Information about Sundial

A sundial is a device that measures time by the position of the Sun. The most commonly seen designs, such as the 'ordinary' or standard garden sundial, cast a shadow on a flat surface marked with the hours of the day. As the position of the sun changes, the time indicated by the shadow changes. However, sundials can be designed for any surface where a fixed object casts a predictable shadow.

Most sundial designs indicate apparent solar time. Minor design variations can measure standard and daylight saving time, as well.

History

Sundials in the form of obelisks (3500 BC) and shadow clocks (1500 BC) are known from ancient Egypt. It was further developed by other cultures, including the Greek^[1], Chinese, and Roman cultures. The latter also built the largest sundial the world has known, the Solarium Augusti.^[2] A type of sundial without a gnomon is described in the Old Testament (Isaiah 38:8).(ca.700 BC).

The mathematician and astronomer Theodosius of Bithynia (ca. 160 BC-ca. 100 BC) is said to have invented a universal sundial that could be used anywhere on Earth. Marcus Vitruvius Pollio the Roman author of De Architectura wrote on the mathematics of gnomons.^[3] The French astronomer Oronce Finé constructed a sundial of ivory in 1524. The Italian astronomer Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Giuseppe Biancani's Constructio instrumenti ad horologia solaria (ca. 1620) discusses how to make a perfect sundial, with accompanying illustrations.

The oldest sundial in Britain is incorporated into the Bewcastle Cross. The dial is divided into four tides, covering the parts of the working day in medieval times.

Terminology

The 'shadow-maker' of the sundial is called a gnomon[1]. In common speech, the gnomon is often called a style. ^[4]

The sun casts a shadow from the gnomon to a surface called the dial face or dial plate (often shortened to face).

Most sundials indicate time on the dial face by the shadow of a line in space called the style[2]. On a standard garden sundial, this line is the top edge of the gnomon. The style should be parallel to the Earth's axis of rotation, and point to the celestial pole.

The line on the dial plate perpendicularly beneath the style is called the substyle[3], that is below the style. The angle the style makes perpendicularly with the dial plate is called the substyle height, an unusual use of the word height to mean an angle. On many wall dials, the substyle is not the same as the noon line. The angle, on the dial plate, the noon line makes to the substyle is called the substyle distance, an unusual use of the word distance to mean an angle.

Some sundials indicate both the time and the date by the shadow of a particular point on the gnomon. That point is called the nodus. The nodus may be the tip of a gnomon with an arbitrary (usually horizontal or vertical) orientation[4].

A few sundials have both a style and a nodus, with the nodus in the form of a small sphere or a notch on a polar-pointing style, or simply the tip of the gnomon.

In addition to the Hour line, the face of the dial can contain further infomation , such as the horizon, the equator and the tropics. These lines are referred to as the dial furniture. It is traditional for a sundial to have a motto.

Ordinary sundials do not correct apparent solar time to clock time. There is a 15-minute variation through the year, known as the equation of time, because the Earth's orbit is slightly elliptical and its axis is tilted relative to the plane of its orbit. A sundial's furniture may include a graph showing the correction needed. More complex sundials may have curved hour-lines, curved gnomons or other arrangements to directly display the clock time.

Design and principles of operation

Equatorial or Equinoctial sundial

The simplest sundial is a disk mounted on a bar. The bar must be parallel to the Earth's axis of rotation. The disk forms a plane parallel to the plane of the Earth's equator. The disk is marked so that one edge of the shadow of the bar shows the time as the Earth rotates. Usually noon will be at the bottom of the disk, 6AM on the western edge, and 6PM on the eastern edge. In the winter, the north side of the disk will be shaded, and hard to read. In the summer, the south side will be shaded.

In the above design, the bar is the style. In the summer, the north end of the bar is the nodus, but in the winter, the south end of the bar is the nodus.

A series of concentric circles can be drawn on the face which plot the path of the shadow of the nodus on specific days, thus the dial can be used as a calendar as well as clock. The style shows the time and the nodus the date. One disadvantage of this design is that with a solid face, near the equinox, when sun is just on the celestial equator, the dial is hard to read.

Garden sundial

See Logo programming language for a sample program to draw a garden sundial

The classic garden sundial uses the same principle, except the lines of the disk are projected, using trigonometry, onto a face that is parallel to the ground. The advantage of the garden sundial is that it keeps time all year, and its face is never completely shaded in the daytime (as vertical sundials are). The top edge of the gnomon is parallel with the axis of the Earth's rotation. The shadow will cross time markings on the face.

