Sundial

A sundial measures time by using the rotation of the Earth.

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.

Design

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 classic garden sundial uses the same principle. 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)).

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. However, they 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.

To correct for daylight savings time, a face should have two sets of numerals, and be adjusted for longitude from the center of the time zone. The admittedly informal standard is to have numerals in hot colors for summer times, and one in cool colors for winter times. A sundial need only be tilted by a maximum of 7.5 degrees to the east or west to adjust to the standard time zone (time zones are 360 degrees/24 hours = 15 degrees wide).

The above types of sundials can be adjusted for latitude just by tilting them so their gnomons parallel the Earth's axis of rotation.

Portable Sundials, for Navigation and Time

The most successful portable sundial was called a triptych. It consisted of two small 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. When both sundials told the same time, the tryptych was correctly aligned both for north and south, and for the latitude. Some triptychs 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) triptychs were used for navigation in ancient times. In later days, triptychs 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 bezel, to adjust for the latitude.

Precision Sundials

The classic shape for a heliochronometer is a semicircle of temperature-invariant steel, with markings on the inner surface. A metal bar 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.

The most precise sundials ever made are monumental instruments constructed by a Caliph in India to set the Islamic religious calendar.

In modern times, some Oriental countries' post offices set their clocks from a precision sundial that determined local noon. These in turn provided the times for the rest of the society.

Traditional sundials are only accurate to about a quarter of an hour because the Earth's orbit is a slight ellipse. Sundials of the above type mount a graph or table to give corrections to the nearest minute based on the current date. [Alas, I don't know the correction; I do know it is yearly, and not synchronized with the equinoxes.]

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. It fits very 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.