Sundial


A sundial is a horological device that tells the time of day when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat plate and a gnomon, which casts a shadow onto the dial. As the Sun appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The style is the time-telling edge of the gnomon, though a single point or nodus may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude.
The term sundial can refer to any device that uses the Sun's altitude or azimuth to show the time. Sundials are valued as decorative objects, metaphors, and objects of intrigue and mathematical study.
The passing of time can be observed by placing a stick in the sand or a nail in a board and placing markers at the edge of a shadow or outlining a shadow at intervals. It is common for inexpensive, mass-produced decorative sundials to have incorrectly aligned gnomons, shadow lengths, and hour-lines, which cannot be adjusted to tell the correct time.

Introduction

There are several different types of sundials. Some sundials use a shadow or the edge of a shadow while others use a line or spot of light to indicate the time.
The shadow-casting object, known as a gnomon, may be a long thin rod or other object with a sharp tip or a straight edge. Sundials employ many types of gnomon. The gnomon may be fixed or moved according to the season. It may be oriented vertically, horizontally, aligned with the Earth's axis, or oriented in an altogether different direction determined by mathematics.
Given that sundials use light to indicate time, a line of light may be formed by allowing the Sun's rays through a thin slit or focusing them through a cylindrical lens. A spot of light may be formed by allowing the Sun's rays to pass through a small hole, window, oculus, or by reflecting them from a small circular mirror. A spot of light can be as small as a pinhole in a solargraph or as large as the oculus in the Pantheon.
Sundials may also use many types of surfaces to receive the light or shadow. Planes are the most common surface, but partial spheres, cylinders, cones and other shapes have been used for greater accuracy or beauty.
Sundials differ in their portability and their need for orientation. The installation of many dials requires knowing the local latitude, the precise vertical direction, and the direction to true north. Portable dials are self-aligning: for example, they may have two dials that operate on different principles, such as a horizontal and analemmatic dial, mounted together on one plate. In these designs, their times agree only when the plate is aligned properly.
Sundials may indicate the local solar time only. To obtain the national clock time, three corrections are required:
  1. The orbit of the Earth is not perfectly circular and its rotational axis is not perpendicular to its orbit. The sundial's indicated solar time thus varies from clock time by small amounts that change throughout the year. This correction—which may be as great as 16 minutes, 33 seconds—is described by the equation of time. A sophisticated sundial, with a curved style or hour lines, may incorporate this correction. The more usual simpler sundials sometimes have a small plaque that gives the offsets at various times of the year.
  2. The solar time must be corrected for the longitude of the sundial relative to the longitude of the official time zone. For example, an uncorrected sundial located west of Greenwich, England but within the same time-zone, shows an earlier time than the official time. It may show "11:45" at official noon, and will show "noon" after the official noon. This correction can easily be made by rotating the hour-lines by a constant angle equal to the difference in longitudes, which makes this a commonly possible design option.
  3. To adjust for daylight saving time, if applicable, the solar time must additionally be shifted for the official difference. This is also a correction that can be done on the dial, i.e. by numbering the hour-lines with two sets of numbers, or even by swapping the numbering in some designs. More often this is simply ignored, or mentioned on the plaque with the other corrections, if there is one.

    Apparent motion of the Sun

The principles of sundials are understood most easily from the Sun's apparent motion. The Earth rotates on its axis, and revolves in an elliptical orbit around the Sun. An excellent approximation assumes that the Sun revolves around a stationary Earth on the celestial sphere, which rotates every 24 hours about its celestial axis. The celestial axis is the line connecting the celestial poles. Since the celestial axis is aligned with the axis about which the Earth rotates, the angle of the axis with the local horizontal is the local geographical latitude.
Unlike the fixed stars, the Sun changes its position on the celestial sphere, being at a positive declination in spring and summer, and at a negative declination in autumn and winter, and having exactly zero declination at the equinoxes. The Sun's celestial longitude also varies, changing by one complete revolution per year. The path of the Sun on the celestial sphere is called the ecliptic. The ecliptic passes through the twelve constellations of the zodiac in the course of a year.
File:Sundial, Singapore Botanic Gardens.jpg|thumb|left|Bowstring sundial in Singapore Botanic Gardens. The design shows that Singapore is located almost at the equator.
This model of the Sun's motion helps to understand sundials. If the shadow-casting gnomon is aligned with the celestial poles, its shadow will revolve at a constant rate, and this rotation will not change with the seasons. This is the most common design. In such cases, the same hour lines may be used throughout the year. The hour-lines will be spaced uniformly if the surface receiving the shadow is either perpendicular or circular about the gnomon.
In other cases, the hour-lines are not spaced evenly, even though the shadow rotates uniformly. If the gnomon is not aligned with the celestial poles, even its shadow will not rotate uniformly, and the hour lines must be corrected accordingly. The rays of light that graze the tip of a gnomon, or which pass through a small hole, or reflect from a small mirror, trace out a cone aligned with the celestial poles. The corresponding light-spot or shadow-tip, if it falls onto a flat surface, will trace out a conic section, such as a hyperbola, ellipse or a circle.
This conic section is the intersection of the cone of light rays with the flat surface. This cone and its conic section change with the seasons, as the Sun's declination changes; hence, sundials that follow the motion of such light-spots or shadow-tips often have different hour-lines for different times of the year. This is seen in shepherd's dials, sundial rings, and vertical gnomons such as obelisks. Alternatively, sundials may change the angle or position of the gnomon relative to the hour lines, as in the analemmatic dial or the Lambert dial.

