial keeps the same functions because the Sun "watches" the sundial in the same way.

Actually something has changed, the solar orbit is not always above the horizon and it isn't in a plane parallel to it; this means the sundial is now influenced by night and day, depending from the latitude; besides there is a particular hour plane wich includes the Meridian line, when the Sun lies in this hour plane it is towards South and it indicates noon. These circumstances allow to identify the noon line and every other hour line.

Finally we can conclude it is possible to make this kind of simply sundial in any place; we have to determine how to place the dial so that it is parallel to the Pole horizon: the pictures in this page suggest we must tilt an horizontal dial towards North (in the Boreal Emisphere) for the co-latitude (90° - latitude).

During this operation the obelisk keeps orthogonal to the dial so it will form an angle with the horizon equal to the latitude. These simply directions are enough to built an 'equinoctial' sundial, also called 'equatorial', the sundial will work in the summer time between the two equinoxes on the upper face and in the lower one in the opposite period.

The shadow length depends on the altitude of the Sun over the dial, that is the Sun declination. As this value is linked to the Gregorian calendar the shadow will draw a circle around the obelisk and the ray of the circle will be related to the date or zodiacal period.
During equinoxes the Sun turns in the plane of the dial, theoretically the shadow length is infinite so this kind of sundial is not fit for watching the declination but it is appreciated for the simplicity of its construction.

The equinoctial sundial has an interesting version; my favourite approach is to imagine to make a hole around the obelisk, called the polar style. The shadow casted on a face of the dial, is casted on the hole side too. This means the hole side has always the shadow casted, whatever face is active. We may consider to use the hole as a dial because there is no time working limit. We can build a ring around the polar style and draw inside the hour lines, these lines should joint the upper and lower hour lines of the equinoctial sundial and they will result 15° one from the other. This sundial will work with any Sun declination.

Close to the equinoxes half a ring should not allow the Sun to cast a shadow over the other half ring, so we may remove the upper half ring allowing the lower one to get the shadow from 6 to 18 all year.

This sundial is called the armillary equinoctial sundial because it is made by armlets, that is bracelets or half bracelets, which are the dial and the polar style standing.

Sometimes the polar style has a knot so that its shadow is visible on the dial. On Equinox the knot shadow describes a half-circle on the half-ring used as dial. If the half-ring is tall enough the shadow of the knot may describe a half-circle above, or below, the equinox half-circle. This displacement is related to the declination of the Sun so this sundial may be used to read the date. The distance between the half-circle of a given declination and the equinox one is equal to the ratio between the ray of the ring and the tangent of the declination.

There are a lot of these sundials with many variants, they are often monumental sundials and their shape may be different depending on the designer creativity, the equinoctial dragon is an example. There are travel versions, they are rings packed one inside the other and they may work adapting to any latitude.

I'd like to conclude this page with some pictures of equinoctial sundials of different kinds. In my hard-disk there are many pictures downloaded from internet, but I should ask for the authorization to publish them here, so I ask the readers to send me their pictures if they have any, with the authorization to publish them here, in this case I will also publish the name of the owners and a link to their web-site.