Making a Horizontal Sundial for 45 Degrees South Latitude

Materials: Advanced

for each sundial you will need...


If you want to make your sundial into a necklace or keychain you might want to drill a hole in the checker, or have someone drill the hole for you, to pass the string through. OR you could screw an eye hook into the top and pass the string through there. BE CREATIVE, and enjoy!


On a sundial, the gnomon is the piece of the sundial which casts its shadow onto the sundial face. In our project we will use a copper nail as the gnomon.

For a horizontal sundial we want the gnomon to be aligned with the South Celestial Pole so that the sun will rotate around it when we face our sundial due south.



Preparing the wooden checker


To align our gnomon along this axis we must position it such that it makes an angle equal to the latitude angle where it will be used with the horizontal face of the sundial. (See below)



The easiest way to get the nail into the wooden checker at this angle is to do the following. First, hammer the nail straight into the center of your wooden checker making sure not to go through the back side.

On an index card draw a line that is inclined from the bottom of the card at an angle equal to your latitude.

Hammer the nail from the side so that it begins to bend over.

Place the index card behind the bent nail, with the start of the line at the base of the nail. Continue to bend the nail over until it is at the same angle as the line you have on your index card.

Now the nail should be making an angle equal to your latitude with the base of the checker. It should look like the image above.

If the nail become loose, a little wood glue at the base should secure it.

Drill a hole in the wooden checker on the opposite side from where the nail is pointing. Make sure to drill the hole large enough so that the cord you have chosen will fit through it.

***Note***
If you do this activity with a large group of young children it is often best to prepare the checkers up to this point ahead of time.
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You are now ready to put on the hourlines for the sundial.

Making the hourlines


On a horizontal sundial the position of the lines that indicate what hour it is depend on the latitude. In this lesson we will calculate these angles and then use a protractor to create a template for placing the lines on the face of our sundial.


The equation below determines at what angle, theta, to draw each hour line. For the angle L you will use your latitide angle, and the angle H is the hour angle, which changes depending on which hour line you are calculating.

The sun travels 360 degrees in 24 hours, or 15 degrees each hour. The hour angle for each given hour line is 15 degrees multiplied by how many lines away from the noon line you are. (For instance, 2 o'clock is two lines away from the noon line, so the hour angle for 2 o'clock is 30 degrees.) You may note that 10 o'clock also has an hour angle of 30 degrees. In fact, your calculations will be completely symmetric. The angles for the hour lines 1-5 p.m. will be the same as those for 11-7 a.m.

Use the equation above to calculate theta for up to six hours away from noon. You can use the table on the left to check you calculations. Once you have calculated the angle values you are ready to construct your hour line template.

To begin construction of the template, place your protractor on a sheet of paper such that the straight edge is near the bottom. Draw a horizontal line on the paper using the bottom edge of the protractor. Without moving the protractor make a pencil tick at the 90 degree mark, which should be at the top of your protractor. Now turn the protractor sideways and use the long edge to draw a vertical line from the tick mark down to the horizontal line. You have just created the noon, and six o'clock lines!



You can now use the values you calculated to draw each hour line at the appropriate angle from the verticle noon line. Begin by placing your protractor sideways on your paper so that it looks like the letter D. You want the long edge along the vertical line and the middle of that long edge where the verticle and horizontal lines cross. If you look at the angle markings on your protractor there should be a zero written at the top, along your verticle line and a 90 written on the right where your horizontal line is drawn. Hold the protractor very still and using the numbers written along the curve of the protractor make a tick with your pencil at each of the angle values in the last column of the table above.

Once you have made all the marks to the right of the verticle line, turn your protractor around so that the curve is now going to the left. Line up the zero with the verticle line and the 90 with your horizontal line and repeat the process of mading tick marks at each angle value from the last column in the table above.

Now use the straight edge of your protractor to connect each tick mark to the intersection of the horizontal and vertical lines. You final template should look like the one at the beginning of this section.

Once you have a hard copy of the hour line template, place your wooden checker on top of the image such that the center of the checker, where the nail hole is, is directly over the intersection of the horizontal and vertical lines. The horizontal line, marked with a six on each side, should run underneath your checker exactly across the center.



Without shifting the checker, rotate it until the head of the nail is pointing up the 12 o'clock line, as seen in the image to the left.




Holding the checker very still make 13 pencil marks on the top face of the wood, each mark inline with the appropriate hourline. It is best to start with pencil so you can redo any mistakes.


Once you have made all of the hour marks go over them in pen and write in the appropriate numbers. Because the face of our sundial is so small, it is best to include only a few of the hour numbers, as in the image to the right.

Finish your sundial by threading the drilled hole with some cording and tie it off to the desired length.



The moment of truth!


To use your new sundial, take it outside on a sunny day, hold it perfectly horizontal, and point the head of the gnomon (nail) due south. The shadow cast by the gnomon should fall on the appropriate hourline.

ENJOY!!!!

***ACCURACY***
To compare the time on the sundial you construct to the time on a clock, there are several adjustments which should be made. The North American Sundial Society has a nice page which discusses these adjustments. Visit: Sundial Time vs. Clock Time .

****REMEMBER****
During daylight savings time you will need to add one hour to the time on your sundial in order to agree with local "clock" time.




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Lesson designed by Michelle B. Larson
mlarson@physics.montana.edu