For thousands of years, humans have used shadows cast by sundials to reckon the passage of time. Sundials measure the position of the Sun as it appears to move across the sky. For observers on different parts of the Earth, the Sun’s apparent motion is different. So depending on their location on the globe, sundials around the world must have their shadows and hour lines set up slightly differently. By observing the motion of sundial shadows around the world at the same time, an observer can get fantastic insight into the nature of planetary motion and our place in the Solar System. The Planetary Society is establishing a worldwide network of nearly identical sundials called “EarthDials.” Images from each EarthDial will be continuously updated and posted on the Web.
As your eye sweeps across the images on this page, the Sun’s shadow will sweep across the faces of the dials. Kids and grownups, classrooms and clubs, around the world will gain a palpable sense of how the Sun illuminates the round globe that is our Earth—and how the Sun’s passage across the sky controls time around the world.
At any moment, EarthDials from half of the world will be in darkness. The path that the Sun traces—and consequently the lines and curves on the faces of the EarthDials—will be very different from Scandinavia to Seattle to South Africa. And while the EarthDials will be made to a common pattern, each one will be decorated in the language and cultural motifs of its host.
The MarsDial A closeup of one of the flight MarsDials shows the gnomon in the center; it will cast shadows on the face. Credit: Cornell University / JPL / NASA
The EarthDials are designed to remind us of the MarsDials aboard NASA’s Spirit and Opportunity rovers that arrived at Mars in January 2004. The MarsDials and the EarthDials bear the common motto “Two Worlds One Sun” because it’s the same Sun that moves across the skies of Earth and Mars.
The EarthDial project will run at least for the duration of the rovers’ operational missions on the surface of Mars, from January through at least April 2004 (and, we hope, much longer). Here are plans and specifications so that you can be part of this exciting project by making your own EarthDial. There are many things in common for all the EarthDials, but also much opportunity to personalize your own.
To set up an EarthDial, there are three main tasks:
Build your EarthDial and decorate it according to your location on the Earth
Set up and align your EarthDial outside
Set up a Webcam to watch your EarthDial and serve its image every 5-10 minutes to your own Web server, where we can link to it from The Planetary Society’s central EarthDial website (If you cannot set up a Webcam, then you can still build and enjoy your EarthDial; please send us a photo of it and we will post it.)
Before you begin, you should first read the instructions all the way through, and make up a list of tools and materials you’ll need. As you proceed through the steps, refer often to the illustrations for guidance. When you begin, please also email us about your plans, including when you expect your EarthDial and Webcam to be operating.
If you follow these instructions carefully, your EarthDial will tell accurate time. The central EarthDial website will have links to all the active EarthDial Webcams. It will also host still photos of EarthDials without Webcams. Depending on response, it may be that only a limited number of EarthDial images can be highlighted on a world map on our website each week. Make your Dial well, so that it will be suitable for selection as one of the featured EarthDials.
Be careful when you measure! Distances should be measured to an accuracy of 2 mm or less. Angles should be measured to an accuracy of one degree or less.
II. Constructing your EarthDial
A. Some Vocabulary
An EarthDial is one of the oldest and simplest types of sundial, consisting of a vertical post, or gnomon, that casts a shadow on to a horizontal surface. You read the time and the date from the position of the center of the shadow of the marker (or nodus), in this case a sphere that is mounted on the top of the post. A network of lines on the dial face indicates the time of day depending on the position of the shadow. The lines consist of hour lines, which mark the time of day (in local solar time) and date curves, which mark the path of the nodus's shadow on special dates of the year (the solstices and equinoxes). The shape of the hour lines and date curves depends upon your latitude.
B. A Sample EarthDial
Here’s an example of what a EarthDial might look like when it’s done.
