Make an Equatorial Sundial

Introduction: (Initial Observation)

As the earth rotates around its axis, it appears that the sun is moving on the sky. The apparent movements of the sun in the sky has many affects in our environment. One thing that we have all noticed is the direction and the size of shadows that change from the morning to the afternoon.
Many scientists have studied the shadows, performed a variety of calculations and tried to use shadows to study the earth movements and . One of the outcomes of such studies have been gnomonic or the construction of sundials.

Gnomonic (pronounced nomonic) is the art or science of dialing, or of constructing dials to show the hour of the day by the shadow of a gnomon.

Sundials are made in many different designs. Each design has its own challenges and its own benefits.

In this project you will construct a special sundial known as the equatorial sundial. You may then use it to demonstrate or explain seasons, short winter days or the long hot summer days. You may also use it to determine the sun time in your area and compare it with your standard time.

Designing and building sundials can be a lot of fun! A sundial is a blend of art and science. Its creation can be as challenging as one wishes to make it. The effort required to make a sundial will be well worth while. It will give you a great sense of satisfaction and enjoyment.

Information Gathering:

First, study sundials. Then, find out how the apparent position of the sun in the sky changes during different hours of the day or different days of the year. Lastly, think about how you can use the changing shadows to construct devices to tell the time or the season.
Following are samples of information that you may find.

Warning: Never look at the sun directly. Doing that will burn the optical nerves of your eyes and cause serious vision problems.

As the earth turns on its axis, the sun appears to move across our sky. The shadows cast by the sun move in a clockwise (hence the definition of clockwise) direction for objects in the northern hemisphere.

Shadow sticks or obelisks are simple sundials. If the sun rose and set at the same time and spot on the horizon every day, they would be fairly accurate clocks. However, the sun’s path through the sky changes every day because the earth’s axis is tilted.

 

 

On the earth’s yearly trip around the sun, the North Pole is tilted toward the sun half of the time and away from the sun the other half. This means the shadows cast by the sun change from day to day.

In addition, because the earth’s surface is curved, the ground at the base of the shadow stick or obelisk is not at the same angle to the sun’s rays as at the equator. This means that the shadow does not move at a uniform rate during the day. That is, if you mark the shadow at sunrise and sunset, you cannot evenly divide the space between for the individual hours. Try changing the latitude in the applet to the right and see how the hour marks change.

There are several ways to overcome these problems. One is to build a horizontal sundial, where the base plate is level, and the “stick,” called the style, is angled so it is parallel to the earth’s axis. The hour marks can then be drawn by trigonometric calculations, correcting for the sundial’s latitude.

 

 

 

Another solution is an equatorial sundial, where the base plate is tilted at an angle equal to the latitude, and the style is perpendicular to the base, which will align it with the earth’s axis. The base can then be marked with regularly-spaced hour marks.

There’s one more thing to remember. Sundials only measure local solar time. If a friend had a sundial 5 degrees longitude to the west of your sundial, his sundial would read a different time than yours. This is a simple calculation: the earth turns 360 degrees in about 24 hours, therefore the sun’s apparent position moves 360/24 = 15 degrees each hour. So your friend’s sundial would be off by 20 minutes (earlier) than yours. This difference is only affected by longitude, not latitude. To standardize things, the earth was divided into 24 time zones in the 1840’s, each to be one hour different from the next.

Did you know that you can measure the height of tall trees, poles and tall buildings without ever having to climb to their top? It is easy!

Simply wait for the time of day that any shadow length is the same as the objects height. Then simply measure the length of the shadow on the ground.

This vertical sundial sits on the Malmesbury House right by St. Ann Gate. Handel, the great Baroque composer, stayed in the Malmesbury House and used the chapel in St. Ann Gate for recitals. The quote on the dial is from Hamlet, of course.

