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North American Sundial Society:

Sundials

Sundials

  • Time and the Sun

  • Dials

  • Placement

  • Construction

  • Finding true north

  • Adjusting for clock time

  • The Seasons

  • The Tropics

  • The Zodiac


    Time and the Sun

    For most of history, man's days and years were governed by the sun and stars. Even after clocks and watches were invented, they were set by the sun so that they read noon when the sun was at its zenith. Time is now delivered to us by the radio and television and told by the digital watch. Morning is when the alarm goes off. Summer is when you need the air conditioner. We know about satellites, galaxies, planets and black holes, but have lost touch with the logic and rhythm of sunrise, sunset, summer and winter.

    These things used to be understood intuitively by everybody, and their rules and special terminology were a part of the intellectual baggage of all well-educated people. Midsummer's day was celebrated at the summer solstice on June 21. Christmas is close to the Winter solstice on December 22. The vernal and autumnal equinoxes mark the beginning of Spring and Fall when the sun moves into Cancer and Capricorn, respectively. It is instructive to learn how a sundial works and watch its shadow advance through the day and vary with the seasons. In this way we can come to a better understanding of these natural phenomena and relearn the meanings of those half-understood, half forgotten names like "gnomon", "ecliptic" and "zodiac."

    Until the end of the 19th century, all time was local and related to the sun. Noon in Boston was not the same time as noon in New York. With the development of railroads and telegraphs widely spaced locations became linked to each other more closely in time and, there was a need to standardize time areas. In 1884 an international convention in Washington D.C. agreed on a worldwide system of time zones of 15° each. Local adjustments were allowed, as necessary, to keep political subdivisions in a single zone.

    Dials

    A sundial consists of the dial plate marked out with hour lines, and a "gnomon", the raised projection that casts the shadow. The inclined edge of the gnomon, called the "style", produces the working edge of the shadow that is used to tell the time. It is oriented parallel to the earth's axis, pointing toward the point in the sky around which the (imaginary) celestial sphere rotates once every 24 hours, which is very close to the location of Polaris, the pole star visible at night. There are many different types of sundials, including vertical dials and tilted dials. Virtually anything casting a shadow can be made into a sundial; the trick is to calculate the proper placement of the time marks. The most straightforward type of dial is the "polar" dial. It has marks placed at equal intervals. Its disadvantage, however, is that it has to be angled to face up toward the north pole. Vertical dials on public buildings used to be widespread. Now, the type of dial seen most often is the horizontal dial, generally used as a decorative element in gardens. Sundials sold in garden shops will not generally tell accurate time, however, except by coincidence.

    Vertical Declining Dial Horizontal Dial

    Placement

    To be accurate, a sundial must be specially designed for the spot it is to be used in and must also be pointed in the right direction. The two dials pictured above were made for a specific location in Maine. Note that the times on the vertical dial are asymmetrical. This is necessary because the dial "declines" from true north by about 20°. The barn was built using a compass but at this point on the earth's surface, magnetic north is about 20° east of true north.

    The angle made by the style with respect to the earth's surface -- or with the plate in the case of a horizontal dial -- must be equal to the local latitude, which will point it to the proper elevation. The time lines are also a function of local latitude; they must be arrayed around the center of the dial differently in different places. Finally, the dial must be oriented so that the gnomon lies on a true north-south axis to insure that it points to the north pole of the sky. When these alignments are all correct, the edge of the gnomon whose shadow marks out the time will be exactly parallel to the axis on which the sky's imaginary globe is turning. When the sun is at its zenith, the gnomon's shadow will fall on the line representing solar noon.

    A garden sundial can be set to tell the right time if it was correctly constructed for some point on the earth's surface. Assuming that the hour lines were drawn correctly to match the elevation of the gnomon at a given latitude the sundial will be accurate if the whole thing, including the plate, is tilted so it sits at the angle of the earth's surface at its "home location" or in other words if the gnomon points to the north celestial pole. If you are at latitude 42° at washington and the gnomon makes an angle of 39° with the plate, simply tip the plate by 3°.

    Construction of a vertical declining dial

    Vertical declining dials are those attached to walls that do not face directly north, south, east or west. Although this is not the most straightforward type of sundial, it is probably the best kind to construct oneself as a project, since it can be put on the side of a house, barn or garage and executed using easily available materials including wood, paint, and pre-made numbers for the dial itself and dowels, pipes, or rods to construct the gnomon-pointer. The following procedure shows how to lay out the angles for the gnomon and the hour lines on paper using a standard geometric methods (straightedge and compass). A protractor will also be necessary to establish the lines dependent on latitude. The drawing should be laid out on a large sheet of pa per and subsequently transferred to the wall. If you are actually going to do this, you will obviously want to send this page to your printer so you can refer to it.

    Since you generally do not have the option of reorienting your garage to line up with the compass, it will probably be necessary for the dial to "decline" from the cardinal points. First, you have to ascertain which of the four categories (shown in figur e 1) your building or wall falls into.


