Sundial | Equinoctial | with Compass | Brass | 2010
Series SOLARES
By: Sílvio Pereira
- Pocket equinoctial (or equatorial) sundial;
- Maker: Unknown
- Material: Brass.
- Dimensions: Diameter 47.0 mm; Thickness 19.7 mm
- Weight: 101.26 g;
- Description: Made up of two parts: 1st, a compass with gnomon and hour indication; 2nd, a world time indication. When the two parts are brought together the sundial is closed.
- How to use it: Place the sundial on a level surface. Set the compass to north. Open the gnomon until it is perpendicular to the sundial. The shadow cast by the tip of the gnomon (where the arrow is) on the sundial's hour scale will show the time.
Note - The sundial shows solar time, which may not be the actual time. The equation of time table on the back of the sundial (last photo) gives the difference in minutes between solar time and actual time. The letter "F" means that a watch should be put forward; "S" means it should be put back.
What an equinoctial (or equatorial) sundial is and how it works
Equinoctial sundial at the La Punta Astronomical Park (Argentina)
All sundials are based on the regularity of the movement of the Sun during its apparent daily path, a reflection of the Earth's rotation. And also on the regularity of its annual cycle.
In this family of sundials (equinoctial), we have:
The indicator (the gnomon):
· is positioned parallel to the Earth's axis;
· lies in the meridian plane of the place;
· and forms with the horizon an angle equal to the latitude of the place where it is set up.
The dial, onto which the shadows are cast:
· is flat and perpendicular to the indicator;
· is therefore parallel to the celestial equator, hence the name of this type of sundial.
Finding the direction of the meridian plane
To determine the direction of the plane of the local meridian, in order to position the gnomon, the meridian line, or local north-south direction, is determined first.
The meridian line, moreover, also coincides with the shadow cast by the gnomon at the moment the Sun crosses the meridian plane of the place.
The hour lines
The dial plate, that is, the layout of the hour lines, is determined by drawing a circle centred on the pole of the dial and dividing it into 24 parts of 15° each (360° = 24 x 15°); the 24 radii corresponding to that division are then drawn.
Noon
Of all the radii drawn, the one that coincides with the intersection of the plane of the local meridian with the plane of the dial, and that points towards the horizon, is the 12 o'clock radius.
East and West (sunrise and sunset)
The hour lines drawn to the west mark the hours before local noon (that is, before the Sun reaches its maximum height for that date) and, after noon, the lines drawn to the east.
The lines that mark the hours 6 and 18 correspond to the east-west direction.
The Astronomical Observatory of Jaipur (India)
This Observatory is in a good state of preservation thanks to Chandra Dhar Sharma Guleril, who restored it in 1901. It is currently managed by the Department of Archaeology and Museums of the state of Rajasthan. A supervisor and a maintenance team are in charge of its conservation.
This “Naked-Eye Observatory” was designed and built by the maharaja Jai Singh II (1681-1743). It contains different and complex instruments, one of them unfinished; some need sunlight and others work with reflected moonlight and starlight.
The monumental instruments of Jaipur provide a precise measurement of time, the solar declination, the azimuth, the position of the constellations in daylight, eclipses and other celestial phenomena. When the sundials could not be used because of rain or an overcast sky, the clepsydra (the water clock) was used to measure time.
Astronomical Observatory of Jaipur
When Jai Singh II designed the observatories, one of his main aims was to create astronomical instruments that would be more accurate and permanent than the metal instruments in use at the time. His solution was to make them large, very large, and to build them of stone and masonry. That simple yet remarkable decision created a collection of large-scale structures for measuring celestial movement that is unrivalled today. Among the many striking impressions for a visitor to one of the observatories is the scale of the instruments: one is literally enveloped and awed by a space that is as aesthetic as it is mathematical.
Plan of the Jaipur astronomical complex
The Samrat Yantra
The Samrat Yantra or Great Samrat, also called the “Supreme Instrument”, is an equinoctial sundial of enormous dimensions. Although it is one of the simplest instruments, and not very different from the sundials developed hundreds of years earlier, the Samrat Yantra is important because it measures time with an accuracy never achieved before. The time scale of the Equatorial Sundial – the Samrat Yantra – in Jaipur, for example, includes subdivisions down to two seconds.
Detail of the interior of the Samrat Yantra
The time scale of all the instruments was originally drawn up using the Indian units of measurement of the period, the old units ghatikas, palas and vipalas; in the 1901 restoration, however, they were converted to hours, minutes and seconds.
The 2-second subdivisions of the Samrat Yantra
The essential parts of the Samrat Yantra are the gnomon, a triangular wall with its hypotenuse parallel to the Earth's axis, and a pair of quadrants on either side, parallel to the plane of the equator.