Location:
Salisbury,
Wiltshire SP1 2EB

Photo by:
Mjausson’s Walks

The vocabulary of sundials
Altitude:	The altitude of the Sun is the vertical angle it makes above the horizon (from -90° to +90°). The Sun’s altitude and azimuth define its position at any given moment. At sunrise the altitude of the Sun is 0°.
Azimuth:	The horizontal angle measured from the meridian. It is positive towards the East and negative towards the West. The Sun’s azimuth at a particular time is its bearing at that moment. The azimuth is 0° when it crosses the meridian of a place.
Co-latitude:	The complementary angle of the latitude of a place, equal to 90°-latitude.
Declination:	of a wall: the angle which a vertical wall makes relative to the meridian. When one designs a vertical sundial, one must take account of the declination of the surface on which it will be placed. In Europe, the declination of a south-facing wall is 0° of an east-facing wall is -90° of a wall facing west +90° and one facing north is 180°. of the Sun: the position of the Sun north or south of the celestial equator.
Dial Plate:	The supporting surface of a horizontal dial. The lines and numbers of a dial are laid out on the dial plate.
Dialist:	An artisan who designs, constructs and installs sundials.
Ecliptic:	The plane containing the orbit of the Earth around the Sun, which by extension projects a circle on the celestial sphere.
Equation of Time:	The value of the difference between Apparent Solar Time and Mean Solar Time. The difference arises from the movement of the Earth in its elliptical orbit as well as the fact that its axis of rotation is inclined to the ecliptic. The difference can vary by as much as +/- 16 minutes. The Equation of Time is sometimes represented in the form of a figure of eight placed on the noon line of a sundial.
Equinoctial line:	The line of declination on a sundial corresponding to the equinox. This line makes a right angle with the gnomon in a plane sundial.
Equinox:	The day of the year when the Sun crosses the celestial equator in its apparent movement. At this moment, the Sun rises exactly in the East and sets exactly in the West. It is the period of the year when night and day are of equal length. The equinox occurs on 20 March and 23 September.
Gnomon:	The name given to a style placed vertically to the plane of a sundial. The shadow cast by the tip of the gnomon can indicate both the time and the date.
Gnomonics:	The science of sundials.
Gnomonist:	An amateur sundial enthusiast.
Hour:	Babylonian Hours: an ancient system which divides the day into 24 hours, commencing at sunrise. They thus measure the number of hours elapsed since sunrise. Italian Hours: an ancient system which divides the day into 24 hours, commencing at sunset. They thus measure the time left until sunset. Standard Time: the time shown by clocks, which will be the same for all inhabitants of a particular time zone. It is Mean Solar Timecorrected for the difference in longitude between a place and the reference longitude of the time zone in which it is located. Mean Solar Time: Obtained by adding the Equation of Time to the Apparent Solar Time. The Mean Solar Time gives a constant hour duration over the year. It varies with the location. Apparent Solar Time: the time naturally shown by a sundial. It is defined as 1/24th of the interval between two successive passages of the Sun across the meridian. This period of time varies throughout the year. Temporary Hour: an ancient system dividing the interval between sunrise and sunset into 12 hours. The length of an hour therefore varied throughout the year! (between 40-80 minutes). These hours are sometimes referred to as Biblical Hours.
Latitude:	the angle formed between the vertical of a place and the plane of the equator. Northern latitudes are positive; southern latitudes are negative.
Lines:	Hour Lines: lines drawn on the dial plate of a sundial which permit us to tell the time from the shadow cast by the style. Hour lines are drawn for hours and sometimes for half-hours or quarter-hours, but much more rarely for 5 minute intervals. Declination Lines: lines drawn on the dial plate of a sundial which permit us to determine the date from the shadow cast by the style. It is conventional to show the dates on which the Sun enters certain signs of the Zodiac.  For example, for the Sun declination 0° (Aries and Libra), +/- 11° 29′ (Pisces and Virgo), +/- 20° 20′ (Gemini and Sagittarius). These lines are also called diurnal arcs.
Longitude:	of a place: the angle formed by the meridian of a place with the Prime Meridian in Greenwich. Longitude is positive for locations to the west of Greenwich and negative for those to the east. Longitude correction: The time difference between the location’s meridian and the time zone’s meridian (Greenwich or local time zone). There is a difference of 4 minutes for each degree of longitude.
Meridian:	of a place: the geographical meridian which passes through a place. geographic: the great circle passing though the poles and the zenith of a place.
Solstice:	The moment in the year when the Sun reaches in maximum declination in the north or south of the celestial equator. The Summer Solstice (21 June) in Europe is the longest day of the year and the Sun is in its highest position in the sky. The Winter Solstice (21 December) is the opposite — the shortest day and the lowest point the Sun reaches in the sky.
Style:	The name given to the shaft or triangle which casts its shadow on a dial. A polar style is oriented parallel to the Earth’s axis. A vertical style or gnomon is placed vertical to the dial plate.
Sub-style:	The line corresponding to the projection of the style on the dial plate of a sundial. The angle which the sub-style makes with the noon hour line indicates the declination of the dial

Question/ Purpose:

What do you want to find out? Write a statement that describes what you want to do. Use your observations and questions to write the statement.

The purpose of this project is to construct an equatorial sundial.

You can then use your sundial to determine:

How different is the standard time from the sun time in your area?

Identify Variables:

When you think you know what variables may be involved, think about ways to change one at a time. If you change more than one at a time, you will not know what variable is causing your observation. Sometimes variables are linked and work together to cause something. At first, try to choose variables that you think act independently of each other.

Independent variable is the local standard time (Watch time).

Dependent variable is the sun time.

Constant is the sundial (type, size and position, orientation)

Hypothesis:

Based on your gathered information, make an educated guess about what types of things affect the system you are working with. Identifying variables is necessary before you can make a hypothesis.

Following is a sample hypothesis:

Sun time will be ahead of standard time in my area. My hypothesis is based on my gathered information about 24 time zones and the fact that my town is at the beginning (far east) of my time zone.

Experiment Design:

Design an experiment to test each hypothesis. Make a step-by-step list of what you will do to answer each question. This list is called an experimental procedure. For an experiment to give answers you can trust, it must have a “control.” A control is an additional experimental trial or run. It is a separate experiment, done exactly like the others. The only difference is that no experimental variables are changed. A control is a neutral “reference point” for comparison that allows you to see what changing a variable does by comparing it to not changing anything. Dependable controls are sometimes very hard to develop. They can be the hardest part of a project. Without a control you cannot be sure that changing the variable causes your observations. A series of experiments that includes a control is called a “controlled experiment.”

Experiment 1: Build a paper equatorial sundial

Note: This simple experiment is an excerpt from a model described in the NASA exploration website with some changes.

Determine your latitude. Using a globe or a map for your area, estimate your latitude (most road maps indicate latitude and longitude). Your latitude will be the number of degrees north if you live in the northern hemisphere, or south if you live in the southern hemisphere.

Or, you can locate your latitude using the internet at one of these sites:

• U.S. Census Bureau (U.S. Only).
• http://gnswww.nima.mil/geonames/GNS/index.jsp (Worldwide)

Print the sundial construction template. Choose a template based on your hemisphere (e.g. if you live above the equator, choose Northern Hemisphere). You will need Adobe Reader to print these files.

• Northern Hemisphere (PDF)
• Southern Hemisphere (PDF)

Construct the sundial. You will need scissors and some tape. The more carefully you make the folds, the more accurate your sundial will be. This set of pictures illustrates the construction at various stages.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Align the sundial. Take your sundial outside, place it on a level surface, and aim the style to the North. You now have a working sundial! When you read the time, remember to take Daylight Savings Time into account (during Daylight Savings Time, the sundial will be an hour behind your clock).

 

 

 

Variations:

To construct your equatorial paper sundial you do not have to use the provided template. Instead you can draw your own dial face on a card and use a straw as a gnomon. The good thing is that in an equatorial sundial, hour lines are exactly 15º apart; so, you can use a protractor to mark hour lines.

To do this you will need:

• a piece of card slightly wider than the protractor and say 25cm (10 in.) long
• a drinking straw or knitting needle
• a protractor

1. Draw lines across the card dividing the length into sections of 1, 10, 14, and 1 cm. (The length of 14 is alright for latitudes of 50 degrees or more, but if you live at a lower latitude, you will need to make this length longer.) We’ll call these lines A, B, and C. Mark the center point of line A, the letter O, and the center point of line C, the letter P. Draw a line from O to P connecting the two center points.
2. Place the center of the protractor on O and draw a half circle. Make a pin hole through O, turn the card over, and place the center of the protractor on the pin hole. Draw another half circle so you have two semicircles back to back
3. Mark 15 degree intervals and number the hours (as shown on the diagram below), on both semi-circles.
4. Score and fold the card along the lines A, B, and C
5. Enlarge the pin hole at O and push the straw through. Make sure the straw is at a 90 degree angle to the card at the point O.
6. Move the bottom end of the straw along the line OP until the angle it makes with the horizontal part of the cardboard is the same as the latitude of the location where you are.
7. When you’ve found the correct location for the bottom end of the straw, use glue or tape to secure the straw at that position.
8. The straw forms the gnomon. The shadow of the gnomon will fall on the hour lines on the top of the dial in the summer, and on the underside in the winter.
9. Place your sundial in a sunny space where the straw is faced to the north.

 

You now have a working equatorial sundial. The dial plate, with the 15 degree angles marked on it, is parallel to the equator plane, and the straw forming the gnomon is parallel to the earth’s axis. The sun appears to revolve round the earth’s axis at 360 degrees every day, which is 15 degrees every hour (which is why you marked out your hour lines at 15 degrees intervals).

 

 

You can also see from your model how a horizontal sundial is constructed. Wait till the shadow is exactly on one of your hour lines, and mark a line where the shadow of the base of your straw falls on the horizontal piece of your card, and mark the hour alongside.

When you have marked out a number of lines in this way, you will see that the angles are not a regular 15 degrees on the horizontal surface. You will also see that the shadow line along the “equator” surface meets the shadow line along the horizontal surface, along the line of the fold B. The hour lines on the horizontal surface are, in fact, the projection on the horizontal surface of the 15 degrees lines on the equatorial surface. This forms the basis of the graphical method of determining the hour lines for horizontal sundials, which of course are different for each latitude.

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Experiment 2: Build a wooden equatorial sundial

Introduction:

In an equatorial sundial, the dial face is parallel to the equator plane and the gnomon is parallel to the earth rotation axis. Dial lines are all 15 degrees apart.

Procedure:

Determine your latitude. Using a globe or a map for your area, estimate your latitude (most road maps indicate latitude and longitude). Your latitude will be the number of degrees north if you live in the northern hemisphere, or south if you live in the southern hemisphere.

Or, you can locate your latitude using the internet at one of these sites:

• U.S. Census Bureau (U.S. Only).
• http://gnswww.nima.mil/geonames/GNS/index.jsp (Worldwide)

Find the direction of true north (Not magnetic north)
True north can be located by using a magnetic compass and making an appropriate correction. Magnetic north is substantially off from true north — the exact amount varies by location. You can use the magnetic declination calculator and enter the latitude and longitude of your area to determine your magnetic declination. You can then use the declination angle and the magnetic north shown by your compass to determine the true north.
For example magnetic declination of New York City is 13ºW, So the true north is 13º on the east of what the magnetic compass shows.

Materials and Equipment:

List of material can be extracted from the experiment section. Material needed for the wooden

1. equatorial sundial are:
2. Round wooden plaque (6″ diameter)
3. Wood dowel or Bamboo Skewer (8″ long)
4. Rectangular wooden board (7″ x 10″)
5. Compass, ruler, protractor, drill and drill bit, tape, glue, pencil, marker, glue gun

Results of Experiment (Observation):

Experiments are often done in series. A series of experiments can be done by changing one variable a different amount each time. A series of experiments is made up of separate experimental “runs.” During each run you make a measurement of how much the variable affected the system under study. For each run, a different amount of change in the variable is used. This produces a different amount of response in the system. You measure this response, or record data, in a table for this purpose. This is considered “raw data” since it has not been processed or interpreted yet. When raw data gets processed mathematically, for example, it becomes results.

Calculations:

No calculations are required for this project.

