# Labs from YSI 94 : Individual Sundial (Cloud/Rain Activity).

April Whitt
CARA Yerkes Summer Institute, August 1994

This is a lab and a Teacher's Guide.

## Objectives

Students will:
• construct a simple sundial
• observe the movements of the shadows on the sundial over a period of time
• relate the movement of the shadows on the sundial to the motion of the Earth or the Sun
• relate the movement of the shadows on the sundial to local time.

## Materials Needed

Manila folder (1 per student), rulers, protractors, tape, pens or pencils

## Procedures

1. Cut the manila folder into two pieces along the center fold. When cut, use a ruler to draw a straight line parallel to the fold and about 2 cm from the cut edge. Find the midpoint of this line and, using a protractor, draw a second line perpendicular to the first line. The second line is the noon line or the 0° line.
2. Locate your latitude on the table provided and determine the hour and half-hour angles from the table; all angles will be measured to the left and to the right of the noon line.
3. Beginning with the noon line and working with a protractor, draw the 11:30 AM line (to the left) and the 12:30 PM line (to the right) at the predetermined angle from the vertical noon line. Follow the same procedure with the 11:00 AM line and the 1:00 PM line, and continue until all the hour and half-hour lines are drawn out to 6:00 AM and 6:00 PM. It may be best to make the hour lines about 4 inches long and the half-hour lines about 2 inches long. Label the hour lines. The lines to the left are "AM" lines, and to the right are "PM" lines. When completed, all of the hour and half-hour lines will come together at the point the noon line intersects the long straight line drawn originally.
4. The gnomon for the sundial is to be made from the other piece of the manila folder. The gnomon must be constructed with an angle equal to your latitude. Use the smooth side of the folder as one edge of the gnomon. Draw a 4-inch line from the smooth side at an angle equal to your latitude. The edge of the folder and the line form two sides of a triangle. The third side may be drawn in any shape desired. Cut out the triangle to use as the sundial's gnomon.
5. Tape the gnomon to the noon line of the sundial. Be certain the smooth edge of the gnomon (the edge from the smooth side of the folder) is right along the noon line and the angle equal to your latitude is at the point where all the hour lines come together. When completed, the gnomon should be vertical to the face of the sundial.
6. Position the sundial so the gnomon is pointing directly North and read the time from the shadow cast by the gnomon on the sundial.

## Extensions

Have the students compare the time from the sundial to the time from a clock. The two will probably not read the same. Three corrections that can be made may be discussed with the students.
1. Daylight saving time. If the sundial is read during daylight saving time, one hour must be added to the reading.
2. Your position compared to the time zone meridian of your time zone. You need to know your longitude and your time zone meridian. The time zone meridians are as follows:
• EST 70°
• CST 90°
• MST 105°
• PST 120°
Subtract your longitude from your time zone meridian. If the result is positive, you live east of your zone meridian and your sundial is reading fast. Since the Earth rotates about 15° in one hour, each degree represents 4 minutes. Accordingly, if you lived at longitude 72°, your sundial would read 12 minutes fast (75° - 72° = 3° x 4 min/° = 12 min).
3. The equation of time. Since the Earth's orbit is an ellipse, the apparent motion of the Sun varies according to the season. It is possible to make the necessary correction with the graph provided. Locate the date of your sighting on the graph, and from the trend line, determine the amount of correction. The positive sign indicates that the amount of correction is to be added to the dial time; a negative sign indicates that the amount of correction is to be subtracted from the dial time.
```LATITUDE                      HOUR ANGLES
1:00 PM  2:00 PM  3:00 PM  4:00 PM  5:00 PM
or 11:00 AM 10:00 AM  9:00 AM  8:00 AM  7:00 AM
---------------------------------------------------------
40°            9.8     20.4     32.7     48.1     67.4
41°           10.0     20.7     33.3     48.7     67.8
42°           10.2     21.1     33.8     49.2     68.2
43°           10.4     21.5     34.3     49.8     68.6
44°           10.5     21.9     34.8     50.3     68.9
45°           10.7     22.2     35.3     50.8     69.2

LATITUDE                   HALF-HOUR ANGLES
12:30 PM  1:30 PM  2:30 PM  3:30 PM  4:30 PM  5:30 PM
or 11:30 AM 10:30 AM  9:30 AM  8:30 AM  7:30 AM  6:30 AM
-------------------------------------------------------------------
40°             4.8     14.9     26.3     40.0     57.2     78.4
41°             4.9     15.2     26.7     40.5     57.7     78.7
42°             5.0     15.5     27.2     41.1     58.2     78.9
43°             5.1     15.8     27.6     41.6     58.7     79.1
44°             5.2     16.1     28.1     42.2     59.2     79.3
45°             5.3     16.3     28.5     42.7     59.6     79.5

```
Important Disclaimers and Caveats: