The sun compass

The sun compass is a true compass, which works for a particular time of the year at a particular latitude. It consists of a vertical stick, which throws a shadow on an underlay. The compass can be calculated mathematically, but it can also be made by noting the passage of the sun throughout the day.

You can download a programme for making sun compasses from the tools menu to the right. It just needs to be unzipped in a folder on your own computer, after which it is ready to run. It just requires that Java's Runtime module is installed.

Double-click on the file suncompass.jar. The programme includes a help function so you can quickly get going and use it.

Firstly, here are some problems that you can solve with the aid of the programme and later there are some suggestions for practical exercises with a sun compass you print-out yourself. You can search for the answers to some of the first problems on the Internet.

• Is it possible to use the same sun compass in Esbjerg (55°N) and at the Skaw (58°N)? (HINT: print out a sun compass for both places and lay one on top of the other).
• At the spring and autumn equinox day and night are of equal length. What do the shadow curves look like at these times? Why do they look like this for all latitudes? What happens to the curves around these dates?
• At the summer solstice the day is longest and at winter solstice the day is shortest. How is this apparent on the sun compass?
• The sun curves are so-called conic sections. According to classical geometry the sun curve is therefore a hyperbola, a parabola or an ellipse. What is the name given to the phenomenon, which produces an elliptical sun curve?
• Thule (77°N) has midnight sun from 23. April to 22. August. The sun compass cannot, for obvious reasons, be used round the clock during this period. Find the first and last date when the sun compass can be used round the clock with a suitable choice of radius and gnomon. What is the reason that it cannot be used round the clock during the whole of the period with midnight sun?
• Midnight sun also occurs in an interval at the summer solstice north of the Arctic Circle (67°N). The sun curves must therefore be hyperbolas before the Arctic Circle, parabolas at the Arctic Circle and ellipses above the Arctic Circle. Set the sun compass to the summer solstice and check the above statement by choosing appropriate latitudes, gnomon and radius. Why do you think the Arctic Circle lies at the above-mentioned latitude?

And now for the practical exercises - these require you to have printed out a sun compass for the correct date and latitude. If it is to be used outdoors it is a good idea to glue it onto a stiff piece of card and cut it to shape so it is easy to handle. You should also remember to hold it horizontally when you use it. Be aware that a single mm’s error on the length of the gnomon can easily become an error of 3-4 mm on the length of shadow late in the afternoon or early in the morning, depending on the latitude.

• Choose a large, open and fairly flat area. Make a mark on the ground – this must not be visible from a distance. Choose a direction with the aid of the sun compass and find a point in the distance, which lies in the appropriate direction. Walk 50-100 steps in the chosen direction and also check the direction on the sun compass underway. Turn round (turn through 180º) and find sighting point and follow it in the opposite direction. Walk the same number of steps back. Did you hit the mark (the direction is the most important)? Carry out the exercise several times until you are fully familiar with the sun compass. Start for example with north/south and east/west.
• Choose a starting point and use the sun compass for the following exercise: 1: walk 100 paces NW. 2: walk 150 paces NE. 3: walk 100 paces SE. 4: walk 150 paces SW. Where do you end up?
• This exercise requires a detailed map of the area in question; for example a cadastral map, which can often be printed out from the local Council’s website. Find a central place from where it is possible to sight various conspicuous objects (house corners etc.), which are depicted on the map. Lay a sun compass over the map and draw the sight lines in on the sun compass (number the objects on the map and on the sun compass). Then go outside and check the directions in practice. The opposite exercise is rather more difficult. Print out a sun compass on ordinary A4 paper and fix it to a drawing board. Ensure a horizontal underlay (for example a table, which can be adjusted in height). Find a central place and try sighting to the various objects (house corners etc.), which are depicted on the map. Draw the sight lines in on the compass and mark them with, for example, a number. Then check your results by laying the sun compass over the map.
• You can also try to construct a little orienteering course with the sun compass where the distance and direction are used from post to post. This requires that you carry out some trials first to find out your average stride length when (gently) running.