Summary of Results:

Summarize what happened. This can be in the form of a table of processed numerical data, or graphs. It could also be a written statement of what occurred during experiments.

It is from calculations using recorded data that tables and graphs are made. Studying tables and graphs, we can see trends that tell us how different variables cause our observations. Based on these trends, we can draw conclusions about the system under study. These conclusions help us confirm or deny our original hypothesis. Often, mathematical equations can be made from graphs. These equations allow us to predict how a change will affect the system without the need to do additional experiments. Advanced levels of experimental science rely heavily on graphical and mathematical analysis of data. At this level, science becomes even more interesting and powerful.

Conclusion:

Using the trends in your experimental data and your experimental observations, try to answer your original questions. Is your hypothesis correct? Now is the time to pull together what happened, and assess the experiments you did.

Related Questions & Answers:

What you have learned may allow you to answer other questions. Many questions are related. Several new questions may have occurred to you while doing experiments. You may now be able to understand or verify things that you discovered when gathering information for the project. Questions lead to more questions, which lead to additional hypothesis that need to be tested.

How does a shadow tell time?

Shadows change direction, depending upon the time of day. A Sun Clock like this one uses a shadow’s position to tell the time.

Why doesn’t the time on my Sun Clock exactly match the time on my watch?

The time you get from your Sun Clock is solar time, not standard time. The two aren’t exactly the same.

According to solar time, it’s noon when the sun reaches its highest point in the sky. But the sun is always moving across the sky–which means that noon where you are is at a slightly different time than noon at a place a few miles to the east or west.

Back before 1883, people used solar time. Each community kept its own time, basing that time on the sun’s position in the sky. Back then, noon in one town would be four minutes later than noon in a town fifty miles to the east.

In 1883, to regulate time for the sake of railroad schedules, the United States adopted what is called standard time, designating time zones and requiring all communities within a time zone to keep the same time–even though that standard time didn’t quite match solar time.

If you are in the middle of your time zone, your Sun Clock will be fairly accurate. If you are at one edge of your time zone, the time on your Sun Clock (solar time) may differ from the time on your watch (standard time) by as much as forty minutes.

Some additional questions:

1. When doesn’t a sundial work?
2. Does your sundial match your watch time? Why?
3. If the earth rotates every 24 hours (approximately), how many degrees does the sun appear to move in one hour? In four minutes? (Hint: one full rotation of the earth is 360 degrees).
4. The sun’s diameter in the sky is about 0.5 degree. About how long does it take for the sun to appear to move its own diameter across the sky?
5. Why don’t we use local solar time instead of time zones in our everyday lives? Would it be easy to know what time your favorite TV program starts?
6. Why do time zones generally run north-south instead of east-west?
7. Does a sundial work the same north and south of the equator?
8. What would be different about a sundial at the North Pole? The South Pole?
9. Why didn’t the ancient Egyptians use watches instead of sundials?
10. Would your sundial read the same time as another sundial 100 miles directly north of you? Would the shadows be the same length?

Possible Errors:

If you did not observe anything different than what happened with your control, the variable you changed may not affect the system you are investigating. If you did not observe a consistent, reproducible trend in your series of experimental runs there may be experimental errors affecting your results. The first thing to check is how you are making your measurements. Is the measurement method questionable or unreliable? Maybe you are reading a scale incorrectly, or maybe the measuring instrument is working erratically.

If you determine that experimental errors are influencing your results, carefully rethink the design of your experiments. Review each step of the procedure to find sources of potential errors. If possible, have a scientist review the procedure with you. Sometimes the designer of an experiment can miss the obvious.

References:

List of References (Websites):

1. USGazetteer
2. Sundial Template 1
3. Sundial Template 2
4. Sundial Template 3
5. http://www.wsanford.com/
6. http://www.sundials.org/
7. An Artistic Design: http://www.sculptoratlarge.com/model/dial/
8. http://www.mts.net/~sabanski/sundial/sotw_israel_sa.htm

List of References (Books):

Anno’s sundial
By: Mitsumasa Anno
Philomel Books, 1987

Sundials; the Art and Science of gnomonics
By: Frank W. Cousins
Pica Press, 1969