When I was about twelve, I saw a sundial in Williamsburg Virginia. It was the first sundial I had ever seen and I was naturally curious about how it worked. Although the dial was beautiful in design, I was surprised to see well over an hour of difference between the time shown on the dial and that shown on my watch. I was left with the impression that sundials were grossly inaccurate and not worth bothering with. I carried that false impression for almost thirty years before discovering that sundials are indeed very accurate. The only thing wrong with that dial I saw was my ignorance of how to properly interpret it's shadow. I have since learned that a properly constructed sundial can give the correct time to within a couple of minutes and that a special type of sundial, called a heliochronometer, can yield the correct time to within a few seconds.
In the sections that follow, I will give instructions on designing a horizontal sundial that should yield the correct time to within a couple of minutes or better. To understand the reasoning behind the instructions, I think it wise to consider for a few moments the daily and yearly motions of the sun, and the essential parts of a sundial.
There are two motions made by the sun, both of which have an effect on the design of a sundial. The first is the apparent motion of the sun across the sky each day as the Earth rotates on it's axis. The second is the apparent motion of the sun across the celestial sphere each year as the Earth revolves about the sun. Notice that these motions are described as "apparent". The sun does not actually move but only "appears" to move due to the Earth's daily and yearly motions.
To measure the apparent motions of the sun, let us first define a base line from which the sun's position is measured. This base line is known as the local meridian and is a line extending from the north pole, through the location of the sundial, to the south pole. This meridian also projects from the surface of the Earth to the celestial sphere and describes an arc that extends from the north celestial pole, through the zenith, to the south celestial pole.
When the center of the sun crosses the local meridian, it is said to transit. The moment of transit is called local apparent noon. The time between two consecutive transits is equal to 24 hours. Since the sun travels through 360 degrees in this time it can be seen that the sun moves through 15 degrees every hour or 1 degree every four minutes. We will use this 15 degree value in laying out the lines on our dial.
A dial designed in such a manner will faithfully and accurately tell us local apparent time. This is apparently what the sundial I saw in Williamsburg was designed for. That dial however, was designed before the advent of time zones and daylight savings time which explains, in part, why the dial did not agree with my watch. The instructions for making your dial include corrections for both time zones and daylight savings time.
There is a third factor which accounts for the difference in time shown on the Williamsburg dial and my watch. This third factor is know as "the equation of time".
The sun's apparent motion across the celestial sphere in the course of a year is not uniform in its rate of travel. This is caused by two factors:
First, the Earth's orbit is not circular, but elliptical with the sun being at one of the foci. The Earth, and thus the apparent motion of the sun, varies in speed as it revolves around the sun. The speed is fastest at perihelion (closest approach to the sun), and slowest at aphelion (furthest distance from the sun). Perihelion occurs around January 4th. This variation in the sun's apparent speed is roughly sinusoidal and repeats once per year.
Second, the Earth is inclined (tilted) with respect to the plane of its orbit by about 23.5 degrees. This inclination causes the sun, at transit, to appear at it's highest point in the sky on June 21st and it's lowest point on December 22nd. These two points in the sun's annual motion are called the Summer Solstice and Winter Solstice respectively. When the sun is halfway between the solstices on March 21st and September 22nd, the points are called the Vernal Equinox and Autumnal Equinox respectively, At the equinoxes the sun is moving at it's fastest rate in its north-south travels. At the solstices, it's north-south travel slows to zero before reversing direction. This changing of speed and reversal in the north-south direction affects the sun's apparent speed as it circles the celestial sphere. This also is roughly sinusoidal and repeats twice each year.
The algebraic sum of the speed variations caused by an elliptical orbit and the Earth's tilt result in a sundial being sometimes fast and sometimes slow when compared to a clock. A clock, by the way, follows what is called the "mean sun"; a fictitious sun that travels across the celestial sphere at the equator. The mean sun travels at a rate equal to the average speed of the apparent sun. The apparent sun and the mean sun agree only four times each year. It is only at those four times that a sundial and a clock will agree. Any other time, there is a difference between sundial time and clock time. This difference is the equation of time.
In summary, three things account for the difference in time shown on a sundial and that of a clock: (1) Time zones (2) Daylight savings time (3) The equation of time
When these three factors are applied to a well designed sundial, its accuracy becomes such that one can set their watch by it to within one or two minutes.
In its simplest form a sundial really only consists of two parts: One part casts a shadow, and the other part is a surface upon which the shadow falls. Given this simple definition, sundials have occured naturally since the creation of the world. The shadow of a tree on the ground or the shadow of a mountain in the valley below are two examples of naturally occuring sundials. Natural sundials can only provide a very rough indication of the age of the day. To gain precision and accuracy, the two essential parts of the sundial have been refined over the centuries. The shadow casting part of the horizontal dial is called the gnomon, while the part that receives the shadow is called the dial plate or face.
The gnomon is the part of the dial that extends into a vertical plane above the horizontal face of the dial. Gnomons for horizontal dials can be of many different shapes, from a simple rod to an intricately scrolled work of art. The most common mental image of a gnomon is that of a triangular piece that extends above the dial plate. The inclined or sloping edge of the gnomon is called the style. The style is the edge that cast the shadow onto the dial plate and is used to indicate the time. The angle the style makes with the face of the dial must be exactly equal to the latitude for which the dial is designed.
All gnomons have a nodus. The nodus is a specific point somewhere along the length of the style. In a simple triangular gnomon, the nodus is the uppermost point of the style. Sometimes a notch, bead or small horizontal bar is placed on the style to serve as the nodus. It defines a particular point on the shadow which is used with special lines on the dial face to indicate a multitude of information other than the time of day. The most common use of the nodus shadow is in conjunction with lines of declination on the dial plate to indicate the time of year. Other uses for the nodus shadow are to show special days of the year, the entrance of the sun into zodiacal constellations, sunrise and sunset in other cities, and the altitude and azimuth of the sun. A vertical line from the nodus to the dial plate is known as the perpendicular style. Both the style and the perpendicular style intersect the dial plate. A line drawn between these two points of intersection is called the substyle. A gnomon consists therefore of four basic parts; a style, a nodus, a perpendicular style and a substyle.
The dial plate is the flat, horizontal surface that receives the shadow of both the style and the nodus. The plate is marked with lines that the shadows move across to indicate time of day and time of year.