The Equatorial Sundial

Although most of us look at our smartphones or smartwatch to tell time, humans have needed reliable ways to measure the time for millennia. At first, we needed to be able to track seasonal changes to understand migration and food. Later we needed to allocate time over the day to define periods of study, prayer, and work. The first examples of calendars date back to about 30,000 years ago. However, the concept of a clock is much more modern - dating to about 500 BCE. These first clocks were Sundials, first developed by the Greeks and then adopted by the Romans. The entire basis of time-telling is astronomy. The annual motion of the Earth around the Sun defines a year, and the daily motion of the Earth rotating on its axis defines a day. Although you can estimate the time just by looking at the sky (and a lot of practice), Sundials were created to break the day into 12 well-defined segments. In Medieval Europe, Sundials were used to set the times for prayer at churches and monasteries. Other inventions such as water clocks, sandglasses, and candle clocks were used on cloudy days and at night, but these other time measurements referenced the Sun's daily motion. The development of mechanical clocks in the 1300s and 1400s eventually replaced Sundials, but they remained popular in the Enlightenment in the 1700s. The Sundials built into the architecture of buildings are visible across Europe.

In this project, I will show you how to build an equatorial or "armillary" sundial that can be mounted in a garden or backyard. This project is an original design inspired by various sundials I have seen in my travels. The basic construction of the project was made using my CNC machine, but other tools such as a bandsaw or saber saw could be used instead. I have included the CNC SVG files, but you may wish to modify the design for your project. In addition to the CNC machine, I used my 3d printer to create the Roman numerals for the dial, various drills, sanders, rasps, and saws to trim the wood, and my router table to clean up the edges of the laminated equatorial ring.

Before I built this project, I had never tried to create bent wooden pieces for a project or used veneer to make laminated pieces. The jigs I built for this could be modified and used for a variety of other projects for indoor and outdoor furniture.

Supplies

1/4 sheet of 3/4 inch furniture grade plywood

1/8 sheet of 3/4 MDF

10 sheets of 1/16 inch veneer - approximately 36 inches long by 8 inches wide

1 brass tube - 1/4 inch diameter

Roman numerals for the hours of the day (or a 3d printer to make them)

stain, finishes, glue, sandpaper

Step 1: Sundial History and Designs

Perhaps the best way to understand the daily motion of the sun is by exploring it from two perspectives. These two links are a great place to start. The Coordinate System Explorer and the Sun Motion Simulator created at the University of Nebraska Lincoln Astronomy Department let you how the sky moves because of the daily rotation of the Earth. Using the first link to the Coordinate System Explorer, you can change your location on Earth and see how the constellations and stars change appear to move. The Sun Motion Simulator link allows you to also change the date you are observing the Sun and then view the effect of the seasonal variation of the Sun's motion caused by our orbit and the tilt of the Earth's axis compared to its orbit. Both of these excellent simulations use Flash, you may need to enable this for your browsers to get them working.

Sundial designs are based on the fact we live on a uniformly rotating sphere. Basically, the device needs to model map the Sun's motion onto a readable dial. Most sundials do this by the use of a shadow stick or "gnomon". If we were located at the North Pole, we could have this gnomon pointing straight up and it would be perfectly aligned with the rotation axis of the earth. We could also use evenly spaced marks for the hours.

Since most of us do not live at the North Pole, we still need our gnomon to be aligned with the Earth's rotation axis. We align our gnomon by tilting it toward the North with an angle above the ground that is equal to the latitude. Using this basic design, we can then project the location of each hour of daylight to a flat surface using some simple trigonometry. However, if we a ring for our dial instead of a flat surface, the hour marks become evenly spaced. This design is known as an equatorial sundial. It is alternatively known as an armillary sundial since the design is based on a model of the star's motion know as an armillary sphere.