The following instructions will take you through the steps of building an EarthDial like this one. But you can build your EarthDial of any materials you want, so long as the final product is sturdy and weatherproof for at least six months, as well as meeting the specifications for the sundial design given below. You’ll have to lay out the dial, draw the hour lines and date curves, add the gnomon, and then decorate the dial according to your own location and language. Are you ready?
C. Summary of EarthDial Specifications
Your EarthDial should be constructed to the following specifications.
1. Consumable Materials
If you are unfamiliar with some of these items, just bring the list to your local hardware store. The most expensive item is the plywood, which should cost between $10 and $30 depending on its quality. The rest of the items will cost under $10—and could cost you nothing if you have a workshop to scrounge around in!
Plywood or particle board
The sample dial shown here is 86 by 86 cm. (about 34 by 34 inch).
The board can be square, round, or any other shape as long as it can contain an 80 cm (31.5 inch) diameter circle; a good thickness is about 12 mm (0.5 inch)
Sandpaper or sanding supplies
1 Stainless steel threaded rod, 9 mm (3/8 inch) diameter, about 20 cm (8 inch) long.
1 Stainless steel washer (same thread size as the threaded rod)
1 Stainless steel nut (same thread size)
1 T-nut, zinc plated (same thread size)
1 Small nail
1 Tube bathtub caulk (silicone sealant)
Black paint, exterior grade, or Black Felt-Tipped Permanent Markers
Light-shade paint, exterior grade, optional (for the background color)
Varnish, exterior grade, waterproof
White glue with water, or découpage adhesive
Paintbrushes and clean-up supplies
1 Ping-Pong ball (40 mm diameter is the modern international standard. The previous standard size was 38 mm; if you use an old ball, measure it to make sure of its size.)
Drill with a 9 mm (3/8 inch) diameter bit
Ruler with millimeter scale
Long straight-edge (use the ruler if it’s long enough)
T-square, right angle tool, triangle, or carpenter’s square
Circle-making compass or a reliable piece of string
Computer with access to the Internet, for determining the hour line angles (alternatively, you may derive the angles yourself using the equations in the Appendix)
Printer with paper, if you want computer-printed numbers and letters for your EarthDial
E. Lay out the Circular Base
Lay out the circular base
For all of the following diagrams, purple lines and text indicate construction lines; mark them lightly. Black lines and text indicate lines and text that will appear on your completed EarthDial.
Using a ruler, define the center (call it point G) of your EarthDial; it should be near the center of the base. Using a hammer, drive a small nail into the center point.
Using a ruler, mark two points on the base, one that is 40 cm from the nail and one that is 35 cm from the nail.
Tie a piece of string to the nail. Grasp the string and the pencil so that the tip of the pencil is at the 40-cm mark with the string stretched taut. Hold the string and pencil tightly so that the string doesn’t slip. Keeping the string taut, draw a circle with the pencil, using the string to keep its radius at a constant 40 cm.
Repeat the previous step, drawing a 35-cm circle.
If you want your base to have a background color other than the color of the wood, paint it first before you begin laying out the EarthDial markings. Inside the 80-cm diameter circle, the background color must be a light shade so that it provides good contrast to the black markings and to the gnomon's shadow. Outside the 80-cm circle, you can use whatever color you like!
How to install the T-nut
Drill a 9 mm (3/8 inch) hole exactly through point G. Make sure that this hole is straight and vertical. This hole will support the gnomon.
Turn the board over. Fit a T-nut into the hole, and pound it into place with a hammer. Be gentle at first to make sure it’s seated properly.
F. Lay out the Hour Lines
Take your time and be careful with your measurements. Distances should be measured to an accuracy of 2 mm or less. Angles should be measured to an accuracy of 1 degree or less.
Note: If you are nearer to the Equator than about 3 degrees of latitude, the following construction method will not work; send us an email to find out how to construct the lines.
