Making a shadow plot

Equipment

• One large piece of white paper (18x24 inches works well)
• One, pencil width, wooden dowel or something similar.
  (12-15 inches long works well for the paper size above)
• A ball of clay
• A flat location that is free from shadows all day long
• One permanent magic marker
• Several heavy objects, rocks or bricks, to hold the paper down

Making a shadow plot of your own can be useful in a many ways. During the course of only one day a shadow plot can help you determine which direction is due north at the location where the shadow plot is made. A compass uses the earth's magnetic field to find north and therefore points toward magnetic north, which is not in the same place as geographic north.
A shadow plot can also help you obtain a feel for how the Sun's path changes across the sky from day to day. To see this effect it is best to work on the shadow plot for several weeks.

Setting up your shadow plot

It is best to set up your shadow plot in the morning, around 9:00.
Once you have found a flat location, clear from shadows, push the ball of clay onto the ground. Insert the wooden dowel into the ball of clay so that it stands vertically. The dowel will need to stand in this exact location for the entire day, or for several weeks, so make sure it is secure. You may need to wrap some duct tape around the base of the dowel and further secure it to the ground in this manner or be creative and find a way to secure the dowel so that it remains perfectly vertical.
Once your dowel is in place look for its shadow. If it is morning, the dowel's shadow should be pointing west. Lie your piece of paper down on the north side of the dowel with the middle of the long edge up against the base of the dowel support. (You can figure out which general direction is north since you know the Sun is in the east and the dowel shadow is facing west.)
The image above will help you set up your materials correctly.
Secure the piece of paper with several rocks. Place the rocks, or other heavy objects, around the edge of the paper so they do not obscure the middle where you will be making your plot.
You are now ready to start making your measurements.
The shadow from the dowel should be on your piece of paper. If it is not wait about an hour and return once the shadow is cast onto the paper. When you have the shadow on the paper, use your permanent marker to make a mark at the very end of the shadow.
Return to your shadow plot about once every half hour and make a mark at the end of the shadow each time. If you begin your plot at 9:00 a.m. you should have enough markings by 3:00 p.m. When you are finished with one day of measurements you plot should look like the one above.
You are now ready to use this plot to find Geographic North.

Using a Shadowplot to find the North-South line

After one day of shadow measurements you are ready to draw the North-South line. On your completed shadow plot draw a smooth curve through all of the marks that you have made, without moving the paper. The more often you have taken your measurements, the easier it will be to draw this curve accurately.
Once you have drawn a smooth curve through the markings, you want to find the shortest distance between the dowel base and this curve. To do this place a meter stick so that one end is at the dowel base and the curve crosses the meter stick at some other point. Pivot the meter stick about the end at the dowel base until the find the location on the curve that is the shortest distance from the dowel base.
Draw a line from the dowel base to this point as in the image below.

This line you have just drawn is called a North-South line. It is the line along which the Sun will cast a shadow at local noon. (Your local noon may not be exactly when the clock says noon depending on where you are in your timezone.)
This North-South line points exactly North and South. A line drawn perpendicular to this line will point East and West. You will need to know the exact direction of North to use your horizontal sundial.


In addition to finding the direction of north you will need to know the latitude of the town or city where you intend to use your sundial in order to build it accurately. If you do not know the latitude of a particular part of the world you can figure it out by looking on a globe or a map that has the latitude lines marked. Latitude is measured in degrees from the equator. The equator is zero degrees latitude, the north and south poles are ninety degrees latitude. Here is a latitude grid of the world.

Use the grid below to find the latitude of the location where your sundial will be used.

 

Now that we understand a little about how the Sun moves through the sky, we know how to find due north and we know the latitude for which we want to build a sundial, we are ready to continue.


The complete construction of a sundial involves the use of a protractor and the understanding of some trigonometric functions like sine and tangent.
The different levels below allow you to construct a sundial no matter what experience you have with these mathematical tools. Select the level appropriate for your understanding from the choices below and we'll get to work!


ADVANCED 
If you are comfortable using a protractor and are familiar with the trig functions sine and tangent this is the level for you!

INTERMEDIATE 
If you are comfortable using a protractor to measure angles, but are not familiar with the trig functions sine and tangent select this level.

NOVICE
If you are not comfortable using a protractor and are not familiar with the trig functions sine and tangent start at this level.