I've seen visited numerous sundials across England ranging from beautiful dial at Oxford University's All Soul's College to the more complicated vertical declining dial at Green Templeton College. There is even a self-guided Sundial tour of Oxford for those interested. The equatorial dials were always the most striking to me, so I wanted to put one in my wife's garden. I kept getting stuck on the design elements. The design I created was prompted by the Instructable's Clocks contest. The final project is temporarily mounted in our garden on a small table until I can get to the hardware to make a permanent mount for it

Step 2: Creating the Equatorial Ring

In most sundials, the gnomon (or shadow stick) casts its shadow on a horizontal or vertical dial plate. For equatorial sundials, the shadow falls on an equatorial ring that is parallel to the equator of the Earth. For this design, we need to create a curved plate. It needs to be relatively thin but strong. For my project, I decided to make this sundial out of wood as an aesthetic choice, but it did introduce some challenges. Some outdoor finishes will protect the dial, creating the curved pieces was challenging. I looked at two possible options - bending wood and laminating wood along a curve. Though bending wood results in strong pieces, I was concerned about how much spring back I needed to plan for in the piece. Without a lot of experimentation, I didn't think I would be able to control for this factor.

I opted instead to use the lamination of veneer strips as the basis for the equatorial ring. The first step in this process is creating a form to use to hold these pieces. Since I have a CNC machine, I designed a 15-inch radius form to hold the pieces together. The design goes about 30 degrees past a half circle to allow room for gluing and trimming the final piece. I decided to make the dial plate 2.25 inches wide, so I cut three pieces from 3/4 inch MDF and then glued them together. I put alignment holes in the CNC design to help put this together. I cleaned up the cuts with a rasp, and I was ready to glue to put the laminated strips in place.

I quickly realized that I needed a way to cut strips of wood inlay with equal widths. I put together a simple jig to hold the inlay pieces so they could be cut on my table saw. A metal miter track was bolted to the bottom of a piece of 3/4 pressboard so that the board overlapped the location of the table saw blade. I ran this through the saw, creating a jig with an edge that precisely aligned with the blade.

Put the pieces of inlay on this jig so that they would be cut to the designed width. You need to account for the table saw blade's width, but aligning them is a pretty easy process. Once the pieces are positioned in the right place, you screw a 1x1 piece of scrap wood in place to sandwich the inlay strips and to hold them tightly to the jig. You can use some small strips of material to make sure the fit was tight along the jib. From there, you can run the jig through the table saw to cut your strips. For the project, you want the pieces to be about 1/8 to 1/4 inch wider than the form you created. You will trim the excess after the glue-up so you have a clean edge.

Once you have cut ten strips of inlay, gluing up the dial plate is relatively easy. You will need to work quickly - and it does help to have slow-drying glue. You add glue to each of the strips and then put them sandwich them together. From there, you need clamping the pieces to the form, starting from one side of the form. Move inch-by-inch along the form, adding more clamps as you go to secure the bent inlay. When it looks like a post-modern porcupine, you are probably close to done. Using a band clamp or other clamping devices would probably work well in this step as long as your inlay strips aren't too long. I realized my mistake after I started the glue-up, so I ended up using my entire clamp supply in this stage of the project.

Once the glued strips are completely dry, you can remove the clamps. I would suggest you wait for at least 24-hours before you proceed to the next step. When you remove the clamps, you can examine the piece you just created. I probably will have some rough edges and be slightly uneven. First, gently trim the ends of the piece using a saw. I used my scroll saw at a slow setting for this step. Now, reattach the laminated piece back onto the form using a band-clamp. You are going to trim the edges of the piece using a flush-cut bit router on your router table.

Trimming the edge on a curve piece like this is tricky, so be very careful about setting the fence on your router table to take only a tiny amount of the material at a time. You shouldn't try to trim more than about 1/16 of an inch per pass. When you are cutting the piece, the bearing on the flush-trim bit should touch the MDF jig, and the fence should provide additional support. Slowly rotate the piece across the flush-cut bit using the router table and the router table fence as reference planes. Adjust the router fence, and then repeat. After several passes, your laminated piece will be trimmed to exactly the size of your form.

I consider trimming the laminate using a hand-held laminate router. After a few experiments, I found I didn't have the precise control I needed to do this without chipping the laminate pieces.

Once all the edges are trimmed, you can put this piece aside and move to the next phase - the verticle structure of the sundial known as the meridian ring.

Step 3: Building the Meridian Ring

The meridian ring of the sundial is a vertical piece that holds the gnomon and equatorial ring in place. I wanted it to be solid and sturdy to contrast the lighter equatorial ring.