On a clear day, as the sun moves from east to west, the shadow of the gnomon falls on the scale of the quadrant, indicating local time. Since a sundial gives the exact time only for its specific location, a formula is used to obtain standard time, compensating for the difference in longitude between the location of the instrument and its time zone, and for the daily adjustment that must be made because of the Earth's orbit around the Sun.
How about building the Samrat Yantra sundial in cardboard?
Models of the Samrat Yantra for construction
A Samrat Yantra was built in each of the Indian observatories to provide a precise measurement of time:
· The largest is in Jaipur, its gnomon being 22.6 metres high.
· The Samrat Yantra in Delhi comes second, at 20.7 metres.
· The heights of the gnomons in Ujjain and Varanasi are 6.7 and 6.8 metres.
The instruments in Jaipur and Delhi can be read to an accuracy of 2 seconds, while those in Ujjain and Varanasi are accurate to 20 and 15 seconds respectively.
The instruments in Jaipur and Delhi included Shasthamsa Yantras built into each of the structures that supported the quadrants.
On the Observatories' website, www.jantarmantar.org, the instruments have been modelled. Several architecture students created models based on measurements by Virendra Sharma, drawings by GR Kaye and Andreas Volwahsen, as well as the panoramic photos presented here. The models and graphic representations in the image gallery above were created by Bei Xu, Cornell M.Arch 2017.
Download the templates and build a model of the Samrat Yantra.
· Template to cut out: https://www.jantarmantar.org/resources/Projects/SY-Model/Samrat-Yantra-Model-Templates.pdf.
· Assembly instructions: https://www.jantarmantar.org/resources/Projects/SY-Model/Instructions-SY-web.pdf.
Improving the accuracy of the time reading
The largest sundials are capable of extremely accurate measurements of time by means of a special way of “reading” the shadow of the gnomon.
One of the common criticisms of the accuracy of the Samrat Yantra is that, because of the distance between the edge of the gnomon and the scale of the quadrant, its shadow has a “soft edge”, that is, it is slightly spread or “blurred”. This means that, although the surface of the quadrant is inscribed with fine markings to indicate time intervals of 2 seconds, the soft edge of the shadow may span 6-7 of those marks and the centre of the shadow can only be estimated.
The solution is to hold a thin object, such as a taut string, parallel to the edge of the shadow and about 1 cm above the surface of the quadrant. Moving the rod in and out of the shadow and observing the point on the surface where its shadow disappears gives an exact indication of the centre of the shadow.
In the simplified version at the La Punta Astronomical Park, all the semi-hard wood posts are square, 10 cm a side; the tallest post is 2.40 metres high, the shortest 90 cm, and the two side posts set at right angles are 1.70 metres high.
Technical Definitions
Equinoctial sundial
Equinoctial sundial: It is characterised by a dial parallel to the equatorial plane, with the polar-pointing gnomon perpendicular to it.
Equatorial sundial: another (historical) name for the equinoctial sundial.
Equatorial plane: The plane through the Earth defined by the Equator.
The equinoctial sundial is the simplest of them all. It can be made without mathematical calculations and used at any latitude. It can be used to determine the hour lines for most other types of sundial by using graphical drawing techniques.
The sundial has equally spaced hour lines, at intervals of 15° around the gnomon. The Figure below illustrates a template for an equinoctial sundial and shows intervals of 5, 10, 15, 30 and 60 minutes.
Dial of the equinoctial sundial
To use the equinoctial sundial at any latitude, the user need only make sure that the gnomon points to the celestial pole. To do so, the dial plate must be at an angle to a horizontal surface equal to the co-latitude (90° - latitude). The
Figure below illustrates how the equinoctial sundial should be positioned.
Correct position of an equinoctial sundial
As the dial plate is parallel to the Equator, there are periods when the Sun is above the dial and others when it is below. From the autumn equinox to the spring equinox, sunlight will fall on the underside of the dial plate. To use the sundial during this period the gnomon must project below the dial plate, as shown in the Figure above. The hour lines must appear on both sides of the dial plate. The numbering on the top of the plate will run clockwise, while that on the bottom will run anticlockwise. The sundial will show the time from sunrise to sunset.
The Figure below shows the upper and lower faces of the dial plate for an equinoctial sundial in the northern hemisphere. The upper dial plate will show the hours, since it is lit between the spring and autumn equinoxes. The lower dial plate will show fewer hours, as it is lit between the autumn and spring equinoxes. For the southern hemisphere the number of hours is reversed.
Upper and lower dials
The dial of the sundial can be rotated to account for the Equation of Time, longitude, Summer Time and time corrections.
As mentioned earlier, the equinoctial sundial can be used to create many other sundials. The Figure below illustrates a number of them and how they can be drawn by projecting the hour lines of an Equatorial dial onto various surfaces.
Various types of sundial
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