Making a sun compass (part 1)

Making a sun compass

The concept of a sun compass is fairly simple – we take a vertical stick called a gnomon that casts a shadow onto a horizontal plate.   For a specific latitude and day of the year, the path of the tip of the shadow on the horizontal plate is unique.  This shape is generally the geometric shape of a hyperbola.    The shadow reaches its shortest length when the sun reaches its highest point in the sky – the local meridian.   If we know this path and draw it out on the plate, we can rotate the plate until the shadow touches this path.  

Figure 1 Sun compass operation.  The tip of the gnomon shadow touches the hyperbolic trace, and the compass 'dial' is aligned to true north.  The levels in the photo were only places to ensure that the plate was level.

If the path is drawn properly, this provides an alignment of the sun compass, so that north/south/east/west and points in between can be measured.  

There is some evidence to support the notion that the Vikings used a sun compass in their voyages to Iceland, Greenland, and Vinland during the Middle Ages. 

More recently, sun compasses were used during World War II.   Infantry on jeeps had to cross large distances across the north African desert, and the metal in the vehicles would screw up magnetic compass readings, so the soldiers were issued sun compasses that allowed them to take their bearings from inside the jeep. 

In addition to being a compass, if the trace carries time information, the sun compass can act as a clock to a reasonable degree of precision (+/- about 10-15 minutes). 

Figure 2 Sun compass made for summer.  Note the length of the gnomon and the shape of the trace.

 Figure 3 Sun compass made for winter.  Note the shorter gnomon and the shape of the trace.

For this exercise, you’ll make a sun compass that’s designed to give you both an approximate time of day, and also work as a compass.

For this exercise, you’ll make a sun compass that’s designed to give you both an approximate time of day, and also work as a compass.

The project

Tools: Excel spreadsheet (link here), flat plate, gnomon (stick), graph paper, protractor, ruler.  

For the flat plate, I recommend a material like Masonite.  It’s thin, lightweight, and reasonably stiff. 

There are three parts to this: 

1.)   Getting the data for the sun compass using the Excel spread sheet

2.)   Making the sun compass itself

3.)   Using the sun compass

1.)   Getting the data

Part A  (Can skip this if you want, but it gives you sunrise and sunset times)

The Excel spread sheet has a lot of intermediate numbers that you don’t have to pay attention to, but there are some numbers that you must enter in order to get it to work properly.  In the top of the spread sheet, there is a sample calculation of the altitude and azimuth of the sun for a given day and latitude/longitude/time of day.  It also provides the time of sunrise and sunset for that location.

Figure 4 Top of spread sheet - inputs are in bold face.

Look at the very top of the spread sheet.   The entries you’ll need to put in are in bold face in this.  The year is obvious, the month should just be the number associated with the month (e.g. January=1, February = 2).  The date of the month is simple.  This particular entry is for June 14^th.

The time zone in UTC is straightforward.   UTC is, effectively, Greenwich time (GMT).   This is for Boston in the summer.   Since Boston is west of Greenwich, it would normally be -5 UTC, but since it’s summer, it’s an hour early, or -4 UTC. 

Latitude and longitude is something that can be looked up readily.  This calculation uses decimal latitude and longitude.   The “day_of_year” is an intermediate calculation step that will happen automatically.

Enter, then, the hour (0-23), minute, and second of the observation.  In this case, I entered the time of 12:42:38, which corresponds to the time of the local noon for Boston, which is the latitude and longitude entered. 

Scroll down a little farther, and you’ll see in bold red the altitude and the azimuth, followed by the sunrise and sunset times in local hours, and local minutes. 

Figure 5 Section of the spread sheet giving the sunrise and sunset in local time.

In the above clip from the spread sheet, for Boston on June 14^th, sunrise is at 5:07, and sunset is at 20:17 (8:17 PM).   The time of sunrise and sunset can be helpful in deciding how to set up the flat plate.

Part B

This is effectively the same calculation as the first part of the spreadsheet, but done for increments of time, and carried out all along rows.   This is in the second part of the spreadsheet.  You enter data under the bold-faced headings.  These include the year, month, day, time zone, latitude, longitude, and time in hours and minutes.   On the spread sheet example, the times are entered in 15 minute intervals.   Getting much finer grained than this is not necessary. 

Figure 6 Portion of spreadsheet for data entry for sun compass construction.

In addition to this, you have to enter the length of the gnomon.  My plate is 20”x8” wide, and I want to get a fairly large chunk of time covered on the plate.   This means that I have to play around with the gnomon length until I get the best coverage.   If I get too close to sunrise and sunset, too much of the board is taken up with that, so I try to get some time after sunrise and sunset.   In this particular case, June 14^th, sunrise is at 5:07 AM, and sunset is at 8:17 PM.   I only put down the time period of 8:15 AM to 17:15 PM. 

Note that the coverage will depend on the gnomon length.  In the photo below, I show two gnomons – one for the summer (long) and one for the winter (short). 

Figure 7 Summer gnomon (left) and winter gnomon (right).  These are constructed to get most of the shadow path during the day onto the plate.

Figure 8 Screen shot of right-hand side of spread sheet, with the gnomon length entered, and the locations of the points on the hyperbolic trace in red.

Next, go to the right-hand side of the spreadsheet.   You have to enter the length of the gnomon.  For the summer months, I used 6”.   I used a 20x8” Masonite plate for my sun compass, with a hole drilled and centered in the middle of the long axis (labeled Lx).  The hole is offset about one inch from the edge of the plate in the short axis (labeled Ly).   The center of the system is 0,0, where the gnomon is located.  In the above example, some of the Ly values are negative, as the sun rises north of east in the summer, and so the shadow will be cast to the south for some times closer to sunrise and sunset.  

Note that the maximum value for Lx is 10 inches to fit onto the plate. 

This list of red numbers is the data you need to plot on the graph paper laid on top of the plate.

1.)   Making the physical sun compass

Here, you will need the following:

a)     Plate – I use a 20”x8” Masonite board, with a hole drilled – centered on the long axis: 10” from each side, and 1” from the edge of the short axis. 

b)    Gnomon: use dowel stock – the hole in the Masonite should match the diameter of the dowel stock. The tip of the gnomon can be sharpened up to make for an obvious shadow-tip.

c)     Graph paper.  Since I’m using inches as the metric, I use a pad of graph paper with 5x5 subdivisions per inch.

Figure 9 Raw materials for making the sun compass.

In addition, I use a ruler and a protractor.

Figure 10 Detail of plate, gnomon, graph paper, and protractor.