To create this piece, I used my CNC machine to carve to mirrored pieces from furniture grade 3/4 inch plywood. The parts have a notch that will hold the equatorial ring in place and holes to make the location where the gnomon will be eventually attached. You will need to drill the actual holes for these later.

You are very welcome to use the meridian ring from my sundial for your project, but you may wish to customize this piece. The critical thing to note is how a sundial is tied to its latitude. The angle of the gnomon should be precisely equal to the latitude of the location of the dial. The equatorial circle should be tilted by 90 degrees to this angle. Since my latitude is 35.8 degrees, the angles of the gnomon and the equatorial plate are set for this location. If you are only a few degrees off, you could just tilt the based of dial by a few degrees to adjust the gnomon is at the correct angle. Being off by a few degrees won't make a huge impact on the accuracy of the dial, but part of the fun of the project is having something customized for your location.

Carving the piece is straightforward on the CNC, but there were some rough edges on the cut because we are using plywood. I used a rasp and some sandpaper to clean them up. I glued the two pieces together and let them dry with clamps holding them in place.

Because CNC machines use cylindrical bits to cut a design, they cannot cut tight interior corners accurately. To use a carved pocket to join a piece of wood, you need to either use "dog bone" cuts or just clean up the cut with a chisel. I opted for using a chisel to keep the grove clean. I simply removed the extra wood in the back corner of the joint. When the groove was close to being square, I did a trial fit between the meridian ring and the equatorial ring. I adjusted the cut as needed to ensure the equatorial ring fit snugly in the pocket.

The plywood edges on the glued piece still looked unfinished. I cut additional veneer strips to just over 1.5 inches in width using my table saw jig. Putting veneer on these curved surfaces was a bit difficult. I couldn't use a band clamp because it wasn't a simple convex surface. I had to resort to ordinary bar clamps to hold everything in place.

When you are done, all the unfinished surfaces will have veneer strips covering them. You can use a combination of Exacto-knives and sandpaper to trim the excess veneer. Cutting the edges is a slow process and, unfortunately, resulted in a few flaws on the surface of my project. However, my overall result was satisfactory.

The next step is to make the base of the Sundial to hold the meridian circle.

Step 4: Building the Base Plate

I used my CNC machine to carve the base plate. The design is simple - a 15-inch radius circle with two rectangular holes in the middle. These rectangular holes fit the feet of the meridian circle piece. As in the previous step, you need to use a chisel to square the corners to ensure a good fit. I made a test piece with just these dado holes to make sure everything would fit snugly and securely in the final assemble. You also need to use a rasp to clean the outer edge of the carve.

At this point, you can dry-fit the meridian circle, the equatorial ring, and the base plate together. Don't use glues or screws to secure it until you have done any preliminary finishing and added the numbers.

Step 5: Final Touches

The final steps to assemble the sundial are pretty easy.

