Using Sundials

Humans have been using the Sun’s position to navigate and tell the time, day, and season for millennia.  Sundials create shadows that make it easier to do these tasks.  In the following sections, explore how to use the simplest sundial (a vertical stick or pole) as a compass, clock, and calendar, then practice with the Sundial Shadow app at the bottom of the page.  But there is a catch – how humans use time is often different than how nature responds to the Sun’s motion during the day and throughout the year! Clock time that humans use does not equal solar time that nature responds to.

Human Use of Time and a Calendar

is different than

Nature’s Response to Time and Season

Since this topic is part of the Earth Systems course, we will focus on using the position of the Sun in the sky to examine nature’s behavior.  However, this information is useful for humans to understand and apply for our needs, particularly designing energy-efficient and aesthetically pleasing buildings, collecting energy with solar panels, all aspects of farming, and quite a bit in our outdoor recreation.

The Sundial Shadow App

Use the Sundial Shadows web app to visualize, conceptualize, estimate, and use shadows and shadow traces as a clock, calendar, and compass.  View the shadows for any latitude, day, and time, and try the unlimited number of challenges that provide visual feedback based on your answers.  The app created the diagrams and animations of sundial shadows on this page.

Earn a Certificate

Answer ten random challenges to earn a certificate to gauge your understanding. Use as a homework assignment, or earn points and clues on the final Earth Systems challenge (when it gets completed): you must identify the best place to inhabit a new planet that you have traveled to. Try as often as you like to earn the most points.

Acknowledgments

I would like to thank Lincoln Berkley, Mattea Horne, Kiley Remiszewski, and Tom Whittaker for sharing their insightful questions, comments, and suggestions to improve the app.

Explore the Math

For a well-written and illustrated review of the math of sun shadows, see Solar Geometry.

Latitude Challenge

Time Challenge

Brief History of Sundials

Humans are planners and organizers. Since the Sun’s diurnal and seasonal heating of the Earth’s surface creates cyclical patterns in nature, humans invented technologies to understand, track, and predict these patterns. Artifacts indicate humans have been tracking solar patterns as early as 20,000 years ago.  By 5,500 years ago, vertical sticks and stones cast shadows that showed solar time and season of the year.  To support growing the needs of communities, trade, and farming, Babylonians and Egyptians refined the process with more advanced sundials.  The unified process to tell time helped organize societies’ activities.

As sundial technology advanced, and identifying time became more precise, humans realized new technologies were needed to support the increasing use in science, commerce, agriculture, navigation at sea, military, global exploration, and industry.  The invention of mechanical clocks created a technology that better supports human needs. Yet, it created a diversion from tracking and understanding one of the most fundamental drivers of nature: the Sun illumination of Earth.  Most humans today, especially those living in cities, are not aware of solar time (the time based on the Sun’s movement). Instead, we rely entirely on the time told by clocks.

Sun Time versus Clock Time

Clocks standardized time for human use, and as time-monitoring technologies advanced, human reliance on nature’s patterns lessened.  Before railroads, towns and cities had their unique reference for clock time that relied somewhat on the timing of local noon.  However, to coordinate the rapid speeds and long distances of railroad travel required unification of time across broader regions.  By 1883, the United States created four time zones across the country, and one year later, the international community divided the world into 24 time zones.

Each time zone is roughly 15º in longitude wide, which means solar time differs by 1 hour between the eastern and western edges of the zone.  Live along the east border, and you experience sunrise and sunset one hour earlier, clock time, than a person living on the western side of this time zone.

To add complication to the difference between a clock and solar time, the Earth’s orbital speed changes throughout the year since its orbit is not perfectly circular (see the section on eccentricity).  A solar day is the time difference between two successive local noons.  If the Earth is moving faster in its orbit, it must rotate more to align with the next day’s local noon, so the day is longer when recorded by a clock.  When Earth moves slower, the solar day is shorter.  The Equation of Time allows humans to account for the difference between a clock and solar time.

Using Declination Circles to Calculate Shadows

Declination circles map the path of the Sun across the sky as viewed from a point on the Earth’s surface at a given latitude and day of the year. A sundial located at this point extends above the surface, so it creates a shadow.  The tip of the shadow points away from the Sun and changes location on the ground throughout the day.  The shape of the shadow trace (the connected tips of the shadows throughout the day) ranges from a circle, ellipse, parabola, and line, whereas the declination circle is always a circle.  The observed shadow’s pattern has a different shape than the declination circle except at the North and South Poles when the sun is above the horizon.

The three views of the declination circle shown below are the position of the Sun in the sky during January 1 at 45ºN.  The yellow lines show the hourly beams of sunlight hitting the Earth’s surface and the tip of a sundial.  Its altitude above the horizon and hour angle identifies the position of the Sun in the sky. The hour angle is zero at local noon, which is when the Sun is highest in the sky as it crosses the local longitude.  Before local noon, the hour angle is negative, and after local noon, the hour angle is positive. Use the horizontal gray lines that are 10º apart to interpolate the altitude of the Sun. Use the vertical arcs that are 10º apart to calculate the hour angle. 

Above is the north-south oriented view of the declination circle for January 1 at 45ºN.  The yellow circles represent the hourly position of the Sun, and the yellow lines represent the hourly beam of sunlight illuminating the center of the horizon.

Above is the east-west oriented view of the declination circle for January 1 at 45ºN.  The yellow circles represent the hourly position of the Sun, and the yellow lines represent the hourly beam of sunlight illuminating the center of the horizon.