    Before we can design the sundial, we must know the latitude (as with all dials) and also the amount of the walls declination. In this example, we will assume that the dial will be going on the wall facing southeast which declines S 24° E, which means that it starting from the south has been twisted around through the east through an angle of 24°. We will also assume the dial is at latitude 40 degrees north.

    The first step is to find the substyle line, which is the line on the dial plate on which the gnomon is to be erected perpendicular to the dial plate -- or in this case, the wall. In a more typical dial, the gnomon would follow the 12-o'clock line, but w ith vertical decliners this is no longer the case. In all vertical dials the 12-o'clock line is vertical, but with declining dials the line on which the gnomon is placed (called the substyle) is twisted out of the vertical, lying to the right or east of the 12-o'clock vertical line and thus among the afternoon hour lines if the dial declines toward the west of south or to the left or west among the morning hour lines with the southeast decliners. (As with the example.) The angle between the vertical 12 -o'clock line and the substyle is called the substyle distance, or SD. To find this substyle graphically we proceed as follows using figure 2.

    The substyle line


    1. Draw AB as the horizontal line.
    2. At C, near the center of AB, draw CD perpendicular to AB
    3. With any convenient radius draw the semi-circle ADB centered at C.
    4. Draw CG making angle DCG equal to the colatitude. The colatitude is the difference 90° minus the local latitude, here 50°. Since our dial declines toward the east, we place CG to the left of CD.
    5. From G draw GH parallel to AB, cutting CD at H.
    6. On the side of CD opposite CG draw CJ with angle DCJ equal to the dial's declination (here 24 degrees).
    7. On CJ lay off CK equal to GH.
    8. Draw KL parallel to AB intersecting CD at L.
    9. On HG lay off HM equal to KL.
    10. Draw CMN. This is the substyle line, and the angle DCN is the substyle distance, SD. This ends our first step.

    The substyle height:

    Having found the substyle on which the gnomon will be placed, we next find the style height, SH, which is the angle the style plate makes with the dial plate. Continuing with figure 2,
    1. Draw KP parallel to CD
    2. Find point R on the semi-circle so that MR = KP.
    3. Draw CR. This represents the style, and angle NCR is the required height of the style, SH.

    The hour lines:

    The hour lines could be added to figure 2, but because of increasing clutter, we will transfer the essential lines to figure 3. AB, CD, CR, and CN are all carried over from the preceding figure.

    1. At any convenient point on CN (as at M) draw SMT perpendicular to CN. The distance taken for CM will determine the scale of the final diagram.
    2. Draw ME perpendicular to CR
    3. On CN lay off MO equal to ME.
    4. With O as center draw a circle of any desired radius. In Figure 3, the radius has been taken equal to OM.
    5. Call the intersection of ST and CD "d." Draw Od.
    6. Divide the circle into 15° arcs starting from Od.
    7. Draw lines from O through the 15° divisions on the circle and continue these radii until they intersect ST at the points indicated by lower case letters.
    8. Draw lines from C to the points just found on ST. These are the hour lines and are numbered counterclockwise with CdD the 12-o'clock line.

    These lines are to be transferred from the worksheet to the dial plate or perhaps directly to the wall, remembering that the 12-o'clock line will be vertical. You will also need the substyle line to attach the gnomon perpendicular to the dial plate.

    Finding true north

    In principle, north can be located by using a magnetic compass and making an appropriate the correction. Magnetic north is substantially off from true north -- the exact amount varies by location. But there are better ways. Polaris, the north star, can be used, but this is inconvenient -- you have to wait for a clear night -- and not entirely accurate either. The most accurate way to find a true north south orientation is by using the sun itself to find the direction of a shadow cast by a vertical object when the sun is at its zenith. This is easier than it sounds, and can be done by measuring the length of the shadow cast by the upright before and after noon. Set up a vertical pole (or a use a rope with a weight) to cast a shadow on the ground. If you use a rope you will need to make the reference point somewhere near the top cast a visible shadow -- like a stick knotted into the rope) The base of the shadow will be the first point for your south-north axis and the reference point or top of the pole will trace the second point. At some time in the morning, mark the spot on the ground where the reference point casts its shadow. Measure the length from the base to the end of the shadow, and using a string of that length, trace out a semi-circle on the ground with the base of the shadow as its center point. As the sun rises higher in the sky, the shadow will first shorten as noon approaches, and and then will lengthen. At some in the afternoon it will reach the semi-circle you traced in the morning. Note the spot when it crosses the arc the second time. The midway point between the morning and afternoon points, will be directly north of the base point of vertical object.

    Adjusting for clock time

    The north "noon" line cast by the sun at its zenith will not correspond to noon clock time. Two adjustments are necessary. The first of these has to do with local placement within the time zone and is different for every longitude; the second is a function of the day of the year and can be found with an Analemma.