History

The earliest sundials known from the archaeological record are shadow clocks from ancient Egyptian astronomy and Babylonian astronomy. By 240 BC, Eratosthenes had estimated the circumference of the world using an obelisk and a water well and a few centuries later, Ptolemy had charted the latitude of cities using the angle of the sun. The people of Kush created sun dials through geometry. The Roman writer Vitruvius lists dials and shadow clocks known at that time in his De architectura. The Tower of the Winds in Athens included both a sundial and a water clock for telling time. A canonical sundial is one that indicates the canonical hours of liturgical acts, and these were used from the 7th to the 14th centuries by religious orders. 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 and horizontal sundials. Giuseppe Biancani's Constructio instrumenti ad horologia solaria discusses how to make a perfect sundial. They have been in common use since the 16th century.
File:Seoul-Gyeongbokgung-Sundial-02.jpg|right|thumb|A Korean sundial first made by Chang Yŏngsil in the Joseon period, displayed in Gyeongbokgung.

Functioning

In general, sundials indicate the time by casting a shadow or throwing light onto a surface known as a dial face or dial plate. Although usually a flat plane, the dial face may also be the inner or outer surface of a sphere, cylinder, cone, helix, and various other shapes.
The time is indicated where a shadow or light falls on the dial face, which is usually inscribed with hour lines. Although usually straight, these hour lines may also be curved, depending on the design of the sundial. In some designs, it is possible to determine the date of the year, or it may be required to know the date to find the correct time. In such cases, there may be multiple sets of hour lines for different months, or there may be mechanisms for setting/calculating the month. In addition to the hour lines, the dial face may offer other data—such as the horizon, the equator and the tropics—which are referred to collectively as the dial furniture.
The entire object that casts a shadow or light onto the dial face is known as the sundial's gnomon. However, it is usually only an edge of the gnomon that casts the shadow used to determine the time; this linear feature is known as the sundial's style. The style is usually aligned parallel to the axis of the celestial sphere, and therefore is aligned with the local geographical meridian. In some sundial designs, only a point-like feature, such as the tip of the style, is used to determine the time and date; this point-like feature is known as the sundial's nodus.
Some sundials use both a style and a nodus to determine the time and date.
The gnomon is usually fixed relative to the dial face, but not always; in some designs such as the analemmatic sundial, the style is moved according to the month. If the style is fixed, the line on the dial plate perpendicularly beneath the style is called the substyle, meaning "below the style". The angle the style makes with the plane of 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 between the noon line and the substyle is called the substyle distance, an unusual use of the word distance to mean an angle.
By tradition, many sundials have a motto. The motto is usually in the form of an epigram: sometimes sombre reflections on the passing of time and the brevity of life, but equally often humorous witticisms of the dial maker. One such quip is, I am a sundial, and I make a botch, Of what is done much better by a watch.
A dial is said to be equiangular if its hour-lines are straight and spaced equally. Most equiangular sundials have a fixed gnomon style aligned with the Earth's rotational axis, as well as a shadow-receiving surface that is symmetrical about that axis; examples include the equatorial dial, the equatorial bow, the armillary sphere, the cylindrical dial and the conical dial. However, other designs are equiangular, such as the Lambert dial, a version of the analemmatic sundial with a moveable style.