The hour lines for your EarthDial will be unique to your latitude. Find the latitude and longitude of the spot where your EarthDial will be set up. For example, the latitude and longitude of Seattle, USA is 47° 41' (47.68°) North, 122° 21' (122.35°) West. You can find your latitude and longitude by inspecting a good map, or by visiting one of these websites:
Here are some examples of what EarthDials look like for different latitudes:
The diagrams for the rest of these instructions show a Northern Hemisphere dial. If you are instead in the Tropics or in the Southern Hemisphere, refer back to these drawings to remind you of the general appearance of an EarthDial.
Go to the EarthDial Calculator to calculate the hour line angles for your latitude. Alternatively, if you know trigonometry, you can calculate the coordinates on your own using the information in Appendix B.
Finding point "C"
The position of the gnomon, or vertical post, is at the center G of the circles. The hour lines will be drawn from a point C directly south (in the Northern Hemisphere) or north (in the Southern Hemisphere) of the gnomon position G. The distance CG depends on your latitude. When you set up your EarthDial, the line CG will be aligned exactly north-south.
Use the EarthDial Calculator to determine distance CG and mark point C on your EarthDial. (Note: if your latitude is less than 14°, point C will plot off the face of your Dial. You can lay the Dial out on the floor and mark point C on the floor in order to do your measuring.)
Lay out the hour lines
From point C, draw in all of the hour lines by carefully measuring their angles B (from the Table). The hour line angles are the angle between each hour line and the north-south (or noon) line. The hour line angle is identical for the same number of hours before or after noon. For instance, the angle will be the same for 11 am and 1 pm, and for 9 am and 3 pm. The 12 noon line is due north-south, so it will also pass through point G, and the 6 am – 6 pm line is due east-west. Because the Sun’s shadow falls opposite to the Sun’s direction, the morning hours are on the west side of the dial, and the afternoon hours are on the east side. Sundials were invented in the Northern Hemisphere. Their shadows go clockwise, and that’s why, to this day, our clocks run clockwise.
G. Draw the Date Curves
The EarthDial Calculator also gives you the information you need to draw date curves on your EarthDial:
Date curves show the graceful track of the ball’s shadow across the face of the dial on four special times of the year: the summer and winter solstices, when the Sun is highest and lowest in the sky, and the autumnal and vernal equinoxes, when the Sun tracks a great circle and is, for observers near the Equator, directly overhead at noon. If you wish, you do not need to draw these Date Curves, but the hour lines are essential.
If your latitude is between the Arctic and Antarctic Circles, the date curves are hyperbolae. You can draw these hyperbolae using the information provided in the EarthDial Calculator. The Calculator gives you three distances along each hour line from point C: the first (CS) is for the summer solstice line, the second (CE) for the equinox line, and the third (CW) for the winter solstice line (see the diagram below).
Lay out the date curves
Note: Depending on your latitude, some of these curves will not fall within the 70-cm inner circle of your EarthDial. If you are farther north or south than 50° latitude, the winter solstice line will fall outside the circle. If you are inside the Arctic or Antarctic Circles, the summer solstice line (and all date curves) will be an ellipse.
Plot the distances CS, CE, and CW along each hour line. Make sure that you carefully measure each distance along the hour line from point C.
Once the points are plotted, connect them with three smooth curves. Terminate all of the date curves at the inside of the ring.
Notice that for any EarthDial anywhere in the world, the equinox line runs due East and West. If the points you plotted for your equinox positions don’t lie in a straight line running exactly East and West, you’ve made a mistake somewhere.
H. Mark and Decorate Your EarthDial
1. Darken the pattern
Darken the pattern
On bare wood, you can use a black felt-tipped marker to darken the lines. Otherwise, you can use black paint. Making the lines by hand with paint can render the lines distinct and handsome.
The finished hour lines should be drawn only between the solstice lines. If your EarthDial has only a summer solstice line (if you are farther north or south than 74° latitude), the hour lines should extend from that summer solstice line to the inner circle.
In order for your EarthDial to be legible through a Web camera, make sure of the following:
All of the lines should be black.
