Sundial
From Wikipedia, the free encyclopedia
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.
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[edit] History
Sundials in the form of obelisks (3500 BC) and shadow clocks (1500 BC) are known from ancient Egypt, and were developed further by other cultures, including the Chinese, Greek[1], and Roman cultures. 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. 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 famous Bewcastle Cross. The dial is divided into four tides, covering the parts of the working day in medieval times.
[edit] Installation of standard sundials
Many ornamental sundials are designed to be used at 45 degrees north. By tilting such a sundial, it may be installed so that it will keep time. However, some mass-produced garden sundials are inaccurate because of poor design and cannot be corrected. 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.
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.
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 quality sundial will include a permanently-mounted table or graph giving this correction for at least each month of the year. Some more complex sundials have curved hour-lines, curved gnomons or other arrangements to directly display the clock time.
[edit] Design and principles of operation
[edit] Terminology
The 'shadow-maker' of the sundial is called a gnomon[1].In common speech, the gnomon is often called a style. [2]
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 general, the best material for a face is a very light color to give a high contrast with the shadow. The surface should have a matt finish to prevent misleading reflections. The numerals should be dark, visible on the unshaded portion of the face. The gnomon should be sturdy, preferably metal, because gnomons are usually thin, and can break easily. The traditional luxury materials are a white marble face, with markings inlaid in black marble. Traditional gnomons are thick bronze to prevent corrosion. In Eastern Europe, there is a tradition of painted dial faces often using fresco techniques.
It is traditional for a sundial to have a motto.
[edit] 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. The disk in the above design is called the face. 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.
[edit] 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). For use in a public area, this sundial can be made visible by placing it in a square, or making the face of frosted glass, elevated high in the air, and visible from underneath. 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
(See Logo programming language for a sample program to draw a garden sundial)
[edit] Vertical sundials
They are easy to see from large distances and inexpensive to arrange. One sturdy method is to paint the sundial on the wall, and construct the gnomon as a tripod of metal bars. Fancy sundials used to have faces of inlaid stone.
[edit] 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 as the hour lines are symmetrical. 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 a cube of stone, and the four direct dials could the inscribed.
[edit] 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.
[edit] 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, the gnomon is aligned and the rest is done by observation rather than calculation.
[edit] Portable sundials, for navigation and time
During the Middle Ages advanced yet portable astronomical instruments were developed.
[edit] Diptych sundial
One popular portable sundial design was called a diptych. It 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. The best material was white ivory, inlaid with black lacquer markings. The best 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.
This means that 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.
[edit] Early 18th century portable sundials
This form of sundial was about 8 cm diameter and made of brass. It had a brass lid, not shown, 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.
This dial was made in Dublin in 1742 by Gabriel Stokes a mathematical instrument maker.
[edit] Elevation sundial
Astrolabes were used as sundials, as well as for calendrical observations, navigation and astronomy.
An even smaller design was the ring. 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.
In recent times, U.S. Special Forces have taken to engraving a simple sundial on their knife-blade. It works even when a watch fails.
[edit] 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.
[edit] 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.
[edit] Precision noonmarks
In some older houses, particularly mansions, a noon-mark can be found carved into a floor or windowsill. Such marks act as sundials to indicate local noon, and they provided a simple and accurate time reference for households that did 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, it is noon!
[edit] Ancient Greek sundials
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.
[edit] 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. [3]
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.[4]
[edit] Reflection sundials
Isaac Newton used a sundial for a south-facing window.[5] 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.
[edit] Analog calculating sundials
A last, interesting variation accurately keeps clock time, while still resembling a conventional garden sundial. It is a horizontal sundial with a face cut on a cardioid (a sort of heart-shape). A cardioid is the shape that 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 is the place where clock time can be read on 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.
[edit] Digital sundials
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.
[edit] 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.
[edit] Footnotes
- ^ Diogenes Laertius - Anaximander
- ^ In technical writing, gnomon can mean the perpendicular height, of a nodus, or the tip of the style from the dial plate. The point that this touches the dial plate, is called the gnomon root.
- ^ “Analemmatic sundials: How to build one and why they work” by C.J. Budd and C.J. Sangwin
- ^ SUNCLOCKS - Human Sundials, using YOUR OWN SHADOW to tell correct time
- ^ Sundials: Their Theory and Construction, Albert E. Waugh, Dover Publications, Inc., 1973, ISBN 0-486-22947-5.
[edit] See also
- Moondial
- Focault pendulum
- Francesco Bianchini
- Scottish sundial — the ancient renaissance sundials of Scotland.
- Sundial Bridge at Turtle Bay — a single spar cable stayed bridge that casts a shadow into a garden where the time may be read. Unfortunately, the style height is wrong for the latitude and it is only accurate two days of the year.
[edit] Sundial Societies, Groups and Organizations
[edit] External links
- The British Sundial Society has a history of sundials and a glossary of sundial terminology*
- 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.
- Sundial links a collection of sundial links ordered by date.
- Sundials on the Internet an eclectic information site on sundials.
