A Sundial as a Clock, Compass, and Calendar

Earth’s axis of rotation orients our coordinate system of latitude and longitude.  Since Earth is a rotating sphere that orbits the Sun, our source of light, Earth’s latitude and longitude are connected to the Sun’s illumination of Earth.  The Sun’s position in the sky tells us time, direction, and location in our orbit.  A sundial lets us track the Sun’s movement throughout the day and year, turning it into a clock, compass, and calendar.

There are many types of sundials, but we will focus on the simplest: a vertically standing object.  These frequently occur in nature: trees!  Humans tend to erect vertical buildings, not ones that tilt (the Tower of Pisa was an accident!).  And if we stand in a flat field with no trees or buildings, we may use our shadow.  So we can apply these simple sundials to tell time, find our way, and prepare for the upcoming seasons any place where the Sun is shining on Earth.

Key Terms and Concepts to Apply

• North and south point in the direction of the local longitude meridian (a half circle), which is toward the axis of rotation.
• East and west point in the direction of the local latitude circle.
• Shadows are always opposite to the Sun’s position in the sky.
• The shortest shadow occurs when the Sun is highest in the sky.
• The longest shadow occurs when the Sun appears on the horizon, so during sunrise and sunset.
• The movement of shadows before local noon is symmetric to those observed after local noon.  The time of the shortest shadow occurs halfway between sunrise and sunset.  This time is called local noon.
• Because the Sun is crossing the local longitude at local noon, the shadow will either point directly north or south or will not be seen if the Sun is directly overhead.

Build and Use A Sundial

Although this may seem like a simple activity, tracking shadows cast by a vertical pole provides insightful experiences of the daily and seasonal patterns of solar illumination for a given latitude. Very few of us take the time to watch shadows move, let alone mark, measure, and use them to understand our natural world. Plus, nothing beats a bit of hands-on science!

Tip 1: Before running the activity, check the weather forecast for cloud cover – clear skies are best to run this activity, and preferably for two consecutive days.

Tip 2: Any vertical pole with level ground around it works well, such as a tetherball pole on the pavement.  Use colored chalk to mark the shadows.

Preparation

This activity needs to run from the morning into the afternoon in order to see the pattern of the Sun’s motion and use the data to measure the direction of true north and calculate when local noon occurred (clock time is different from Sun time). Set up the sundial and begin taking measurements and marking with the colored yarn by 10 AM at the latest. Pick a location with adequate availability of open sky above and around the post.

Procedures

Every 10-15 minutes, mark the position of the end of the shadow with a marker. Secure the tag in the ground. To help visualize past shadows, connect colored yarn between the tag and the base of the PVC pipe. Local noon is the time of day when the Sun is highest in the sky, and the shadow will be the shortest. Local noon occurs when the Sun is due south of the observer if you are north of 23.5ºN latitude, so the shadow at local noon points toward true north. If you are south of 23.5ºS, then the Sun’s position at local noon will always be due north of you. Between the Tropic of Cancer (23.5ºN) and Tropic of Capricorn (23.5ºS), the Sun will either be directly overhead, due north or due south of you depending on the time of year.

Clock Time versus Sun Time

Being in Boston, with a longitude of 72ºW, we are very close to the eastern edge of the Eastern Time zone, and our local noon is nearly an hour before to that experienced by someone close to the western edge of the Eastern Time zone. The eastern side of a time zone experiences sunrise, local noon, and sunset an hour earlier than the west edge of that time zone. Remember, we use standard time during the winterish months and daylight savings time during the summerish months, so local noon may occur after 1 PM, depending on your location and day of the year. By marking shadow positions every 10-15 minutes, you will be able to calculate the time of local noon and where true north is oriented. Look at the trace of the shadows and notice that they were long in the morning, became shortest around noon, and then got long in the afternoon. The key is that the shadows’ lengths are symmetric about the shortest shadow.

Finding the Clock Time of Local Noon

Use the circle, shadow trace, and intersections described below to calculate the time of local noon:

1) Estimate the time the trace of the shadow (orange) first crosses the circle (black). In this example, it appears to be near 10:15 AM.

2) Estimate the time the shadow moved outside the circle. For this example, it appears to be near 12:45 PM.

3) The midpoint between these two times is the clock time of local noon:

(10:15 + 12:45) / 2 = 23 / 2 = 11:30 AM

Suggestions

If you are running this activity at school, it works great if there are multiple classes working on it through the day making measurements. Learn how to use it as a clock, compass, and a calendar after a day of data collecting. If a single class did the activity, I gave homework to work in teams to make measurements throughout the school day.

If you have a block of time to spend at the sundial, bring additional tools with you. A globe (or a ball and chalk to mark on the ball), compass, pencil and notebook/drawing pad are good. Use the globe/ball to help visualize why the Sun appears to be moving as it is for your location – and any location on Earth. Also, explore how latitude and longitude come into play with the direction and timing of the motion of the Sun. For example, was sunrise north of east, east, or south of east that morning? Why is the Sun south of you at local noon (if you are north of 23.5ºN)? Where would it be if you were south of 23.5ºS?

Finding Local Noon and True North Using a Shadow Trace

True north points to the axis of the Earth’s rotation. At all latitudes north of 23.5ºN,  the direction of the shortest daily shadow points toward true north. To find the exact direction of the shortest shadow:

1) Using a string tied to the base of the sundial, create a circle (black) from the center post

2) Mark where the trace of the shadows (orange line) crosses the circle (blue line).

3) Find the midpoint of the blue line (place a string along the blue line and fold it in half) and extend the green line from the center post through this point. The green line is pointing true north.

Using a compass, compare true north to magnetic north in your location.  This is a valuable mini-experiment that will be used to explore what creates Earth’s magnetic field.  The difference between true north and magnetic north is the magnetic declination.

Using a Sundial as a Calendar

If you can save the markings, run this activity every week or two and compare the differences in the location and shape of the shadow trace (orange line above). If you are after December 21 and before June 21, the shadows get closer to the sundial each day. And between June 21 and December 21, the shadows move away from the sundial each day. If you have saved each week’s shadow trace, you have a calendar!

Sundial Shadow Traces Throughout the Year

Local noon is when the Sun is at its highest point in the sky.  The Sun crosses your longitude at local noon, so it is precisely north, south, or overhead at that moment.  Because the Sun is highest in the sky, the shadows are shortest, and they point in the opposite direction from the Sun.  Finally, the shadow patterns are symmetric about local noon.  The shadow length an hour before local noon is the same as that an hour later, and the direction pointing away from the local noon shadow is the same an hour before and after local noon.

Two latitudes don’t experience local noon: the North and South Poles. Why?

Each of these ways to think about local noon are important for navigation, telling the time of day and the day of the year, using solar panels and other solar-based technologies, building energy-efficient buildings, gardening, and understanding the seasons and climate regimes.

Extension: Calculating the Altitude of the Sun in the Sky

You need to be familiar with the tangent function (see Right Triangles and Vectors).

If you measure the angle of the sun at local noon during an equinox (March 21 or September 21), you may calculate your latitude.

Latitude = 90º – local noon sun angle

For other days of the year, if you are north of 23.5ºN:

Latitude = 90º – local noon sun angle + solar declination

Solar declination depends on the day of the year.

To explore the Sun’s illumination patterns of Earth, see the Sun-Earth Connection, and for more detail on solar declination, see Declination, Latitude, and Solar Illumination.