The two large circles making up the outer ring should be drawn in a line about 2 mm thick.
The hour lines and date curves should be about 4 mm thick.
2. Add text to the EarthDial
You can either do this by hand with paint or markers, or print the numbers and words on your printer and glue them to the EarthDial’s surface with white glue or decoupage adhesive.
Add the hour numerals
The hour markings are for local solar time; thus, local solar noon (labeled 12) is the hour line running from point C exactly north (in the Northern Hemisphere) or south (in the Southern Hemisphere); time increases clockwise in the Northern Hemisphere and anti-clockwise in the Southern Hemisphere. (When clocks were being developed in Europe during the Middle Ages, why do you think they chose to have the hours on the clock face increase in one particular way?)
Write the hour line numerals 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, and 6. The numerals should be at least 3.0 cm high in order to be legible through the camera. Write them in an arc near the outer ring of your Dial, or, if there is room outside your winter solstice line, just along the outside of that line.
Place the motto “Two Worlds One Sun” in the southern portion of the outer ring, in your own language, in black capital letters at least 3.5 cm high. Examples: English is TWO WORLDS ONE SUN; Dutch is TWEE WERELDEN ÉÉN ZON; French is DEUX MONDES UN SOLEIL.
Place the phrase “EARTH 2004” in the northern portion of the ring in your own language, in black capital letters at least 3.5 cm high (e.g. English is EARTH 2004; Dutch is AARDE 2004; French is TERRE 2004). If you wish to use your culture’s own date (e.g., Islamic, Jewish, or Chinese), please do so. The date should correspond to January 4, 2004 when the first of the two Mars Exploration Rovers (Spirit) arrived on the surface of Mars.
Add the text
Write the name of your town and country in English in black capital letters at least 3.0 cm high just to the south of point C (if in the Northern Hemisphere) or to the north of C (if in the Southern Hemisphere). For example, if your EarthDial is located in the Italian city known in Italy as “Milano, Italia,” this portion of the dial should be labeled with the English usage: MILAN, ITALY. For opportunities to use your native language elsewhere on the design, see below.
Write the latitude and longitude of the EarthDial in English in black letters 3.0 cm high, just below the name of the location, with the latitude on top. Use the following style:
47° 41' N 122° 21' W
3. Add Optional Features
Add any desired artwork to the areas outside the circles, or in the empty area to the south (Northern Hemisphere) or north (Southern Hemisphere) of your summer solstice line. The diagram below shows gray areas where you may add decorations.
Add optional features
This artwork can be of any design and any color. We especially ask for images and designs reflecting your local culture. Or you could put in further information about the location and circumstances of your EarthDial. You have complete freedom as to what to include here – be creative! Examples include your location in the local language and alphabet, builders’ signatures, the institution or group that constructed the dial, etc. Make the EarthDial your own! The EarthDial design standards are minimal to allow for creativity. You should not, however, add 3-dimensional features that might cast shadows onto the dial, nor decorations that obscure or confuse the key information on the dial (hour lines, date curves, hour markers, and location information).
You can add secondary labels on the hour lines. These might depict Daylight Saving or Summer Time, as they do in our example EarthDial, or you could add numbers in Roman numerals or your language’s numerical system or alphabet. These numbers should be placed near the southern ends of the hour lines (or northern ends if your EarthDial is in the Southern Hemisphere), but not too close to point C. These numbers should be at least 3.0 cm high and black.
You could also add a small mirror (perhaps 10 cm square) to the outer edge. The reflection in this mirror will indicate the blue sky or clouds above, just as small mirrors of polished aluminum do for the reddish Martian sky on the MarsDials.
You can also draw extra hour lines that depict important times during the day (for example, the start and end of the local school day!)—but don’t forget that the local solar time shown on the dial will differ from your clock time. You could also add in extra date curves for special days of the year—your New Year, Independence Day, or first and last days of school. To add your own hour lines and date curves, you will have to calculate their positions using the equations in Appendix B. If you do add extra hour lines and date curves, distinguish them from the solstice and equinox lines by making them thinner than 4 mm. You might also make them a color other than black.
4. Final Finishing
When you are done with your artwork and decorating, weatherproof your EarthDial with a coat or two of varnish.
The center of the gnomon should be 8 centimeters above the board
Cut the threaded rod so that it will support the center of the Ping-Pong ball at exactly 10.0 cm above the EarthDial’s surface. Accuracy is extremely important in this step. In the sample Seattle EarthDial, the rod is 13.5 cm long. This allows for the rod to touch the top of the inside of the ball and penetrate the surface of the board by about 1.5 cm.
Poke or drill a hole into the Ping-Pong ball that is big enough for the threaded rod to fit through.
Squirt a few spoonfuls of silicone sealant into the ball, and fit the ball onto the rod.
Let it cure for as long as the instructions on the silicone sealant recommend.
When it has cured, paint the ball black in order to prevent the Sun’s ultraviolet light from damaging the ball.
Mount the threaded rod into the T-nut in the center of the Dial. Turn the rod in or out until the ball’s center is exactly 10.0 cm above the EarthDial’s surface. Make sure that the gnomon is exactly vertical. Lock it in place with the nut and washer. If you are using a standard sized (40 mm diameter) Ping-Pong ball, the bottom of the ball should be exactly 8.0 cm above the surface. Again, it is very important to mount the gnomon accurately.
And now, step back and gaze upon your beautiful EarthDial!
Find a site for your EarthDial where it will not be subject to vandalism or inadvertent misalignment. It must be able to stay in place 24 hours a day in all weather from January through at least April of 2004 (and, we hope, longer).
Make sure there is space on the south side of your EarthDial for a camera mount.
The EarthDial must be located where the Sun will shine on it for as much of the middle of the day as possible, from January to June 2004. The more sunlight hours, the better. In the Northern Hemisphere this means having a good exposure to generally southern directions, that is, no nearby trees or buildings blocking the sky from the southeast through the southwest. In the Southern Hemisphere, the good exposure needs to be to the North.
To help gauge shadowing problems, Table A shows the maximum altitude angle of the Sun (when it is due south in the Northern Hemisphere, or due north in the Southern Hemisphere) for early January and late June. An altitude angle of 90° means that the Sun is straight overhead; 0° means that the sun lies on the horizon. Remember that these are the maximum altitudes (at noon); the Sun will be at lower and lower altitudes as one moves away from noon. You can see that the altitude angle of the Sun depends very much on your latitude!
Table A: Maximum Altitudes of the Sun
B. Align Your EarthDial
Any sundial, if it is to read correctly, must be leveled and aligned north and south. This must be done very precisely! Each degree that it is misaligned will lead to about a 4-minute error in telling the time.
Level your EarthDial. First, make your best guess as to the proper alignment of your EarthDial, then use a carpenter’s level to check its level. Use wooden or metal shims to make the Dial level. Make sure that your EarthDial does not wobble and that the base is sturdy.
There are three main techniques for alignment, listed below. The magnetic compass technique is least accurate and the gnomon technique is most accurate. If you have to shift the EarthDial significantly in order to align it, it may have gotten out of level. Recheck the level when you’re done.
1. Use a Magnetic Compass
This will get you roughly aligned, but you need to have a good quality compass (larger faces are better), have a locale with no metal nearby (buildings are full of steel), and know the number of degrees by which magnetic north or south (which the compass indicates) deviates from true north or south (the direction to the North or South Pole) at your location. This difference is called the magnetic declination and can be found at this website:
At that exact time, rotate your dial to the correct hour line. To make sure it’s positioned correctly, check by repeating with a different hour on a different day.