The markings of each edge are aligned with the edge of the gnomon that produces the shadow. The angle of the face markings from the root of the gnomon (the substyle) are calculated from the formula:

• face-angle = arctan(sin(latitude)*tan(hour-angle))

The angle of the style:

• style height = latitude

Installation of ornamental garden sundials

Many ornamental sundials are designed to be used at 45 degrees north. A sundial designed for one latitude can be adjusted for use at another latitude by tilting its base so that its style, or gnomon, is parallel to the Earth's axis of rotation and pointing in the direction of the north celestial pole in the northern hemisphere, or the south celestial pole in the southern hemisphere. Some mass-produced garden sundials fail to calculate the hourlines so can never be corrected.

A local standard time zone is nominally 15 degrees wide, but may be modified to follow geographic or political boundaries. A sundial can be rotated around its style (which must remain pointed at the celestial pole) to adjust to the local time zone. In most cases, a rotation in the range of 7.5 degrees east to 23 degrees west suffices. This will introduce error in sundials that do not have equal hour angles.

To correct for daylight saving time, a face needs two sets of numerals or a correction table. An informal standard is to have numerals in hot colors for summer, and in cool colors for winter.

Vertical sundials

They are easy to see from large distances and inexpensive to arrange. The face may be painted on the wall, or displayed in inlaid stone, and the gnomon may be single metal bar or tripod of metal bars for rigidity.

Vertical Direct

These are placed on surfaces that align directly with the cardinal points of the compass. As mediaeval churches were aligned to face due east, this is actually quite common.

A vertical direct south dial may be recognised by the symmetrical hour lines. The hours run counter clockwise.They are similar to garden sundials in construction. The formula for a south-facing sundial face :

• face-angle = arctan(cos(latitude)*tan(hour-angle))

The angle of the style:

• style height = co-latitude = 90-latitude.

A vertical direct east or west dial has a gnomon that is parallel but raised from the wall that supports it. The hourlines run parallel to the gnomon, at an angle to the horizon. This angle is the location's latitude. The east dial drops to the right, and the west to the left.

A vertical direct north dial is a mirror image of a south direct dial, it is of limited use as it only displays the hours before 6 am, and after 6 pm.

It used to be traditional to place four sundials on the roof or sides of a tower to provide the time. In this way, the time was available to all for the entire day. Further a pillar could be erected to hold a cube of stone, and the four direct dials could the inscribed.

Vertical declining dials

A declining dial is any dial that does not directly face N, S, E or W. It can be recognised by hourlines that are not symmetrical. In every case the gnomon will point to the celestial north pole. In every case, the midday line or meridian line is vertical, but the gnomon will not be vertical. The line marked XII or 12 will be close to the meridian, but may not be exactly there as the dial has been corrected for longitude.

Inclining dials, inclining declining dials

Inclining dials, sometimes called reclining dials, are dials on a slope. In principle, sundials can be placed on any surface, at any angle, given the correct trigonometric projection of the face. Sundials on sloping roofs can be calculated. This is rarely done; usually the gnomon is aligned and the rest is done by observation rather than calculation.

Analemmatic sundials

Analemmatic sundials correct solar time to mean solar time or another standard time. These usually have hour lines shaped like "figure eights" (analemmas) according to the equation of time. This compensates for the slight eccentricity in the Earth's orbit that causes up to a 15 minute variation from mean solar time. Very accurate dials of this type fit nicely in a public square, using a ball at the tip of a flagpole as the nodus, with the face painted on or inlaid in the pavement.

The geometrical construction of an analemmatic sundial is simple. First imagine an equatorial sundial floating in the air: a vertical bar directed towards the pole and a ring in the plane perpendicular to the bar. Label the lowest point of the ring "12", and the other hour marks as usual. At a certain time and date, the shadow of a certain point A on the bar (which falls here or there depending on the time of year) falls on a certain point B of the ring (which depends on the hour, and the position in the Earth's orbit). Now draw the point B' in the ground just below B and the point A' just below A. Now if you stand at A' your shadow will point at B', because the sun is somewhere in the plane A B A' B'.

In middle latitudes, the ellipse with the hour-marks should be about six meters wide, so the shadow of the head of the beholder will fall near it most of the time. ^[5]

A less accurate version of the sundial is to lay out the hour marks on concrete, and then let the user stand in a square marked with the month. The month squares are arranged to correct the sundial for the time of year. The user's head then forms the gnomon of the dial. If the sundial is molded into the concrete, it resists vandalism and is engaging and reasonably accurate. ^[6]

Portable sundials, for navigation and time

During the Middle Ages advanced yet portable astronomical instruments were developed.