1. Begin the finishing process by sanding the pieces down to at least 400 grit paper. Using a tack cloth, clean up the dust leftover from the sanding.
2. For the meridian circle, I decided to use a darker stain to accent the piece. I used two coats of a simple wood stain to get to a uniform color. I waited about 4 hours between coats, and then let the final coat dry for 24 hours.
3. Create a strip of material to cover the edge of the base. Since the base is made of a single piece of 3/4 plywood, use the table saw veneer cutter jig to make one or two strips to go around the circumference of the circle. I stained the veneer before I applied it. Gluing the veneer in place was relatively easy. Masking tape holds the pieces in place while a band clamp to apply pressure to the circumference.
4. Seal the equatorial circle before adding the roman numerals. I used spray-on shellac for both the equatorial circle and for the base plate. I sprayed three coats for each, allowing about an hour between the coats. I also put three coats of shellac on the stained meridian circle after it was completely dry.
5. Print out a set of roman numerals on your 3d printer. I made the very simple design in Fusion 360. They have a vertical size of 1 inch and a thickness of 0.1 inches. I decided to use a copper color filament for the numbers. Since I hadn't used this kind of plastic before, it took a few tries to dial it in. The final filament temperature for my particular filament and printer (a Prusa MK3) was 200C with a bed temperature of 60C. Because the plastic didn't adhere well to the bed, I used the Brim setting to help "tack down" the pieces. Although the resulting numbers weren't perfect, I was very happy with the results. Given the stay at home orders, going to the local hobby stores to purchase better numbers wasn't a possible choice.
6. Once the shellac on the equatorial circle has dried for 24 hours, glue the numbers in place. The roman numeral XII should be at the midpoint on the piece. Because this is a 15-inch circle and each hour of the Earth's rotation changes the angle by 15 degrees, the spacing between the centers of the numbers should be 1.96 inches. I used a ruler and made some pencil marks at the centers of each of the numbers. I glued the pieces in place using a cyanoacrylate glue with a bottle of accelerant to make sure the pieces dried in place.
7. Drill a hole for the gnomon through the top of the meridian circle and halfway through the bottom of the meridian circle. The holes should be aligned so the brass gnomon fits cleanly through the top hole and feeds into the bottom hole. The drill marks from the carve were put in place to help guide you through the process. However, you can always go back to the plans to find the location. I used a meter stick to help me visualize where the hole was and an electric hand drill to do the drilling.
8. Cut the bass tube to the right length for your gnomon. I decided to let the top of the tube go past the top hole in the meridian circle. Although this is often done as just a design choice, it is not required. I used a hacksaw to do trim the piece. Using 400 grit sandpaper, I cleaned up the tarnish on the rod to make it look shiny. The gnomon is placed through the hole. I will probably use epoxy glue to seal up the holes before the final finishing coats to keep water from seeping into the wood.
9. Once all the glues and finishes are dry, assemble the Sundial. Do a final dry fit to make sure the pieces all fit together. Be sure the roman numeral XII on the equatorial circle is directly aligned with the center of the meridian circle. After you have double-checked the fit, apply glue to the surfaces then clamp the assembly in place. You may wish to use screws to hold the assembly together as well.
10. Apply your final finishing coats to the assembly. I recommend using a weather-resistant poly finish designed for outdoor furniture.

Now we are ready for the final assembly step - installation.

Step 6: Installation

Installing the Sundial is straight forward. In my wife's garden, I put the dial on a small outdoor coffee table in the flowers. You need to find level the base plate and make sure the gnomon is pointing toward true north. If you use a compass to align the dial, you should be aware of the differences between magnetic north and true north. For most of North America, the magnetic declination is just a few degrees. However, there is a helpful calculator here if you want to be more accurate.

As an alternative, you can align the gnomon with Polaris - the North Star. The gnomon should point directly at Polaris since this star is located almost exactly above the Earth's North Pole.

When you look at the dial, you might be disappointed in how accurate the time is. In the last step, we will talk about the differences between solar time and mean solar time, and how to account for these differences.

Step 7: Telling Time With Your Sundial

Even if you have perfectly aligned the sundial in your yard, you will notice the time you see on the dial is not the same time that is on your watch. The reason this happens is because of the conventions we now use to measure time.

As mechanical clocks were perfected In the 1800s, most countries moved away from the local solar time to mean solar time. Mean solar time is based on mechanical and digital clocks. Each hour is the same, and there are 24 hours in a day. Because the Earth follows an orbit that is slightly elliptical, we move a bit faster in our orbit when we are closest to the sun in January. The effect of this changing speed is the length of the solar day changes during the year as measured by accurate mechanical and digital timepieces. The differences are subtle - only about 20 seconds per day. However, the effect of these changes accumulates. At some times during the year, the solar time is 20 minutes off compared to the local mean solar time. The difference between the mean solar time and the local solar time is known as the equation of time.

As mechanical clocks were developed, the US and England introduced the idea of "zone time" to deal the difficulties in scheduling trains between cities. Before we had time zones, every longitude had a slightly different time. Every 1 degree of longitude changed the time by 4 minutes. By using of geographic time zones spanning approximately 15 degrees of longitude, everyone within a single zone can use the same clock time. People in Nashville can have the same time on their clocks as people in Fargo. However, the local solar time doesn't follow zone time, so you need to account for the time shift between your longitude and the center of the timezone.