3. Use the Gnomon
This method is elegant and very accurate. It works because the Sun makes an apparent path across the sky that is perfectly symmetric around solar noon, the moment when the Sun is highest in the sky.
Cover the dial face with a piece of paper and let the shadow of the gnomon fall on it. Track the location of the tip of the shadow over about 3 hours, starting at roughly an hour and a half before solar noon and continuing until an hour and a half after solar noon (solar noon is roughly 12 noon Standard Time or 1 pm Daylight Saving Time).
Carefully mark and measure the length and direction of the shadow at a time roughly an hour and a half before local solar noon. The exact time isn’t important, but carefully measuring the length of the shadow is; measure to the center of the ball’s shadow. This is your reference shadow length. As time passes (bring a book!), the shadow will shorten as the Sun moves higher in the sky. After solar noon, the Sun starts down, and the shadow lengthens.
Keep track of the length of the shadow relative to the reference shadow length. You can do this by tying around the gnomon a string whose length equals your reference length (but be careful not to stretch the string by pulling too strongly). As the shadow begins to approach the reference shadow length, mark the length of the shadow every couple of minutes. Once the shadow has lengthened past the reference shadow length, you can stop marking.
Find the point that most exactly matches the reference shadow length. Finally, draw a line that bisects the angle between those two shadow directions. You now have a true north-south line! Keep in mind that the two corresponding times are equally before and after solar noon, not clock noon. Making a graph of shadow length versus time is useful. The more pairs of points you measure, the more accurately you will determine a true north-south line.
In order for all of the EarthDials to have a consistent appearance on the website, the Web camera must be on the south side of the EarthDial, aiming north. Regardless of which hemisphere you’re in, have your camera point north. When picking your EarthDial’s location, be sure to make room for a camera mount on the south side.
Design your Web camera mount so that it casts the least shadows possible. This will not be a problem for Southern Hemisphere cameras, but camera mounts in the Northern Hemisphere will often cast shadows on the EarthDial faces. The example below shows a Northern Hemisphere mount that does not cast a shadow; the yellow Webcam is pointed at the dial from the south side.
Because the Web camera will be located outside, it must be weatherproof. The following instructions are one way you can set up a weatherproof Web camera.
Ideally, the camera should be able to run 24 hours a day (or at least from before sunrise to after sunset).
Computer with access to the Internet and a fixed IP address or domain name
A Web Camera. Any type that is compatible with your computer will work. A USB camera is much better than a parallel port camera because it will be able to draw power through its cable, and the cable end is small. A wireless camera has no need for a cable from indoors to outdoors, but requires batteries that need to be regularly checked.
Extension cable to connect the Web camera with the computer. If you have to run the cable very far, you may need to place USB hubs along the route to boost the camera’s signal.
Tripod or other mounting post to hold the camera. The mounting system must be weatherproof.
Square water-tight flashlight (torch), the type that would float if it fell overboard from a boat. The flashlight body must be large enough to hold the camera inside.
Stainless steel screw, nut, and washer for mounting the camera to the tripod or other mounting post.
Material to secure the camera, for example adhesive tape, bits of foam padding, etc.
Utility knife or drill for making a hole in the flashlight body.
B. Install your Web Camera and Serve it over the Internet
Follow the camera manufacturer’s instructions to install and set up the camera on your computer.
Set up the Web camera so that it captures and saves an image on your Web server at least every five or ten minutes. This saved image should always have the same filename and should be accessible over the Internet; it should also have the clock time and date "stamped" on it (most Webcams allow for this). This image will be linked to from The Planetary Society’s central EarthDial website. Most Web cameras today come with software and instructions for doing this. If you have an older camera, you may need to consult the manufacturer’s web site, or your computer’s operating system web site. You can do it.
C. Weatherproof your Web camera
A weatherproof Webcam enclosure
The waterproof flashlight body will be used as an enclosure for your camera. The handle will be mounted to a tripod.