Shadows & Sun Position Depend on Latitude, Day, & Time

Shadows point away from the Sun, and the position of the Sun in the sky means applying declination circles and how they involve latitude, day, and time. Therefore shadow length and direction depend on the latitude, day, and time.

When a variable depends on several variables, there is a dependency between each variable to the others. For example, to calculate the area of a rectangle, multiply the width and length.  If the area and the width are known, then the length may be calculated by dividing the area by the width. Similarly, if we know the latitude, day, and time, shadow length and direction may be calculated.  If the shadow and two of the variables latitude, day, and time are known, then the third may be calculated.  This flexibility is how we use shadows as a compass, clock, and calendar.

In the animations and illustrations that follow, the blue dots represent the tips of a sundial’s shadow every 30 minutes.  The set of blue dots represents the shadow trace. The orange lines show the shadow at sunrise and sunset.  The black line is the shadow at the time displayed in the upper left corner.

The white lines are direction every 10º, and the white circles are the relative length of the shadow compared to the height of the sundial.  Use the relative shadow lengths to calculate and/or interpolate the altitude of the Sun above the horizon (see the table on the right).

Using the Sun and Shadows as a Compass

The first step is to become familiar with how shadows change across the globe with the season.  Below are animations of shadow traces for three seasons: December 21, when the Northern Hemisphere is most illuminated; an equinox, when both hemispheres are evenly illuminated; and December 21, when the Southern Hemisphere is most illuminated.  Latitude begins at 90ºN and decreases at 15º intervals until it reaches 90ºS.

On December 21, the Sun’s declination is 23.5ºS, so all shadows at sunrise and sunset across the globe are north of east and west, respectively.  At and northward of 66.5ºN, the sun remains below the horizon all day.  At and south of 66.5ºS, the Sun remains above the horizon all day. Northward of 23.5ºN, the local noon shadow will always point northward.  South of 23.5ºS, the local noon shadow will always point southward.

Except for the poles, on the equinoxes, the Sun rises exactly east and sets exactly west at all latitudes, creating 12 hours of sunlight and darkness.  At the poles, the Sun remains on the horizon for 24 hours.

Key Patterns of Shadows with Season

• Except at the Poles, shadow traces curve less near the equinoxes (March 21/22 and September 21/22).  At the Poles, when the Sun is above the horizon, the shadow trace is circular.
• Near the December 21 solstice, shadow traces curve northward for all latitudes that experience a period of darkness that day.  The closer toward the solstice, the more pronounced the curvature.
• Near the June 21 solstice, shadow traces curve southward for all latitudes that experience a period of darkness that day. The closer toward the solstice, the greater the curvature.
• North of 23.5ºN, the Tropic of Cancer, the shadow at local noon always points north.  The shadows are longer near December 21 compared to those near June 21.
• South of 23.5ºS, the Tropic of Capricorn, the shadow at local noon always points south.  The shadows are longer near June 21 compared to those near December 21.
• Between the Tropics of Cancer and Capricorn, the Sun is directly overhead at local noon twice a year, so there won’t be a shadow at that time.  For these latitudes,

the local noon shadow will point north when Latitude – Declination > 0º

and will point south when Latitude – Declination < 0º

The Sun will be directly overhead when Latitude – Declination = 0º

Recall that southern latitudes are negative, so 10ºS = -10º.

Solar declination is essential for calculating the angle of the local noon sun above the horizon in the Northern Hemisphere:

90º – Latitude + Declination = Local Noon Sun Angle 

and for the Southern Hemisphere:

90º + Latitude – Declination = Local Noon Sun Angle 

Using the Sun and Shadows as a Clock

Although a shadow trace shows how the shadows move throughout the day, we often don’t have this available at a snapshot in time.  The more familiar you are with how shadow traces change at a given latitude at different times of the year, the easier it is to envision the complete shadow trace from one shadow at a particular time of the year. Below are the hourly shadow positions for 45ºN at three times of the year: December 21, March 22, and June 21.  Compare these animations to the shadow traces for 45ºN every 30 days throughout the year.

Hourly shadow motion during December 21 at 45ºN.

Hourly shadow motion during March 22 at 45ºN.

Key Patterns of Shadows as a Clock

• Since the Earth rotates from west to east, the Sun appears to move with a westward component throughout the day.  This means that shadows appear to move with an eastward component. Before local noon, shadows are west of north/south, and after local noon, shadows are east of north/south.
• Near local noon, shadows have the most consistent eastward movement.
• Shadows decrease in length from sunrise to local noon and increase from local noon to sunset.

Using the Sun and Shadows as a Calendar

In the Northern Hemisphere, shadows before and after local noon are longer than the previous day’s between the June 21 solstice and the December 21 solstice.  On the other days, shadows are shorter than the previous day’s.

In the Southern Hemisphere, the opposite trend occurs for morning and afternoon shadows.  Shadows are shorter the previous day’s between June 21 and December 21.

The above trends hold for local noon shadows when poleward of the Tropic Circles (23.5ºN and 23.5ºS).  Since the Sun will be directly overhead at local noon twice a year, and there won’t be a shadow at these times.  These occur when:

latitude + declination = 0º.

Above is an animation of the shadow that occurs at 3 PM (solar time) at 45ºN every 30 days throughout the year.

Above is an animation of the shadow that occurs at 3 PM (solar time) at 15ºN every 30 days throughout the year.