    Time Zones

    Since there are 360° in a circle and the earth makes one rotation in 24 hours, each time zone covers 15° (15 X 24 = 360). Time zones are counted in 15° increments from Greenwich, England, the point of reference, so that the "center" of each time zone (i.e. the point where solar time is the same as clock time) lies on 15° increments moving west from Greenwich. Eastern Standard Time is set to noon when the sun crosses over the 75th meridian (5 hour increments west of Greenwich) which falls near Philadelphia. Since each° represents 1/15 of an hour, it counts for 4 minutes of time, and it is necessary to subtract or add 4 minutes for each° of difference from the center of the time zone. For Eastern standard time, when it is noon by the clock, it is exactly 8 minutes earlier by the sun at the Capitol building in Washington at 77° longitude -- two° west of the 75 meridian line at Philadelphia.

    The Equation of Time

    The second adjustment is more complex and is captured in what is by tradition called "the equation of time." This results from the fact that the apparent motion of the sun across a spherical sky is a fiction; the earth actually orbits around the sun in an elliptical path. Therefore the sun's apparent motion across the sky is not uniform throughout the year and can run almost 15 minutes fast or slow. For practical purposes, however, it is important that the hour-unit of time be kept constant and the days divided into 24 equal sized hours, regardless of the season. This means that for clock time it is necessary to create a "mean sun" -- an imaginary sun that moves across the sky at a constant rate. The equation of time is is the sum of two curves, one caused by the earth's eliptical orbit; the other caused by its inclination. The equation has long ago been worked out with great precision and incorporated in tables. If plotted against the days of the year, it looks like an irregular pattern with four peaks and four troughs. It is commonly represented graphically on old globes and sundials by the "Analemma," a figure-8 shaped device that shows the number of minutes that must be added or subtracted from solar time at each date in the year.

    The Seasons

    A line traced around the center of the celestial sphere perpendicular to the pole it rotates around is called the celestial equator. This line is not directly overhead, but is tilted as a function of the observer's local latitude. In the northern hemisphere it angles toward the south. In the Washington DC area, it makes an angle with the horizon of 52 degrees. Through the course of a year, the sun migrates around the celestial sphere. If it moved along the equator, there would be no seasons. But because the earth's axis is tilted with respect to its orbit around the sun, this requires another imaginary line on the imaginary celestial sphere, known as the ecliptic. On the longest day of the year (the summer solstice), the ecliptic is 23.4° higher than the equator so that the sun reaches 75.4° at high noon. At the winter solstice, the year's shortest day, the sun only reaches 28.6° above the horizon. At the vernal and autumnal equinoxes when days and nights are equal, the sun's path along the ecliptic coincides with the celestial equator and the sun reaches 52° elevation above south at the latitude of Washington.

    This is confusing and difficult to visualize. It may help to bear in mind that the equator line is related to the sky's daily rotation, while the sun moves on the ecliptic by only a short distance every day. The sun therefore moves across the sky on a path (almost) parallel each day to the equator, but displaced from it by a distance that varies slowly throughout the year. In this figure, which is meant to represent the sky, the sun is at its high point, the summer solstice. It rotates in one day on the axis of the pole, parallel to the celestial equator. It does not rise in the east and set in the west, but cuts the horizon quite far north side of an east-west line, The sun's motion along the ecliptic takes a year to complete. When it has moved to the opposite side as shown in the diagram, its path will be very low and it will rise and set south of an east-west line through the horizon.

    The Tropics: Cancer and Capricorn

    The word "tropic" has an older meaning from which the present use is derived. What we call "the tropics" lies between two lines, the tropics of Cancer and Capricorn that when drawn on the surface of the earth represent the northernmost and southernmost points at which the sun can be found overhead on the longest day. The words derive from the lines drawn on a sundial (at any latitude) which represent the longest (and shortest) days of the year. The length of the shadow cast at a given time by a sundial's gnomon -- or any other shadow-- is a function of the season. It is longer in winter than in summer. The line that is traced out on the ground by the tip of a shadow from dawn to dusk has a different shape depending on the season and is called the "line of declination". If, on the summer solstice you were to plot the sun's shadow cast by the tip of the style (the nodus) on a sundial at short intervals over a full day, the line traced out crossing the hour lines would form a parabola. Similarly, the line traced out by the shorter series of shadows on December 21 is also a parabola, but faces in the opposite direction. These two lines were called "tropics" and on old dials are sometimes labelled the tropics of Cancer and Capricorn. These names come from the fact that they are traced out at the times of year when the sun is in the respective constellation.

    The Zodiac

    During the day, the stars lying along the ecliptic cannot be seen, but they are nevertheless there. The constellations near the ecliptic have a special status. There are 12 of them, which collectively make up the zodiac, which aside from their use in the newspaper astrology column, represent traditional star patterns in the night sky and hold official sway over 15° of arc each. At the summer solstice the sun enters the constellation Cancer. When it sets in the evening of June 21 along with (then invisible) Cancer, the constellation on the opposite side of the zodiac, Capricorn, will be rising into view. At the winter solstice, the sun is in Capricorn. The shadow traced by the nodus is the tropic of Capricorn, and as Capricorn sets at dusk, Cancer will be rising in the night sky. On the two equinoxes, March 21 and September 21, the nodus traces out a straight line.