Remove the clear window, its mounting ring, the battery, the bulb, and the reflector from the flashlight.
Cut a hole with a knife or a drill on the underside of the flashlight body for the camera’s wire to exit.
Drill a hole in the handle of the flashlight, so that it can be mounted to something upright and stable, like a tripod. On most floatable flashlights, the handle is designed so that it is not part of the water-tight battery and bulb compartment. You can modify it without losing the integrity of the enclosure.
Attach the flashlight body to the mounting post or tripod using a stainless steel screw, nut, and washer.
Cable hub in a bag
Thread the camera’s cable through the hole you cut in the underside of the flashlight body. Settle the camera inside and secure it in place. We secured one with an old pencil eraser (rubber) and some double-stick adhesive tape. It doesn’t take much, just something to take up the space around the camera, keeping it immobile. Seal the wire to the body of the enclosure with bathtub caulk.
Secure a route for your cable to run from outside, where the camera is, to the inside, where your computer is. You may need to add USB hubs along the cable to boost the camera’s signal. Seal the electrical connections in plastic bags and tie them tight. A good technique is to mount the connections above the cable run so that water drips down off the connections, rather than running along the cable and into the connections.
D. Set Up the Camera to View Your EarthDial
Set up the camera on its mount outside so that it can see the EarthDial. The camera must be looking at the EarthDial from the south.
Set up the Webcam
Mount the camera so that its look-down angle is at least 30° below horizontal; steeper is better. Mounting the camera directly above the dial and pointing it straight down is acceptable.
Let the world see your dial and, if possible, not your tripod or camera mount or its shadow. At right is an example camera mount for the Northern Hemisphere that does not cast a shadow on the face of the Dial.
Aim and zoom the camera so that the Dial takes up the entire field of view (see the illustration).
Observe the camera image and, if necessary, adjust the focus. Most cameras adjust for the light level automatically.
Once everything is set up, let us know the URL for the Webcam images so that we can link to them from the EarthDial website. You have now joined the worldwide EarthDial community!
Over the succeeding weeks and months, frequently check your EarthDial’s physical and electronic setup to make sure it’s serving good quality images all day long, day after day.
Send us some text (less than 500 words) with information and links about your organization, your town, your culture, your philosophy of time and timekeeping, ideas about space exploration, or anything else you think might be of interest to visitors to the EarthDial site. The text should be mostly in English. We can only post statements using the Latin (Roman) alphabet (that is, the alphabet that is used for English). Email your text to email@example.com.
Try combining images to make an all-day "movie" showing the shadow sweeping across the dial face. Make such a movie at one-month intervals and notice the different tracks.
A. Converting Between Sundial Time and Clock Time
Many would say that sundial time is truer and provides more insight into the nature of our world than our artificially constructed clock time. A sundial indicates local solar time, which is time measured by the Sun at a given location; in general, this time differs from clock time. For example, it is local solar noon when the Sun is highest in the sky. At local solar noon the Sun is generally due south for observers in the Northern Hemisphere, or due north for observers in the Southern Hemisphere. Between the Tropics of Cancer and Capricorn, however, the noontime Sun is to the south on some dates and to the north on others (depending on the latitude).
If you wish to read clock time with your EarthDial (or any sundial), there are three adjustments you need to make:
1. Adjustment for Location Within Your Time Zone
The Earth’s rotation causes the Sun to appear to move from east to west. So the Sun arrives on the eastern edge of a time zone long before it arrives on the western edge. Consider Seattle, which keeps Pacific Standard Time (PST) on its clocks. At Seattle’s latitude, the two edges of the Pacific Time Zone are over 800 kilometers apart. When sundials on the eastern edge correctly read 12:30 pm, sundials on the western edge (also correctly) read 11:30 am. The sundials differ by an hour, while everyone’s watch in the Pacific Time Zone reads exactly 12:00 noon. Yikes! Imagine two people at the Pacific Time Zone’s edge. They are shaking hands and admiring a sundial correctly telling local solar time, while their watches disagree by one full hour. (In a sundial-admirer’s sense, the sundial is the only trustworthy timepiece available.) We need a rule to compensate for the width of time zones.