The image in this section shows the equation of time calculated for my home in Murfreesboro Tennessee. It includes both the correction to the Zone time and the equation of time into a simple graph.

Daylight savings time adds a final level of complexity. We arbitrarily chance the clocks by one hour in the spring to allow more light in the evening when people are usually more active. This s yearly ritual sets all the Sundials off by a full hour.

The good news is that all these factors can be calculated and built into a table or graph to let you determine the local clock time from your sundial. Given a bit more time until the contest deadline, I would have etched this onto a brass plate and mounted it on the side of the sundial for reference. However, my attempts to use the "glossy paper" method to transfer patterns to brass for etching failed repeatedly. I would have also included a motto for the dial on the brass plaque. My favorite is from the Sundial at York Minster - "LUCEM DEMONSTRAT UMBRA" - a Latin phrase that translates into "The shadow shows the light."

Of course, determining the exact time is never the point of any sundial project. Sitting in the garden, smelling the flowers, and petting the cat should not be done on a strict schedule. Watching the shadow of the gnomon move across the dial on a lazy afternoon reminds us to take time to enjoy the hours of our lives.

Step 8: ​Adapting the Sundial to ANY Latitude

Adapting this design to ANY latitude is relatively easy, but it helps to understand the underlying principles.

When we in the Northern Hemisphere on Earth, the sky’s rotation when facing north is counter-clockwise. The stars and other celestial objects all appear to go around the North Celestial Pole near the location of the star Polaris. When we look south, celestial objects rise along the eastern half of the horizon and set on along the western half of the horizon. The stars are following a circular path around the South Celestial Pole even though our location in the Northern Hemisphere prevents us from seeing it directly. The Sun follows this general arc from east to west through its daily motion. From the Northern Hemisphere, the Sun rises to the left of south and sets to the right of south. The Sun’s shadow moves from the west to the east, or from left to right if you are facing north. Of course, the reason we see this motion is because of the rotation of the Earth. If viewed from above the North Pole, the Earth would appear to rotate in a counter-clockwise direction.

From the Southern Hemisphere, you observe the same motion from a different perspective. If you look to the north, stars move counter-clockwise around the North Celestial. Of course, you can’t see the North Celestial Pole directly because the Earth blocks it in the same way the South Celestial Pole is blocked by the Earth when you are in the Northern Hemisphere. Looking to the south, observers in the Southern Hemisphere would observe stars going clockwise around the South Celestial Pole.

For any observer who can see a sunrise and sunset, the Sun generally rises in the east half of the sky and sets in the western half of the sky. In the Arctic and Antarctic, there are days when the Sun never sets. The motion of the Sun is still east to west but in a circle above the horizon. However, for observers in the Southern Hemisphere, the Sun’s path will be to the north of the observer. When you are facing north, the Sun will appear to rise to the right of north and set to the left of north.

Knowing all these things means we need to make minor modifications in our Sundial:

1. Just as before, the gnomon should draw a line that connects the North and South Celestial Poles. For all observers, this means the angle between the horizon and the gnomon is your latitude.
2. In the Southern Hemisphere, we align the Sundial so the top of the gnomon points toward the South Celestial Pole. Since there isn’t a star like Polaris to align the gnomon with, using a compass or shadow circle would be a natural alternative. Using a shadow circle to determine direction is simple and works everywhere. Place a vertical stick in the ground in the morning and draw a circle around it. Mark the two locations where the stick’s shadow hits the ring. The line between the two points is directly west-to-east, so the direction of north is perpendicular to this line.
3. The numbers on Southern Hemisphere Sundials run from the right to the left instead of from left to right. Noon is still in the same place, but 11 AM is 15 degrees RIGHT of the noon on the equatorial dial instead of 15 degrees to the left of noon as in the original design.

To help visualize all of this, I have included a couple of additional pictures with this note. Note in the first image how all sundials align to between the North and South Celestial Poles. The only difference is which direction you are facing when you observe them. The arrows pointing to the Zenith (the location directly above the head) of each observer should help you visualize how this would appear from different places on Earth. The second image hopefully helps put all this into perspective. Sundials are a projection of the Earth’s rotation, and Equatorial Sundials are aligned such that the shadow follows the rotation of Earth.