Diptych sundial

The diptych consisted of two small flat faces, joined by a hinge. Diptychs usually folded into little flat boxes suitable for a pocket. The gnomon was a string between the two faces. When the string was tight, the two faces formed both a vertical and horizontal sundial. These were made of white ivory, inlaid with black lacquer markings. The gnomons were black braided silk, linen or hemp.

With a knot or bead on the string as a nodus, and the correct markings, a diptych can keep a calendar well-enough to plant crops.

By making the two sundials have different angles to the string (and thus different projections), a diptych can be self-aligning. When both faces show the same time, and the hinge is level, the diptych shows the local apparent solar time. Additionally, the hinge will point north (in the northern hemisphere), and the diptych will be angled so the gnomon is parallel to the Earth's axis of rotation. At solar noon, sunrise and sunset, the latitude adjustment of the diptych can't affect the time of either sundial, but at 9am and 3pm, each degree of latitude error (from holding the sundial at the wrong angle) creates four minutes of difference between the two faces. A diptych can also act as a compass and even measure latitude. Some diptychs included a small scale and a plumb-bob to read the latitude. Some others included a compass rose to measure angles to geographic features. Large (meter-sized) diptychs may have been used for navigation in ancient times.

Early 18th century portable sundials

One form of sundial was about 8 cm diameter and made of brass. It had a brass lid to protect it when travelling. Several features enabled precision to be achieved. It had an iron compass needle so that North could be accurately set. The scale division is to 5 minutes.

Elevation sundial

Astrolabes were used as sundials, as well as for calendrical observations, navigation and astronomy.

Ring dials

Ring dials came in several forms. The principle component was a ring suspended vertically.

Ring, Poke or Astronomical Ring: Sometimes referred to as an Aquitaine. It had a small handle, or was a fob or the decoration of a necklace. When held by its handle, a hole would cast a shadow on the inside of the ring, telling the time by markings on the inside. The user had to know if it was morning or evening. Usually the hole was mounted in a sliding lockable piece of metal, which was adjusted to correct date. The name poke comes from an old term for pocket; hence a pocket dial.

Universal Equinoctial Ring Dial: This dial has a vertical meridian ring that was graduated with latitude. This permits the user to align the device with the celestial sphere by setting the ring to his location. Mounted inside the meridian ring was an equatorial or hour ring. It was mounted so that it could be folded into the outer ring when not in use. When used, it was opened to a position at right angles to the meridian ring. This ring was marked with the time. The third component of the dial was the central bar. It was often in the form of a flat plate with a sliding plate in it. This bar could pivot about its end points and was parallel to the celestial polar axis. The slider was positioned to the month and day according to a scale scribed on the bar. The sliding plate had a hole in it through which the sun would shine. By orienting the bar towards the sun, the light shining through the hole would fall on the hour ring indicating the time. Usually constructed of brass, these were self-orienting, universal and accurate. Larger ringscould yield local time to the minute.

Precision sundials (heliochronometers)

A precision sundial, called a heliochronometer,corrects apparent solar time to mean solar time or another standard time. Heliochronometers usually indicate the minutes to within 1 minute of Universal Time. See this discussion of the limits of Sundial Accuracy.

Equatorial bow sundial

The classic shape for a heliochronometer is an equatorial bow sundial. A bar, slot or stretched wire parallel to the earth's axis forms the style. The face is a semicircle with markings on the inner surface. This pattern, built a couple of meters wide out of temperature-invariant steel invar, was used to keep the trains running on time in France before World War I.

One of the simplest sundials that reads clock time is an equatorial bow with a gnomon shaped like two vases [5]. The vase-shape directly shades the hour line in the correct place as the year passes, and the sun changes elevation.

The most precise sundials ever made are monumental equatorial bows constructed of masonry, part of the Yantra mandir (Jaipur), in India, built as part of a set of astronomical instruments.

Precision noonmarks

In some older houses a noon-mark can be found carved into a floor or windowsill. Such marks indicate local noon, and they provide a simple and accurate time reference for households that do not possess accurate clocks.

In modern times, some Asian countries' post offices have set their clocks from a precision noon-mark. These in turn provided the times for the rest of the society. The typical noon-mark sundial was a lens set above an analemmatic plate. The plate has an engraved figure-eight shape. When the edge of the sun's image touches the part of the shape for the current month, this indicates that it is noon.

Further Methods

Vitruvius

Marcus Vitruvius Pollio, a 1st century BC Roman, in Book IX of De Architectura gave a list of sundials known at that time and their inventors.

• semicircular, hollowed out of a square block, and cut under to correspond to the polar altitude - Berosus the Chaldean
• scaphe or hemisphere - Aristarchus of Samos
• disc on a plane surface - Aristarchus of Samos
• arachne - Eudoxus of Cnidus or Apollonius of Perga
• plinthium or lacunar (example in the Circus Flaminius) - Scopinas of Syracuse
• pros ta historoumena - Parmenio
• pros pan klima - Theodosius of Bithynia and Andreas
• pelecinum - Patrocles
• cone - Dionysodorus
• quiver - Apollonius of Perga
• conarachne
• conical plinthium
• antiborean
• portable sundials
• analemma

Pelekinon

The ancient Greeks used a type of sundial sometimes referred to as pelekinon (axe-like, apparently because shape of the hour and day lines suggest the ancient double-headed ax pelekus). The gnomon was a rod or pole upright in a horizontal face or half-spherical face. The shadow of the tip of the rod sweeps out hyperbolic curves on a flat face, or circles on a spherical face. The advantage of these dials is that they can be marked to tell the exact time for all times of year.

Reflection sundials

Isaac Newton used a sundial for a south-facing window.^[7] He placed a tiny mirror on the windowsill, and painted the sundial's face in a mirror-image pelekinon on the ceiling and walls. The mirror formed the gnomon by reflecting a spot of light. This provides a large, accurate, perfectly correctable sundial with minimal material, and no wasted space at all. This design could easily be made analemmatic.

Analog calculating sundials

A horizontal sundial with a face cut on a cardioid keeps clock time, while still resembling a conventional garden sundial. The cardioid shape connects the intersections between the solar-time marks of a conventional sundial, and the equal-angles of a true clock-time face. The place where The shadow crosses the cardioid's edge, and the clock time can be read from the underlying clock-time dial. The sundial is adjusted for daylight saving time by rotating the underlying equal-angle clock-time face. The sun-time face does not move.

The Optical Sundial - The Benoy Dial

In a Benoy Dial the time is indicated by a clear pointer of light. Sunlight is focused through a clear liquid within what would be recognised as the gnomon. This makes the dial unique as the only one that does not stop but focuses light to show time. Benoy dials (called a Sunclock by its maker) can be seen at :

• Upton Hall British Horological Institute Newark-on-Trent Nottinghamshire UK
• Within the collections of St Edmundsbury Heritage Service Bury St Edmunds UKhttp://www.stedmundsbury.gov.uk/sebc/visit/Telling-the-Story-of-Time-Measurement.cfm
• Carnfunnock Country Park Antrim Northern Ireland
• Longleat Warminster Wiltshire UK
• Jodrell Bank Science Centre and Arboretum
• Birmingham Botanical Gardens Edgebaston UK
• Science Museum UK - (inventory number 1975-318)

Digital sundials

Main article: Digital sundial

A digital sundial uses light and shadow to 'write' the time in numerals rather than marking time with position. One such design uses two parallel masks to screen sunlight into patterns appropriate for the time of day.

References

• Sundials: Their Theory and Construction, Albert E. Waugh, Dover Publications, Inc., 1973, ISBN 0-486-22947-5.
• "Sundials Old and New", A.P.Herbert, Methuen & Co. Ltd, 1967.
• "Illustrating Shadows", Simon Wheaton-Smith, ISBN 0-9765286-8-1, LCN: 2005900674
• also see "Illustrating More Shadows", Simon Wheaton-Smith, both books are over 300 pages long.
• Gerard L'E. Turner, Antique Scientific Instruments, Blandford Press Ltd. 1980 ISBN 0-7137-1068-3
• Make A Sundial, (The Education Group British Sundial Society) Editors Jane Walker and David Brown, British Sundial Society 1991 ISBN 0-9518404-0

Footnotes

See also

• Moondial
• Foucault pendulum
• Francesco Bianchini
• Scottish sundial — the ancient renaissance sundials of Scotland.
• Tide (time) - devisions of the day on early sundials.
• Nocturnal - device for determining time by the stars at night.

Sundial Societies, Groups and Organizations

• The British Sundial Society
• The North American Sundial Society
• Societat Catalana de Gnomònica
• The Italian Sundial Society (CGI)

External links

• Sundial Websites Catalogue An indexed and edited site of Sundial related sites.
• Sunbeams and Sundials Children's guide to the sun, the seasons and sundials.
• A major source of information Information about sundial design and building, small indoor, glass, clay, and concrete, designing programs in many languages for sundials, and VRML models.
• Sundial links a collection of sundial links ordered by date.
• Shakhes An Iranian sundial website (in Farsi and English)including sundial in Iran, sundial making and ....