The Rule. For every degree of longitude you live west of the center of your time zone, add 4 minutes to the sundial reading to adjust to clock time. If you live east of the center, then subtract 4 minutes for each degree.
Most time zones are one hour or 15 degrees of longitude wide. With 60 minutes in an hour, it thus takes 4 minutes for the Sun to sweep through 1 degree. Seattle is at 122.3° West longitude, so dials in Seattle are 2.3° x 4 = 9.2 minutes behind clocks and watches. One should add 9.2 minutes to the dial reading.
You can find the center longitude of your time zone by noting how many hours your clocks are ahead of or behind Greenwich Mean Time GMT (also called Universal Time), where longitude is defined to be 0°. For each hour that you are ahead of (behind) GMT, the center of your time zone is shifted 15° of longitude to the East (West). For example, PST is 8 hours behind GMT, and thus its center longitude is 120° West. For another example, India Standard Time is 4.5 hours ahead of GMT, and thus its center longitude is 67.5° East.
2. Adjustment for Summer Time
If Daylight Saving Time (Summer Time) is in force, add one hour to the sundial time to get clock time.
3. Adjustment for the Non-Uniformity of Solar Time
We have created clock time so that it proceeds absolutely uniformly - a second is a second, an hour is an hour, day after day after day. But the rate of solar time turns out to be slightly variable. The interval from one solar noon to the next averages exactly 24 hours over a year, but it can be as much as 30 seconds longer or shorter on any given day. This behavior of the sun’s apparent motion is caused by the slight non-circularity (1.7%) of the Earth’s orbit and by the famous 23.4° tilt of the Earth’s rotation axis. The net effect is that dial time can differ as much as 15 minutes from clock time (even if you are at the center of your time zone). This adjustment is called the Equation of Time. This is an old usage of the word “equation”; think of it as equating one system of time to another. The required time to add or subtract for each day of the year is given at this website:
Be careful to make this adjustment with the correct sign; “dial slow” or “sun slow” means that sundial time lags behind clock time.
B. Equations for Hour Lines and Date Curves
1. Distance CG
The hour lines will be drawn from a point C directly south (in the Northern Hemisphere) or north (in the Southern Hemisphere) of the gnomon position G. The distance CG depends on your latitude and the height of the gnomon. The distance CG is given by
CG = (gnomon height) / tan(latitude)
The EarthDial gnomon is 10 cm tall.
2. Hour Lines
The angle B of an hour line that is H hours before or after noon is given by
tan B = sin(latitude) x tan(H x 15°)
Example: for a latitude of 30°, the angle of the hour line for both 11 am and 1 pm (H = 1 hour), measured with respect to the noon (north-south) line, is B = 7.6°. For H = 6 hours, the value of B is 90° for all latitudes.
The hours always increase from west to east, regardless of the latitude, with the result that in the Northern Hemisphere, the shadow moves clockwise during the course of the day. In the Southern Hemisphere, the shadow moves anticlockwise during the day.
3. Date Curves
Date curves are drawn for special dates of the year: the equinoxes, when the solar declination D is 0°, and the solstices, when the solar declination is ±23.4°.
For each value of H, define F to be
F = tan-1 [ tan(latitude) / cos(H x 15°) ] ,
and define R to be
For each value of H, calculate R for solar declinations D of –23.4° (December), 0° (March and September), and +23.4° (June).
These values of R are the distances along each hour line, measured from point C, to the intersection points with each date curve. The summer solstice curve lies closer to point C than the winter solstice curve. The equinox curve will lie in between and will be a straight line. If you want to draw a date curve for some other special date, first find the solar declination for that date at this website: