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# Sundial

A normal sundial measures apparent solar time. Mild design variations can measure standard and daylight savings time, as well.

Sundials were first invented in ancient Egypt. They were perfected by the Greeks and Romans and ironically, just as Newton enabled their greatest perfection, they were replaced by mechanical clocks.

Tilting a sundial is the only practical way to install a mass-produced garden sundial so that it will keep time. Some mass-produced garden sundials are improperly designed, and unable to keep time. Most are made to 45 degrees north.

A sundial can be adjusted to another latitude by tilting it so its gnomon(s) is (are) parallel the Earth's axis of rotation. That is, the end of a gnomon should point at the north celestial pole in the northern hemisphere, or the south celestial pole in the southern hemisphere.

A sundial need only be tilted by a maximum of 7.5 degrees to the east or west to adjust to the local standard time zone (time zones are 360 degrees/24 hours = 15 degrees wide). Tilt the sundial so that it is oriented as if it were at the longitude of the center of your local time zone.

To correct for daylight savings time, a face needs two sets of numerals or a correction table, and must be adjusted for longitude from the center of the time zone. The admittedly 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, because the Earth's orbit is slightly eilliptical. A quality sundial will include a permanently-mounted table giving this correction for at least each month of the year.

Twisting a sundial to obtain daylight savings time will not work, because the time angles on the faces of most sundials are not equal.

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.

The 'shadow-maker' of the sundial is called a gnomon. In the above design, the bar is the gnomon. The disk in the above design is called the face. In general, the best material for a face is a very light color to give a high contrast with the shadow. 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.

### The 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 making the face of frosted glass, elevated high in the air with the bottom of the glass visible. 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 are calculated from the formula face-angle = arctan(sin(latitude)*(gnomon-length)*tan(hour-angle)).

### Vertical Sundials

Although they are rare in modern life, sundials on vertical south-facing walls (north-facing in the southern hemisphere) are a traditional ancient convenience. 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.

A problem is that vertical sundials only keep time for the part of the year in which the sun illuminates the wall. They are very similar to garden sundials. The formula for a south-facing sundial face is face-angle = arctan(cos(latitude)*(gnomon-length)*tan(hour-angle)). Traditionally, the gnomon is a tripod of metal bars (bronze or iron), and the face is painted, molded, carved or inlaid on the south wall.

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 year. In principle, sundials can be placed on any surface, at any angle, given the correct trigonometric projection of the face.

The most successful portable sundial was called a diptych. It consisted of two small flat faces, joined by a hinge. 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 or linen.

If the hinge of a diptych is level (parallel to the ground), and both faces show the same time, the diptych shows the local mean 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 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 inclded a compass rose to measure angles to geographic features. Large (meter-sized) diptychs were used for navigation in ancient times. Diptychs usually folded into little flat boxes suitable for a pocket.

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, to adjust for the latitude.

In recent times, U.S. special forces have taken to engraving a simple sundial on their knife-blade.

Traditional sundials are only accurate to about a quarter of an hour because the Earth's orbit is a slight ellipse. Simple, quality sundials often mount a graph or table to give corrections to the nearest minute based on the current date.

The classic shape for a heliochronometer is an equatorial bow sundial, a semicircle of temperature-invariant steel invar[?], with markings on the inner surface. A metal bar parallel to the earth's axis forms the gnomon. This pattern, built a couple of meters wide, 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 sundial with a gnomon shaped like two vases. 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 by a Mogul Caliph in India to set the Islamic religious calendar.

### Precision Noonmarks

In modern times, some Oriental countries' post offices have set their clocks from a precision noon-mark, a sundial that determined local noon. 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.

### Plekhnatons

The ancient greeks used a type of sundial called a plekhnaton. 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 great-circles on a spherical face. The advantage of a plekhnaton is that it can be corrected to tell the exact time for all times of year.

A particularly fun version of the plekhnaton is to lay out the hour lines 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 plekhnaton. If the sundial is molded into the concrete, it is almost perfectly immune to vandalism, as well as truly fun and reasonably accurate.

Plekhnatons fit nicely in a public square, using a flagpole as the gnomon, with the face painted on or inlaid in the pavement.

Isaac Newton invented a variant of the plekhnaton for a south-facing window. He placed a tiny mirror on the windowsill, and painted the plekhnaton's face in a mirror-image 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 only small amounts of material, and no wasted space at all.

### 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 savings time by rotating the underlying equal-angle clock-time face. The sun-time face does not move.

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